{"id": "2606.18833", "title": "Seed-Guided Semi-Supervised Clustering by A-Contrario Anomaly Detection", "abstract": "This paper introduces a semi-supervised clustering framework grounded in the statistical duality between grouping principles and anomaly detection. We address the challenge of robust cluster definition in noisy environments -- a task where partitioning algorithms often over-assign outliers and density-based methods remain sensitive to heuristic global parameters. Drawing on \\textit{a-contrario} statistical reasoning and Gestalt proximity principles, we define a cluster as a maximal subset of data points containing no anomalies relative to a null hypothesis of uniform randomness. Central to this approach is the Perception algorithm, which utilises a principled expectation-based threshold ($\\mathbb{E} < 1$) to identify outliers without manual parameter tuning. By treating clustering as the dual of anomaly detection, we employ an iterative ``clustering-by-exclusion'' mechanism. The algorithm is seed-guided, leveraging minimal user-provided labels to initialise robust cluster medians and form initial groups, which are subsequently expanded by admitting non-anomalous points. This approach naturally isolates fringe points, isolated noise, and emerging unknown clusters. We evaluate the method on synthetic and real-world benchmarks, including image and text datasets represented through raw, linear-reduced, and neighbourhood-preserving embeddings. Results demonstrate that with as few as 10--30 seeds per cluster, the proposed method achieves competitive and often very strong performance under a practical low-tuning benchmarking protocol, while maintaining linear scalability with respect to both observations and dimensionality for a fixed number of seeded clusters and iterations.", "date": "2026-06-17", "categories": []}
{"id": "2606.18972", "title": "FOSC-X: An Extended Framework for Optimal Local Cuts and Non-Horizontal Cluster Selection from Clustering Hierarchies", "abstract": "Extracting a flat clustering solution from a hierarchy is a common task in practical cluster analysis and can be formulated as an optimisation problem. Existing approaches focus on finding a single optimal solution. We introduce FOSC-X, a framework for extracting the top-M globally optimal flat clusterings from local, non-horizontal cuts of a hierarchical cluster tree, while optionally enforcing constraints on the number of clusters. This enables automatic identification of multiple high-quality alternative clusterings that capture different aspects of the hierarchical structure. Without constraints, the top-M problem can be solved in polynomial time using dynamic programming, exploiting the property that locally optimal partial candidates within subtrees can be combined to form globally optimal solutions while automatically determining the number of clusters. However, this can lead to solutions with numbers of clusters that are ultimately undesirable -- e.g., too large to be meaningful or practically analysed within a particular application domain. Imposing cluster-count constraints breaks the optimality property underlying the unconstrained dynamic programming approach, since locally optimal partial candidates may no longer combine into feasible globally optimal solutions. FOSC-X addresses this challenge through a dynamic programming strategy that maintains compact sets of feasible candidates using lower and upper feasibility bounds while pruning infeasible or dominated combinations. The resulting method guarantees optimal rankings of the top-M solutions with linear-time complexity in the number of cluster nodes and dataset size, both with and without cluster-count constraints. Experiments show that FOSC-X efficiently reveals alternative clustering structures overlooked by single-solution extraction methods.", "date": "2026-06-17", "categories": []}
{"id": "2511.19162", "title": "BioArtlas: Computational Clustering of Multi-Dimensional Complexity in Bioart", "abstract": "Bioart brings living material into artistic practice, where a single work can be at once an aesthetic object, a scientific instrument, and an ethical provocation. Traditional categories sort such works along one axis at a time, which flattens the very hybridity that defines the field and leaves curators no way to compare works across many dimensions together. I introduce BioArtlas, a computational atlas that represents each bioartwork along many curated dimensions at once and organizes the field by conceptual similarity rather than by medium or chronology. My method embeds the keywords of all 81 works on each of thirteen interpretive axes, groups related concepts into a shared codebook that tames inconsistent terminology, and then searches systematically for a clustering that is both statistically clean and interpretable. Among the methods that place every work on the map, agglomerative clustering separates the field far more cleanly than the usual k-means baseline (silhouette 0.664 versus 0.483), whereas density-based methods reach higher scores only by discarding most of the corpus as noise. By separating rigorous analysis from public storytelling, BioArtlas turns the tangled complexity of bioart into a navigable landscape, openly available as an interactive interface (https://www.bioartlas.com) and dataset (https://github.com/joonhyungbae/BioArtlas).", "date": "2025-09-27", "categories": []}
{"id": "2604.23628", "title": "Characterizing Admissible Objective Functions for Hierarchical Clustering", "abstract": "Hierarchical clustering is a fundamental task in data analysis, but classical methods have long lacked a principled objective function. Dasgupta [STOC 2016] took an important step toward addressing this gap by proposing a well-motivated objective function for cluster trees. Cohen-Addad et al. [J. ACM 2019] subsequently introduced the notion of admissibility: an objective function is admissible if, whenever the input similarity matrix admits generating trees, its minimizers are precisely those generating trees. They also gave a necessary and sufficient condition for admissibility within a family of objective functions based on aggregate intercluster similarity. We refer to this family as sum-type objective functions. However, apart from Dasgupta's original objective function, no explicit admissible objective functions in this family were provided.\n  In this paper, we study admissible objective functions for hierarchical clustering in two directions. For sum-type objective functions, we give a complete characterization when the scaling function is a symmetric polynomial of degree at most two, and we derive sufficient conditions for degree-three polynomials. We also show that the recursive sparsest cut algorithm achieves an O$(\\phi)$-approximation ratio for the admissible objective functions covered by our characterization, where $\\phi$ is the approximation factor of the sparsest cut subroutine. We then introduce max-type objective functions, where cluster interaction is measured by maximum, rather than aggregate, intercluster similarity. For this class, we characterize which objective functions are admissible for arbitrary symmetric scaling functions and give a complete characterization when the scaling function is a symmetric polynomial of degree at most two.", "date": "2026-04-26", "categories": []}
{"id": "2504.18179", "title": "Label-independent hyperparameter-free self-supervised single-view deep subspace clustering", "abstract": "Deep subspace clustering (DSC) algorithms face several challenges that hinder their widespread adoption across variois application domains. First, clustering quality is typically assessed using only the encoder's output layer, disregarding valuable information present in the intermediate layers. Second, most DSC approaches treat representation learning and subspace clustering as independent tasks, limiting their effectiveness. Third, they assume the availability of a held-out dataset for hyperparameter tuning, which is often impractical in real-world scenarios. Fourth, learning termination is commonly based on clustering error monitoring, requiring external labels. Finally, their performance often depends on post-processing techniques that rely on labeled data. To address this limitations, we introduce a novel single-view DSC approach that: (i) minimizes a layer-wise self expression loss using a joint representation matrix; (ii) optimizes a subspace-structured norm to enhance clustering quality; (iii) employs a multi-stage sequential learning framework, consisting of pre-training and fine-tuning, enabling the use of multiple regularization terms without hyperparameter tuning; (iv) incorporates a relative error-based self-stopping mechanism to terminate training without labels; and (v) retains a fixed number of leading coefficients in the learned representation matrix based on prior knowledge. We evaluate the proposed method on six datasets representing faces, digits, and objects. The results show that our method outperforms most linear SC algorithms with careffulyl tuned hyperparameters while maintaining competitive performance with the best performing linear appoaches.", "date": "2025-04-25", "categories": []}
{"id": "2606.13146", "title": "Robust State-Conditional Feature-Weighted Jump Models for Temporal Clustering", "abstract": "We propose a robust feature-weighted jump model for time-dependent clustering. A penalty is used to encourage smoothness of transitions over time, while robustness is achieved through the use of a Tukey's biweight loss function. An additional parameter controls the variability of feature weights across states, allowing the model to assign state-specific relevance to each feature. We illustrate in simulation how the method accurately recovers the true cluster sequence and reliably identifies relevant features, outperforming competing approaches, particularly in the presence of outliers. We conclude with two empirical applications, one on the number of conflict-related homicides in Kosovo in the period 1998-2000, and another on macroeconomic performance of twelve European countries in the period 1949-2024.", "date": "2026-06-11", "categories": []}
{"id": "2606.13444", "title": "Clustering Node Attributed Networks with Graph Neural Networks and Self Learning", "abstract": "Graph clustering - partitioning the node set of a graph into disjoint subsets that reflect some latent information - is a fundamental problem as it finds applications in a myriad of different scenarios. While this classic problem has been tackled for decades by different communities, a recent variation of the problem driven by real data considers the scenario where nodes have attributes that are also informative. This has triggered novel methods that simultaneously leverage network information (edges) and node information (attributed) in the design of novel clustering algorithms. This work proposes a novel framework that builds on prior works that have applied graph neural networks (GNN) to graph clustering. The proposed framework operates in rounds of self learning in a fully unsupervised setting. In each round, a GNN generates representations for nodes that are used to cluster the nodes. This clustering influences the graph used to generate the node representation in the next round. Moreover, a context graph built in each round using the original graph is used to generate the node representations. Empirical results show that the proposed methodology extracts information from both network edges and node attributes in synthetic data, outperforming algorithms focused solely on the network or attributes when neither are very informative. Multiple rounds of learning also improve the performance and always outperforms a long single round of training (i.e., classic GNN graph clustering). When considering real datasets, empirical results indicate that the proposed methodology is competitive to state-of-the-art methods when cluster sizes are balanced.", "date": "2026-06-11", "categories": []}
{"id": "2409.00743", "title": "Interpretable Clustering: A Survey", "abstract": "In recent years, much of the research on clustering algorithms has primarily focused on enhancing their accuracy and efficiency, frequently at the expense of interpretability. However, as these methods are increasingly being applied in high-stakes domains such as healthcare, finance, and autonomous systems, the need for transparent and interpretable clustering outcomes has become a critical concern. This is not only necessary for gaining user trust but also for satisfying the growing ethical and regulatory demands in these fields. Ensuring that decisions derived from clustering algorithms can be clearly understood and justified is now a fundamental requirement. To address this need, this paper provides a comprehensive and structured review of the current state of explainable clustering algorithms, identifying key criteria to distinguish between various methods. These insights can effectively assist researchers in making informed decisions about the most suitable explainable clustering methods for specific application contexts, while also promoting the development and adoption of clustering algorithms that are both efficient and transparent. For convenient access and reference, an open repository organizes representative and emerging interpretable clustering methods under the taxonomy proposed in this survey, available at https://github.com/hulianyu/Awesome-Interpretable-Clustering", "date": "2024-09-01", "categories": []}
{"id": "2606.11737", "title": "Machine-learning clustering of close-in exoplanet populations: links to pebble accretion", "abstract": "Close-in exoplanets exhibit a wide range of orbital architectures and physical properties shaped by both formation conditions and migration processes. Although population-synthesis models predict distinct planetary populations, establishing a quantitative connection between observed exoplanets and synthetic populations remains challenging. We investigate the intrinsic organisation of close-in exoplanets using physically motivated dynamical parameters and connect the resulting populations to pebble-accretion formation pathways. A two-stage Gaussian mixture model (GMM) is applied to an observed sample of close-in exoplanets, performing unsupervised probabilistic clustering in a feature space dominated by dynamical descriptors of planet-star interactions. The resulting clusters are mapped onto a pebble-accretion synthetic population within a statistically motivated three-dimensional parameter space. Formation-related quantities, including gas availability, gas fraction, and ice-rock mass ratio, are then used to interpret the mapped populations. We identify statistically supported sub-populations without imposing predefined classification boundaries, including very-massive gas giants, hot giants, warm-Jupiter-dominated systems, and lower-mass giants. The mapped synthetic populations reveal systematic differences in formation timing, gas accretion, and solid growth histories. In particular, very-massive gas giants are preferentially associated with earlier formation epochs than hot-giant and warm-Jupiter-dominated populations. These results demonstrate that physically motivated machine-learning approaches can provide a statistically robust framework for linking observed exoplanet populations to theoretical planet formation pathways.", "date": "2026-06-10", "categories": []}
{"id": "2606.12077", "title": "Efficient Time Series Clustering from Multiscale Reservoir Dynamics with Granular-Ball Anchoring Graph Optimization", "abstract": "Time-series clustering remains challenging due to the inherent trade-off between clustering effectiveness and computational efficiency. Similarity-based methods often suffer from quadratic complexity caused by pairwise distance computations, while deep learning-based approaches typically rely on costly iterative training and a large number of trainable parameters. In this paper, we propose MSRGC-Net, an efficient time-series clustering framework that integrates multiscale reservoir computing, granular-ball-based anchoring graph construction, and consensus learning. MSRGC-Net adopts a training-free reservoir computing paradigm to extract multiscale temporal representations from raw time series without backpropagation, significantly reducing computational overhead. To capture the intrinsic structure of the resulting representations, granular-ball computing is employed to adaptively model data distributions via density-consistent regions, yielding compact and robust anchor graph representations. Furthermore, a consensus-based anchoring graph optimization strategy is introduced to effectively align multiscale reservoir representations and integrate complementary information across temporal scales. Extensive experiments on widely used univariate and multivariate benchmark datasets demonstrate that MSRGC-Net consistently outperforms state-of-the-art methods in clustering performance while maintaining superior computational efficiency.", "date": "2026-06-10", "categories": []}
{"id": "2606.10673", "title": "ClusBench: The Clustering Benchmark Data Resource You've All Been Waiting For (?)", "abstract": "Although some very common test beds exist for assessing the performance of clustering methods, large scale benchmarking is typically limited to relatively simplistic simulation set-ups. Here we describe the production and curation of close to 3000 synthetic data sets, derived from more than 200 publicly available data sets; the majority of which arose from real-world applications. By fitting a flexible non-parametric distribution to each base data set we are able to retain much of the nuance in real-world data which is difficult to reproduce in standard simulations, while also producing data sets whose sizes are sometimes substantially greater than the data sets from which they are derived. The synthetic data sets, plus an accompanying R package, are available for download from https://github.com/DavidHofmeyr/ClusBench.", "date": "2026-06-09", "categories": []}
{"id": "2606.10896", "title": "Flash-GMM: A Memory-Efficient Kernel for Scalable Soft Clustering", "abstract": "We present \\textbf{Flash-GMM}, a fused Triton kernel for efficient computation of Gaussian Mixture Models (GMMs) over large-scale data in a single GPU pass. By eliminating the need to materialize the full responsibility matrix in GPU memory, Flash-GMM achieves a \\textbf{20$\\times$} speedup over existing implementations and enables training on datasets more than \\textbf{100$\\times$} larger than previously feasible on one device. To demonstrate its impact, we integrate Flash-GMM into the IVF coarse quantizer for approximate nearest-neighbor (ANN) search. We show that soft GMM clustering is now a viable drop-in replacement for $k$-means, and that GMM responsibilities can be leveraged to assign border vectors to multiple clusters. Our approach reaches fixed recall targets with up to $1.7\\times$ fewer distance computations, or equivalently, yields $+2$--$12$ recall@10 at matched computational cost. We release the kernel as an open-source project.", "date": "2026-06-09", "categories": []}
{"id": "2606.08322", "title": "Orthogonality and Dimensionality in Airline Cluster Analysis using PCA and Kernel PCA", "abstract": "To characterize the US airline profit cycles from 1995 to 2020, the authors of Renold et al. (2023) combine k-means clustering, principal component analysis, and system dynamic modelling. We replicate their clustering experiment in three spaces -- the original 7-dimensional raw-variable space, a 3-dimensional PC score space, and a 4-dimensional PC score space using their dataset gratefully included in the paper. We show that the six-cluster taxonomy is geometrically robust: k-means in 3-PC space produces bit-for-bit identical cluster assignments relative to 7D raw space. As a nonlinearity check we apply kernel PCA under six kernels spanning three families plus a linear baseline. All six kernels preserve the six-cluster assignment in 2D. A 1D diagnostic tightens this: the linear kernel conflates the COVID year C_3 with the peak-profit cluster C_0, whereas all five non-baseline kernels shift C_3 to overlap only the post-financial-crisis cluster C_5. Agreement across the kernel families confirms an intrinsically linear manifold with no hidden curvature. The silhouette criterion reveals that the dataset structurally supports only three clusters, not six. Collinearity in the raw 7D space suppresses the silhouette signal that would otherwise identify k=3 as the structurally motivated choice.", "date": "2026-06-06", "categories": []}
{"id": "2606.09340", "title": "Thresholded Local Hyper-Flow Diffusion", "abstract": "Local Hyper-Flow Diffusion (HFD) gives an edge-size-independent Cheeger-type guarantee for seeded clustering in general submodular hypergraphs, but existing HFD solvers do not keep intermediate computation local at every iteration. We introduce Thresholded Local HFD (TL-HFD), a first-order method that maintains an active region around the seeds, performs projected subgradient updates on that region and its immediate boundary, and expands via thresholded (top-k) boundary activation. We prove that the local update is exact: the degree-preconditioned projected subgradient step restricted to the active region and its boundary coincides with the unrestricted global update. We establish finite-time dual suboptimality for both exact and thresholded updates, treating the latter as inexact projected subgradient steps with explicit skipped-boundary error. We further derive an additive activated-volume bound controlled by realized local subgradient norms and the minimum boundary-push among newly activated vertices, and translate approximate dual optimality with localized support into a robust sweep-cut guarantee for early-stopped iterates. For general submodular cut-costs, each iteration is local in the scanned region and oracle-sensitive in the hyperedge primitive. Empirically, TL-HFD often matches or improves over HFD while activating less volume, with the largest gains on noisy instances where diffusion tends to absorb non-target vertices.", "date": "2026-06-08", "categories": []}
{"id": "2606.04777", "title": "UniFair: A unified fair clustering approach based on separation and compactness", "abstract": "Clustering is increasingly used to support high-impact decisions, yet standard objectives such as k-means can produce clusterings that treat demographic groups unequally. Existing fair clustering methods typically optimize a single notion of fairness and often overlook how clustering costs interact with the geometry of the induced decision boundaries. We propose UniFair, a unified framework that jointly optimizes separation fairness and social fairness. Separation fairness encourages protected groups to lie farther from the induced decision boundaries, while social fairness reduces disparities in within-cluster distortion by penalizing group-wise clustering costs. We develop gradient-based optimization procedures for separation-fair and unified k-means objectives, and extend them to deep clustering by enforcing the same criteria in the latent space of an autoencoder. Experiments on tabular and image datasets show that UniFair reduces both boundary-related and cost-based group disparities with only a modest increase in clustering loss.", "date": "2026-06-03", "categories": []}
{"id": "2606.05230", "title": "Central Description Length (CDL) Clustering Validation Index", "abstract": "Selecting a clustering algorithm and its hyperparameters without labels is a common difficulty in engineering machine learning pipelines that work with unsupervised analysis of sensor, image, or process data. Clustering validation indices (CVIs) provide internal scores for ranking candidate clusterings, but most popular CVIs are built from Euclidean compactness and separation terms and so tend to favour compact, convex partitions. Their performance is known to degrade on non convex, irregular, or variable density data, where kernel transformations or alternative distance measures are typically used at the cost of additional tuning and computation. This paper introduces the Central Description Length (CDL) clustering validation index. CDL uses the observed within cluster compactness, the estimated cluster centers, and the estimated cluster covariances to compute a probabilistic upper bound on the description length associated with the unobservable true cluster centers. The bound condenses intra cluster compactness and centroid displacement into a single computable quantity and is evaluated on the partition produced by any clustering algorithm. The implementation uses only observable quantities (the data, the partition, the estimated centers, and the estimated covariances) and does not use ground truth labels. On synthetic benchmarks with non convex and arbitrary shape clusters, CDL-CVI selected the reference number of clusters more often and reached higher Adjusted Rand Index (ARI) values than the conventional CVIs we tested, without an additional kernel preprocessing stage. On image benchmarks (MNIST, CIFAR-10, STL-10) clustered from frozen unsupervised embeddings, CDL-CVI returned cluster numbers close to the reference class counts across K-means, DBSCAN, and spectral clustering in the reported trials.", "date": "2026-06-02", "categories": []}
{"id": "2412.03008", "title": "Local Clustering on Complex Graphs and Complex Hypergraphs", "abstract": "Local/seeded clustering aims to find a compact cluster near the given starting instances. While most existing studies on graph clustering assume a discrete graph setting (i.e., unweighted, undirected graphs without self-loops), real-world graphs can be more complex. In this paper, we extend the classic non-approximating Andersen-Chung-Lang (ACL) clustering algorithm beyond discrete graphs and generalize its quadratic optimality to a wider range of complex graphs, including weighted, directed, and self-looped graphs and hypergraphs with edge-dependent vertex weights. Specifically, by leveraging PageRank, we propose two algorithms: GeneralACL for graphs and HyperACL for hypergraphs. We prove that, under two mild conditions, both algorithms can identify a quadratically optimal cluster in terms of conductance. Additionally, we provide experiments to validate our theoretical findings. Our code is available at https://github.com/iDEA-iSAIL-Lab-UIUC/HyperACL.", "date": "2024-12-04", "categories": []}
{"id": "2509.25289", "title": "ClustRecNet: A Novel End-to-End Deep Learning Framework for Clustering Algorithm Recommendation", "abstract": "Identifying an effective clustering algorithm for a given dataset remains a fundamental unsupervised learning issue. We introduce ClustRecNet, a novel end-to-end deep learning framework that recommends suitable clustering algorithm(s) by directly learning high-order representations of raw tabular data. To facilitate robust meta-learning, we first construct a comprehensive repository of 34,000 synthetic datasets encompassing a large variety of clustering scenarios, run 10 popular clustering algorithms, and use Adjusted Rand Index (ARI) to establish ground-truth labels. ClustRecNet's architecture incorporates a convolution block, two residual blocks, and an attention block to capture local and global structural patterns, effectively bypassing the knowledge bottleneck associated with manual feature engineering. Extensive evaluation on both synthetic and real-world benchmarks demonstrates that ClustRecNet consistently outperforms traditional internal cluster validity indices such as Silhouette, Calinski-Harabasz, Davies-Bouldin, and Dunn as well as state-of-the-art Automated Machine Learning (AutoML) approaches such as ML2DAC, AutoCluster, and AutoML4Clust. For example, our framework achieves an average 0.497 ARI gain over the Calinski-Harabasz cluster validity index on synthetic data and an average 44.16% ARI improvement over the leading AutoML approach (ML2DAC) on real-world benchmarks. Code and data are available at: https://github.com/mrbakhtyari/ClustRecNet", "date": "2025-09-29", "categories": []}
{"id": "2511.03000", "title": "Unifying Information-Theoretic and Pair-Counting Clustering Similarity", "abstract": "Comparing clusterings is central to evaluating unsupervised models, yet the many existing similarity measures can produce widely divergent, sometimes contradictory, evaluations. Clustering similarity measures are typically organized into two principal families, pair-counting and information-theoretic, reflecting whether they quantify agreement through element pairs or aggregate information across full cluster contingency tables. Prior work has uncovered parallels between these families and applied empirical normalization or chance-correction schemes, but their deeper analytical connection remains only partially understood. Here, we develop an analytical framework that unifies these families through two complementary perspectives. First, both families are expressed as weighted expansions of observed versus expected co-occurrences, with pair-counting arising as a quadratic, low-order approximation and information-theoretic measures as higher-order, frequency-weighted extensions. Second, we generalize pair-counting to k-tuple agreement and show that information-theoretic measures can be viewed as systematically accumulating higher-order co-assignment structure beyond the pairwise level. We illustrate the approaches analytically for the Rand index and Mutual Information, and show how other indices in each family emerge as natural extensions. Together, these views clarify when and why the two regimes diverge, relating their sensitivities directly to weighting and approximation order, and provide a principled basis for selecting, interpreting, and extending clustering similarity measures across applications.", "date": "2025-11-04", "categories": []}
{"id": "2606.04343", "title": "Robust Multi-view Clustering against Imperfect Information", "abstract": "Real-world multi-view data always suffer from imperfect information problem, where the view-specific observations are absent (i.e., Incomplete Views, IV) and cross-view correspondences are mismatched (i.e., Noisy Correspondences, NC) for certain instances. As a remedy, numerous IV- and NC-oriented multi-view clustering (MvC) methods have been proposed, which however require either reliable correspondences or sufficiently complete instances, thus stopping short of addressing the imperfect information problem. In contrast, we observe that both IV and NC challenges originate from the same issue of imperfect cross-view counterpart information, where the counterpart of an anchor instance in another view might be either unavailable or unreliable. Based on the observation, we propose a novel robust MvC framework, termed Posterior-guided Latent Counterpart Inference (PLCI), which could handle both IV and NC in a unified manner. Specifically, PLCI formulates the desired cross-view counterpart of each anchor instance as a latent variable, and integrates both instance-level reliability and prototype-level semantic transport to infer the posterior distribution of the latent counterpart. Extensive experiments on six widely-used multi-view datasets against 10 state-of-the-art MvC methods demonstrate the effectiveness of PLCI for tackling the imperfect information problem. The code will be released upon acceptance.", "date": "2026-06-03", "categories": []}
{"id": "2605.30225", "title": "ExDBSCAN: Explaining DBSCAN with Counterfactual Reasoning -- Additional Material", "abstract": "Clustering is an unsupervised technique for grouping data points by similarity. While explainability methods exist for supervised machine learning, they are not directly applicable to clustering, making it challenging to understand cluster assignments. This interpretability gap is particularly evident in the popular density-based method DBSCAN, which assigns points as inliers (cluster members in dense regions) or outliers (noise points in sparse regions). DBSCAN does not provide insight into why a particular point receives its assignment or whether its assignment is robust to small changes in the data. To address the lack of explainability, we introduce ExDBSCAN, a density-aware, post-hoc explanation method. ExDBSCAN offers actionable counterfactual explanations, with theoretical guarantees for validity. It generates multiple counterfactuals using a density connected weighted graph, adopting a physics-inspired model that repels counterfactual candidates from one another (diversity), while pulling them toward the instance to explain (proximity). Empirical evaluation on 30 tabular datasets comparing against four baselines shows that ExDBSCAN outperforms all baselines while attaining perfect validity and retrieving diverse, proximal counterfactuals.", "date": "2026-05-28", "categories": []}
{"id": "2212.07944", "title": "Variable Clustering via Distributionally Robust Nodewise Regression", "abstract": "We study a multi-factor block model for variable clustering and connect it to regularized subspace clustering through a distributionally robust version of nodewise regression. To solve the latter problem, we derive a convex relaxation, provide a data-driven approach for selecting the size of the robust region, and develop an ADMM algorithm for efficient implementation. We validate our method in extensive numerical studies and demonstrate its superior performance.", "date": "2022-12-15", "categories": []}
{"id": "2411.12438", "title": "Dimension Reduction via Sum-of-Squares and Improved Clustering Algorithms for Non-Spherical Mixtures", "abstract": "We develop a new approach for clustering non-spherical (i.e., arbitrary component covariances) Gaussian mixture models via a subroutine, based on the sum-of-squares method, that finds a low-dimensional separation-preserving projection of the input data. Our method gives a non-spherical analog of the classical dimension reduction, based on singular value decomposition, that, among several other applications, forms a key component of the celebrated spherical clustering algorithm of Vempala and Wang [VW04].\n  As applications, we obtain an algorithm to (1) cluster an arbitrary total-variation separated mixture of $k$ centered (i.e., zero-mean) Gaussians with $n\\geq \\operatorname{poly}(d) f(w_{\\min}^{-1})$ samples and $\\operatorname{poly}(n)$ time, and (2) cluster an arbitrary total-variation separated mixture of $k$ Gaussians with identical but arbitrary unknown covariance with $n \\geq d^{O(\\log w_{\\min}^{-1})} f(w_{\\min}^{-1})$ samples and $n^{O(\\log w_{\\min}^{-1})}$ time. Here, $w_{\\min}$ is the minimum mixing weight of the input mixture, and $f$ does not depend on the dimension $d$. Our algorithms naturally extend to tolerating a dimension-independent fraction of arbitrary outliers. Before this work, the techniques in the state-of-the-art non-spherical clustering algorithms needed $d^{O(k)} f(w_{\\min}^{-1})$ samples and time for clustering such mixtures.\n  Our results may come as a surprise in the context of the $d^{\\Omega(k)}$ statistical query and sum-of-squares lower bounds [DKS17, DKPP24] for clustering non-spherical Gaussian mixtures. While these results are usually thought to rule out $d^{o(k)}$ cost algorithms for the problem, our results show that the lower bounds can in fact be circumvented for a remarkably general class of Gaussian mixtures.", "date": "2024-11-19", "categories": []}
{"id": "2504.19419", "title": "Advancing Local Clustering on Graphs via Compressive Sensing: Semi-supervised and Unsupervised Methods", "abstract": "Local clustering aims to identify specific substructures within a large graph without any additional structural information of the graph. These substructures are typically small compared to the overall graph, enabling the problem to be approached by finding a sparse solution to a linear system associated with the graph Laplacian. In this work, we first propose a method for identifying specific local clusters when very few labeled data are given, which we term semi-supervised local clustering. We then extend this approach to the unsupervised setting when no prior information on labels is available. The proposed methods involve randomly sampling the graph, applying diffusion through local cluster extraction, then examining the overlap among the results to find each cluster. We establish the co-membership conditions for any pair of nodes, and rigorously prove the correctness of our methods. Additionally, we conduct extensive experiments to demonstrate that the proposed methods achieve state of the art results in the low-label rates regime.", "date": "2025-04-28", "categories": []}
{"id": "2511.00064", "title": "SPORE: Skeleton Propagation Over Recalibrating Expansions", "abstract": "Many real-world datasets are not linearly separable, limiting the effectiveness of centroid-based clustering methods such as K-means. Density-based clustering methods address this limitation by identifying clusters with arbitrary geometric structure; however, existing approaches exhibit two persistent shortcomings. First, they often underperform in the presence of heterogeneous local densities, where a single density threshold cannot adequately capture clusters across multiple density scales. Second, they generally lack the clear boundary delineation naturally induced by the linear partitioning mechanism of centroid-based methods. This paper introduces SPORE (Skeleton Propagation Over Recalibrating Expansions), a clustering algorithm designed to address both challenges while preserving the geometric flexibility of density-based approaches. SPORE operates in two stages: an adaptive cluster expansion phase followed by a proximity-driven boundary propagation phase that maintains discriminative capability even under weak density contrast. The proposed method is evaluated on 28 benchmark datasets against established density-based baselines, with K-means included as a reference centroid-based method. Experimental results demonstrate that SPORE achieves significantly improved cluster recovery relative to all evaluated baselines (p < 0.01), while strong-performing configurations can be identified within five random-search evaluations.", "date": "2025-10-29", "categories": []}
{"id": "2602.24047", "title": "Unsupervised Baseline Clustering and Incremental Adaptation for IoT Device Traffic Profiling", "abstract": "The growth and heterogeneity of IoT devices create security challenges where static identification models can degrade as traffic evolves. This paper presents a two-stage, flow-feature-based pipeline for unsupervised IoT device traffic profiling and incremental model updating, evaluated on selected long-duration captures from the Deakin IoT dataset. For baseline profiling, density-based clustering (DBSCAN) isolates a substantial outlier portion of the data and produces the strongest alignment with ground-truth device labels among tested classical methods (NMI 0.78), outperforming centroid-based clustering on cluster purity. For incremental adaptation, we evaluate stream-oriented clustering approaches and find that BIRCH supports efficient updates (0.13 seconds per update) and forms comparatively coherent clusters for a held-out novel device (purity 0.87), but with limited capture of novel traffic (share 0.72) and a measurable trade-off in known-device accuracy after adaptation (0.71). Overall, the results highlight a practical trade-off between high-purity static profiling and the flexibility of incremental clustering for evolving IoT environments.", "date": "2026-02-27", "categories": []}
{"id": "2605.28209", "title": "Robust Contrastive Graph Clustering with Adaptive Local-Global Integration", "abstract": "Graph clustering is essential in graph analysis for revealing structural patterns and node communities. Despite recent advances in self-supervised contrastive learning that have improved clustering via structural and attribute signals, existing methods still struggle to flexibly capture high-order local structures and often overlook global semantics in complex graphs. These limitations lead to suboptimal node representations, especially in real-world graphs with fragmented structures and ambiguous cluster boundaries. To address these limitations, a contrastive graph clustering framework is proposed to jointly integrate multi-scale local structures with global semantics via attention mechanisms. At the local level, GNN-based topological signals extracted from multiple propagation depths are adaptively fused through attention-based weighting to capture multi-scale neighborhood features. At the global level, semantic prototypes derived from dynamically evolving cluster centers are adaptively aggregated through attention to guide node representations and enhance inter-cluster separability. The model is trained under a dual-view contrastive learning paradigm with a hybrid objective that combines instance-level and structure-aware losses to improve representation robustness and discrimination. Experiments on eight real-world graph datasets demonstrate that our method achieves competitive clustering performance. Code is available at https://github.com/vege12138/w2.", "date": "2026-05-27", "categories": []}
{"id": "2606.00302", "title": "ERICA: Quantifying Replicability of Cluster Analysis", "abstract": "Despite being ubiquitous in science, clustering remains a technique whose results are not quantitatively scrutinized via a framework. We present an analysis called evaluating replicability via iterative clustering assignments (ERICA) that is applied to a dataset to determine whether clusters are identified in a replicable manner. The pipeline computes a statistic that describes whether structure is found in a dataset. Quantitative visualization methods are presented to answer important questions such as the similarity between clusters, and the identity of points that may be outliers. When tested on synthetic data, the findings show clusters being discovered in a replicable manner. However, we note a possibility for non-replicable results when the pipeline is applied to three gene expression datasets for breast cancer subtype validation. The study underscores the need for rigorous inspection and offers a practical tool for doing so.", "date": "2026-05-29", "categories": []}
{"id": "2606.00327", "title": "Cluster Analysis with Resampling for Validation and Exploration (CARVE)", "abstract": "Clustering is widely used across the sciences as the foundation for downstream data-driven scientific discoveries. However, clustering results are highly sensitive to the choice of algorithm, preprocessing, and the number of clusters $k$, producing scientific claims that are often not reproducible. The current state of the art for validating clustering solutions consists of clustering validation indices (CVIs) such as Silhouette, Davies-Bouldin, and Calinski-Harabasz, which rely on geometric assumptions that break down on the heavy-tailed, high-dimensional, and nonlinearly structured data encountered in biomedical research. Resampling-based alternatives - grounded in the ideas of clustering stability and generalizability - have been proposed but remain scattered across specialized tools with no unified, accessible software. We fill this gap with CARVE (Cluster Analysis with Resampling for Validation and Exploration), an open-source Python and R package that jointly evaluates multiple clustering algorithms and hyperparameters, returning stability and generalizability diagnostics at the global, cluster, and sample level together with principled selection rules and consensus-based cluster labels. Across six synthetic benchmarks CARVE consistently recovers near-optimal clusterings where classical indices degrade substantially. On experimental genomics and proteomics data sets, CARVE recovers finer biological structure when classical CVIs collapse entirely. CARVE is available with a scikit-learn-compatible Python API and an analogous R interface compatible with Seurat workflows.", "date": "2026-05-29", "categories": []}
{"id": "2606.00342", "title": "PE-means: Improved Differentially Private $k$-means Clustering through Private Evolution", "abstract": "We study the problem of differentially private (DP) $k$-means clustering in Euclidean space. Previous solutions rely on summing the private data directly, which induces a sensitivity proportional to the domain. We introduce PE-means, an extension of the private evolution (PE) algorithm (an increasingly popular method for synthetic data generation), to the problem of $k$-means clustering. The key advantage of PE is that it only computes a private histogram with constant sensitivity to guide the evolution. Our adaptation of PE includes new evolutionary operators for clustering, as well as other algorithmic improvements of independent interest. Overall, PE-means achieves an average improvement of 20% in clustering loss over state-of-the-art baselines.", "date": "2026-05-29", "categories": []}
{"id": "2606.01255", "title": "Agentic Clustering: Controllable Text Taxonomies via Multi-Agent Refinement", "abstract": "Recent text-clustering methods use large language models to propose a cluster taxonomy from a corpus and then assign each text to it. These pipelines are fundamentally programmatic: the sequence of LLM calls and the rules for stopping, merging, and splitting clusters are fixed in code in advance, so they generalise poorly across corpora of different structure and cannot easily incorporate user-supplied constraints such as a target cluster count or a clustering intent. We propose an agentic alternative in which an orchestrator LLM inspects the state of the discovery process at each step and dispatches one of a small set of specialised agents - proposer, synthesizer, auditor, investigator, and critic - adapting the pipeline to the corpus rather than executing a fixed one. On seven public text-clustering benchmarks the method achieves state-of-the-art performance, beating the strongest prior LLM baseline by up to 32% in ARI.", "date": "2026-05-31", "categories": []}
{"id": "2606.01525", "title": "Semi-Supervised Hyperbolic Hierarchical Clustering with Set-Level Structural Priors", "abstract": "Semi-supervised hierarchical clustering aims to learn a tree structure consistent with data patterns and user-provided supervision. Supervision is usually given as leaf-level relations, such as pairwise must-link/cannot-link constraints or triplet-wise must-link-before constraints. Although useful for regulating local sample relations, such supervision does not directly indicate which samples should form coherent subtrees. Consequently, the non-leaf structure of the learned tree may deviate from the hierarchical organization preferred by ground-truth labels. To address this limitation, we propose a semi-supervised hyperbolic hierarchical clustering method with set-level structural priors. The main contribution is to introduce sets as basic modeling units for hierarchy learning. Each set denotes samples expected to cohere within a subtree and is induced from leaf-level supervision together with a learned constraint-consistent similarity structure. These sets act as soft structural priors for subtree-level supervision, allowing supervision to guide non-leaf hierarchy formation beyond local leaf-level relations. Specifically, we first learn constraint-consistent embeddings to obtain a reliable set partition, then construct constraint-induced sets and estimate inter-set similarities to form set-level structural priors. Finally, these priors are incorporated into a hyperbolic hierarchy objective for continuous tree optimization. Experiments on eleven benchmark datasets and ablation studies show that the proposed method consistently improves label consistency over representative hierarchical clustering baselines while also enhancing similarity-based tree quality.", "date": "2026-06-01", "categories": []}
{"id": "2605.30700", "title": "Mathematical Morphology in Machine Learning", "abstract": "This work introduces mathematical morphology-an established visual computing theory-into machine learning to exploit shape and density aspects often overlooked by standard techniques. We propose a fast clustering algorithm based on morphological reconstruction that accurately preserves cluster shapes and density. This scheme offers unique features: an intrinsic sense of maximal clusters, cost-free noise removal, and diverse growth patterns controlled by structuring elements.Additionally, we propose a novel distance metric combining Minkowski and Chebyshev distances, highly efficient for morphological dilations. In $Z^2$ discrete neighbourhood iterations, it is roughly 1.3 times faster than Manhattan and 329.5 times faster than Euclidean distances. When evaluated using a k-Nearest Neighbours (k-NN) classifier across 33 UCI datasets against 14 other distances, our metric achieved above-average accuracies most frequently (26 of 33 cases) and the best overall accuracy in 9 cases.Finally, we introduce novel morphological classifiers. Unlike current literature, this proposal uniquely models shape, density, and fractal information in datasets.", "date": "2026-05-29", "categories": []}
{"id": "2601.01162", "title": "Bridging the Semantic Gap for Categorical Data Clustering via Large Language Models", "abstract": "Qualitative data are widespread in domains such as healthcare, marketing, and bioinformatics, where clustering offers a fundamental tool for pattern discovery. A core difficulty of qualitative-data clustering lies in measuring similarity among attribute values that carry no inherent ordering or distance. To recover such relationships, existing studies typically rely on within-dataset co-occurrence statistics. This statistical route, however, becomes unreliable once the sample size is small, and the semantic context of each value is therefore left underexploited. Motivated by this limitation, this paper proposes BREVE (Balanced Representation via External Value Enrichment), a clustering framework that enriches each qualitative value with extra semantic dimensions drawn from an external knowledge base. That is, every unique value is expanded by a dense embedding that encodes its semantic content. To prevent the original value identity from being diluted by the added dimensions, a lightweight one-hot component is further appended. An adaptive weight, guided by cluster compactness, then determines how strongly the enrichment dimensions enter the final representation. With this design, experiments on eight benchmark datasets yield an average ARI rank of 1.3 against seven representative competitors.", "date": "2026-01-03", "categories": []}
{"id": "2605.29933", "title": "CLUBench: A Clustering Benchmark", "abstract": "Clustering is a fundamental problem in data science with a long-standing research history, yielding numerous insightful algorithms. Despite this progress, a systematic and large-scale empirical evaluation that jointly considers conventional algorithms, deep learning-based methods, and recent foundation model-based clustering remains largely absent, leading to limited guidance on algorithm selection and deployment. To address this gap, we introduce CLUBench, a comprehensive clustering benchmark comprising 24 algorithms of diverse principles evaluated on 131 datasets across tabular, text, and image data, involving 178,815 experiments. Importantly, our analyses of (i) the impact of hyperparameter tuning,(ii) the impact of data types and characteristics,(iii) the impact of pretrained embeddings,(iv) large language model-based clustering,(v) the similarity of algorithms, and (vi) the low-rank structures of performance matrices, yield meaningful insights and promising pathways for clustering research. For instance, our study reveals that: 1) All evaluated deep clustering methods do not exhibit a significant advantage compared with the top-performing conventional clustering algorithms (e.g., KMeans, SpeClu) in terms of average performance; 2) For image and text clustering tasks, combining pretrained embeddings with conventional clustering algorithms (e.g., KMeans, SpeClu) offers effective and efficient clustering; 3) Clustering remains a challenging and nontrivial problem, even in the era of increasingly dominant foundation models. Moreover, we propose to use the low-rank structure in cross-model performance matrices to efficiently approximate the overall performance evaluation in practical applications. We further demonstrate the feasibility of model selection based on the performance matrices across all hyperparameter configurations.", "date": "2026-05-28", "categories": []}
{"id": "2605.30175", "title": "A new completely parameter-free clustering algorithm for unsupervised classification of BATSE gamma-ray bursts", "abstract": "Cluster analysis is a widely applied machine learning technique to understand the existing patterns in the population of gamma-ray bursts (GRBs), in order to explore their physical sources. In the present scenario, the number of clusters corresponding to differentiable groups is still under conflict, in spite of numerous attempts with the state-of-the-art clustering procedures. This crucial unknown parameter needs to be evaluated, either directly or indirectly in terms of other tuning parameters, to produce the clusters in GRBs through implementation of an appropriate clustering algorithm. While most of the applied algorithms reached two physically explained groups of merger and collapsar predominated by the short and long bursts respectively, other statistical approaches violated this binary partition. However, physical establishment of any additional cluster(s) is not yet confirmed. Therefore, we propose a new algorithm, from a different stream of clustering referred to as `completely parameter-free', which carries out the classification of GRBs in a manner that has not been tried so far. It indicates two main groups, of short and long duration bursts from the BATSE sample, compatible with the merger-collapsar theory.", "date": "2026-05-28", "categories": []}
{"id": "2310.01285", "title": "Automated regime classification in multidimensional time series data using sliced Wasserstein k-means clustering", "abstract": "Recent work has proposed Wasserstein k-means (Wk-means) clustering as a powerful method to classify regimes in time series data, and one-dimensional asset returns in particular. In this paper, we begin by studying in detail the behaviour of the Wasserstein k-means clustering algorithm applied to synthetic one-dimensional time series data. We extend the previous work by studying, in detail, the dynamics of the clustering algorithm and how varying the hyperparameters impacts the performance over different random initialisations. We compute simple metrics that we find to be useful in identifying high-quality clusterings. We then extend the technique of Wasserstein k-means clustering to multidimensional time series data by approximating the multidimensional Wasserstein distance as a sliced Wasserstein distance, resulting in a method we call 'sliced Wasserstein k-means (sWk-means) clustering'. We apply the sWk-means clustering method to the problem of automated regime classification in multidimensional time series data, using synthetic data to demonstrate the validity and effectiveness of the approach. Finally, we show that the sWk-means method is able to identify distinct market regimes in real multidimensional financial time series, using publicly available foreign exchange spot rate data as a case study. We conclude with remarks about some limitations of our approach and potential complementary or alternative approaches.", "date": "2023-10-02", "categories": []}
{"id": "2601.10494", "title": "CROCS: A Two-Stage Clustering Framework for Behaviour-Centric Consumer Segmentation with Smart Meter Data", "abstract": "With grid operators confronting rising uncertainty from renewable integration and a broader push toward electrification, Demand-Side Management (DSM) -- particularly Demand Response (DR) -- has attracted significant attention as a cost-effective mechanism for balancing modern electricity systems. Unprecedented volumes of consumption data from a continuing global deployment of smart meters enable consumer segmentation based on real usage behaviours, promising to inform the design of more effective DSM and DR programs. However, existing clustering-based segmentation methods insufficiently reflect the behavioural diversity of consumers, often relying on rigid temporal alignment, and faltering in the presence of anomalies, missing data, or large-scale deployments.\n  To address these challenges, we propose a novel two-stage clustering framework -- Clustered Representations Optimising Consumer Segmentation (CROCS). In the first stage, each consumer's daily load profiles are clustered independently to form a Representative Load Set (RLS), providing a compact summary of their typical diurnal consumption behaviours. In the second stage, consumers are clustered using the Weighted Sum of Minimum Distances (WSMD), a novel set-to-set measure that compares RLSs by accounting for both the prevalence and similarity of those behaviours. Finally, community detection on the WSMD-induced graph reveals higher-order prototypes that embody the shared diurnal behaviours defining consumer groups, enhancing the interpretability of the resulting clusters.\n  Extensive experiments on both synthetic and real Australian smart meter datasets demonstrate that CROCS captures intra-consumer variability, uncovers both synchronous and asynchronous behavioural similarities, and remains robust to anomalies and missing data, while scaling efficiently through natural parallelisation. These results...", "date": "2026-01-15", "categories": []}
{"id": "2601.16091", "title": "Delayed Assignments in Online Non-Centroid Clustering with Stochastic Arrivals", "abstract": "Clustering is a fundamental problem, aiming to partition a set of elements, like agents or data points, into clusters such that elements in the same cluster are closer to each other than to those in other clusters. In this paper, we present a new framework for studying online non-centroid clustering with delays, where elements, that arrive one at a time as points in a finite metric space, should be assigned to clusters, but assignments need not be immediate. Specifically, upon arrival, each point's location is revealed, and an online algorithm has to irrevocably assign it to an existing cluster or create a new one containing, at this moment, only this point. However, we allow decisions to be postponed at a delay cost, instead of following the more common assumption of immediate decisions upon arrival. This poses a critical challenge: the goal is to minimize both the total distance costs between points in each cluster and the overall delay costs incurred by postponing assignments. In the classic worst-case arrival model, where points arrive in an arbitrary order, no algorithm has a competitive ratio better than sublogarithmic in the number of points. To overcome this strong impossibility, we focus on a stochastic arrival model, where points' locations are drawn independently across time from an unknown and fixed probability distribution over the finite metric space. We offer hope for beyond worst-case adversaries: we devise an algorithm that is constant competitive in the sense that, as the number of points grows, the ratio between the expected overall costs of the output clustering and an optimal offline clustering is bounded by a constant.", "date": "2026-01-22", "categories": []}
{"id": "2605.12961", "title": "Reducing Bias and Variance: Generative Semantic Guidance and Bi-Layer Ensemble for Image Clustering", "abstract": "Image clustering aims to partition unlabeled image datasets into distinct groups. A core aspect of this task is constructing and leveraging prior knowledge to guide the clustering process. Recent approaches introduce semantic descriptions as prior information, most of which typically relying on matching-based techniques with predefined vocabularies. However, the limited matching space restricts their adaptability to downstream clustering tasks. Moreover, these methods primarily focus on reducing bias to improve performance, frequently overlooking the importance of variance reduction. To address these limitations, we propose GSEC (Image Clustering based on Generative Semantic Guidance and Bi-Layer Ensemble), a framework designed to reduce bias through generative semantic guidance and mitigate variance via ensemble learning. Our method employs Multimodal Large Language Models to generate semantic descriptions and derive image embeddings via weighted averaging. Additionally, a bi-layer ensemble strategy integrates cross-modal information through BatchEnsemble in the inner layer and aligns outputs via an alignment mechanism in the outer layer. Comparative experiments demonstrate that GSEC outperforms 18 state-of-the-art methods across six benchmark datasets, while further analysis confirms its effectiveness in simultaneously reducing both bias and variance. The code is available at https://github.com/2017LI/GSEC.git.", "date": "2026-05-13", "categories": []}
{"id": "2605.24422", "title": "Clustering based on Stochastic Dominance with application for risk averters and risk seekers", "abstract": "Stochastic Dominance (SD) theory provides a rigorous framework for selecting superior assets tailored to the asset allocation needs of investors with varying risk preferences (i.e., risk-averse, risk-seeking, and risk-neutral). However, traditional stock clustering methods typically rely on geometric metrics such as Euclidean distance, which often fail to effectively capture the intrinsic risk dominance relationships among assets. To address this limitation, this paper proposes an innovative clustering analysis framework based on SD test statistics. Methodologically, this study deeply integrates SD theory with machine learning algorithms. Transcending the limitations of traditional reliance on geometric distance, we innovatively utilize test statistics from first-, second-, and third-order SD to construct a \"Stochastic Dominance Coefficient Matrix.\" Building upon this matrix, we modify the classic K-means and Hierarchical Clustering algorithms. Specifically, we derive 12 distinct algorithm variants tailored to different orders of SD relationships. Simultaneously, we construct the SD-SC coefficient and the SD-DBI index as specialized validity indices to evaluate the clustering performance. Empirically, we analyze constituent stock data from a representative developed market (the US NASDAQ Index) and an emerging market (China's CSI 100 Index). The results verify the effectiveness and robustness of the proposed method. Furthermore, we apply the clustering results to the modification of the Single Index Model and the construction of Global Minimum Variance Portfolios (GMVP). The findings demonstrate that the proposed method effectively facilitates customized asset allocation for investors, holding significant theoretical value and practical implications.", "date": "2026-05-23", "categories": []}
{"id": "2605.24673", "title": "Affinity Graph Connectivity in Convex Clustering", "abstract": "We generalize finite-sample bounds for convex clustering to the setting where affinity weights appearing in the objective correspond to a general connected graph. These bounds and their analysis lead to a better understanding of clustering behavior under various implied connectivity structures behind the data and to new rates of convergence for centroid recovery. The new theoretical framework is based on random walks, which allow application of concentration inequalities related to random graph models, and formalizes the relationship between the clustering performance and the connectivity of the graph structures. Through the form of the bound and empirical results, we argue proper tuning of hyperparameters to convex clustering problems should also include tuning of input affinity weights.", "date": "2026-05-23", "categories": []}
{"id": "2510.16335", "title": "On the Provable Importance of Gradients for Language-Assisted Image Clustering", "abstract": "This paper investigates the recently emerged problem of Language-assisted Image Clustering (LaIC), where textual semantics are leveraged to improve the discriminability of visual representations to facilitate image clustering. Due to the unavailability of true class names, one of core challenges of LaIC lies in how to filter positive nouns, i.e., those semantically close to the images of interest, from unlabeled wild corpus data. Existing filtering strategies are predominantly based on the off-the-shelf feature space learned by CLIP; however, despite being intuitive, these strategies lack a rigorous theoretical foundation. To fill this gap, we propose a novel gradient-based framework, termed as GradNorm, which is theoretically guaranteed and shows strong empirical performance. In particular, we measure the positiveness of each noun based on the magnitude of gradients back-propagated from the cross-entropy between the predicted target distribution and the softmax output. Theoretically, we provide a rigorous error bound to quantify the separability of positive nouns by GradNorm and prove that GradNorm naturally subsumes existing filtering strategies as extremely special cases of itself. Empirically, extensive experiments show that GradNorm achieves the state-of-the-art clustering performance on various benchmarks. Code is publicly available at \\href{https://github.com/60pen9/On-the-Provable-Importance-of-Gradients-for-Language-Assisted-Image-Clustering}{here}.", "date": "2025-10-18", "categories": []}
{"id": "2512.15436", "title": "Online Partitioned Local Depth for semi-supervised applications", "abstract": "We introduce an extension of the partitioned local depth (PaLD) algorithm that is adapted to online applications such as semi-supervised prediction. PaLD is best known for unsupervised, parameter-free clustering, but its robustness is based on triples of data points, making exact analysis computationally expensive. Research is ongoing to improve the scalability of the underlying discrete algorithm and expand the breath of PaLD's applications.\n  The new algorithm we present, online PaLD, is well-suited to situations where it is possible to pre-compute a cohesion network from a reference dataset. After $O(n^3)$ steps to construct a queryable data structure, online PaLD can extend the cohesion network to a new data point in $O(n^2)$ time. Our approach complements previous speed up approaches based on approximation and parallelism. In practical terms, online PaLD makes larger datasets accessible to exact analysis with a relatively simple implementation. We present applications to online anomaly detection and semi-supervised classification for health-care datasets as initial illustrations of online PaLD's potential to expand applications of the PaLD framework.", "date": "2025-12-17", "categories": []}
{"id": "2603.25958", "title": "Cluster-Adaptive Feature Extraction and its Theoretical Foundation with Minkowski Weighted k-Means", "abstract": "The Minkowski weighted $k$-means ($mwk$-means) algorithm extends classical $k$-means by incorporating feature weights and a Minkowski distance. We first show that the $mwk$-means objective can be expressed as a power-mean aggregation of within-cluster dispersions, with the order determined by the Minkowski exponent $p$. This formulation reveals how $p$ controls the transition between selective and uniform use of features. Using this representation, we derive bounds for the objective function and characterise the structure of the feature weights, showing that they depend only on relative dispersion and follow a power-law relationship with dispersion ratios. This leads to explicit guarantees on the suppression of high-dispersion features, and we establish convergence of the algorithm. Building on these theoretical results, we introduce Cluster-Adaptive Feature Extraction (CAFE), a method that uses the $mwk$-means feature weights to rescale the data prior to unsupervised feature extraction. We prove that this rescaling reverses the within-cluster dispersion ordering, suppressing noisy features and amplifying informative ones. Numerous experiments conducted under controlled within-cluster noise show that CAFE consistently improves the results of traditional feature extraction methods.", "date": "2026-03-26", "categories": []}
{"id": "2605.22410", "title": "Minimum Description Length based Granular-Ball Tree Regularization for Spectral Clustering", "abstract": "Spectral clustering largely depends on the affinity graph, yet constructing a graph that preserves reliable local connectivity while adapting to heterogeneous data structures remains challenging. Existing granular-ball-based spectral clustering methods usually reduce graph complexity by using coarse-grained representatives. However, the learned local regions are often treated as graph nodes or anchors, and their structural information is not sufficiently used to regularize the original sample-level graph. To address this issue, this paper proposes a Minimum Description Length based Granular-Ball Tree-Regularized Spectral Clustering method, termed MDL-GBTRSC. The proposed method constructs a granular-ball tree through local MDL model selection, with reciprocal neighborhood continuity used to discourage splits that break reliable local connections. The stable leaf balls obtained from the tree provide coding-scale information for regularizing the sample-level affinity graph. In addition, a shared-neighbor bridge code is introduced to adjust weak local bridge relations without requiring an additional user-specified threshold. In this way, MDL-GBTRSC connects interpretable local representation learning with affinity graph construction in a unified spectral clustering framework. Experiments on real and synthetic datasets show that MDL-GBTRSC achieves the best average ARI and NMI under the adopted fixed-configuration protocol compared with classical spectral clustering baselines and representative granular-ball, micro-cluster, and anchor-based methods.", "date": "2026-05-21", "categories": []}
{"id": "2605.21301", "title": "Automatic Discovery of Disease Subgroups by Contrasting with Healthy Controls", "abstract": "In biomedical Subgroup Discovery, practitioners are interested in discovering interpretable and homogeneous subgroups within a group of patients. In this paper, assuming that healthy subjects (i.e., controls) share common but irrelevant factors of variation with the patients, we motivate and develop a Contrastive Subgroup Discovery method, entitled Deep UCSL. By contrasting patients with controls, Deep UCSL identifies subgroups driven solely by pathological factors, ignoring common variability shared with healthy subjects. Our framework employs a deep feature extractor to learn a discriminative representation space. Mathematically, we derive a novel loss based on the conditional joint likelihood of latent clusters and patient/control labels, optimized via an Expectation-Maximization strategy alternating between subgroup inference and feature encoder updates. A regularization term further encourages representations to capture disease-specific variability while ignoring variability shared with controls. Compared to previous related works, our approach quantitatively improves the quality of the estimated subgroups, as demonstrated on a MNIST example and four distinct real medical imaging datasets. Code and datasets are available at: https://github.com/rlouiset/deep_ucsl.", "date": "2026-05-20", "categories": []}
{"id": "2404.16676", "title": "Multilayer Correlation Clustering", "abstract": "We establish Multilayer Correlation Clustering, a novel generalization of Correlation Clustering to the multilayer setting. In this model, we are given a series of inputs of Correlation Clustering (called layers) over the common set $V$ of $n$ elements. The goal is to find a clustering of $V$ that minimizes the $\\ell_p$-norm ($p\\geq 1$) of the multilayer-disagreements vector, which is defined as the vector (with dimension equal to the number of layers), each element of which represents the disagreements of the clustering on the corresponding layer. For this generalization, we first design an $O(L\\log n)$-approximation algorithm, where $L$ is the number of layers. We then study an important special case of our problem, namely the problem with the so-called probability constraint. For this case, we first give an $(\\alpha+2)$-approximation algorithm, where $\\alpha$ is any possible approximation ratio for the single-layer counterpart. Furthermore, we design a $4$-approximation algorithm, which improves the above approximation ratio of $\\alpha+2=4.5$ for the general probability-constraint case. Computational experiments using real-world datasets support our theoretical findings and demonstrate the practical effectiveness of our proposed algorithms.", "date": "2024-04-25", "categories": []}
{"id": "2510.23507", "title": "A Deep Latent Factor Graph Clustering with Fairness-Utility Trade-off Perspective", "abstract": "Fair graph clustering seeks partitions that respect network structure while maintaining proportional representation across sensitive groups, with applications spanning community detection, team formation, resource allocation, and social network analysis. Many existing approaches enforce rigid constraints or rely on multi-stage pipelines (e.g., spectral embedding followed by $k$-means), limiting trade-off control, interpretability, and scalability. We introduce \\emph{DFNMF}, an end-to-end deep nonnegative tri-factorization tailored to graphs that directly optimizes cluster assignments with a soft statistical-parity regularizer. A single parameter $\\lambda$ tunes the fairness--utility balance, while nonnegativity yields parts-based factors and transparent soft memberships. The optimization uses sparse-friendly alternating updates and scales near-linearly with the number of edges. Across synthetic and real networks, DFNMF achieves substantially higher group balance at comparable modularity, often dominating state-of-the-art baselines on the Pareto front. The code is available at https://github.com/SiamakGhodsi/DFNMF.git.", "date": "2025-10-27", "categories": []}
{"id": "2605.18880", "title": "A Multi-Dimensional Clustering Approach for Identifying Inborn Errors of Immunity", "abstract": "Rare diseases such as inborn errors of immunity (IEI) require early diagnosis to prevent end organ damage and improve quality of life. Hurdles in accessing and curating large scale electronic health record (EHR) data limit routine data driven analyses to remain on the forefront of IEI and other rare disease trends. Development of machine learning (ML) algorithms in IEI for pattern recognition as well as published methodology examining how to systematically process and integrate complex medical data is limited. Our proposed pipeline, including data curation and ML clustering algorithms, is designed to recognize novel rare disease patterns and extract IEI- associated features from a national data registry. Our methodology for EHR data formatting and processing presents the pipeline that transforms raw immunologic lab data into vectors. This is further combined with hyperparameter tuning for diseases pattern recognition via clustering. This study refines IEI feature awareness, develops data tool kits for rare disease populations analysis, and expands on transforming complex medical records in data structures interpretable by unsupervised ML.", "date": "2026-05-16", "categories": []}
{"id": "2406.15797", "title": "$\\texttt{SynC}$: Synergistic Boosting of Structure and Representation for Deep Graph Clustering", "abstract": "Employing graph neural networks (GNNs) for graph clustering has shown promising results in deep graph clustering. However, existing methods disregard the reciprocal relationship between representation learning and structure augmentation: the more homogeneous the graph, the more cohesive the node representations; the more cohesive the node representations, the more reliable the structure augmentation becomes. Moreover, the generalization ability of existing GNN-based models on the low homophily graph is relatively poor. To this end, we propose a graph clustering framework named Synergistic Deep Graph Clustering Network (SynC). SynC employs a Transform Input Graph Auto-Encoder (TIGAE) to obtain high-quality embeddings via mitigating the representations collapse issue of GAE for guiding structure augmentation. Then, we re-capture neighborhood representations on the refined graph to obtain clustering-friendly embeddings and conduct self-supervised clustering. Notably, these two stages share weights, resulting in synergistic boosting while significantly reducing the number of model parameters. Additionally, we introduce a structure fine-tuning strategy to improve the model's generalization on the low homophily graph. Extensive experiments on benchmark datasets demonstrate the superiority of SynC. The code is released at GitHub.", "date": "2024-06-22", "categories": []}
{"id": "2605.16320", "title": "AdaGraph: A Graph-Native Clustering Algorithm That Overcomes the Curse of Dimensionality and Enables Scientific Discovery", "abstract": "We present AdaGraph, a graph-native clustering algorithm born from the Structure-Centric Machine Learning (SC-ML) paradigm -- a new field of unsupervised learning that replaces geometry-centric (distance-based) computation with structure-centric (topology-based) computation, fundamentally dissolving the curse of dimensionality. AdaGraph operates entirely within the kNN graph topology, a representation that retains meaningful relational structure in arbitrarily high dimensions where Euclidean distance metrics become uninformative. AdaGraph requires no a priori specification of the number of clusters k, handles noise natively, and scales via the SLCD (Sample-Learn-Calibrate-Deploy) prototype-deployment framework. As its unsupervised tuning objective, AdaGraph pairs with Graph-SCOPE, the topology-based cluster validity index introduced as a separate SC-ML contribution. On 10 synthetic benchmarks spanning d=10 to d=5000, Graph-SCOPE achieves mean ARI=0.900 and correctly selects k on 9/10 datasets -- outperforming Silhouette, Davies-Bouldin, and Calinski-Harabasz -- while maintaining Kendall tau >= 0.92 with ground-truth cluster quality across all dimensionalities (Silhouette: tau ~= 0.46). We validate AdaGraph across three scientific domains: (1) gene co-expression discovery in hepatocellular carcinoma (GSE14520, 10,000 genes, 488 patients, no dimensionality reduction), where AdaGraph identifies condition-specific gene modules that WGCNA, ICA, NMF, and Spectral Biclustering fail to resolve; (2) natural language text clustering, where AdaGraph achieves ARI=0.751 on 20NG-6cat versus HDBSCAN's 0.464 (62% relative improvement); (3) materials science clustering of superconductors (145-dimensional Magpie features), perovskites, and JARVIS-DFT materials, where AdaGraph achieves the highest Graph-SCOPE on all three datasets.", "date": "2026-05-05", "categories": []}
{"id": "2605.18460", "title": "When Fireflies Cluster; Enhancing Automatic Clustering via Centroid-Guided Firefly Optimization", "abstract": "This work presents a novel variant of the Firefly Algorithm (FA) for data clustering, addressing limitations of traditional methods like K-Means that struggle with non-uniform cluster shapes, densities, and the need for pre-defining the number of clusters. The proposed algorithm introduces a centroid movement strategy and a multi-objective fitness function that balances compactness, separation, and a novel TSP-based navigation penalty. It automatically estimates the optimal number of clusters and dynamically adjusts cluster boundaries. Application to robotic sensor networks highlights its practical value, with experiments showing improved clustering quality and reduced intra-cluster path distances compared to K-Means. These results confirm the algorithm's robustness in complex spatial clustering tasks, with potential for future extensions to higher-dimensional and adaptive scenarios.", "date": "2026-05-18", "categories": []}
{"id": "2605.15640", "title": "Learning Disentangled Representations for Generalized Multi-view Clustering", "abstract": "Multi-View Clustering (MVC) has gained significant attention for its ability to leverage complementary information across diverse views. However, existing deep MVC methods often struggle with view-distribution entanglement during cross-view fusion, which hampers the quality of the shared latent space and leads to suboptimal Figures. To address this issue, we propose the Generalized Multi-view Auto-Encoder (GMAE), a framework designed to preserve cross-view complementarity through disentangled representation learning. Specifically, GMAE employs dual-path autoencoders to decouple source features into view-specific and view-common embeddings, facilitating the discovery of clearer clustering structures. We further construct cross-view adversarial discriminators to guide view-specific encoders in capturing more discriminative features. By strategically modulating mutual information, GMAE effectively aligns distributions and prevents representation collapse, ensuring the generation of robust, non-trivial embeddings. Comprehensive experiments on 13 benchmark datasets demonstrate that GMAE consistently outperforms state-of-the-art methods in both complete and incomplete MVC tasks. Our code implementation is available at the repository: https://github.com/obananas/GMAE.", "date": "2026-05-15", "categories": []}
{"id": "2511.05159", "title": "A New Framework for Convex Clustering in Kernel Spaces: Finite Sample Bounds, Consistency and Performance Insights", "abstract": "Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges them. Despite its advantages, this method can fail when dealing with data exhibiting linearly non-separable or non-convex structures. To mitigate the limitations, we propose a kernelized extension of the convex clustering method. This approach projects the data points into a Reproducing Kernel Hilbert Space (RKHS) using a feature map, enabling convex clustering in this transformed space. This kernelization not only allows for better handling of complex data distributions but also produces an embedding in a finite-dimensional vector space. We provide a comprehensive theoretical underpinning for our kernelized approach, proving algorithmic convergence and establishing finite sample bounds for our estimates. The effectiveness of our method is demonstrated through extensive experiments on both synthetic and real-world datasets, showing superior performance compared to state-of-the-art clustering techniques. This work marks a significant advancement in the field, offering an effective solution for clustering in non-linear and non-convex data scenarios.", "date": "2025-11-07", "categories": []}
{"id": "2601.21656", "title": "TabClustPFN: A Prior-Fitted Network for Tabular Data Clustering", "abstract": "Clustering tabular data is a fundamental yet challenging problem due to heterogeneous feature types, diverse data-generating mechanisms, and the absence of transferable inductive biases across datasets. Prior-fitted networks (PFNs) have recently demonstrated strong generalization in supervised tabular learning by amortizing Bayesian inference under a broad synthetic prior. Extending this paradigm to clustering is nontrivial: clustering is unsupervised, admits a combinatorial and permutation-invariant output space, and requires inferring the number of clusters. We introduce TabClustPFN, a prior-fitted network for tabular data clustering that performs amortized Bayesian inference over both cluster assignments and cluster cardinality. Pretrained on synthetic datasets drawn from a flexible clustering prior, TabClustPFN clusters unseen datasets in a single forward pass, without dataset-specific retraining or hyperparameter tuning. The model naturally handles heterogeneous numerical and categorical features and adapts to a wide range of clustering structures. Experiments on synthetic data and curated real-world tabular benchmarks show that TabClustPFN outperforms classical, deep, and amortized clustering baselines, while exhibiting strong robustness in out-of-the-box exploratory settings. Code is available at https://github.com/Tianqi-Zhao/TabClustPFN.", "date": "2026-01-29", "categories": []}
{"id": "2602.18435", "title": "CAKE: Confidence in Assignments via K-partition Ensembles", "abstract": "Clustering is widely used for unsupervised structure discovery, yet it offers limited insight into how reliable each individual assignment is. Diagnostics, such as convergence behavior or objective values, may reflect global quality, but they do not indicate whether particular instances are assigned confidently, especially for initialization-sensitive algorithms like k-means. This assignment-level instability can undermine both accuracy and robustness. Ensemble approaches improve global consistency by aggregating multiple runs, but they typically lack tools for quantifying pointwise confidence in a way that combines cross-run agreement with geometric support from the learned cluster structure. This work introduces CAKE (Confidence in Assignments via K-partition Ensembles), a framework that evaluates each point using two complementary statistics computed over a clustering ensemble: assignment stability and consistency of local geometric fit. These are combined into a single, interpretable score in [0,1]. The theoretical analysis shows that CAKE remains effective under noise and separates stable from unstable points. Experiments on synthetic and real-world datasets indicate that CAKE effectively highlights ambiguous points and stable core members, providing a confidence ranking over instances that can be used for selection or prioritization in downstream clustering workflows.", "date": "2026-02-20", "categories": []}
{"id": "2605.14828", "title": "K-Models: a Flexible and Interpretable Method for Ordinal Clustering with Application to Antigen-Antibody Interaction Profiles", "abstract": "Existing clustering methods for functional data often prioritize partitioning accuracy over interpretability, making it challenging to extract meaningful insights when the data-generating process follows a specific underlying structure and an ordinal relationship among clusters is suspected. This work introduces K-Models, a novel framework that integrates ordinal constraints and estimates key underlying elements of the random process generating the observed functional profiles, improving both interpretability and structure identification. The proposed method is evaluated through simulations and real-world applications. In particular, it is tested on Region of Interest (ROI) curves, which represent reaction profiles from a reflectometric sensor monitoring biomolecular interactions, such as antigen-antibody binding. These curves represent changes in reflected light intensity over time at multiple measurement spots with immobilized antigens during analyte exposure, capturing the binding dynamics of the system. The goal is to identify intrinsic signal patterns solely from the observed dynamics, making this dataset an ideal benchmark for assessing the added interpretability of the proposed approach. By incorporating structural assumptions into the clustering process, K-Models enhances interpretability while maintaining performance comparable to state-of-the-art techniques, providing a valuable tool for analyzing functional data with an underlying ordinal structure.", "date": "2026-05-14", "categories": []}
{"id": "2601.09051", "title": "Deep Incomplete Multi-View Clustering via Hierarchical Imputation and Alignment", "abstract": "Incomplete multi-view clustering (IMVC) aims to discover shared cluster structures from multi-view data with partial observations. The core challenges lie in accurately imputing missing views without introducing bias, while maintaining semantic consistency across views and compactness within clusters. To address these challenges, we propose DIMVC-HIA, a novel deep IMVC framework that integrates hierarchical imputation and alignment with four key components: (1) view-specific autoencoders for latent feature extraction, coupled with a view-shared clustering predictor to produce soft cluster assignments; (2) a hierarchical imputation module that first estimates missing cluster assignments based on cross-view contrastive similarity, and then reconstructs missing features using intra-view, intra-cluster statistics; (3) an energy-based semantic alignment module, which promotes intra-cluster compactness by minimizing energy variance around low-energy cluster anchors; and (4) a contrastive assignment alignment module, which enhances cross-view consistency and encourages confident, well-separated cluster predictions. Experiments on benchmarks demonstrate that our framework achieves superior performance under varying levels of missingness.", "date": "2026-01-14", "categories": []}
{"id": "2605.08759", "title": "MDL-GBG: A Non-parametric and Interpretable Granular-Ball Generation Method for Clustering", "abstract": "Existing granular-ball generation methods are still mainly driven by handcrafted quality measures and heuristic splitting or stopping criteria, which may weaken the transparency of local generation decisions in clustering. To address this issue, this paper proposes Minimum Description Length based Granular-Ball Generation (MDL-GBG), a non-parametric and interpretable granular-ball generation method for clustering. MDL-GBG reformulates granular-ball generation as a local model selection problem under the Minimum Description Length principle. For each granular ball, three candidate explanations are compared, namely a single-ball model, a two-ball model, and a core-ball-plus-residual model, and the model with the shortest description length is selected. In this way, ball retention, splitting, and residual peeling are unified within a common coding-theoretic framework. A residual reassignment mechanism is further introduced to re-evaluate peeled-off boundary samples after stable granular-balls are formed. Experiments on 20 UCI datasets show that the stable granular-balls generated by MDL-GBG provide an effective upstream representation for clustering. In particular, MDL-GBG+AC achieves the best average ranks in ARI, ACC, and NMI among the compared methods. These results indicate that MDL-GBG offers a principled and interpretable alternative to heuristic granular-ball generation strategies.", "date": "2026-05-09", "categories": []}
{"id": "2605.13128", "title": "Amortized Neural Clustering of Time Series based on Statistical Features", "abstract": "This paper introduces an algorithm-agnostic approach to feature-based time series clustering via amortized neural inference. By training neural networks to approximate the optimal partitioning rule from simulated data, the proposed framework reduces reliance on conventional clustering methods, such as $K$-means, $K$-medoids, or hierarchical clustering, and their associated objective functions and heuristics. Leveraging statistical features, such as autocorrelations and quantile autocorrelations, the approach learns a data-driven affinity structure from which clustering partitions can be recovered, without requiring explicit prior specification of cluster shapes or structures. In addition, one version of the method can automatically determine the number of clusters, avoiding ad-hoc selection procedures. Comprehensive empirical studies show that the proposed framework achieves competitive or superior clustering accuracy relative to traditional methods, even in challenging scenarios where competing techniques are provided with the true number of clusters. An application to financial time series of stock returns illustrates its practical utility. By reducing the need for algorithm selection and calibration, the proposed framework opens new possibilities for automated, adaptive, and data-driven clustering of temporal data across scientific and industrial domains.", "date": "2026-05-13", "categories": []}
{"id": "2605.13759", "title": "Fast and effective algorithms for fair clustering at scale", "abstract": "Clustering is an unsupervised machine learning task that consists of identifying groups of similar objects. It has numerous applications and is increasingly used in fairness-sensitive domains where objects represent individuals, such as customers, employees, or students. We address a fair clustering problem in which objects belong to protected groups. The problem consists of partitioning the objects into a predefined number of clusters while attaining a user-defined target level of fairness, meaning that each protected group is sufficiently represented in each cluster. The objective is to minimize the clustering cost, defined as the sum of squared Euclidean distances between the objects and the centers of their clusters. Since clustering cost and fairness are generally in conflict, managing the trade-off between them is essential in practical applications. Existing methods provide limited control over this trade-off and either fail to scale to large datasets or, when they scale, produce low-quality solutions. We propose a general framework for fair clustering that provides precise control over the cost-fairness trade-off and introduce three heuristics based on it. The first heuristic focuses on solution quality and the flexibility to incorporate additional constraints, the second improves scalability while retaining high solution quality, and the third is designed for maximum scalability, producing solutions for instances with millions of objects in seconds. The proposed heuristics outperform existing approaches in comprehensive numerical experiments on benchmark datasets. The source code of our heuristics and instructions for reproducing the experiments are publicly available on GitHub.", "date": "2026-05-13", "categories": []}
{"id": "2305.01507", "title": "A Parameter-free Adaptive Resonance Theory-based Topological Clustering Algorithm Capable of Continual Learning", "abstract": "In general, a similarity threshold (i.e., a vigilance parameter) for a node learning process in Adaptive Resonance Theory (ART)-based algorithms has a significant impact on clustering performance. In addition, an edge deletion threshold in a topological clustering algorithm plays an important role in adaptively generating well-separated clusters during a self-organizing process. In this paper, we propose an ART-based topological clustering algorithm that integrates parameter estimation methods for both the similarity threshold and the edge deletion threshold. The similarity threshold is estimated using a determinantal point process-based criterion, while the edge deletion threshold is defined based on the age of edges. Experimental results with synthetic and real-world datasets show that the proposed algorithm has superior clustering performance to state-of-the-art clustering algorithms without requiring parameter specifications specific to the datasets. Source code is available at https://github.com/Masuyama-lab/CAE", "date": "2023-05-01", "categories": []}
{"id": "2504.14697", "title": "Quantitative Clustering in Mean-Field Transformer Models", "abstract": "The evolution of tokens through deep transformer models can be modeled as an interacting particle system that has been shown to exhibit an asymptotic clustering behavior akin to the synchronization phenomenon in Kuramoto models. In this work, we investigate the long-time clustering of mean-field transformer models. More precisely, under suitable assumptions on the transformer model parameters, we establish that any suitably regular mean-field initialization synchronizes exponentially fast to a Dirac point mass, with explicit quantitative convergence rates.", "date": "2025-04-20", "categories": []}
{"id": "2510.07136", "title": "Differentially Private Spectral Graph Clustering: Balancing Privacy, Accuracy, and Efficiency", "abstract": "We study spectral graph clustering under edge differential privacy. We propose a matrix shuffling mechanism that combines randomized edge flipping with a random permutation of the adjacency matrix. While edge flipping alone provides only a constant $\\varepsilon$ guarantee as the graph grows, shuffling amplifies privacy so that the effective $\\varepsilon$ tends to zero with the number of nodes. We develop a unified error analysis framework -- based on Davis--Kahan perturbation theory and a classification-margin bound -- that gives explicit misclassification rates for all the mechanisms considered as a function of the privacy budget, eigengap, and number of communities. Applying this framework, we show that the matrix shuffling mechanism achieves an error rate scaling of $\\tilde{O}(1/n)$, a clear improvement over two canonical DP baselines from the private PCA literature: the Gaussian mechanism applied directly to the adjacency matrix (Analyze Gauss) and the noisy power method, both of which scale as $\\tilde{O}(1)$ in $n$. We further propose a private spectral gap detection algorithm for estimating the number of communities. Experiments on synthetic and real-world networks validate our theoretical findings.", "date": "2025-10-08", "categories": []}
{"id": "2605.08673", "title": "PHIDA: Persistence-Guided Node-to-Cluster Mapping for Online Clustering", "abstract": "Online clustering methods that adaptively create and update nodes as data arrive often make node learning explicit, whereas the mapping from the learned node state to output clusters often remains implicit or simplified. Implicit mappings make output clusters sensitive to weak graph bridges or local relations based on distance in the graph over learned nodes, leaving no explicit constraint on which node groups remain intact during mapping. This paper addresses this gap by proposing PHIDA, a persistence-guided node-to-cluster mapping method for online clustering with learned nodes. PHIDA implements this mapping within Adaptive Resonance Theory (ART)-based online clustering by combining Inverse-Distance ART (IDA) node learning with node-to-cluster mapping constrained by Persistent Homology (PH). Experiments on 24 benchmark datasets show that PHIDA achieves the best average ranks in stationary comparisons that include the recent stationary-only clustering methods, while also improving aggregate performance in the nonstationary setting over the evaluated online methods that adaptively create and update nodes. Ablations and comparisons with conventional node-to-cluster mappings indicate that the observed gains are associated with PH-constrained mapping that preserves raw PH components, together with the use of the PH component view during node learning. Source code is available at https://github.com/Masuyama-lab/PHIDA", "date": "2026-05-09", "categories": []}
{"id": "2605.07119", "title": "Classification Fields: Arbitrarily Fine Recursive Hierarchical Clustering From Few Examples", "abstract": "Classical clustering methods usually return either a finite partition of the observed data or a finite dendrogram over it. This finite-sample view is inadequate when the hierarchy of interest is a recursive geometric object with fine-scale refinements that continue beyond the levels directly observed. We introduce classification fields: infinite-depth hierarchical cluster structures on $\\mathbb{R}^d$ generated by a local parent-to-child refinement rule. A classification field generator maps each parent centre to an ordered, bounded, and separated tuple of child residuals. Together with a root and a scale factor, this rule recursively generates cluster centres, Voronoi cells, and a metric DAG encoding the hierarchy. Given only a finite prefix of such a hierarchy, we learn a classification field predictor that approximates the generator and can be rolled out to unseen depths. We prove exponential truncation convergence in the completed cell metric and ReLU realizability with width $O(\\varepsilon^{-\\gamma})$ and depth $\\widetilde O(\\varepsilon^{-3\\gamma/2})$, where $\\gamma=\\log K/(-\\log s)$, up to finite-window aspect-ratio factors. The approximation holds at the level of the induced compact metric structures, measured in the completed cell-metric Hausdorff distance. Experimental validation on matched CFG-generated hierarchies, IFS fractals, and image-induced recursive clustering hierarchies shows that learned predictors preserve ordered child slots, unordered geometry, and hierarchy-level path metrics under recursive rollout. These results support the claim that finite hierarchical observations can reveal local refinement rules capable of generating substantially deeper classification fields.", "date": "2026-05-08", "categories": []}
{"id": "2605.07130", "title": "Simple KNN-Based Outlier Detection Achieves Robust Clustering", "abstract": "Being robust to the presence of outliers is crucial for applying clustering algorithms in practice. In the $\\textit{robust $k$-Means}$ problem (i.e., $k$-Means with outliers), the goal is to remove $z$ outliers and minimize the $k$-Means cost on the remaining points. Despite the close connection between robust $k$-Means and outlier detection, both theoretical and empirical understanding of the effectiveness of $\\textit{classic outlier detection heuristics}$ for robust $k$-Means remains limited. In this paper, we prove that under a practical assumption on the optimal cluster sizes, simply removing points with large $K$-Nearest-Neighbor distances achieves performance comparable to prior work in terms of approximation guarantees: it yields a constant-factor reduction from robust $k$-Means to standard $k$-Means, without introducing additional centers or discarding extra outliers, as is commonly required by existing approaches. Empirically, experiments on real-world datasets show that our method outperforms or matches several more sophisticated algorithms in terms of clustering cost and runtime. These results demonstrate that simple KNN-based heuristics can be surprisingly effective for robust clustering, highlighting new opportunities to bridge techniques from outlier detection and clustering.", "date": "2026-05-08", "categories": []}
{"id": "2605.07424", "title": "A Flexible Adaptive Stable Clustering Algorithm for Archive-Scale Online Mass Spectrometry", "abstract": "Modern online mass spectrometry generates multi-terabyte data streams critical for understanding Earth's environmental systems. However, extracting actionable chemical insights from these repositories is impeded by a computational bottleneck: existing clustering methods force a compromise among scalability, metric flexibility, and algorithmic stability. Here, we introduce Flexible Adaptive Stable Clustering (FASC), a dynamical systems framework that resolves these constraints by architecturally decoupling the similarity kernel from rigorous optimization logic. Unlike legacy heuristics that suffer from stochastic drift and algorithmic blending, FASC employs a Density-Augmented Similarity Selection rule and geometric constraints to guarantee deterministic, order-independent convergence. After validating FASC on canonical machine-learning ground truths (achieving >99.5% cluster purity and 0.99 Adjusted Rand Index), we deployed the framework on 25 million mass spectra of atmospheric aerosols. Demonstrating strictly linear empirical runtime scaling (O(N)), FASC autonomously mapped atmospheric aging pathways of secondary inorganic aerosols while isolating ultra-rare industrial tracers (<0.2% abundance), providing a scalable infrastructure for mining environmental big data.", "date": "2026-05-08", "categories": []}
{"id": "2605.05996", "title": "Gaussian mixture models in Hilbert spaces via kernel methods", "abstract": "Modern datasets across many disciplines increasingly consist of time-evolving, potentially infinite-dimensional random objects, such as dynamic functional data, which are naturally modeled in Hilbert spaces. In these settings, characterizing probability measures, for example, through densities, can be ill-defined or technically challenging. Motivated by clustering applications, we propose a Gaussian mixture framework for Hilbert-space-valued data based on kernel mean embeddings and develop efficient optimization algorithms for estimation. We establish theoretical guarantees showing that the proposed algorithm is well defined and that the model yields a dense class of approximations in infinite-dimensional spaces. We evaluate the framework through extensive experiments on diverse structures and data geometries, including $L^2$-functional data and random graphs in Laplacian spaces arising in modern medical applications.", "date": "2026-05-07", "categories": []}
{"id": "2505.00359", "title": "TNStream: Applying Tightest Neighbors to Micro-Clusters to Define Multi-Density Clusters in Streaming Data", "abstract": "In data stream clustering, systematic theory of stream clustering algorithms remains relatively scarce. Recently, density-based methods have gained attention. However, existing algorithms struggle to simultaneously handle arbitrarily shaped, multi-density, high-dimensional data while maintaining strong outlier resistance. Clustering quality significantly deteriorates when data density varies complexly. This paper proposes a clustering algorithm based on the novel concept of Tightest Neighbors and introduces a data stream clustering theory based on the Skeleton Set. Based on these theories, this paper develops a new method, TNStream, a fully online algorithm. The algorithm adaptively determines the clustering radius based on local similarity, summarizing the evolution of multi-density data streams in micro-clusters. It then applies a Tightest Neighbors-based clustering algorithm to form final clusters. To improve efficiency in high-dimensional cases, Locality-Sensitive Hashing (LSH) is employed to structure micro-clusters, addressing the challenge of storing k-nearest neighbors. TNStream is evaluated on various synthetic and real-world datasets using different clustering metrics. Experimental results demonstrate its effectiveness in improving clustering quality for multi-density data and validate the proposed data stream clustering theory.", "date": "2025-05-01", "categories": []}
{"id": "2603.03235", "title": "The elbow statistic: Multiscale clustering statistical significance", "abstract": "Selecting the number of clusters remains a fundamental challenge in unsupervised learning. Existing approaches typically focus on identifying a single \"optimal\" partition, often overlooking statistically meaningful structure present across multiple resolutions. We introduce ElbowSig, a general inferential framework for assessing clustering structure over a range of resolutions. The method formalizes the elbow heuristic by defining a normalized discrete curvature statistic based on the sequence of within-cluster heterogeneity values, and evaluates its significance relative to a null distribution of unstructured data. This yields hypothesis tests across resolutions, enabling simultaneous inference at multiple clustering scales. We derive the asymptotic behavior of the null statistic in both large-sample and high-dimensional regimes, characterizing its limiting form and variability. Because it depends only on the heterogeneity sequence, ElbowSig is compatible with a wide range of clustering algorithms, including hard, fuzzy, and model-based methods. Experiments on synthetic and real datasets show that the procedure controls Type-I error under unstructured data while providing power to detect multiscale organization, revealing structure that is often missed by single-resolution selection criteria.", "date": "2026-03-03", "categories": []}
{"id": "2605.00390", "title": "Towards Robust and Scalable Density-based Clustering via Graph Propagation", "abstract": "We present \\textit{CluProp}, a novel framework that reimagines varied-density clustering in high-dimensional spaces as a label propagation process over neighborhood graphs. Our approach formally bridges the gap between density-based clustering and graph connectivity, leveraging efficient propagation mechanisms from network science to mitigate the parameter sensitivity inherent in traditional density-based methods. Specifically, we introduce a deterministic density-based propagation strategy to ensure scalable neighborhood identification. The framework is agnostic to the choice of distance metric and exhibits superior performance on large-scale data, processing millions of points in minutes while consistently outperforming existing baselines in accuracy.", "date": "2026-05-01", "categories": []}
{"id": "2604.22655", "title": "Associativity-Peakiness Metric for Contingency Tables", "abstract": "For the use case of comparing the performance of clustering algorithms whose output is a contingency table, a single performance metric for contingency tables is needed. Such a metric is vital for comparative performance analysis of clustering algorithms. A survey of publicly available literature did not show the presence of such a metric. Metrics do exist for vector pairs of truth values and predicted values, which are an alternative form of output of clustering algorithms. However, the metrics for vector pairs do not reveal the presence of detailed features that are apparent in contingency tables. This paper presents the Associativity Peakiness (AP) metric, which characterizes aspects of clustering algorithm performance that are critical for predicting a clustering algorithm's performance when deployed. The AP metric is analogous to measures of quality for confusion matrices that are outputs of supervised learning algorithms. This paper presents results from simulations in which 500 contingency tables were generated for multiple test scenarios. The results show that for the use case of evaluating clustering algorithms, the AP metric characterizes performance of contingency tables with higher dynamic range than publicly available metrics, and that it is computationally more efficient than comparable publicly available metrics.", "date": "2026-04-24", "categories": []}
{"id": "2604.26972", "title": "How Hard Is Continuous Clustering? Lower Bounds from the Existential Theory of the Reals", "abstract": "This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it contains certain cluster structures. Four natural questions are examined. First, do there exist several points with high density that are far apart from each other. Second, do two high density points have a midpoint with low density, creating a valley between them. Third, does the region where the density is above a threshold have at least a given number of separate connected pieces. Fourth, does that same region contain a hole, meaning a loop that cannot be shrunk to a point. We prove that the first two problems, separated points and valley detection, are exactly as hard as the existential theory of the reals, a complexity class that contains NP and is believed to be strictly larger. In contrast, the topological problems of counting connected pieces and detecting holes are at least as hard as the existential theory of the reals, but their exact complexity remains open. Placing them inside that class would need a major advance in real algebraic geometry. These results give the first rigorous classification of exact continuous clustering inside the real polynomial hierarchy. They also show that even basic clustering criteria are not NP complete unless unexpected collapses occur.", "date": "2026-04-24", "categories": []}
{"id": "2604.27721", "title": "Physically-Informed Fuzzy Clustering of Vertical Sounding Ionograms", "abstract": "This paper presents a physically-informed fuzzy clustering of vertical sounding ionograms for automatically separating the ionogram into tracks suitable for further interpretation and determining their optimal number. The model is designed for use not only in conditions where the number of tracks is known, but also in disturbed ionospheric conditions where the number of tracks is preliminary unknown.\n  The method is based on an expectation-maximization algorithm, used for clustering, and on parametrically specified distributions of distances from points to parametrically specified curves. The curves used as track models are close to model tracks in the parabolic ionospheric layer model. The resulting model of each track has six parameters: three standard ones (the critical frequency, the lower boundary of the layer, and its half-width), and three additional ones to take into account possible underlying layer effects. By sequentially increasing the number of tracks and optimizing their parameters, the model finds the optimal number of tracks on the ionogram by minimizing the modified Bayesian information criterion. The Sequential Least Squares Quadratic Programming algorithm is used to find the parameters of a single track. The width of each single track is assumed to be unknown constant found during fitting process.\n  To improve the quality of ionogram clustering, automatic adaptive noise filtering is performed before clustering. This filtering is based on a combination of the DBSCAN and Gaussian Mixture algorithms. Also, to improve clustering quality on an ionosonde without hardware separation of the ordinary and extraordinary components, a preliminary approximate removal of points belonging to the extraordinary mode is performed.", "date": "2026-04-30", "categories": []}
{"id": "2411.17838", "title": "Rock the KASBA: Blazingly Fast and Accurate Time Series Clustering", "abstract": "Time series data has become increasingly prevalent across numerous domains, driving a growing demand for time series machine learning techniques. Among these, time series clustering (TSCL) stands out as one of the most popular machine learning tasks. TSCL serves as a powerful exploratory analysis tool and is also employed as a preprocessing step or subroutine for various tasks, including anomaly detection, segmentation, and classification.\n  The most popular TSCL algorithms are either fast (in terms of run time) but perform poorly on benchmark problems, or perform well on benchmarks but scale poorly. We present a new TSCL algorithm, the $k$-means (K) accelerated (A) Stochastic subgradient (S) Barycentre (B) Average (A) (KASBA) clustering algorithm. KASBA is a $k$-means clustering algorithm that uses the Move-Split-Merge (MSM) elastic distance at all stages of clustering, applies a randomised stochastic subgradient gradient descent to find barycentre centroids, links each stage of clustering to accelerate convergence and exploits the metric property of MSM distance to avoid a large proportion of distance calculations. It is a versatile and scalable clusterer designed for real-world TSCL applications. It allows practitioners to balance run time and clustering performance. We demonstrate through extensive experimentation that KASBA produces significantly better clustering than the faster state of the art clusterers and is offers orders of magnitude improvement in run time over the most performant $k$-means alternatives.", "date": "2024-11-26", "categories": []}
{"id": "2309.00578", "title": "Consistency of Lloyd's Algorithm Under Perturbations", "abstract": "In the context of unsupervised learning, Lloyd's algorithm is one of the most widely used clustering algorithms. It has inspired a plethora of work investigating the correctness of the algorithm under various settings with ground truth clusters. In particular, in 2016, Lu and Zhou have shown that the mis-clustering rate of Lloyd's algorithm on $n$ independent samples from a sub-Gaussian mixture is exponentially bounded after $O(\\log(n))$ iterations, assuming proper initialization of the algorithm. However, in many applications, the true samples are unobserved and need to be learned from the data via pre-processing pipelines such as spectral methods on appropriate data matrices. We show that the mis-clustering rate of Lloyd's algorithm on perturbed samples from a sub-Gaussian mixture is also exponentially bounded after $O(\\log(n))$ iterations under the assumptions of proper initialization and that the perturbation is small relative to the sub-Gaussian noise. In canonical settings with ground truth clusters, we derive bounds for algorithms such as $k$-means$++$ to find good initializations and thus leading to the correctness of clustering via the main result. We show the implications of the results for pipelines measuring the statistical significance of derived clusters from data such as SigClust. We use these general results to derive implications in providing theoretical guarantees on the misclustering rate for Lloyd's algorithm in a host of applications, including high-dimensional time series, multi-dimensional scaling, and community detection for sparse networks via spectral clustering.", "date": "2023-09-01", "categories": []}
{"id": "2601.11883", "title": "Approximation Algorithm for Constrained $k$-Center Clustering: A Local Search Approach", "abstract": "Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any improvement to a ratio of 2 - {\\epsilon} would imply P = NP. In this work, we study the constrained k-center clustering problem, where instance-level cannot-link (CL) and must-link (ML) constraints are incorporated as background knowledge. Although general CL constraints significantly increase the hardness of approximation, previous work has shown that disjoint CL sets permit constant-factor approximations. However, whether local search can achieve such a guarantee in this setting remains an open question. To this end, we propose a novel local search framework based on a transformation to a dominating matching set problem, achieving the best possible approximation ratio of 2. The experimental results on both real-world and synthetic datasets demonstrate that our algorithm outperforms baselines in solution quality.", "date": "2026-01-17", "categories": []}
{"id": "2604.22909", "title": "Deep Clustering for Climate: Analyzing Teleconnections through Learned Categorical States", "abstract": "Understanding and representing complex climate variability is essential for both scientific analysis and predictive modeling. However, identifying meaningful climate regimes from raw variables is challenging, as they exhibit high noise and nonlinear dependencies. In this work, we explore the use of Masked Siamese Networks to discretize climate time series into semantically rich clusters. Focusing on daily minimum and maximum temperature, we show that the resulting representations: (i) yield clusters that reflect meaningful climate states under our modeling assumptions, offering a simplified representation for downstream use; (ii) enable sampling and analysis of specific climate scenarios; and (iii) exhibit statistical associations with El Ni\\~no events, underscoring their scientific relevance. Our findings highlight the potential of self-supervised discretization as a tool for climate data analysis and open avenues for incorporating richer climate indicators in future work.", "date": "2026-04-24", "categories": []}
{"id": "2604.23083", "title": "Turtle shell clustering: A mixture approach to discriminative clustering with applications to flow cytometry and other data", "abstract": "Generative approaches to clustering provide information on geometric properties of clusters, whereas discriminative approaches provide boundaries between clusters. Ideas from both approaches are incorporated to present a fully unsupervised, probabilistic, and discriminative clustering method via a regularized mutual information objective function, wherein a mixture of mixtures of Gaussian and uniform distributions is used for formulation of the conditional model. Automatic selection of the number of components is established with the introduction of the regularizing term and a merge step, similar to those applied in reversible jump Markov chain Monte Carlo methods used in Bayesian clustering. Consequently, the turtle shell method -- a fully unsupervised clustering method capable of estimating non-linear boundary lines, automatically selecting the number of components, and capturing intuitive clusters in the presence of data abnormalities such as noise and/or irregular cluster shapes -- is introduced. We test this method on various simulated and real datasets commonly explored in clustering research, and extend the analysis to datasets arising from flow cytometry experiments.", "date": "2026-04-25", "categories": []}
{"id": "2604.23912", "title": "Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering", "abstract": "Learning low-dimensional representations from multi-view relational data is challenging when underlying geometries differ across views. We propose Bary-GWMDS, a Gromov-Wasserstein-based method that operates directly on distance matrices to learn a consensus embedding preserving shared relational structure. By leveraging intrinsic distances, the approach naturally handles nonlinear distortions across views. We also introduce Mean-GWMDS-C, a clustering-oriented formulation that averages distance matrices and learns reduced-support representations via a consensus Gromov-Wasserstein transport. Experiments on synthetic and real-world datasets show that the proposed framework yields stable and geometrically meaningful embeddings.", "date": "2026-04-26", "categories": []}
{"id": "2604.24611", "title": "Uncovering Latent Patterns in Social Media Usage and Mental Health: A Clustering-Based Approach Using Unsupervised Machine Learning", "abstract": "The widespread adoption of social media has heightened interest in its psychological effects, particularly on mental health indicators such as anxiety, depression, loneliness, and sleep quality, as these platforms increasingly influence social interactions and well-being. Although previous research has examined correlations between social media use and mental health, few studies have utilized unsupervised machine learning to segment users based on behavioral and psychological patterns, leaving a gap in identifying distinct risk profiles across diverse groups. This study seeks to address this by segmenting individuals according to their social media usage and psychological well-being, employing clustering to reveal hidden patterns and evaluate their mental health implications. Data from 551 participants, collected via an online survey, were preprocessed using KNN imputation for missing values, one-hot encoding for categorical variables like Gender with 5 unique values, and outlier detection via IQR and Z-score methods. K-Means clustering, optimized at 6 clusters using the Elbow Method and a Silhouette Score of 0.32, was applied, with PCA reducing 22 dimensions for visualization and a correlation heatmap highlighting relationships, such as a 0.28 correlation between social media hours and anxiety.", "date": "2026-04-27", "categories": []}
{"id": "2406.14111", "title": "Expander Hierarchies for Normalized Cuts on Graphs", "abstract": "Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their inherent intricacies and large hidden factors in their asymptotic running times. Here, we introduce the first practically efficient algorithm for computing expander decompositions and their hierarchies and demonstrate its effectiveness and utility by incorporating it as the core component in a novel solver for the normalized cut graph clustering objective. Our extensive experiments on a variety of large graphs show that our expander-based algorithm outperforms state-of-the-art solvers for normalized cut with respect to solution quality by a large margin on a variety of graph classes such as citation, e-mail, and social networks or web graphs while remaining competitive in running time.", "date": "2024-06-20", "categories": []}
{"id": "2604.22405", "title": "Robust Fuzzy local k-plane clustering with mixture distance of hinge loss and L1 norm", "abstract": "K-plane clustering (KPC), hyperplane clustering, and mixture regression all essentially fall within the same class of problems. This problem can be conceptualized as clustering in relatively high-dimensional K subspaces or K linear manifolds. Traditional KPC or fuzzy KPC models demonstrate a pronounced susceptibility to outliers, as they presuppose that the projection distance between data points and the plane normal vector adheres to the L2 distance. Meanwhile, the assumption of infinitely extending clusters adversely affects clustering performance. To solve these problems, this paper proposed a new robust fuzzy local k-plane clustering (RFLkPC) method that combines the mixture distance of hinge loss and L1 norm. The RFLkPC model assumes that each plane cluster is bounded to a finite area, which can flexibly and robustly handle plane clustering tasks with outliers or not. The corresponding model and optimization algorithms of RFLkPC were provided. Compared to other related models on this topic, a large number of experiments verify the efficiency of RFLkPC on simulated data and real data. The source code for the proposed RFLkPC method is publicly available at https://github.com/xuelin-xie/RFLkPC.", "date": "2026-04-24", "categories": []}
{"id": "2604.21798", "title": "An effective variant of the Hartigan $k$-means algorithm", "abstract": "The k-means problem is perhaps the classical clustering problem and often synonymous with Lloyd's algorithm (1957). It has become clear that Hartigan's algorithm (1975) gives better results in almost all cases, Telgarsky-Vattani note a typical improvement of $5\\%$ -- $10\\%$. We point out that a very minor variation of Hartigan's method leads to another $2\\%$ -- $5\\%$ improvement; the improvement tends to become larger when either dimension or $k$ increase.", "date": "2026-04-23", "categories": []}
{"id": "2512.05623", "title": "Bounded Graph Clustering with Graph Neural Networks", "abstract": "In community detection, many methods require the user to specify the number of clusters in advance since an exhaustive search over all possible values is computationally infeasible. While some classical algorithms can infer this number directly from the data, this is typically not the case for graph neural networks (GNNs): even when a desired number of clusters is specified, standard GNN-based methods often fail to return the exact number due to the way they are designed. In this work, we address this limitation by introducing a flexible and principled way to control the number of communities discovered by GNNs. Rather than assuming the true number of clusters is known, we propose a framework that allows the user to specify a plausible range and enforce these bounds during training. However, if the user wants an exact number of clusters, it may also be specified and reliably returned.", "date": "2025-12-05", "categories": []}
{"id": "2512.21510", "title": "Missing Pattern Tree based Decision Grouping and Ensemble for Enhancing Pair Utilization in Deep Incomplete Multi-View Clustering", "abstract": "Real-world multi-view data often exhibit highly inconsistent missing patterns, posing significant challenges for incomplete multi-view clustering (IMVC). Although existing IMVC methods have made progress from both imputation-based and imputation-free routes, they largely overlook the issue of pair underutilization. Specifically, inconsistent missing patterns prevent incomplete but available multi-view pairs from being fully exploited, thereby limiting the model performance. To address this limitation, we propose a novel missing-pattern tree based IMVC framework. Specifically, to fully leverage available multi-view pairs, we first introduce a missing-pattern tree model to group data into multiple decision sets according to their missing patterns, and then perform multi-view clustering within each set. Furthermore, a multi-view decision ensemble module is proposed to aggregate clustering results across all decision sets. This module infers uncertainty-based weights to suppress unreliable clustering decisions and produce robust outputs. Finally, we develop an ensemble-to-individual knowledge distillation module module, which transfers ensemble knowledge to view-specific clustering models. This design enables mutual enhancement between ensemble and individual modules by optimizing cross-view consistency and inter-cluster discrimination losses. Extensive theoretical analysis supports our key designs, and empirical experiments on multiple benchmark datasets demonstrate that our method effectively mitigates the pair underutilization issue and achieve superior IMVC performance.", "date": "2025-12-25", "categories": []}
{"id": "2602.03562", "title": "NPCNet: Navigator-Driven Pseudo Text for Deep Clustering of Early Sepsis Phenotyping", "abstract": "Electronic Health Records (EHRs) provide high-dimensional temporal data essential for patient modeling; however, conventional algorithmic approaches often rely on data aggregation or imputation, which distorts temporal disease trajectories. Such computational limitations are particularly critical in sepsis, a heterogeneous syndrome where clustering-based stratification plays a key role in identifying clinically distinct phenotypes for precise treatment strategies. Furthermore, existing clustering processes seldom incorporate domain-driven constraints, often resulting in phenotypes that lack clear clinical distinction. We propose a novel clustering network, NPCNet, that comprises a text embedding generator, a clustering operator, and a target navigator. We first transform EHRs into pseudo texts by discretizing continuous clinical measurements, then integrate them with static variables to construct the embeddings. The target navigator then infuses clinical knowledge into the embeddings through auxiliary tasks, constraining clustering results to better align sepsis phenotypes with clinical significance. Finally, the clustering operator employs an iterative refinement mechanism to jointly optimize phenotype centroids and patient representations under domain-driven constraints. Extensive experiments on public datasets validate that NPCNet achieves superior performance on both internal clustering benchmarks and clinical validity metrics, offering a viable pathway for precision treatment strategies in the management of sepsis.", "date": "2026-02-03", "categories": []}
{"id": "2604.07562", "title": "Reasoning-Based Refinement of Unsupervised Text Clusters with LLMs", "abstract": "Unsupervised methods are widely used to induce latent semantic structure from large text collections, yet their outputs often contain incoherent, redundant, or poorly grounded clusters that are difficult to validate without labeled data. We propose a reasoning-based refinement framework that leverages large language models (LLMs) not as embedding generators, but as semantic judges that validate and restructure the outputs of arbitrary unsupervised clustering algorithms. Our framework introduces three reasoning stages: (i) coherence verification, where LLMs assess whether cluster summaries are supported by their member texts; (ii) redundancy adjudication, where candidate clusters are merged or rejected based on semantic overlap; and (iii) label grounding, where clusters are assigned interpretable labels through a two-stage process that generates and consolidates semantically similar labels in a fully unsupervised manner. This design decouples representation learning from structural validation and mitigates the common failure modes of embedding-only approaches. We evaluate the framework in real-world social media corpora from two platforms with distinct interaction models, demonstrating consistent improvements in cluster coherence and human-aligned labeling quality over classical topic models and recent representation-based baselines. Human evaluation shows strong agreement with LLM-generated labels, despite the absence of gold-standard annotations. We further conduct robustness analysis under matched temporal and volume conditions to assess cross-platform stability. Beyond empirical gains, our results suggest that LLM-based reasoning can serve as a general mechanism for validating and refining unsupervised semantic structure, enabling more reliable and interpretable analysis of large text collections without supervision.", "date": "2026-04-08", "categories": []}
{"id": "2604.16959", "title": "Hyperbolic Enhanced Representation Learning for Incomplete Multi-view Clustering", "abstract": "Incomplete Multi-View Clustering (IMVC) faces the challenge of learning discriminative representations from fragmentary observations while maintaining robustness against missing views. However, prevalent Euclidean-based methods suffer from a geometric mismatch when modeling real-world data with intrinsic hierarchies, leading to semantic blurring where representations drift towards spatially proximal but semantically distinct neighbors. To bridge this gap, we propose HERL, a Hyperbolic Enhanced Representation Learning framework for IMVC. Operating within the Poincar\\'e ball, HERL constructs a structure-aware latent space to enhance representation learning. Specifically, we design a dual-constraint hyperbolic contrastive mechanism optimizing: an angular-based loss to preserve semantic identity via directional alignment, and a distance-based loss to enforce hierarchical compactness. Furthermore, a hyperbolic prototype head is introduced to rectify global structural drift by aligning cross-view hierarchy-aware prototype distributions. Consequently, HERL disentangles fine-grained semantic correlations to sharpen cluster boundaries and imposes geometric constraints to rectify the data recovery process. Extensive experimental results demonstrate that HERL consistently outperforms state-of-the-art approaches.", "date": "2026-04-18", "categories": []}
{"id": "2604.18024", "title": "Clusterability-Based Assessment of Potentially Noisy Views for Multi-View Clustering", "abstract": "In multi-view clustering, the quality of different views may vary substantially, and low-quality or degraded views can impair overall clustering performance. However, existing studies mainly address this issue within the clustering process through view weighting or noise-robust optimization, while paying limited attention to data-level assessment before clustering. In this paper, we study the problem of pre-clustering noisy-view analysis in multi-view data from a clusterability perspective. To this end, we propose a Multi-View Clusterability Score (MVCS), which quantifies the strength of latent cluster-related structures in multi-view data through three complementary components: per-view structural clusterability, joint-space clusterability, and cross-view neighborhood consistency. To the best of our knowledge, this is the first clusterability score specifically designed for multi-view data. We further use it to perform potentially noisy view analysis and noisy-view detection before clustering. Extensive experiments on real-world datasets demonstrate that noisy views can significantly degrade clustering performance, and that, compared with existing clusterability measures designed for single-view data, the proposed method more effectively supports noisy-view analysis and detection.", "date": "2026-04-20", "categories": []}
{"id": "2603.03188", "title": "Scalable Posterior Uncertainty for Flexible Density-Based Clustering", "abstract": "We introduce a novel framework for uncertainty quantification in clustering that combines martingale posterior distributions with density-based clustering. Unlike classical model-based approaches, which define clusters at the latent level of a mixture model, we treat clusters as explicit functionals of the data-generating density, without assuming any specific parametric form. To characterize density uncertainty, we obtain martingale posterior samples via a predictive resampling scheme driven by model score evaluations. This allows us to leverage state-of-the-art differentiable density estimators, such as normalizing flows, making density resampling efficient in large-scale settings and fully parallelizable on modern GPU hardware. Martingale posterior samples of the clustering structure are then obtained by applying density-based clustering to the density draws, enabling principled inference on any clustering-related quantity. Casting the inference target as a density functional further enables a rigorous theoretical analysis of the procedure's convergence properties. We apply our methodology to image and single-cell RNA sequencing data, demonstrating the computational efficiency afforded by its GPU compatibility as well as its ability to recover meaningful clustering structures, with associated uncertainty, across diverse domains.", "date": "2026-03-03", "categories": []}
{"id": "2604.15738", "title": "Why Colors Make Clustering Harder:Global Integrality Gaps, the Price of Fairness, and Color-Coupled Algorithms in Chromatic Correlation Clustering", "abstract": "Chromatic Correlation Clustering (CCC) extends Correlation Clustering by assigning semantic colors to edges and requiring each cluster to receive a single color label. Unlike standard CC, whose LP relaxation has integrality gap 2 on complete graphs and admits a 2.06-approximation, the analogous LP for CCC has a strict lower bound of 2.11, and the best known LP-rounding algorithm achieves 2.15. We explain this gap by isolating the source of difficulty: cross-edge chromatic interference. Neutral edges, whose color does not match the candidate cluster color, create an irreducible cost absent from standard CC and force any color-independent rounding scheme to pay an additional mismatch penalty.\n  We make four contributions. First, we prove a Global Integrality Gap Decomposition Theorem showing that the gap of any color-independent CCC rounding algorithm equals the standard CC gap plus an irreducible chromatic penalty Delta(L) > 0. Second, we solve the associated min-max problem and derive the staircase formula Delta(L) = ((L-1)/L) Delta_infinity, where Delta_infinity is approximately 0.0734. In particular, the two-color gap is 2.0967, separating CCC from standard CC already at L = 2. Third, we introduce Color-Coupled Correlation Clustering (C4). Adding the valid global constraint sum_c x_uv^c >= L-1 and a correlated interval-packing rounding scheme makes neutral edges behave like classical negative edges, recovering the optimal 2.06 approximation and bypassing the 2.11 lower bound for the uncoupled LP. Fourth, experiments on extremal instances, real multi-relational networks, and fairness benchmarks validate the theory: empirical LP gaps follow the predicted staircase, and C4 matches the unconstrained approximation ratio under fairness constraints.", "date": "2026-04-17", "categories": []}
{"id": "2604.16061", "title": "Constant-Factor Approximations for Doubly Constrained Fair k-Center, k-Median and k-Means", "abstract": "We study discrete k-clustering problems in general metric spaces that are constrained by a combination of two different fairness conditions within the demographic fairness model. Given a metric space (P,d), where every point in P is equipped with a protected attribute, and a number k, the goal is to partition P into k clusters with a designated center each, such that a center-based objective function is minimized and the attributes are fairly distributed with respect to the following two fairness concepts: 1) group fairness: We aim for clusters with balanced numbers of attributes by specifying lower and upper bounds for the desired attribute proportions. 2) diverse center selection: Clusters have natural representatives, i.e., their centers. We ask for a balanced set of representatives by specifying the desired number of centers to choose from each attribute.\n  Dickerson, Esmaeili, Morgenstern and Zhang (2023) denote the combination of these two constraints as doubly constrained fair clustering. They present algorithms whose guarantees depend on the best known approximation factors for either of these problems. Currently, this implies an 8-approximation with a small additive violation on the group fairness constraint. For k-center, we improve this approximation factor to 4 with a small additive violation. This guarantee also depends on the currently best algorithm for DS-fair k-center given by Jones, Nguyen and Nguyen (2020). For k-median and k-means, we propose the first constant-factor approximation algorithms. Our algorithms transform a solution that satisfies diverse center selection into a doubly constrained fair clustering using an LP-based approach. Furthermore, our results are generalizable to other center-selection constraints, such as matroid k-clustering and knapsack constraints.", "date": "2026-04-17", "categories": []}
{"id": "2512.22897", "title": "Federated Multi-Task Clustering", "abstract": "Spectral clustering has emerged as one of the most effective clustering algorithms due to its superior performance. However, most existing models are designed for centralized settings, rendering them inapplicable in modern decentralized environments. Moreover, current federated learning approaches often suffer from poor generalization performance due to reliance on unreliable pseudo-labels, and fail to capture the latent correlations amongst heterogeneous clients. To tackle these limitations, this paper proposes a novel framework named Federated Multi-Task Clustering (i.e.,FMTC), which intends to learn personalized clustering models for heterogeneous clients while collaboratively leveraging their shared underlying structure in a privacy-preserving manner. More specifically, the FMTC framework is composed of two main components: client-side personalized clustering module, which learns a parameterized mapping model to support robust out-of-sample inference, bypassing the need for unreliable pseudo-labels; and server-side tensorial correlation module, which explicitly captures the shared knowledge across all clients. This is achieved by organizing all client models into a unified tensor and applying a low-rank regularization to discover their common subspace. To solve this joint optimization problem, we derive an efficient, privacy-preserving distributed algorithm based on the Alternating Direction Method of Multipliers, which decomposes the global problem into parallel local updates on clients and an aggregation step on the server. To the end, several extensive experiments on multiple real-world datasets demonstrate that our proposed FMTC framework significantly outperforms various baseline and state-of-the-art federated clustering algorithms.", "date": "2025-12-28", "categories": []}
{"id": "2604.14810", "title": "Scalable Model-Based Clustering with Sequential Monte Carlo", "abstract": "In online clustering problems, there is often a large amount of uncertainty over possible cluster assignments that cannot be resolved until more data are observed. This difficulty is compounded when clusters follow complex distributions, as is the case with text data. Sequential Monte Carlo (SMC) methods give a natural way of representing and updating this uncertainty over time, but have prohibitive memory requirements for large-scale problems. We propose a novel SMC algorithm that decomposes clustering problems into approximately independent subproblems, allowing a more compact representation of the algorithm state. Our approach is motivated by the knowledge base construction problem, and we show that our method is able to accurately and efficiently solve clustering problems in this setting and others where traditional SMC struggles.", "date": "2026-04-16", "categories": []}
{"id": "2503.00379", "title": "Improving clustering quality evaluation in noisy Gaussian mixtures", "abstract": "Clustering is a well-established technique in machine learning and data analysis, widely used across various domains. Cluster validity indices, such as the Average Silhouette Width, Calinski-Harabasz, and Davies-Bouldin indices, play a crucial role in assessing clustering quality when external ground truth labels are unavailable. However, these measures can be affected by different degrees of feature relevance, potentially leading to unreliable evaluations in high-dimensional or noisy data sets.\n  We introduce a theoretically grounded Feature Importance Rescaling (FIR) method that enhances the quality of clustering validation by adjusting feature contributions based on their dispersion. It attenuates noise features, clarifies clustering compactness and separation, and thereby aligns clustering validation more closely with the ground truth. Through extensive experiments on synthetic data sets under different configurations and a case study on real-world data, we demonstrate that FIR consistently improves the correlation between the values of cluster validity indices and the ground truth, particularly in settings with noisy or irrelevant features.\n  The results show that FIR increases the robustness of clustering evaluation, reduces variability in performance across different data sets, and remains effective even when clusters exhibit significant overlap. These findings highlight the potential of FIR as a valuable enhancement of clustering validation, making it a practical tool for unsupervised learning tasks where labelled data is unavailable.", "date": "2025-03-01", "categories": []}
{"id": "2604.13307", "title": "Deep Spatially-Regularized and Superpixel-Based Diffusion Learning for Unsupervised Hyperspectral Image Clustering", "abstract": "An unsupervised framework for hyperspectral image (HSI) clustering is proposed that incorporates masked deep representation learning with diffusion-based clustering, extending the Spatially-Regularized Superpixel-based Diffusion Learning ($S^2DL$) algorithm. Initially, a denoised latent representation of the original HSI is learned via an unsupervised masked autoencoder (UMAE) model with a Vision Transformer backbone. The UMAE takes spatial context and long-range spectral correlations into account and incorporates an efficient pretraining process via masking that utilizes only a small subset of training pixels. In the next stage, the entropy rate superpixel (ERS) algorithm is used to segment the image into superpixels, and a spatially regularized diffusion graph is constructed using Euclidean and diffusion distances within the compressed latent space instead of the HSI space. The proposed algorithm, Deep Spatially-Regularized Superpixel-based Diffusion Learning ($DS^2DL$), leverages more faithful diffusion distances and subsequent diffusion graph construction that better reflect the intrinsic geometry of the underlying data manifold, improving labeling accuracy and clustering quality. Experiments on Botswana and KSC datasets demonstrate the efficacy of $DS^2DL$.", "date": "2026-04-14", "categories": []}
{"id": "2604.13484", "title": "Joint Representation Learning and Clustering via Gradient-Based Manifold Optimization", "abstract": "Clustering and dimensionality reduction have been crucial topics in machine learning and computer vision. Clustering high-dimensional data has been challenging for a long time due to the curse of dimensionality. For that reason, a more promising direction is the joint learning of dimension reduction and clustering. In this work, we propose a Manifold Learning Framework that learns dimensionality reduction and clustering simultaneously. The proposed framework is able to jointly learn the parameters of a dimension reduction technique (e.g. linear projection or a neural network) and cluster the data based on the resulting features (e.g. under a Gaussian Mixture Model framework). The framework searches for the dimension reduction parameters and the optimal clusters by traversing a manifold,using Gradient Manifold Optimization. The obtained The proposed framework is exemplified with a Gaussian Mixture Model as one simple but efficient example, in a process that is somehow similar to unsupervised Linear Discriminant Analysis (LDA). We apply the proposed method to the unsupervised training of simulated data as well as a benchmark image dataset (i.e. MNIST). The experimental results indicate that our algorithm has better performance than popular clustering algorithms from the literature.", "date": "2026-04-15", "categories": []}
{"id": "2604.13816", "title": "Composite Silhouette: A Subsampling-based Aggregation Strategy", "abstract": "Determining the number of clusters is a central challenge in unsupervised learning, where ground-truth labels are unavailable. The Silhouette coefficient is a widely used internal validation metric for this task, yet its standard micro-averaged form tends to favor larger clusters under size imbalance. Macro-averaging mitigates this bias by weighting clusters equally, but may overemphasize noise from under-represented groups. We introduce Composite Silhouette, an internal criterion for cluster-count selection that aggregates evidence across repeated subsampled clusterings rather than relying on a single partition. For each subsample, micro- and macro-averaged Silhouette scores are combined through an adaptive convex weight determined by their normalized discrepancy and smoothed by a bounded nonlinearity; the final score is then obtained by averaging these subsample-level composites. We establish key properties of the criterion and derive finite-sample concentration guarantees for its subsampling estimate. Experiments on synthetic and real-world datasets show that Composite Silhouette effectively reconciles the strengths of micro- and macro-averaging, yielding more accurate recovery of the ground-truth number of clusters.", "date": "2026-04-15", "categories": []}
{"id": "2406.17952", "title": "LINSCAN -- A Linearity Based Clustering Algorithm", "abstract": "DBSCAN and OPTICS are powerful algorithms for identifying clusters of points in domains where few assumptions can be made about the structure of the data. In this paper, we leverage these strengths and introduce a new algorithm, LINSCAN, designed to seek lineated clusters that are difficult to find and isolate with existing methods. In particular, by embedding points as normal distributions approximating their local neighborhoods and leveraging a distance function derived from the Kullback Leibler Divergence, LINSCAN can detect and distinguish lineated clusters that are spatially close but have orthogonal covariances. We demonstrate how LINSCAN can be applied to seismic data to identify active faults, including intersecting faults, and determine their orientation. Finally, we discuss the properties a generalization of DBSCAN and OPTICS must have in order to retain the stability benefits of these algorithms.", "date": "2024-06-25", "categories": []}
{"id": "2410.17976", "title": "metasnf: Meta Clustering with Similarity Network Fusion in R", "abstract": "metasnf is an R package that enables users to apply meta clustering, a method for efficiently searching a broad space of cluster solutions by clustering the solutions themselves, to clustering workflows based on similarity network fusion (SNF). SNF is a multi-modal data integration algorithm commonly used for biomedical subtype discovery. The package also contains functions to assist with cluster visualization, characterization, and validation. This package can help researchers identify SNF-derived cluster solutions that are guided by context-specific utility over context-agnostic measures of quality.", "date": "2024-10-23", "categories": []}
{"id": "2501.06268", "title": "Clustering with Uniformity- and Neighbor-Based Random Geometric Graphs", "abstract": "We propose a graph-based clustering method based on Cluster Catch Digraphs (CCDs) that extends their applicability to\n  moderate-dimensional data settings. Existing CCD variants, such as RK-CCDs, rely on spatial randomness tests based on\n  Ripley's K function, which exhibit performance degradation as dimensionality increases. To address this limitation, we\n  introduce a nearest-neighbor-distance (NND) based Monte Carlo spatial randomness test (MC-SRT) for determining\n  covering radii, resulting in the proposed Uniformity- and Neighbor-based CCDs (UN-CCDs). The proposed method is\n  designed for datasets of moderate size and dimension, particularly in settings with complex cluster geometry and\n  uniformly distributed background noise. Through Monte Carlo simulations and experiments on benchmark datasets, we show\n  that UN-CCDs provide stable and competitive performance relative to several established clustering methods within the\n  evaluated regimes, while remaining largely parameter-free. We also discuss computational trade-offs and identify the\n  practical regimes in which the method is most effective. -- Keywords:\n  Graph-based clustering; Cluster catch digraphs; Moderate-dimensional data; the nearest neighbor distance; Spatial\n  randomness test.", "date": "2025-01-09", "categories": []}
{"id": "2604.12460", "title": "Enhancing Clustering: An Explainable Approach via Filtered Patterns", "abstract": "Machine learning has become a central research area, with increasing attention devoted to explainable clustering, also known as conceptual clustering, which is a knowledge-driven unsupervised learning paradigm that partitions data into $\\theta$ disjoint clusters, where each cluster is described by an explicit symbolic representation, typically expressed as a closed pattern or itemset. By providing human-interpretable cluster descriptions, explainable clustering plays an important role in explainable artificial intelligence and knowledge discovery. Recent work improved clustering quality by introducing k-relaxed frequent patterns (k-RFPs), a pattern model that relaxes strict coverage constraints through a generalized kcover definition. This framework integrates constraint-based reasoning, using SAT solvers for pattern generation, with combinatorial optimization, using Integer Linear Programming (ILP) for cluster selection. Despite its effectiveness, this approach suffers from a critical limitation: multiple distinct k-RFPs may induce identical k-covers, leading to redundant symbolic representations that unnecessarily enlarge the search space and increase computational complexity during cluster construction. In this paper, we address this redundancy through a pattern reduction framework. Our contributions are threefold. First, we formally characterize the conditions under which distinct k-RFPs induce identical kcovers, providing theoretical foundations for redundancy detection. Second, we propose an optimization strategy that removes redundant patterns by retaining a single representative pattern for each distinct k-cover. Third, we investigate the interpretability and representativeness of the patterns selected by the ILP model by analyzing their robustness with respect to their induced clusters. Extensive experiments conducted on several real-world datasets demonstrate that the proposed approach significantly reduces the pattern search space, improves computational efficiency, preserves and enhances in some cases the quality of the resulting clusters.", "date": "2026-04-14", "categories": []}
{"id": "2410.05217", "title": "Organizing Unstructured Image Collections using Natural Language", "abstract": "In this work, we introduce and study the novel task of Open-ended Semantic Multiple Clustering (OpenSMC). Given a large, unstructured image collection, the goal is to automatically discover several, diverse semantic clustering criteria (e.g., Activity or Location) from the images, and subsequently organize them according to the discovered criteria, without requiring any human input. Our framework, X-Cluster: eXploratory Clustering, treats text as a reasoning proxy: it concurrently scans the entire image collection, proposes candidate criteria in natural language, and groups images into meaningful clusters per criterion. This radically differs from previous works, which either assume predefined clustering criteria or fixed cluster counts. To evaluate X-Cluster, we create two new benchmarks, COCO-4C and Food-4C, each annotated with four distinct grouping criteria and corresponding cluster labels. Experiments show that X-Cluster can effectively reveal meaningful partitions on several datasets. Finally, we use X-Cluster to achieve various real-world applications, including uncovering hidden biases in text-to-image (T2I) generative models and analyzing image virality on social media. Project page: https://oatmealliu.github.io/xcluster.html", "date": "2024-10-07", "categories": []}
{"id": "2601.20628", "title": "Sparse clustering via the Deterministic Information Bottleneck algorithm", "abstract": "Cluster analysis relates to the task of assigning objects into groups which ideally present some desirable characteristics. When a cluster structure is confined to a subset of the feature space, traditional clustering techniques face unprecedented challenges. We present an information theoretic framework that overcomes the problems associated with sparse data, allowing for joint feature weighting and clustering. Our proposal constitutes a competitive alternative to existing clustering algorithms for sparse data, as demonstrated through simulations on synthetic data. The effectiveness of our method is established by an application on a real-world genomics data set.", "date": "2026-01-28", "categories": []}
{"id": "2604.10368", "title": "A Structured Clustering Approach for Inducing Media Narratives", "abstract": "Media narratives wield tremendous power in shaping public opinion, yet computational approaches struggle to capture the nuanced storytelling structures that communication theory emphasizes as central to how meaning is constructed. Existing approaches either miss subtle narrative patterns through coarse-grained analysis or require domain-specific taxonomies that limit scalability. To bridge this gap, we present a framework for inducing rich narrative schemas by jointly modeling events and characters via structured clustering. Our approach produces explainable narrative schemas that align with established framing theory while scaling to large corpora without exhaustive manual annotation.", "date": "2026-04-11", "categories": []}
{"id": "2604.10865", "title": "Beyond Statistical Co-occurrence: Unlocking Intrinsic Semantics for Tabular Data Clustering", "abstract": "Deep Clustering (DC) has emerged as a powerful tool for tabular data analysis in real-world domains like finance and healthcare. However, most existing methods rely on data-level statistical co-occurrence to infer the latent metric space, often overlooking the intrinsic semantic knowledge encapsulated in feature names and values. As a result, semantically related concepts like `Flu' and `Cold' are often treated as symbolic tokens, causing conceptually related samples to be isolated. To bridge the gap between dataset-specific statistics and intrinsic semantic knowledge, this paper proposes Tabular-Augmented Contrastive Clustering (TagCC), a novel framework that anchors statistical tabular representations to open-world textual concepts. Specifically, TagCC utilizes Large Language Models (LLMs) to distill underlying data semantics into textual anchors via semantic-aware transformation. Through Contrastive Learning (CL), the framework enriches the statistical tabular representations with the open-world semantics encapsulated in these anchors. This CL framework is jointly optimized with a clustering objective, ensuring that the learned representations are both semantically coherent and clustering-friendly. Extensive experiments on benchmark datasets demonstrate that TagCC significantly outperforms its counterparts.", "date": "2026-04-13", "categories": []}
{"id": "2604.11118", "title": "Distributionally Robust K-Means Clustering", "abstract": "K-means clustering is a workhorse of unsupervised learning, but it is notoriously brittle to outliers, distribution shifts, and limited sample sizes. Viewing k-means as Lloyd--Max quantization of the empirical distribution, we develop a distributionally robust variant that protects against such pathologies. We posit that the unknown population distribution lies within a Wasserstein-2 ball around the empirical distribution. In this setting, one seeks cluster centers that minimize the worst-case expected squared distance over this ambiguity set, leading to a minimax formulation. A tractable dual yields a soft-clustering scheme that replaces hard assignments with smoothly weighted ones. We propose an efficient block coordinate descent algorithm with provable monotonic decrease and local linear convergence. Experiments on standard benchmarks and large-scale synthetic data demonstrate substantial gains in outlier detection and robustness to noise.", "date": "2026-04-13", "categories": []}
{"id": "2604.11144", "title": "Hierarchical Textual Knowledge for Enhanced Image Clustering", "abstract": "Image clustering aims to group images in an unsupervised fashion. Traditional methods focus on knowledge from visual space, making it difficult to distinguish between visually similar but semantically different classes. Recent advances in vision-language models enable the use of textual knowledge to enhance image clustering. However, most existing methods rely on coarse class labels or simple nouns, overlooking the rich conceptual and attribute-level semantics embedded in textual space. In this paper, we propose a knowledge-enhanced clustering (KEC) method that constructs a hierarchical concept-attribute structured knowledge with the help of large language models (LLMs) to guide clustering. Specifically, we first condense redundant textual labels into abstract concepts and then automatically extract discriminative attributes for each single concept and similar concept pairs, via structured prompts to LLMs. This knowledge is instantiated for each input image to achieve the knowledge-enhanced features. The knowledge-enhanced features with original visual features are adapted to various downstream clustering algorithms. We evaluate KEC on 20 diverse datasets, showing consistent improvements across existing methods using additional textual knowledge. KEC without training outperforms zero-shot CLIP on 14 out of 20 datasets. Furthermore, the naive use of textual knowledge may harm clustering performance, while KEC provides both accuracy and robustness.", "date": "2026-04-13", "categories": []}
{"id": "2604.07744", "title": "The Condition-Number Principle for Prototype Clustering", "abstract": "We develop a geometric framework that links objective accuracy to structural recovery in prototype-based clustering. The analysis is algorithm-agnostic and applies to a broad class of admissible loss functions. We define a clustering condition number that compares within-cluster scale to the minimum loss increase required to move a point across a cluster boundary. When this quantity is small, any solution with a small suboptimality gap must also have a small misclassification error relative to a benchmark partition. The framework also clarifies a fundamental trade-off between robustness and sensitivity to cluster imbalance, leading to sharp phase transitions for exact recovery under different objectives. The guarantees are deterministic and non-asymptotic, and they separate the role of algorithmic accuracy from the intrinsic geometric difficulty of the instance. We further show that errors concentrate near cluster boundaries and that sufficiently deep cluster cores are recovered exactly under strengthened local margins. Together, these results provide a geometric principle for interpreting low objective values as reliable evidence of meaningful clustering structure.", "date": "2026-04-09", "categories": []}
{"id": "2510.20220", "title": "Alternatives to the Laplacian for Scalable Spectral Clustering with Group Fairness Constraints", "abstract": "Recent research has focused on mitigating algorithmic bias in clustering by incorporating fairness constraints into algorithmic design. Notions such as disparate impact, community cohesion, and cost per population have been implemented to enforce equitable outcomes. Among these, group fairness (balance) ensures that each protected group is proportionally represented within every cluster. However, incorporating balance as a metric of fairness into spectral clustering algorithms has led to computational times that can be improved. This study aims to enhance the efficiency of spectral clustering algorithms by reformulating the constrained optimization problem using a new formulation derived from the Lagrangian method and the Sherman-Morrison-Woodbury (SMW) identity, resulting in the Fair-SMW algorithm. Fair-SMW employs three alternatives to the Laplacian matrix with different spectral gaps to generate multiple variations of Fair-SMW, achieving clustering solutions with comparable balance to existing algorithms while offering improved runtime performance. We present the results of Fair-SMW, evaluated using the Stochastic Block Model (SBM) to measure both runtime efficiency and balance across real-world network datasets, including LastFM, FacebookNet, Deezer, and German. We achieve an improvement in computation time that is twice as fast as the state-of-the-art, and also flexible enough to achieve twice as much balance.", "date": "2025-10-22", "categories": []}
{"id": "2604.06864", "title": "A Data-Informed Variational Clustering Framework for Noisy High-Dimensional Data", "abstract": "Clustering in high-dimensional settings with severe feature noise remains challenging, especially when only a small subset of dimensions is informative and the final number of clusters is not specified in advance. In such regimes, partition recovery, feature relevance learning, and structural adaptation are tightly coupled, and standard likelihood-based methods can become unstable or overly sensitive to noisy dimensions. We propose DIVI, a data-informed variational clustering framework that combines global feature gating with split-based adaptive structure growth. DIVI uses informative prior initialization to stabilize optimization, learns feature relevance in a differentiable manner, and expands model complexity only when local diagnostics indicate underfit. Beyond clustering performance, we also examine runtime scalability and parameter sensitivity in order to clarify the computational and practical behavior of the framework. Empirically, we find that DIVI performs competitively under severe feature noise, remains computationally feasible, and yields interpretable feature-gating behavior, while also exhibiting conservative growth and identifiable failure regimes in challenging settings. Overall, DIVI is best viewed as a practical variational clustering framework for noisy high-dimensional data rather than as a fully Bayesian generative solution.", "date": "2026-04-08", "categories": []}
{"id": "2604.07143", "title": "Lumbermark: Resistant Clustering by Chopping Up Mutual Reachability Minimum Spanning Trees", "abstract": "We introduce Lumbermark, a robust divisive clustering algorithm capable of detecting clusters of varying sizes, densities, and shapes. Lumbermark iteratively chops off large limbs connected by protruding segments of a dataset's mutual reachability minimum spanning tree. The use of mutual reachability distances smoothens the data distribution and decreases the influence of low-density objects, such as noise points between clusters or outliers at their peripheries. The algorithm can be viewed as an alternative to HDBSCAN that produces partitions with user-specified sizes. A fast, easy-to-use implementation of the new method is available in the open-source 'lumbermark' package for Python and R. We show that Lumbermark performs well on benchmark data and hope it will prove useful to data scientists and practitioners across different fields.", "date": "2026-04-08", "categories": []}
{"id": "2511.10809", "title": "Near-optimal Linear Predictive Clustering in Non-separable Spaces via MIP and QPBO Reductions", "abstract": "Linear Predictive Clustering (LPC) partitions samples based on shared linear relationships between feature and target variables, with numerous applications including marketing, medicine, and education. Greedy optimization methods, commonly used for LPC, alternate between clustering and linear regression but lack global optimality. While effective for separable clusters, they struggle in non-separable settings where clusters overlap in feature space. In an alternative constrained optimization paradigm, Bertsimas and Shioda (2007) formulated LPC as a Mixed-Integer Program (MIP), ensuring global optimality regardless of separability but suffering from poor scalability. This work builds on the constrained optimization paradigm to introduce two novel approaches that improve the efficiency of global optimization for LPC. By leveraging key theoretical properties of separability, we derive near-optimal approximations with provable error bounds, significantly reducing the MIP formulation's complexity and improving scalability. Additionally, we can further approximate LPC as a Quadratic Pseudo-Boolean Optimization (QPBO) problem, achieving substantial computational improvements in some settings. Comparative analyses on synthetic and real-world datasets demonstrate that our methods consistently achieve near-optimal solutions with substantially lower regression errors than greedy optimization while exhibiting superior scalability over existing MIP formulations.", "date": "2025-11-13", "categories": []}
{"id": "2511.15424", "title": "LLM-MemCluster: Empowering Large Language Models with Dynamic Memory for Text Clustering", "abstract": "Large Language Models (LLMs) are reshaping unsupervised learning by offering an unprecedented ability to perform text clustering based on their deep semantic understanding. However, their direct application is fundamentally limited by a lack of stateful memory for iterative refinement and the difficulty of managing cluster granularity. As a result, existing methods often rely on complex pipelines with external modules, sacrificing a truly end-to-end approach. We introduce LLM-MemCluster, a novel framework that reconceptualizes clustering as a fully LLM-native task. It leverages a Dynamic Memory to instill state awareness and a Dual-Prompt Strategy to enable the model to reason about and determine the number of clusters. Evaluated on several benchmark datasets, our tuning-free framework significantly and consistently outperforms strong baselines. LLM-MemCluster presents an effective, interpretable, and truly end-to-end paradigm for LLM-based text clustering.", "date": "2025-11-19", "categories": []}
{"id": "2604.05337", "title": "Individual-heterogeneous sub-Gaussian Mixture Models", "abstract": "The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the individual-heterogeneous sub-Gaussian mixture model, a flexible framework that assigns each observation its own heterogeneity parameter, thereby explicitly capturing the heterogeneity inherent in practical applications. Built upon this model, we propose an efficient spectral method that provably achieves exact recovery of the true cluster labels under mild separation conditions, even in high-dimensional settings where the number of features far exceeds the number of samples. Numerical experiments on both synthetic and real data demonstrate that our method consistently outperforms existing clustering algorithms, including those designed for classical Gaussian mixture models.", "date": "2026-04-07", "categories": []}
{"id": "2604.05857", "title": "Weight-Informed Self-Explaining Clustering for Mixed-Type Tabular Data", "abstract": "Clustering mixed-type tabular data is fundamental for exploratory analysis, yet remains challenging due to misaligned numerical-categorical representations, uneven and context-dependent feature relevance, and disconnected and post-hoc explanation from the clustering process. We propose WISE, a Weight-Informed Self-Explaining framework that unifies representation, feature weighting, clustering, and interpretation in a fully unsupervised and transparent pipeline. WISE introduces Binary Encoding with Padding (BEP) to align heterogeneous features in a unified sparse space, a Leave-One-Feature-Out (LOFO) strategy to sense multiple high-quality and diverse feature-weighting views, and a two-stage weight-aware clustering procedure to aggregate alternative semantic partitions. To ensure intrinsic interpretability, we further develop Discriminative FreqItems (DFI), which yields feature-level explanations that are consistent from instances to clusters with an additive decomposition guarantee. Extensive experiments on six real-world datasets demonstrate that WISE consistently outperforms classical and neural baselines in clustering quality while remaining efficient, and produces faithful, human-interpretable explanations grounded in the same primitives that drive clustering.", "date": "2026-04-07", "categories": []}
{"id": "2405.03083", "title": "Causal K-Means Clustering", "abstract": "Causal effects are often characterized with population summaries. These might provide an incomplete picture when there are heterogeneous treatment effects across subgroups. Since the subgroup structure is typically unknown, it is more challenging to identify and evaluate subgroup effects than population effects. We propose a new solution to this problem: \\emph{Causal k-Means Clustering}, which leverages the k-means clustering algorithm to uncover the unknown subgroup structure. Our problem differs significantly from the conventional clustering setup since the variables to be clustered are unknown counterfactual functions. We present a plug-in estimator which is simple and readily implementable using off-the-shelf algorithms, and study its rate of convergence. We also develop a new bias-corrected estimator based on nonparametric efficiency theory and double machine learning, and show that this estimator achieves fast root-n rates and asymptotic normality in large nonparametric models. Our proposed methods are especially useful for modern outcome-wide studies with multiple treatment levels. Further, our framework is extensible to clustering with generic pseudo-outcomes, such as partially observed outcomes or otherwise unknown functions. Finally, we explore finite sample properties via simulation, and illustrate the proposed methods using a study of mobile-supported self-management for chronic low back pain.", "date": "2024-05-05", "categories": []}
{"id": "2603.28816", "title": "ASTRA: Mapping Art-Technology Institutions via Conceptual Axes, Text Embeddings, and Unsupervised Clustering", "abstract": "The global landscape of art-technology institutions, including festivals, biennials, research labs, conferences, and hybrid organizations, has grown increasingly diverse, yet systematic frameworks for analyzing their multidimensional characteristics remain scarce. This paper proposes ASTRA (Art-technology Institution Spatial Taxonomy and Relational Analysis), a computational methodology combining an eight-axis conceptual framework (Curatorial Philosophy, Territorial Relation, Knowledge Production Mode, Institutional Genealogy, Temporal Orientation, Ecosystem Function, Audience Relation, and Disciplinary Positioning) with a text-embedding and clustering pipeline to map 78 cultural-technology institutions into a unified analytical space. Each institution is characterized through qualitative descriptions along the eight axes, encoded via E5-large-v2 sentence embeddings and quantized through a word-level codebook into TF-IDF feature vectors. Dimensionality reduction using UMAP, followed by agglomerative clustering (Average linkage, k=10), yields a composite score of 0.825, a silhouette coefficient of 0.803, and a Calinski-Harabasz index of 11196. Non-negative matrix factorization extracts ten latent topics, and a neighbor-cluster entropy measure identifies boundary institutions bridging multiple thematic communities. An interactive React-based tool enables curators, researchers, and policymakers to explore institutional similarities and cross-disciplinary connections. Results reveal coherent groupings such as an art-science hub cluster anchored by ZKM and ArtScience Museum, an innovation and industry cluster including Ars Electronica, transmediale, and Sonar, an ACM academic cluster comprising TEI, DIS, and NIME, and an electronic music cluster including CTM Festival, MUTEK, and Sonic Acts. Code and data: https://github.com/joonhyungbae/astra", "date": "2026-03-28", "categories": []}
{"id": "2604.03306", "title": "Deep Image Clustering Based on Curriculum Learning and Density Information", "abstract": "Image clustering is one of the crucial techniques in multimedia analytics and knowledge discovery. Recently, the Deep clustering method (DC), characterized by its ability to perform feature learning and cluster assignment jointly, surpasses the performance of traditional ones on image data. However, existing methods rarely consider the role of model learning strategies in improving the robustness and performance of clustering complex image data. Furthermore, most approaches rely solely on point-to-point distances to cluster centers for partitioning the latent representations, resulting in error accumulation throughout the iterative process. In this paper, we propose a robust image clustering method (IDCL) which, to our knowledge for the first time, introduces a model training strategy using density information into image clustering. Specifically, we design a curriculum learning scheme grounded in the density information of input data, with a more reasonable learning pace. Moreover, we employ the density core rather than the individual cluster center to guide the cluster assignment. Finally, extensive comparisons with state-of-the-art clustering approaches on benchmark datasets demonstrate the superiority of the proposed method, including robustness, rapid convergence, and flexibility in terms of data scale, number of clusters, and image context.", "date": "2026-03-31", "categories": []}
{"id": "2604.04302", "title": "CavMerge: Merging K-means Based on Local Log-Concavity", "abstract": "K-means clustering, a classic and widely-used clustering technique, is known to exhibit suboptimal performance when applied to non-linearly separable data. Numerous adjustments and modifications have been proposed to address this issue, including methods that merge K-means results from a relatively large K to obtain a final cluster assignment. However, existing methods of this nature often encounter computational inefficiencies and suffer from hyperparameter tuning. Here we present \\emph{CavMerge}, a novel K-means merging algorithm that is intuitive, free of parameter tuning, and computationally efficient. Operating under minimal local distributional assumptions, our algorithm demonstrates strong consistency and rapid convergence guarantees. Empirical studies on various simulated and real datasets demonstrate that our method yields more reliable clusters in comparison to current state-of-the-art algorithms.", "date": "2026-04-05", "categories": []}
{"id": "2604.01943", "title": "A Novel Theoretical Analysis for Clustering Heteroscedastic Gaussian Data without Knowledge of the Number of Clusters", "abstract": "This paper addresses the problem of clustering measurement vectors that are heteroscedastic in that they can have different covariance matrices. From the assumption that the measurement vectors within a given cluster are Gaussian distributed with possibly different and unknown covariant matrices around the cluster centroid, we introduce a novel cost function to estimate the centroids. The zeros of the gradient of this cost function turn out to be the fixed-points of a certain function. As such, the approach generalizes the methodology employed to derive the existing Mean-Shift algorithm. But as a main and novel theoretical result compared to Mean-Shift, this paper shows that the sole fixed-points of the identified function tend to be the cluster centroids if both the number of measurements per cluster and the distances between centroids are large enough. As a second contribution, this paper introduces the Wald kernel for clustering. This kernel is defined as the p-value of the Wald hypothesis test for testing the mean of a Gaussian. As such, the Wald kernel measures the plausibility that a measurement vector belongs to a given cluster and it scales better with the dimension of the measurement vectors than the usual Gaussian kernel. Finally, the proposed theoretical framework allows us to derive a new clustering algorithm called CENTRE-X that works by estimating the fixed-points of the identified function. As Mean-Shift, CENTRE-X requires no prior knowledge of the number of clusters. It relies on a Wald hypothesis test to significantly reduce the number of fixed points to calculate compared to the Mean-Shift algorithm, thus resulting in a clear gain in complexity. Simulation results on synthetic and real data sets show that CENTRE-X has comparable or better performance than standard clustering algorithms K-means and Mean-Shift, even when the covariance matrices are not perfectly known.", "date": "2026-04-02", "categories": []}
{"id": "2510.14710", "title": "MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homology", "abstract": "Datasets often possess an intrinsic multiscale structure with meaningful descriptions at different levels of coarseness. Such datasets are naturally described as multi-resolution clusterings, i.e., not necessarily hierarchical sequences of partitions across scales. To analyse and compare such sequences, we use tools from topological data analysis and define the Multiscale Clustering Bifiltration (MCbiF), a 2-parameter filtration of abstract simplicial complexes that encodes cluster intersection patterns across scales. The MCbiF is a complete invariant of (non-hierarchical) sequences of partitions and can be interpreted as a higher-order extension of Sankey diagrams, which reduce to dendrograms for hierarchical sequences. We show that the multiparameter persistent homology (MPH) of the MCbiF yields a finitely presented and block decomposable module, and its stable Hilbert functions characterise the topological autocorrelation of the sequence of partitions. In particular, at dimension zero, the MPH captures violations of the refinement order of partitions, whereas at dimension one, the MPH captures higher-order inconsistencies between clusters across scales. We then demonstrate through experiments the use of MCbiF Hilbert functions as interpretable topological feature maps for downstream machine learning tasks, and show that MCbiF feature maps outperform both baseline features and representation learning methods on regression and classification tasks for non-hierarchical sequences of partitions. We also showcase an application of MCbiF to real-world data of non-hierarchical wild mice social grouping patterns across time.", "date": "2025-10-16", "categories": []}
{"id": "2603.20507", "title": "Distributed Gradient Clustering: Convergence and the Effect of Initialization", "abstract": "We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a local dataset and communicates only with its immediate neighbours, with the aim of finding a global clustering of the joint data. We perform extensive numerical experiments, evaluating the effects of center initialization on the performance of our family of methods, demonstrating that our methods are more resilient to the effects of initialization, compared to centralized gradient clustering [2]. Next, inspired by the $K$-means++ initialization [3], we propose a novel distributed center initialization scheme, which is shown to improve the performance of our methods, compared to the baseline random initialization.", "date": "2026-03-20", "categories": []}
{"id": "2603.26744", "title": "CNMBI: Determining the Number of Clusters Using Center Pairwise Matching and Boundary Filtering", "abstract": "One of the main challenges in data mining is choosing the optimal number of clusters without prior information. Notably, existing methods are usually in the philosophy of cluster validation and hence have underlying assumptions on data distribution, which prevents their application to complex data such as large-scale images and high-dimensional data from the real world. In this regard, we propose an approach named CNMBI. Leveraging the distribution information inherent in the data space, we map the target task as a dynamic comparison process between cluster centers regarding positional behavior, without relying on the complete clustering results and designing the complex validity index as before. Bipartite graph theory is then employed to efficiently model this process. Additionally, we find that different samples have different confidence levels and thereby actively remove low-confidence ones, which is, for the first time to our knowledge, considered in cluster number determination. CNMBI is robust and allows for more flexibility in the dimension and shape of the target data (e.g., CIFAR-10 and STL-10). Extensive comparison studies with state-of-the-art competitors on various challenging datasets demonstrate the superiority of our method.", "date": "2026-03-23", "categories": []}
{"id": "2603.26746", "title": "TDEC: Deep Embedded Image Clustering with Transformer and Distribution Information", "abstract": "Image clustering is a crucial but challenging task in multimedia machine learning. Recently the combination of clustering with deep learning has achieved promising performance against conventional methods on high-dimensional image data. Unfortunately, existing deep clustering methods (DC) often ignore the importance of information fusion with a global perception field among different image regions on clustering images, especially complex ones. Additionally, the learned features are usually clustering-unfriendly in terms of dimensionality and are based only on simple distance information for the clustering. In this regard, we propose a deep embedded image clustering TDEC, which for the first time to our knowledge, jointly considers feature representation, dimensional preference, and robust assignment for image clustering. Specifically, we introduce the Transformer to form a novel module T-Encoder to learn discriminative features with global dependency while using the Dim-Reduction block to build a friendly low-dimensional space favoring clustering. Moreover, the distribution information of embedded features is considered in the clustering process to provide reliable supervised signals for joint training. Our method is robust and allows for more flexibility in data size, the number of clusters, and the context complexity. More importantly, the clustering performance of TDEC is much higher than recent competitors. Extensive experiments with state-of-the-art approaches on complex datasets show the superiority of TDEC.", "date": "2026-03-23", "categories": []}
{"id": "2603.26963", "title": "On the Optimal Number of Grids for Differentially Private Non-Interactive $K$-Means Clustering", "abstract": "Differentially private $K$-means clustering enables releasing cluster centers derived from a dataset while protecting the privacy of the individuals. Non-interactive clustering techniques based on privatized histograms are attractive because the released data synopsis can be reused for other downstream tasks without additional privacy loss. The choice of the number of grids for discretizing the data points is crucial, as it directly controls the quantization bias and the amount of noise injected to preserve privacy. The widely adopted strategy selects a grid size that is independent of the number of clusters and also relies on empirical tuning. In this work, we revisit this choice and propose a refined grid-size selection rule derived by minimizing an upper bound on the expected deviation in the K-means objective function, leading to a more principled discretization strategy for non-interactive private clustering. Compared to prior work, our grid resolution differs both in its dependence on the number of clusters and in the scaling with dataset size and privacy budget. Extensive numerical results elucidate that the proposed strategy results in accurate clustering compared to the state-of-the-art techniques, even under tight privacy budgets.", "date": "2026-03-27", "categories": []}
{"id": "2603.27417", "title": "Kempe Swap K-Means: A Scalable Near-Optimal Solution for Semi-Supervised Clustering", "abstract": "This paper presents a novel centroid-based heuristic algorithm, termed Kempe Swap K-Means, for constrained clustering under rigid must-link (ML) and cannot-link (CL) constraints. The algorithm employs a dual-phase iterative process: an assignment step that utilizes Kempe chain swaps to refine current clustering in the constrained solution space and a centroid update step that computes optimal cluster centroids. To enhance global search capabilities and avoid local optima, the framework incorporates controlled perturbations during the update phase. Empirical evaluations demonstrate that the proposed method achieves near-optimal partitions while maintaining high computational efficiency and scalability. The results indicate that Kempe Swap K-Means consistently outperforms state-of-the-art benchmarks in both clustering accuracy and algorithmic efficiency for large-scale datasets.", "date": "2026-03-28", "categories": []}
{"id": "2603.23518", "title": "Cluster-R1: Large Reasoning Models Are Instruction-following Clustering Agents", "abstract": "General-purpose embedding models excel at recognizing semantic similarities but fail to capture the characteristics of texts specified by user instructions. In contrast, instruction-tuned embedders can align embeddings with textual instructions yet cannot autonomously infer latent corpus structures, such as determining the optimal number of clusters. To address both limitations, we reframe instruction-following clustering as a generative task and train large reasoning models (LRMs) as autonomous clustering agents. Our reasoning-driven training pipeline enables LRMs to interpret high-level clustering instructions and then infer the corresponding latent groupings. To evaluate this paradigm, we introduce ReasonCluster, a comprehensive benchmark comprising 28 diverse tasks spanning daily dialogue, legal cases, and financial reports. Experiments across diverse datasets and clustering scenarios show that our approach consistently outperforms strong embedding-based methods and LRM baselines, demonstrating that explicit reasoning fosters more faithful and interpretable instruction-based clustering.", "date": "2026-03-06", "categories": []}
{"id": "2603.23581", "title": "The Mass Agreement Score: A Point-centric Measure of Cluster Size Consistency", "abstract": "In clustering, strong dominance in the size of a particular cluster is often undesirable, motivating a measure of cluster size uniformity that can be used to filter such partitions. A basic requirement of such a measure is stability: partitions that differ only slightly in their point assignments should receive similar uniformity scores. A difficulty arises because cluster labels are not fixed objects; algorithms may produce different numbers of labels even when the underlying point distribution changes very little. Measures defined directly over labels can therefore become unstable under label-count perturbations. I introduce the Mass Agreement Score (MAS), a point-centric metric bounded in [0, 1] that evaluates the consistency of expected cluster size as measured from the perspective of points in each cluster. Its construction yields fragment robustness by design, assigning similar scores to partitions with similar bulk structure while remaining sensitive to genuine redistribution of cluster mass.", "date": "2026-03-24", "categories": []}
{"id": "2603.24275", "title": "Language-Assisted Image Clustering Guided by Discriminative Relational Signals and Adaptive Semantic Centers", "abstract": "Language-Assisted Image Clustering (LAIC) augments the input images with additional texts with the help of vision-language models (VLMs) to promote clustering performance. Despite recent progress, existing LAIC methods often overlook two issues: (i) textual features constructed for each image are highly similar, leading to weak inter-class discriminability; (ii) the clustering step is restricted to pre-built image-text alignments, limiting the potential for better utilization of the text modality. To address these issues, we propose a new LAIC framework with two complementary components. First, we exploit cross-modal relations to produce more discriminative self-supervision signals for clustering, as it compatible with most VLMs training mechanisms. Second, we learn category-wise continuous semantic centers via prompt learning to produce the final clustering assignments. Extensive experiments on eight benchmark datasets demonstrate that our method achieves an average improvement of 2.6% over state-of-the-art methods, and the learned semantic centers exhibit strong interpretability. Code is available in the supplementary material.", "date": "2026-03-25", "categories": []}
{"id": "2511.05876", "title": "MoEGCL: Mixture of Ego-Graphs Contrastive Representation Learning for Multi-View Clustering", "abstract": "In recent years, the advancement of Graph Neural Networks (GNNs) has significantly propelled progress in Multi-View Clustering (MVC). However, existing methods face the problem of coarse-grained graph fusion. Specifically, current approaches typically generate a separate graph structure for each view and then perform weighted fusion of graph structures at the view level, which is a relatively rough strategy. To address this limitation, we present a novel Mixture of Ego-Graphs Contrastive Representation Learning (MoEGCL). It mainly consists of two modules. In particular, we propose an innovative Mixture of Ego-Graphs Fusion (MoEGF), which constructs ego graphs and utilizes a Mixture-of-Experts network to implement fine-grained fusion of ego graphs at the sample level, rather than the conventional view-level fusion. Additionally, we present the Ego Graph Contrastive Learning (EGCL) module to align the fused representation with the view-specific representation. The EGCL module enhances the representation similarity of samples from the same cluster, not merely from the same sample, further boosting fine-grained graph representation. Extensive experiments demonstrate that MoEGCL achieves state-of-the-art results in deep multi-view clustering tasks. The source code is publicly available at https://github.com/HackerHyper/MoEGCL.", "date": "2025-11-08", "categories": []}
{"id": "2511.09211", "title": "Parameter-Free Clustering via Self-Supervised Consensus Maximization (Extended Version)", "abstract": "Clustering is a fundamental task in unsupervised learning, but most existing methods heavily rely on hyperparameters such as the number of clusters or other sensitive settings, limiting their applicability in real-world scenarios. To address this long-standing challenge, we propose a novel and fully parameter-free clustering framework via Self-supervised Consensus Maximization, named SCMax. Our framework performs hierarchical agglomerative clustering and cluster evaluation in a single, integrated process. At each step of agglomeration, it creates a new, structure-aware data representation through a self-supervised learning task guided by the current clustering structure. We then introduce a nearest neighbor consensus score, which measures the agreement between the nearest neighbor-based merge decisions suggested by the original representation and the self-supervised one. The moment at which consensus maximization occurs can serve as a criterion for determining the optimal number of clusters. Extensive experiments on multiple datasets demonstrate that the proposed framework outperforms existing clustering approaches designed for scenarios with an unknown number of clusters.", "date": "2025-11-12", "categories": []}
{"id": "2603.20829", "title": "Beyond the Academic Monoculture: A Unified Framework and Industrial Perspective for Attributed Graph Clustering", "abstract": "Attributed Graph Clustering (AGC) is a fundamental unsupervised task that partitions nodes into cohesive groups by jointly modeling structural topology and node attributes. While the advent of graph neural networks and self-supervised learning has catalyzed a proliferation of AGC methodologies, a widening chasm persists between academic benchmark performance and the stringent demands of real-world industrial deployment. To bridge this gap, this survey provides a comprehensive, industrially grounded review of AGC from three complementary perspectives. First, we introduce the Encode-Cluster-Optimize taxonomic framework, which decomposes the diverse algorithmic landscape into three orthogonal, composable modules: representation encoding, cluster projection, and optimization strategy. This unified paradigm enables principled architectural comparisons and inspires novel methodological combinations. Second, we critically examine prevailing evaluation protocols to expose the field's academic monoculture: a pervasive over-reliance on small, homophilous citation networks, the inadequacy of supervised-only metrics for an inherently unsupervised task, and the chronic neglect of computational scalability. In response, we advocate for a holistic evaluation standard that integrates supervised semantic alignment, unsupervised structural integrity, and rigorous efficiency profiling. Third, we explicitly confront the practical realities of industrial deployment. By analyzing operational constraints such as massive scale, severe heterophily, and tabular feature noise alongside extensive empirical evidence from our companion benchmark, we outline actionable engineering strategies. Furthermore, we chart a clear roadmap for future research, prioritizing heterophily-robust encoders, scalable joint optimization, and unsupervised model selection criteria to meet production-grade requirements.", "date": "2026-03-21", "categories": []}
{"id": "2603.21590", "title": "Feature Incremental Clustering with Generalization Bounds", "abstract": "In many learning systems, such as activity recognition systems, as new data collection methods continue to emerge in various dynamic environmental applications, the attributes of instances accumulate incrementally, with data being stored in gradually expanding feature spaces. How to design theoretically guaranteed algorithms to effectively cluster this special type of data stream, commonly referred to as activity recognition, remains unexplored. Compared to traditional scenarios, we will face at least two fundamental questions in this feature incremental scenario. (i) How to design preliminary and effective algorithms to address the feature incremental clustering problem? (ii) How to analyze the generalization bounds for the proposed algorithms and under what conditions do these algorithms provide a strong generalization guarantee? To address these problems, by tailoring the most common clustering algorithm, i.e., $k$-means, as an example, we propose four types of Feature Incremental Clustering (FIC) algorithms corresponding to different situations of data access: Feature Tailoring (FT), Data Reconstruction (DR), Data Adaptation (DA), and Model Reuse (MR), abbreviated as FIC-FT, FIC-DR, FIC-DA, and FIC-MR. Subsequently, we offer a detailed analysis of the generalization error bounds for these four algorithms and highlight the critical factors influencing these bounds, such as the amounts of training data, the complexity of the hypothesis space, the quality of pre-trained models, and the discrepancy of the reconstruction feature distribution. The numerical experiments show the effectiveness of the proposed algorithms, particularly in their application to activity recognition clustering tasks.", "date": "2026-03-23", "categories": []}
{"id": "2501.11421", "title": "Online Clustering of Data Sequences with Bandit Information", "abstract": "We study the problem of online clustering of data sequences in the multi-armed bandit (MAB) framework under the fixed-confidence setting. There are $M$ arms, each providing i.i.d. samples from a parametric distribution whose parameters are unknown. The $M$ arms form $K$ clusters based on the distance between the true parameters. In the MAB setting, one arm can be sampled at each time. The objective is to estimate the clusters of the arms using as few samples as possible from the arms, subject to an upper bound on the error probability. Our setting allows for: arms within a cluster to have non-identical distributions, vector parameter arms, vector observations, and $K \\le M$ clusters. We propose and analyze the Average Tracking Bandit Online Clustering (ATBOC) algorithm. ATBOC is asymptotically order-optimal for multivariate Gaussian arms, with expected sample complexity grows at most twice as fast as the lower bound as $\\delta \\rightarrow 0$, and this guarantee extends to multivariate sub-Gaussian arms. For single-parameter exponential family arms, ATBOC is asymptotically optimal, matching the lower bound. We also propose a computationally more efficient alternatives Lower and Upper Confidence Bound based Bandit Online Clustering Algorithm (LUCBBOC), and Bandit Online Clustering-Elimination (BOC-ELIM). We derive the computational complexity of the proposed algorithms and compare their per-sample runtime through simulations. LUCBBOC and BOC-ELIM require lower per-sample runtime than ATBOC while achieving comparable performance. All the proposed algorithms are $\\delta$-Probably correct, i.e., the error probability of cluster estimate at the stopping time is atmost $\\delta$. We validate the asymptotic optimality guarantees through simulations, and present the comparison of our proposed algorithms with other related work through simulations on both synthetic and real-world datasets.", "date": "2025-01-20", "categories": []}
{"id": "2509.08625", "title": "An upper bound on the silhouette evaluation metric for clustering", "abstract": "The silhouette coefficient quantifies, for each observation, the balance between within-cluster cohesion and between-cluster separation, taking values in the range [-1,1]. The average silhouette width (ASW) is a widely used internal measure of clustering quality, with higher values indicating more cohesive and well-separated clusters. However, the dataset-specific maximum of ASW is typically unknown, and the standard upper limit of 1 is rarely attainable. In this work, we derive for each data point a sharp upper bound on its silhouette width and aggregate these to obtain a canonical upper bound for the ASW. This bound-often substantially below 1-enhances the interpretability of empirical ASW values by providing guidance on how close a given clustering result is to the best possible outcome for that dataset. We evaluate the usefulness of the upper bound on a variety of datasets and conclude that it can meaningfully enrich cluster quality evaluation; however, its practical relevance depends on the specific dataset. Finally, we extend the framework to establish an upper bound for the macro-averaged silhouette.", "date": "2025-09-10", "categories": []}
{"id": "2602.14855", "title": "A Pragmatic Method for Comparing Clusterings with Overlaps and Outliers", "abstract": "Clustering algorithms are an essential part of the unsupervised data science ecosystem, and extrinsic evaluation of clustering algorithms requires a method for comparing the detected clustering to a ground truth clustering. In a general setting, the detected and ground truth clusterings may have outliers (objects belonging to no cluster), overlapping clusters (objects may belong to more than one cluster), or both, but methods for comparing these clusterings are currently undeveloped. In this note, we define a pragmatic similarity measure for comparing clusterings with overlaps and outliers, show that it has several desirable properties, and experimentally confirm that it is not subject to several common biases afflicting other clustering comparison measures.", "date": "2026-02-16", "categories": []}
{"id": "2603.19840", "title": "Explainable cluster analysis: a bagging approach", "abstract": "A major limitation of clustering approaches is their lack of explainability: methods rarely provide insight into which features drive the grouping of similar observations. To address this limitation, we propose an ensemble-based clustering framework that integrates bagging and feature dropout to generate feature importance scores, in analogy with feature importance mechanisms in supervised random forests. By leveraging multiple bootstrap resampling schemes and aggregating the resulting partitions, the method improves stability and robustness of the cluster definition, particularly in small-sample or noisy settings. Feature importance is assessed through an information-theoretic approach: at each step, the mutual information between each feature and the estimated cluster labels is computed and weighted by a measure of clustering validity to emphasize well-formed partitions, before being aggregated into a final score. The method outputs both a consensus partition and a corresponding measure of feature importance, enabling a unified interpretation of clustering structure and variable relevance. Its effectiveness is demonstrated on multiple simulated and real-world datasets.", "date": "2026-03-20", "categories": []}
{"id": "2603.20009", "title": "A Super Fast K-means for Indexing Vector Embeddings", "abstract": "We present SuperKMeans: a k-means variant designed for clustering collections of high-dimensional vector embeddings. SuperKMeans' clustering is up to 7x faster than FAISS and Scikit-Learn on modern CPUs and up to 4x faster than cuVS on GPUs (Figure 1), while maintaining the quality of the resulting centroids for vector similarity search tasks. SuperKMeans acceleration comes from reducing data-access and compute overhead by reliably and efficiently pruning dimensions that are not needed to assign a vector to a centroid. Furthermore, we present Early Termination by Recall, a novel mechanism that early-terminates k-means when the quality of the centroids for retrieval tasks stops improving across iterations. In practice, this further reduces runtimes without compromising retrieval quality. We open-source our implementation at https://github.com/cwida/SuperKMeans", "date": "2026-03-20", "categories": []}
{"id": "2603.14601", "title": "$K-$means with learned metrics", "abstract": "We study the Fr\\'echet $k-$means of a metric measure space when both the measure and the distance are unknown and have to be estimated. We prove a general result that states that the $k-$means are continuous with respect to the measured Gromov-Hausdorff topology. In this situation, we also prove a stability result for the Voronoi clusters they determine. We do not assume uniqueness of the set of $k-$means, but when it is unique, the results are stronger. This framework provides a unified approach to proving consistency for a wide range of metric learning procedures. As concrete applications, we obtain new consistency results for several important estimators that were previously unestablished, even when $k=1$. These include $k-$means based on: (i) Isomap and Fermat geodesic distances on manifolds, (ii) difussion distances, (iii) Wasserstein distances computed with respect to learned ground metrics. Finally, we consider applications beyond the statistical inference paradigm like (iv) first passage percolation and (v) discrete approximations of length spaces.", "date": "2026-03-15", "categories": []}
{"id": "2505.04389", "title": "Clust-Splitter - an Efficient Nonsmooth Optimization-Based Algorithm for Clustering Large Datasets", "abstract": "Clustering is a fundamental task in data mining and machine learning, particularly for analyzing large-scale data. In this paper, we introduce Clust-Splitter, an efficient algorithm based on nonsmooth optimization, designed to solve the minimum sum-of-squares clustering problem in very large datasets. The clustering task is approached through a sequence of three nonsmooth optimization problems: two auxiliary problems used to generate suitable starting points, followed by a main clustering formulation. To solve these problems effectively, the limited memory bundle method is combined with an incremental approach to develop the Clust-Splitter algorithm. We evaluate Clust-Splitter on real-world datasets characterized by both a large number of attributes and a large number of data points and compare its performance with several state-of-the-art large-scale clustering algorithms. Experimental results demonstrate the efficiency of the proposed method for clustering very large datasets, as well as the high quality of its solutions, which are on par with those of the best existing methods.", "date": "2025-05-07", "categories": []}
{"id": "2506.01324", "title": "Near-Optimal Clustering in Mixture of Markov Chains", "abstract": "We study the problem of clustering $T$ trajectories of length $H$, each generated by one of K unknown ergodic Markov chains over a finite state space of size $S$. We derive an instance-dependent, high-probability lower bound on the clustering error rate, governed by the stationary-weighted KL divergence between transition kernels. We then propose a two-stage algorithm: Stage I applies spectral clustering via a new injective Euclidean embedding for ergodic Markov chains, a contribution of independent interest enabling sharp concentration results; Stage II refines clusters with a single likelihood-based reassignment step. We prove that our algorithm achieves near-optimal clustering error with high probability under reasonable requirements on $T$ and $H$. Preliminary experiments support our approach, and we conclude with discussions of its limitations and extensions.", "date": "2025-06-02", "categories": []}
{"id": "2510.24318", "title": "Transformers can do Bayesian Clustering", "abstract": "Bayesian clustering accounts for uncertainty but is computationally demanding at scale. Furthermore, real-world datasets often contain missing values, and simple imputation ignores the associated uncertainty, resulting in suboptimal results. We present Cluster-PFN, a Transformer-based model that extends Prior-Data Fitted Networks (PFNs) to unsupervised Bayesian clustering. Trained entirely on synthetic datasets generated from a finite Gaussian Mixture Model (GMM) prior, Cluster-PFN learns to estimate the posterior distribution over both the number of clusters and the cluster assignments. Our method estimates the number of clusters more accurately than handcrafted model selection procedures such as AIC, BIC and Variational Inference (VI), and achieves clustering quality competitive with VI while being orders of magnitude faster. Cluster-PFN can be trained on complex priors that include missing data, outperforming imputation-based baselines on real-world genomic datasets, at high missingness. These results show that the Cluster-PFN can provide scalable and flexible Bayesian clustering.", "date": "2025-10-28", "categories": []}
{"id": "2411.14727", "title": "HyReaL: Clustering Attributed Graph via Hyper-Complex Space Representation Learning", "abstract": "Clustering complex data in the form of attributed graphs has attracted increasing attention, where powerful graph representation is a critical prerequisite. However, the well-known Over-Smoothing (OS) effect makes Graph Convolutional Networks tend to homogenize the representation of graph nodes, while the existing OS solutions focus on alleviating the homogeneity of nodes' embeddings from the aspect of graph topology information, which is inconsistent with the attributed graph clustering objective. Therefore, we introduce hyper-complex space with powerful quaternion feature transformation to enhance the representation learning of the attributes. A generalized \\textbf{Hy}per-complex space \\textbf{Re}present\\textbf{a}tion \\textbf{L}earning (\\textbf{HyReaL}) model is designed to: 1) bridge arbitrary dimensional attributes to the well-developed quaternion algebra with four parts, and 2) connect the learned representations to more generalized clustering objective without being restricted to a given number of clusters $k$. The novel introduction of quaternion benefits attributed graph clustering from two aspects: 1) enhanced attribute coupling learning capability allows complex attribute information to be sufficiently exploited in clustering, and 2) stronger learning capability makes it unnecessary to stack too many graph convolution layers, naturally alleviating the OS problem. It turns out that the node representations learned by HyReaL are more discriminative and widely suit downstream clustering with different $k$s. Extensive experiments including significance tests, ablation studies, qualitative results, etc., show the superiority of HyReaL.", "date": "2024-11-22", "categories": []}
{"id": "2506.19837", "title": "Convergence and clustering analysis for Mean Shift with radially symmetric, positive definite kernels", "abstract": "The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In this paper, we show that for\\textit{ sufficiently large bandwidth} convergence is guaranteed in any dimension with \\textit{any radially symmetric and strictly positive definite kernels}. Although the author acknowledges that our result is partially more restrictive than that of \\cite{YT} due to the lower limit of the bandwidth, our kernel class is not covered by the kernel class in \\cite{YT}, and the proof technique is different. Moreover, we show theoretically and experimentally that while for Gaussian kernel, accurate clustering at \\textit{large bandwidths} is generally impossible, it may still be possible for other radially symmetric, strictly positive definite kernels.", "date": "2025-06-24", "categories": []}
{"id": "2512.12436", "title": "Rough Sets for Explainability of Spectral Graph Clustering", "abstract": "Graph Spectral Clustering methods (GSC) allow representing clusters of diverse shapes, densities, etc. However, the results of such algorithms, when applied e.g. to text documents, are hard to explain to the user, especially due to embedding in the spectral space which has no obvious relation to document contents. Furthermore, the presence of documents without clear content meaning and the stochastic nature of the clustering algorithms deteriorate explainability. This paper proposes an enhancement to the explanation methodology, proposed in an earlier research of our team. It allows us to overcome the latter problems by taking inspiration from rough set theory.", "date": "2025-12-13", "categories": []}
{"id": "2602.09586", "title": "Delving into Spectral Clustering with Vision-Language Representations", "abstract": "Spectral clustering is known as a powerful technique in unsupervised data analysis. The vast majority of approaches to spectral clustering are driven by a single modality, leaving the rich information in multi-modal representations untapped. Inspired by the recent success of vision-language pre-training, this paper enriches the landscape of spectral clustering from a single-modal to a multi-modal regime. Particularly, we propose Neural Tangent Kernel Spectral Clustering that leverages cross-modal alignment in pre-trained vision-language models. By anchoring the neural tangent kernel with positive nouns, i.e., those semantically close to the images of interest, we arrive at formulating the affinity between images as a coupling of their visual proximity and semantic overlap. We show that this formulation amplifies within-cluster connections while suppressing spurious ones across clusters, hence encouraging block-diagonal structures. In addition, we present a regularized affinity diffusion mechanism that adaptively ensembles affinity matrices induced by different prompts. Extensive experiments on \\textbf{16} benchmarks -- including classical, large-scale, fine-grained and domain-shifted datasets -- manifest that our method consistently outperforms the state-of-the-art by a large margin.", "date": "2026-02-10", "categories": []}
{"id": "2603.13254", "title": "Introducing Feature-Based Trajectory Clustering, a clustering algorithm for longitudinal data", "abstract": "We present a new algorithm for clustering longitudinal data. Data of this type can be conceptualized as consisting of individuals and, for each such individual, observations of a time-dependent variable made at various times. Generically, the specific way in which this variable evolves with time is different from one individual to the next. However, there may also be commonalities; specific characteristic features of the time evolution shared by many individuals. The purpose of the method we put forward is to find clusters of individual whose underlying time-dependent variables share such characteristic features. This is done in two steps. The first step identifies each individual to a point in Euclidean space whose coordinates are determined by specific mathematical formulae meant to capture a variety of characteristic features. The second step finds the clusters by applying the Spectral Clustering algorithm to the resulting point cloud.", "date": "2026-02-24", "categories": []}
{"id": "2603.13339", "title": "AdaBox: Adaptive Density-Based Box Clustering with Parameter Generalization", "abstract": "Density-based clustering algorithms like DBSCAN and HDBSCAN are foundational tools for discovering arbitrarily shaped clusters, yet their practical utility is undermined by acute hyperparameter sensitivity -- parameters tuned on one dataset frequently fail to transfer to others, requiring expensive re-optimization for each deployment.\n  We introduce AdaBox (Adaptive Density-Based Box Clustering), a grid-based density clustering algorithm designed for robustness across diverse data geometries. AdaBox features a six-parameter design where parameters capture cluster structure rather than pairwise point relationships. Four parameters are inherently scale-invariant, one self-corrects for sampling bias, and one is adjusted via a density scaling stage, enabling reliable parameter transfer across 30-200x scale factors. AdaBox processes data through five stages: adaptive grid construction, liberal seed initialization, iterative growth with graduation, statistical cluster merging, and Gaussian boundary refinement.\n  Comprehensive evaluation across 111 datasets demonstrates three key findings: (1) AdaBox significantly outperforms DBSCAN and HDBSCAN across five evaluation metrics, achieving the best score on 78\\% of datasets with p < 0.05; (2) AdaBox uniquely exhibits parameter generalization. Protocol A (direct transfer to 30-100x larger datasets) shows AdaBox maintains performance while baselines collapse. (3) Ablation studies confirm the necessity of all five architectural stages for maintaining robustness.", "date": "2026-03-06", "categories": []}
{"id": "2603.13799", "title": "Node Role-Guided LLMs for Dynamic Graph Clustering", "abstract": "Dynamic graph clustering aims to detect and track time-varying clusters in dynamic graphs, revealing how complex real-world systems evolve over time. However, existing methods are predominantly black-box models. They lack interpretability in their clustering decisions and fail to provide semantic explanations of why clusters form or how they evolve, severely limiting their use in safety-critical domains such as healthcare or transportation. To address these limitations, we propose an end-to-end interpretable framework that maps continuous graph embeddings into discrete semantic concepts through learnable prototypes. Specifically, we first decompose node representations into orthogonal role and clustering subspaces, so that nodes with similar roles (e.g., hubs, bridges) but different cluster affiliations can be properly distinguished. We then introduce five node role prototypes (Leader, Contributor, Wanderer, Connector, Newcomer) in the role subspace as semantic anchors, transforming continuous embeddings into discrete concepts to facilitate LLM understanding of node roles within communities. Finally, we design a hierarchical LLM reasoning mechanism to generate both clustering results and natural language explanations, while providing consistency feedback as weak supervision to refine node representations. Experimental results on four synthetic and six real-world benchmarks demonstrate the effectiveness, interpretability, and robustness of DyG-RoLLM. Code is available at https://github.com/Clearloveyuan/DyG-RoLLM.", "date": "2026-03-14", "categories": []}
{"id": "2603.14783", "title": "Orthogonal Subspace Clustering: Enhancing High-Dimensional Data Analysis through Adaptive Dimensionality Reduction and Efficient Clustering", "abstract": "This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in a statistical sense, whose form exactly matches the paradigm of Q-type factor analysis. This theorem lays a solid mathematical foundation for dimensionality reduction via matrix decomposition and factor analysis. Based on this theorem, we propose the OSC framework to address the \"curse of dimensionality\" -- a critical challenge that degrades clustering effectiveness due to sample sparsity and ineffective distance metrics. OSC integrates orthogonal subspace construction with classical clustering techniques, introducing a data-driven mechanism to select the subspace dimension based on cumulative variance contribution. This avoids manual selection biases while maximizing the retention of discriminative information. By projecting high-dimensional data into an uncorrelated, low-dimensional orthogonal subspace, OSC significantly improves clustering efficiency, robustness, and accuracy. Extensive experiments on various benchmark datasets demonstrate the effectiveness of OSC, with thorough analysis of evaluation metrics including Cluster Accuracy (ACC), Normalized Mutual Information (NMI), and Adjusted Rand Index (ARI) highlighting its advantages over existing methods.", "date": "2026-03-16", "categories": []}
{"id": "2501.03584", "title": "Discriminative Representation learning via Attention-Enhanced Contrastive Learning for Short Text Clustering", "abstract": "Contrastive learning has gained significant attention in short text clustering, yet it has an inherent drawback of mistakenly identifying samples from the same category as negatives and then separating them in the feature space (false negative separation), which hinders the generation of superior representations. To generate more discriminative representations for efficient clustering, we propose a novel short text clustering method, called Discriminative Representation learning via \\textbf{A}ttention-\\textbf{E}nhanced \\textbf{C}ontrastive \\textbf{L}earning for Short Text Clustering (\\textbf{AECL}). The \\textbf{AECL} consists of two modules which are the pseudo-label generation module and the contrastive learning module. Both modules build a sample-level attention mechanism to capture similarity relationships between samples and aggregate cross-sample features to generate consistent representations. Then, the former module uses the more discriminative consistent representation to produce reliable supervision information for assist clustering, while the latter module explores similarity relationships and consistent representations optimize the construction of positive samples to perform similarity-guided contrastive learning, effectively addressing the false negative separation issue. Experimental results demonstrate that the proposed \\textbf{AECL} outperforms state-of-the-art methods. If the paper is accepted, we will open-source the code.", "date": "2025-01-07", "categories": []}
{"id": "2501.15194", "title": "Reliable Pseudo-labeling via Optimal Transport with Attention for Short Text Clustering", "abstract": "Short text clustering has gained significant attention in the data mining community. However, the limited valuable information contained in short texts often leads to low-discriminative representations, increasing the difficulty of clustering. This paper proposes a novel short text clustering framework, called Reliable \\textbf{P}seudo-labeling via \\textbf{O}ptimal \\textbf{T}ransport with \\textbf{A}ttention for Short Text Clustering (\\textbf{POTA}), that generate reliable pseudo-labels to aid discriminative representation learning for clustering. Specially, \\textbf{POTA} first implements an instance-level attention mechanism to capture the semantic relationships among samples, which are then incorporated as a semantic consistency regularization term into an optimal transport problem. By solving this OT problem, we can yield reliable pseudo-labels that simultaneously account for sample-to-sample semantic consistency and sample-to-cluster global structure information. Additionally, the proposed OT can adaptively estimate cluster distributions, making \\textbf{POTA} well-suited for varying degrees of imbalanced datasets. Then, we utilize the pseudo-labels to guide contrastive learning to generate discriminative representations and achieve efficient clustering. Extensive experiments demonstrate \\textbf{POTA} outperforms state-of-the-art methods. The code is available at: \\href{https://github.com/YZH0905/POTA-STC/tree/main}{https://github.com/YZH0905/POTA-STC/tree/main}.", "date": "2025-01-25", "categories": []}
{"id": "2603.12684", "title": "Federated Hierarchical Clustering with Automatic Selection of Optimal Cluster Numbers", "abstract": "Federated Clustering (FC) is an emerging and promising solution in exploring data distribution patterns from distributed and privacy-protected data in an unsupervised manner. Existing FC methods implicitly rely on the assumption that clients are with a known number of uniformly sized clusters. However, the true number of clusters is typically unknown, and cluster sizes are naturally imbalanced in real scenarios. Furthermore, the privacy-preserving transmission constraints in federated learning inevitably reduce usable information, making the development of robust and accurate FC extremely challenging. Accordingly, we propose a novel FC framework named Fed-$k^*$-HC, which can automatically determine an optimal number of clusters $k^*$ based on the data distribution explored through hierarchical clustering. To obtain the global data distribution for $k^*$ determination, we let each client generate micro-subclusters. Their prototypes are then uploaded to the server for hierarchical merging. The density-based merging design allows exploring clusters of varying sizes and shapes, and the progressive merging process can self-terminate according to the neighboring relationships among the prototypes to determine $k^*$. Extensive experiments on diverse datasets demonstrate the FC capability of the proposed Fed-$k^*$-HC in accurately exploring a proper number of clusters.", "date": "2026-03-13", "categories": []}
{"id": "2603.13177", "title": "Clustering Astronomical Orbital Synthetic Data Using Advanced Feature Extraction and Dimensionality Reduction Techniques", "abstract": "The dynamics of Saturn's satellite system offer a rich framework for studying orbital stability and resonance interactions. Traditional methods for analysing such systems, including Fourier analysis and stability metrics, struggle with the scale and complexity of modern datasets. This study introduces a machine learning-based pipeline for clustering approximately 22,300 simulated satellite orbits, addressing these challenges with advanced feature extraction and dimensionality reduction techniques. The key to this approach is using MiniRocket, which efficiently transforms 400 timesteps into a 9,996-dimensional feature space, capturing intricate temporal patterns. Additional automated feature extraction and dimensionality reduction techniques refine the data, enabling robust clustering analysis. This pipeline reveals stability regions, resonance structures, and other key behaviours in Saturn's satellite system, providing new insights into their long-term dynamical evolution. By integrating computational tools with traditional celestial mechanics techniques, this study offers a scalable and interpretable methodology for analysing large-scale orbital datasets and advancing the exploration of planetary dynamics.", "date": "2026-03-13", "categories": []}
{"id": "2506.12878", "title": "Silhouette-Driven Instance-Weighted $k$-means", "abstract": "Clustering is a fundamental unsupervised learning task with applications across a wide range of domains. Popular algorithms such as $k$-means are efficient and widely used, but can be sensitive to outliers, ambiguous boundary points, and heterogeneous cluster geometry, which may distort centroid estimates and yield suboptimal partitions. We introduce K-Sil, a silhouette-driven $k$-means variant that, at each iteration, weights points using a centroid-margin proxy for the silhouette score, emphasizing confidently assigned instances while down-weighting borderline or noisy regions. Centroid updates take the form of a softmax-weighted mean, and an adaptive temperature automatically calibrates the sharpness of the weight distribution using a cluster-balanced, macro-averaged, silhouette criterion. Under standard separation conditions, we establish a local convergence result for the induced weighted centroid updates. Experiments on 15 real-world datasets spanning tabular, biomedical, text, and image representations show consistent gains in internal validation metrics and typical improvements in external validation metrics over $k$-means and competitive instance-weighted baselines.", "date": "2025-06-15", "categories": []}
{"id": "2510.13065", "title": "Absolute indices for determining compactness, separability and number of clusters", "abstract": "Finding \"true\" clusters in a data set is a challenging problem. Clustering solutions obtained using different models and algorithms do not necessarily provide compact and well-separated clusters or the optimal number of clusters. Cluster validity indices are commonly applied to identify such clusters. Nevertheless, these indices are typically relative, and they are used to compare clustering algorithms or choose the parameters of a clustering algorithm. Moreover, the success of these indices depends on the underlying data structure. This paper introduces novel absolute cluster indices to determine both the compactness and separability of clusters. We define a compactness function for each cluster and a set of neighboring points for cluster pairs. This function is utilized to determine the compactness of each cluster and the whole cluster distribution. The set of neighboring points is used to define the margin between clusters and the overall distribution margin. The proposed compactness and separability indices are applied to identify the true number of clusters. Using a number of synthetic and real-world data sets, we demonstrate the performance of these new indices and compare them with other widely-used cluster validity indices.", "date": "2025-10-15", "categories": []}
{"id": "2603.10132", "title": "Unbalanced Optimal Transport Dictionary Learning for Unsupervised Hyperspectral Image Clustering", "abstract": "Hyperspectral images capture vast amounts of high-dimensional spectral information about a scene, making labeling an intensive task that is resistant to out-of-the-box statistical methods. Unsupervised learning of clusters allows for automated segmentation of the scene, enabling a more rapid understanding of the image. Partitioning the spectral information contained within the data via dictionary learning in Wasserstein space has proven an effective method for unsupervised clustering. However, this approach requires balancing the spectral profiles of the data, blurring the classes, and sacrificing robustness to outliers and noise. In this paper, we suggest improving this approach by utilizing unbalanced Wasserstein barycenters to learn a lower-dimensional representation of the underlying data. The deployment of spectral clustering on the learned representation results in an effective approach for the unsupervised learning of labels.", "date": "2026-03-10", "categories": []}
{"id": "2603.10287", "title": "MultiwayPAM: Multiway Partitioning Around Medoids for LLM-as-a-Judge Score Analysis", "abstract": "LLM-as-a-Judge is a flexible framework for text evaluation, which allows us to obtain scores for the quality of a given text from various perspectives by changing the prompt template. Two main challenges in using LLM-as-a-Judge are computational cost of LLM inference, especially when evaluating a large number of texts, and inherent bias of an LLM evaluator. To address these issues and reveal the structure of score bias caused by an LLM evaluator, we propose to apply a tensor clustering method to a given LLM-as-a-Judge score tensor, whose entries are the scores for different combinations of questions, answerers, and evaluators. Specifically, we develop a new tensor clustering method MultiwayPAM, with which we can simultaneously estimate the cluster membership and the medoids for each mode of a given data tensor. By observing the medoids obtained by MultiwayPAM, we can gain knowledge about the membership of each question/answerer/evaluator cluster. We experimentally show the effectiveness of MultiwayPAM by applying it to the score tensors for two practical datasets.", "date": "2026-03-11", "categories": []}
{"id": "2603.10721", "title": "Sample-and-Search: An Effective Algorithm for Learning-Augmented k-Median Clustering in High dimensions", "abstract": "In this paper, we investigate the learning-augmented $k$-median clustering problem, which aims to improve the performance of traditional clustering algorithms by preprocessing the point set with a predictor of error rate $\\alpha \\in [0,1)$. This preprocessing step assigns potential labels to the points before clustering. We introduce an algorithm for this problem based on a simple yet effective sampling method, which substantially improves upon the time complexities of existing algorithms. Moreover, we mitigate their exponential dependency on the dimensionality of the Euclidean space. Lastly, we conduct experiments to compare our method with several state-of-the-art learning-augmented $k$-median clustering methods. The experimental results suggest that our proposed approach can significantly reduce the computational complexity in practice, while achieving a lower clustering cost.", "date": "2026-03-11", "categories": []}
{"id": "2403.03666", "title": "Provable Filter for Real-world Graph Clustering", "abstract": "Graph clustering, an important unsupervised problem, has been shown to be more resistant to advances in Graph Neural Networks (GNNs). In addition, almost all clustering methods focus on homophilic graphs and ignore heterophily. This significantly limits their applicability in practice, since real-world graphs exhibit a structural disparity and cannot simply be classified as homophily and heterophily. Thus, a principled way to handle practical graphs is urgently needed. To fill this gap, we provide a novel solution with theoretical support. Interestingly, we find that most homophilic and heterophilic edges can be correctly identified on the basis of neighbor information. Motivated by this finding, we construct two graphs that are highly homophilic and heterophilic, respectively. They are used to build low-pass and high-pass filters to capture holistic information. Important features are further enhanced by the squeeze-and-excitation block. We validate our approach through extensive experiments on both homophilic and heterophilic graphs. Empirical results demonstrate the superiority of our method compared to state-of-the-art clustering methods.", "date": "2024-03-06", "categories": []}
{"id": "2603.06602", "title": "Khatri-Rao Clustering for Data Summarization", "abstract": "As datasets continue to grow in size and complexity, finding succinct yet accurate data summaries poses a key challenge. Centroid-based clustering, a widely adopted approach to address this challenge, finds informative summaries of datasets in terms of few prototypes, each representing a cluster in the data. Despite their wide adoption, the resulting data summaries often contain redundancies, limiting their effectiveness particularly in datasets characterized by a large number of underlying clusters. To overcome this limitation, we introduce the Khatri-Rao clustering paradigm that extends traditional centroid-based clustering to produce more succinct but equally accurate data summaries by postulating that centroids arise from the interaction of two or more succinct sets of protocentroids.\n  We study two central approaches to centroid-based clustering, namely the well-established k-Means algorithm and the increasingly popular topic of deep clustering, under the lens of the Khatri-Rao paradigm. To this end, we introduce the Khatri-Rao k-Means algorithm and the Khatri-Rao deep clustering framework. Extensive experiments show that Khatri-Rao k-Means can strike a more favorable trade-off between succinctness and accuracy in data summarization than standard k-Means. Leveraging representation learning, the Khatri-Rao deep clustering framework offers even greater benefits, reducing even more the size of data summaries given by deep clustering while preserving their accuracy.", "date": "2026-02-17", "categories": []}
{"id": "2603.09370", "title": "From Representation to Clusters: A Contrastive Learning Approach for Attributed Hypergraph Clustering", "abstract": "Contrastive learning has demonstrated strong performance in attributed hypergraph clustering. Typically, existing methods based on contrastive learning first learn node embeddings and then apply clustering algorithms, such as k-means, to these embeddings to obtain the clustering results.However, these methods lack direct clustering supervision, risking the inclusion of clustering-irrelevant information in the learned graph.To this end, we propose a Contrastive learning approach for Attributed Hypergraph Clustering (CAHC), an end-to-end method that simultaneously learns node embeddings and obtains clustering results. CAHC consists of two main steps: representation learning and cluster assignment learning. The former employs a novel contrastive learning approach that incorporates both node-level and hyperedge-level objectives to generate node embeddings.The latter joint embedding and clustering optimization to refine these embeddings by clustering-oriented guidance and obtains clustering results simultaneously.Extensive experimental results demonstrate that CAHC outperforms baselines on eight datasets.", "date": "2026-03-10", "categories": []}
{"id": "2509.25376", "title": "Cold-Start Active Correlation Clustering", "abstract": "We study active correlation clustering where pairwise similarities are not provided upfront and must be queried in a cost-efficient manner through active learning. Specifically, we focus on the cold-start scenario, where no true initial pairwise similarities are available for active learning. To address this challenge, we propose a coverage-aware method that encourages diversity early in the process. We demonstrate the effectiveness of our approach through several synthetic and real-world experiments.", "date": "2025-09-29", "categories": []}
{"id": "2601.20157", "title": "PASS: Certified Subset Repair for Classical and Quantum Pairwise Constrained Clustering", "abstract": "Pairwise-constrained clustering incorporates side information through must-link (ML) and cannot-link (CL) relations between samples. While these constraints can improve cluster quality, they complicate optimization at scale and limit quantum and hybrid approaches through the size of the encoded problem. PASS is a scalable framework for pairwise-constrained k-means that concentrates optimization on a small working subset while updating remaining assignments through re-centering. Cannot-link feasibility under subset-restricted updates is formalized as a list-coloring problem on the induced constraint subgraph, yielding a checkable repair certificate with verifiable outcomes. The same subset restriction produces reduced classical subproblems and smaller quantum formulations, enabling a reduction-based hybrid evaluation under a simulation protocol. Infeasible constraint sets are handled explicitly: the pipeline returns a verifiable repair under stated conditions or reports residual conflicts under the same evaluation protocol. Across diverse benchmarks, PASS attains competitive SSE with lower runtime and returns solutions on instances where strong baselines do not finish within a fixed time budget.", "date": "2026-01-28", "categories": []}
{"id": "2603.05318", "title": "GALACTIC: Global and Local Agnostic Counterfactuals for Time-series Clustering", "abstract": "Time-series clustering is a fundamental tool for pattern discovery, yet existing explainability methods, primarily based on feature attribution or metadata, fail to identify the transitions that move an instance across cluster boundaries. While Counterfactual Explanations (CEs) identify the minimal temporal perturbations required to alter the prediction of a model, they have been mostly confined to supervised settings. This paper introduces GALACTIC, the first unified framework to bridge local and global counterfactual explainability for unsupervised time-series clustering. At instance level (local), GALACTIC generates perturbations via a cluster-aware optimization objective that respects the target and underlying cluster assignments. At cluster level (global), to mitigate cognitive load and enhance interpretability, we formulate a representative CE selection problem. We propose a Minimum Description Length (MDL) objective to extract a non-redundant summary of global explanations that characterize the transitions between clusters. We prove that our MDL objective is supermodular, which allows the corresponding MDL reduction to be framed as a monotone submodular set function. This enables an efficient greedy selection algorithm with provable $(1-1/e)$ approximation guarantees. Extensive experimental evaluation on the UCR Archive demonstrates that GALACTIC produces significantly sparser local CEs and more concise global summaries than state-of-the-art baselines adapted for our problem, offering the first unified approach for interpreting clustered time-series through counterfactuals.", "date": "2026-03-05", "categories": []}
{"id": "2603.06889", "title": "Single-pass Possibilistic Clustering with Damped Window Footprints", "abstract": "Streaming clustering is a domain that has become extremely relevant in the age of big data, such as in network traffic analysis or in processing continuously-running sensor data. Furthermore, possibilistic models offer unique benefits over approaches from the literature, especially with the introduction of a \"fuzzifier\" parameter that controls how quickly typicality degrades as one gets further from cluster centers. We propose a single-pass possibilistic clustering (SPC) algorithm that is effective and easy to apply to new datasets. Key contributions of SPC include the ability to model non-spherical clusters, closed-form footprint updates over arbitrarily sized damped windows, and the employment of covariance union from the multiple hypothesis tracking literature to merge two cluster mean and covariance estimates. SPC is validated against five other streaming clustering algorithm on the basis of cluster purity and normalized mutual information.", "date": "2026-03-06", "categories": []}
{"id": "2511.05826", "title": "CADM: Cluster-customized Adaptive Distance Metric for Categorical Data Clustering", "abstract": "An appropriate distance metric is crucial for categorical data clustering, as the distance between categorical data cannot be directly calculated. However, the distances between attribute values usually vary in different clusters induced by their different distributions, which has not been taken into account, thus leading to unreasonable distance measurement. Therefore, we propose a cluster-customized distance metric for categorical data clustering, which can competitively update distances based on different distributions of attributes in each cluster. In addition, we extend the proposed distance metric to the mixed data that contains both numerical and categorical attributes. Experiments demonstrate the efficacy of the proposed method, i.e., achieving an average ranking of around first in fourteen datasets. The source code is available at https://anonymous.4open.science/r/CADM-47D8", "date": "2025-11-08", "categories": []}
{"id": "2603.03056", "title": "Incremental Graph Construction Enables Robust Spectral Clustering of Texts", "abstract": "Neighborhood graphs are a critical but often fragile step in spectral clustering of text embeddings. On realistic text datasets, standard $k$-NN graphs can contain many disconnected components at practical sparsity levels (small $k$), making spectral clustering degenerate and sensitive to hyperparameters. We introduce a simple incremental $k$-NN graph construction that preserves connectivity by design: each new node is linked to its $k$ nearest previously inserted nodes, which guarantees a connected graph for any $k$. We provide an inductive proof of connectedness and discuss implications for incremental updates when new documents arrive. We validate the approach on spectral clustering of SentenceTransformer embeddings using Laplacian eigenmaps across six clustering datasets from the Massive Text Embedding Benchmark. Compared to standard $k$-NN graphs, our method outperforms in the low-$k$ regime where disconnected components are prevalent, and matches standard $k$-NN at larger $k$.", "date": "2026-03-03", "categories": []}
{"id": "2603.04458", "title": "Learning Unified Distance Metric for Heterogeneous Attribute Data Clustering", "abstract": "Datasets composed of numerical and categorical attributes (also called mixed data hereinafter) are common in real clustering tasks. Differing from numerical attributes that indicate tendencies between two concepts (e.g., high and low temperature) with their values in well-defined Euclidean distance space, categorical attribute values are different concepts (e.g., different occupations) embedded in an implicit space. Simultaneously exploiting these two very different types of information is an unavoidable but challenging problem, and most advanced attempts either encode the heterogeneous numerical and categorical attributes into one type, or define a unified metric for them for mixed data clustering, leaving their inherent connection unrevealed. This paper, therefore, studies the connection among any-type of attributes and proposes a novel Heterogeneous Attribute Reconstruction and Representation (HARR) learning paradigm accordingly for cluster analysis. The paradigm transforms heterogeneous attributes into a homogeneous status for distance metric learning, and integrates the learning with clustering to automatically adapt the metric to different clustering tasks. Differing from most existing works that directly adopt defined distance metrics or learn attribute weights to search clusters in a subspace. We propose to project the values of each attribute into unified learnable multiple spaces to more finely represent and learn the distance metric for categorical data. HARR is parameter-free, convergence-guaranteed, and can more effectively self-adapt to different sought number of clusters $k$. Extensive experiments illustrate its superiority in terms of accuracy and efficiency.", "date": "2026-03-03", "categories": []}
{"id": "2603.04625", "title": "K-Means as a Radial Basis function Network: a Variational and Gradient-based Equivalence", "abstract": "This work establishes a rigorous variational and gradient-based equivalence between the classical K-Means algorithm and differentiable Radial Basis Function (RBF) neural networks with smooth responsibilities. By reparameterizing the K-Means objective and embedding its distortion functional into a smooth weighted loss, we prove that the RBF objective $\\Gamma$-converges to the K-Means solution as the temperature parameter $\\sigma$ vanishes. We further demonstrate that the gradient-based updates of the RBF centers recover the exact K-Means centroid update rule and induce identical training trajectories in the limit. To address the numerical instability of the Softmax transformation in the low-temperature regime, we propose the integration of Entmax-1.5, which ensures stable polynomial convergence while preserving the underlying Voronoi partition structure. These results bridge the conceptual gap between discrete partitioning and continuous optimization, enabling K-Means to be embedded directly into deep learning architectures for the joint optimization of representations and clusters. Empirical validation across diverse synthetic geometries confirms a monotone collapse of soft RBF centroids toward K-Means fixed points, providing a unified framework for end-to-end differentiable clustering.", "date": "2026-03-04", "categories": []}
{"id": "2603.05067", "title": "Synchronization-based clustering on the unit hypersphere", "abstract": "Clustering on the unit hypersphere is a fundamental problem in various fields, with applications ranging from gene expression analysis to text and image classification. Traditional clustering methods are not always suitable for unit sphere data, as they do not account for the geometric structure of the sphere. We introduce a novel algorithm for clustering data represented as points on the unit sphere $\\mathbf{S}^{d-1}$. Our method is based on the $d$-dimensional generalized Kuramoto model. The effectiveness of the introduced method is demonstrated on synthetic and real-world datasets. Results are compared with some of the traditional clustering methods, showing that our method achieves similar or better results in terms of clustering accuracy.", "date": "2026-03-05", "categories": []}
{"id": "2408.06958", "title": "AuToMATo: An Out-Of-The-Box Persistence-Based Clustering Algorithm", "abstract": "We present AuToMATo, a novel clustering algorithm based on persistent homology. While AuToMATo is not parameter-free per se, we provide default choices for its parameters that make it into an out-of-the-box clustering algorithm that performs well across the board. AuToMATo combines the existing ToMATo clustering algorithm with a bootstrapping procedure in order to separate significant peaks of an estimated density function from non-significant ones. We perform a thorough comparison of AuToMATo (with its parameters fixed to their defaults) against many other state-of-the-art clustering algorithms. We find not only that AuToMATo compares favorably against parameter-free clustering algorithms, but in many instances also significantly outperforms even the best selection of parameters for other algorithms. AuToMATo is motivated by applications in topological data analysis, in particular the Mapper algorithm, where it is desirable to work with a clustering algorithm that does not need tuning of its parameters. Indeed, we provide evidence that AuToMATo performs well when used with Mapper. Finally, we provide an open-source implementation of AuToMATo in Python that is fully compatible with the standard scikit-learn architecture.", "date": "2024-08-13", "categories": []}
{"id": "2603.03387", "title": "Learning Order Forest for Qualitative-Attribute Data Clustering", "abstract": "Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute values, e.g., the nominal values of attributes like symptoms, marital status, etc. This paper, therefore, discovered a tree-like distance structure to flexibly represent the local order relationship among intra-attribute qualitative values. That is, treating a value as the vertex of the tree allows to capture rich order relationships among the vertex value and the others. To obtain the trees in a clustering-friendly form, a joint learning mechanism is proposed to iteratively obtain more appropriate tree structures and clusters. It turns out that the latent distance space of the whole dataset can be well-represented by a forest consisting of the learned trees. Extensive experiments demonstrate that the joint learning adapts the forest to the clustering task to yield accurate results. Comparisons of 10 counterparts on 12 real benchmark datasets with significance tests verify the superiority of the proposed method.", "date": "2026-03-03", "categories": []}
{"id": "2301.00061", "title": "A Global Optimization Algorithm for K-Center Clustering of One Billion Samples", "abstract": "This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a reduced-space branch and bound scheme and guarantees convergence to the global optimum in a finite number of steps by only branching on the regions of centers. To improve efficiency, we have designed a two-stage decomposable lower bound, the solution of which can be derived in a closed form. In addition, we also propose several acceleration techniques to narrow down the region of centers, including bounds tightening, sample reduction, and parallelization. Extensive studies on synthetic and real-world datasets have demonstrated that our algorithm can solve the K-center problems to global optimal within 4 hours for ten million samples in the serial mode and one billion samples in the parallel mode. Moreover, compared with the state-of-the-art heuristic methods, the global optimum obtained by our algorithm can averagely reduce the objective function by 25.8% on all the synthetic and real-world datasets.", "date": "2022-12-30", "categories": []}
{"id": "2305.02850", "title": "Impossibility of Depth Reduction in Explainable Clustering", "abstract": "Over the last few years Explainable Clustering has gathered a lot of attention. Dasgupta et al. [ICML'20] initiated the study of explainable $k$-means and $k$-median clustering problems where the explanation is captured by a threshold decision tree which partitions the space at each node using axis parallel hyperplanes. Recently, Laber et al. [Pattern Recognition'23] made a case to consider the depth of the decision tree as an additional complexity measure of interest.\n  In this work, we prove that even when the input points are in the Euclidean plane, then any depth reduction in the explanation incurs unbounded loss in the $k$-means and $k$-median cost. Formally, we show that there exists a data set $X\\subseteq \\mathbb{R}^2$, for which there is a decision tree of depth $k-1$ whose $k$-means/$k$-median cost matches the optimal clustering cost of $X$, but every decision tree of depth less than $k-1$ has unbounded cost w.r.t. the optimal cost of clustering. We extend our results to the $k$-center objective as well, albeit with weaker guarantees.", "date": "2023-05-04", "categories": []}
{"id": "2406.16227", "title": "VICatMix: variational Bayesian clustering and variable selection for discrete biomedical data", "abstract": "Effective clustering of biomedical data is crucial in precision medicine, enabling accurate stratifiction of patients or samples. However, the growth in availability of high-dimensional categorical data, including `omics data, necessitates computationally efficient clustering algorithms. We present VICatMix, a variational Bayesian finite mixture model designed for the clustering of categorical data. The use of variational inference (VI) in its training allows the model to outperform competitors in term of efficiency, while maintaining high accuracy. VICatMix furthermore performs variable selection, enhancing its performance on high-dimensional, noisy data. The proposed model incorporates summarisation and model averaging to mitigate poor local optima in VI, allowing for improved estimation of the true number of clusters simultaneously with feature saliency. We demonstrate the performance of VICatMix with both simulated and real-world data, including applications to datasets from The Cancer Genome Atlas (TCGA), showing its use in cancer subtyping and driver gene discovery. We demonstrate VICatMix's utility in integrative cluster analysis with different `omics datasets, enabling the discovery of novel subtypes.\n  \\textbf{Availability:} VICatMix is freely available as an R package, incorporating C++ for faster computation, at https://github.com/j-ackierao/VICatMix.", "date": "2024-06-23", "categories": []}
{"id": "2602.08542", "title": "Incremental (k, z)-Clustering on Graphs", "abstract": "Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center. In the dynamic setting, the graph is subject to adversarial edge updates, and the goal is to maintain explicitly an exact $(k, z)$-clustering solution in the induced shortest-path metric.\n  While efficient dynamic $k$-center approximation algorithms on graphs exist [Cruciani et al. SODA 2024], to the best of our knowledge, no prior work provides similar results for the dynamic $(k,z)$-clustering problem. As the main result of this paper, we develop a randomized incremental $(k, z)$-clustering algorithm that maintains with high probability a constant-factor approximation in a graph undergoing edge insertions with a total update time of $\\tilde O(k m^{1+o(1)}+ k^{1+\\frac{1}{\\lambda}} m)$, where $\\lambda \\geq 1$ is an arbitrary fixed constant. Our incremental algorithm consists of two stages. In the first stage, we maintain a constant-factor bicriteria approximate solution of size $\\tilde{O}(k)$ with a total update time of $m^{1+o(1)}$ over all adversarial edge insertions. This first stage is an intricate adaptation of the bicriteria approximation algorithm by Mettu and Plaxton [Machine Learning 2004] to incremental graphs. One of our key technical results is that the radii in their algorithm can be assumed to be non-decreasing while the approximation ratio remains constant, a property that may be of independent interest.\n  In the second stage, we maintain a constant-factor approximate $(k,z)$-clustering solution on a dynamic weighted instance induced by the bicriteria approximate solution. For this subproblem, we employ a dynamic spanner algorithm together with a static $(k,z)$-clustering algorithm.", "date": "2026-02-09", "categories": []}
{"id": "2603.00210", "title": "Universal NP-Hardness of Clustering under General Utilities", "abstract": "Clustering is a central primitive in unsupervised learning, yet practice is dominated by heuristics whose outputs can be unstable and highly sensitive to representations, hyperparameters, and initialisation. Existing theoretical results are largely objective-specific and do not explain these behaviours at a unifying level. We formalise the common optimisation core underlying diverse clustering paradigms by defining the Universal Clustering Problem (UCP): the maximisation of a polynomial-time computable partition utility over a finite metric space. We prove the NP-hardness of UCP via two independent polynomial-time reductions from graph colouring and from exact cover by 3-sets (X3C). By mapping ten major paradigms -- including k-means, GMMs, DBSCAN, spectral clustering, and affinity propagation -- to the UCP framework, we demonstrate that each inherits this fundamental intractability. Our results provide a unified explanation for characteristic failure modes, such as local optima in alternating methods and greedy merge-order traps in hierarchical clustering. Finally, we show that clustering limitations reflect interacting computational and epistemic constraints, motivating a shift toward stability-aware objectives and interaction-driven formulations with explicit guarantees.", "date": "2026-02-27", "categories": []}
{"id": "2602.23528", "title": "Neural Operators Can Discover Functional Clusters", "abstract": "Operator learning is reshaping scientific computing by amortizing inference across infinite families of problems. While neural operators (NOs) are increasingly well understood for regression, far less is known for classification and its unsupervised analogue: clustering. We prove that sample-based neural operators can learn any finite collection of classes in an infinite-dimensional reproducing kernel Hilbert space, even when the classes are neither convex nor connected, under mild kernel sampling assumptions. Our universal clustering theorem shows that any $K$ closed classes can be approximated to arbitrary precision by NO-parameterized classes in the upper Kuratowski topology on closed sets, a notion that can be interpreted as disallowing false-positive misclassifications.\n  Building on this, we develop an NO-powered clustering pipeline for functional data and apply it to unlabeled families of ordinary differential equation (ODE) trajectories. Discretized trajectories are lifted by a fixed pre-trained encoder into a continuous feature map and mapped to soft assignments by a lightweight trainable head. Experiments on diverse synthetic ODE benchmarks show that the resulting practical SNO recovers latent dynamical structure in regimes where classical methods fail, providing evidence consistent with our universal clustering theory.", "date": "2026-02-26", "categories": []}
{"id": "2602.22568", "title": "Quality-Aware Robust Multi-View Clustering for Heterogeneous Observation Noise", "abstract": "Deep multi-view clustering has achieved remarkable progress but remains vulnerable to complex noise in real-world applications. Existing noisy robust methods predominantly rely on a simplified binary assumption, treating data as either perfectly clean or completely corrupted. This overlooks the prevalent existence of heterogeneous observation noise, where contamination intensity varies continuously across data. To bridge this gap, we propose a novel framework termed Quality-Aware Robust Multi-View Clustering (QARMVC). Specifically, QARMVC employs an information bottleneck mechanism to extract intrinsic semantics for view reconstruction. Leveraging the insight that noise disrupts semantic integrity and impedes reconstruction, we utilize the resulting reconstruction discrepancy to precisely quantify fine-grained contamination intensity and derive instance-level quality scores. These scores are integrated into a hierarchical learning strategy: at the feature level, a quality-weighted contrastive objective is designed to adaptively suppress the propagation of noise; at the fusion level, a high-quality global consensus is constructed via quality-weighted aggregation, which is subsequently utilized to align and rectify local views via mutual information maximization. Extensive experiments on five benchmark datasets demonstrate that QARMVC consistently outperforms state-of-the-art baselines, particularly in scenarios with heterogeneous noise intensities.", "date": "2026-02-26", "categories": []}
{"id": "2510.14640", "title": "LUMI: Unsupervised Intent Clustering with Multiple Pseudo-Labels", "abstract": "In this paper, we propose an intuitive, training-free and label-free method for intent clustering in conversational search. Current approaches to short text clustering use LLM-generated pseudo-labels to enrich text representations or to identify similar text pairs for pooling. The limitations are: (1) each text is assigned only a single label, and refining representations toward a single label can be unstable; (2) text-level similarity is treated as a binary selection, which fails to account for continuous degrees of similarity. Our method LUMI is designed to amplify similarities between texts by using shared pseudo-labels. We first generate pseudo-labels for each text and collect them into a pseudo-label set. Next, we compute the mean of the pseudo-label embeddings and pool it with the text embedding. Finally, we perform text-level pooling: Each text representation is pooled with its similar pairs, where similarity is determined by the degree of shared labels. Our evaluation on four benchmark sets shows that our approach achieves competitive results, better than recent state-of-the-art baselines, while avoiding the need to estimate the number of clusters during embedding refinement, as is required by most methods. Our findings indicate that LUMI can effectively be applied in unsupervised short-text clustering scenarios.", "date": "2025-10-16", "categories": []}
{"id": "2602.21509", "title": "Fair Model-based Clustering", "abstract": "The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that modify standard K-means clustering to satisfy a given fairness constraint. A critical limitation of several existing fair clustering algorithms is that the number of parameters to be learned is proportional to the sample size because the cluster assignment of each datum should be optimized simultaneously with the cluster center, and thus scaling up the algorithms is difficult. In this paper, we propose a new fair clustering algorithm based on a finite mixture model, called Fair Model-based Clustering (FMC). A main advantage of FMC is that the number of learnable parameters is independent of the sample size and thus can be scaled up easily. In particular, mini-batch learning is possible to obtain clusters that are approximately fair. Moreover, FMC can be applied to non-metric data (e.g., categorical data) as long as the likelihood is well-defined. Theoretical and empirical justifications for the superiority of the proposed algorithm are provided.", "date": "2026-02-25", "categories": []}
{"id": "2509.07766", "title": "Toward Quantum Utility in Finance: A Robust Data-Driven Algorithm for Asset Clustering", "abstract": "Clustering financial assets based on return correlations is a fundamental task in portfolio optimization and statistical arbitrage. However, classical clustering methods often fall short when dealing with signed correlation structures, typically requiring lossy transformations and heuristic assumptions such as a fixed number of clusters. In this work, we apply the Graph-based Coalition Structure Generation algorithm (GCS-Q) to directly cluster signed, weighted graphs without relying on such transformations. GCS-Q formulates each partitioning step as a QUBO problem, enabling it to leverage quantum annealing for efficient exploration of exponentially large solution spaces. We validate our approach on both synthetic and real-world financial data, benchmarking against state-of-the-art classical algorithms such as SPONGE and k-Medoids. Our experiments demonstrate that GCS-Q consistently achieves higher clustering quality, as measured by Adjusted Rand Index and structural balance penalties, while dynamically determining the number of clusters. These results highlight the practical utility of near-term quantum computing for graph-based unsupervised learning in financial applications.", "date": "2025-09-09", "categories": []}
{"id": "2601.09768", "title": "CLiMB: A Domain-Informed Novelty Detection Clustering Framework for Galactic Archaeology and Scientific Discovery", "abstract": "In data-driven scientific discovery, a challenge lies in classifying well-characterized phenomena while identifying novel anomalies. Current semi-supervised clustering algorithms do not always fully address this duality, often assuming that supervisory signals are globally representative. Consequently, methods often enforce rigid constraints that suppress unanticipated patterns or require a pre-specified number of clusters, rendering them ineffective for genuine novelty detection. To bridge this gap, we introduce CLiMB (CLustering in Multiphase Boundaries), a domain-informed framework decoupling the exploitation of prior knowledge from the exploration of unknown structures. Using a sequential two-phase approach, CLiMB first anchors known clusters using metric-adaptive constrained partitioning, and subsequently applies density-based clustering to residual data to reveal arbitrary topologies. We demonstrate this framework on RR Lyrae stars data from the Gaia Data Release 3. CLiMB attains an Adjusted Rand Index of 0.829 with 90% seed coverage in recovering known Milky Way substructures, outperforming heuristic and constraint-based baselines, which stagnate below 0.20. Furthermore, sensitivity analysis confirms CLiMB's superior data efficiency, showing monotonic improvement as knowledge increases. Finally, the framework successfully isolates three distinct dynamical features (Shiva, Shakti, and the Galactic Disk) in the unlabelled field, validating its potential for scientific discovery.", "date": "2026-01-14", "categories": []}
{"id": "2501.10471", "title": "VillageNet: Graph-based, Easily-interpretable, Unsupervised Clustering for Broad Biomedical Applications", "abstract": "Clustering large high-dimensional datasets with diverse variable is essential for extracting high-level latent information from these datasets. Here, we developed an unsupervised clustering algorithm, we call \"Village-Net\". Village-Net is specifically designed to effectively cluster high-dimension data without priori knowledge on the number of existing clusters. The algorithm operates in two phases: first, utilizing K-Means clustering, it divides the dataset into distinct subsets we refer to as \"villages\". Next, a weighted network is created, with each node representing a village, capturing their proximity relationships. To achieve optimal clustering, we process this network using a community detection algorithm called Walk-likelihood Community Finder (WLCF), a community detection algorithm developed by one of our team members. A salient feature of Village-Net Clustering is its ability to autonomously determine an optimal number of clusters for further analysis based on inherent characteristics of the data. We present extensive benchmarking on extant real-world datasets with known ground-truth labels to showcase its competitive performance, particularly in terms of the normalized mutual information (NMI) score, when compared to other state-of-the-art methods. The algorithm is computationally efficient, boasting a time complexity of O(N*k*d), where N signifies the number of instances, k represents the number of villages and d represents the dimension of the dataset, which makes it well suited for effectively handling large-scale datasets.", "date": "2025-01-16", "categories": []}
{"id": "2508.05493", "title": "Exact and Heuristic Algorithms for Constrained Biclustering", "abstract": "Biclustering, also known as co-clustering or two-way clustering, simultaneously partitions the rows and columns of a data matrix to reveal submatrices with coherent patterns. Incorporating background knowledge into clustering to enhance solution quality and interpretability has attracted growing interest in mathematical optimization and machine learning research. Extending this paradigm to biclustering enables prior information to guide the joint grouping of rows and columns. We study constrained biclustering with pairwise constraints, namely must-link and cannot-link constraints, which specify whether objects should belong to the same or different biclusters. As a model problem, we address the constrained version of the k-densest disjoint biclique problem, which aims to identify k disjoint complete bipartite subgraphs (called bicliques) in a weighted complete bipartite graph, maximizing the total density while satisfying pairwise constraints. We propose both exact and heuristic algorithms. The exact approach is a tailored branch-and-cut algorithm based on a low-dimensional semidefinite programming (SDP) relaxation, strengthened with valid inequalities and solved in a cutting-plane fashion. Exploiting integer programming tools, a rounding scheme converts SDP solutions into feasible biclusterings at each node. For large-scale instances, we introduce an efficient heuristic based on the low-rank factorization of the SDP. The resulting nonlinear optimization problem is tackled with an augmented Lagrangian method, where the subproblem is solved by decomposition through a block-coordinate projected gradient algorithm. Extensive experiments on synthetic and real-world datasets show that the exact method significantly outperforms general-purpose solvers, while the heuristic achieves high-quality solutions efficiently on large instances.", "date": "2025-08-07", "categories": []}
{"id": "2602.16688", "title": "On the Hardness of Approximation of the Fair k-Center Problem", "abstract": "In this work, we study the hardness of approximation of the fair $k$-center problem. In this problem, we are given a set of data points in a metric space that is partitioned into groups and the task is to choose a subset of $k$-data points, called centers, such that a prescribed number of data points from each group are chosen while minimizing the maximum distance from any point to its closest center. Although a polynomial-time $3$-approximation is known for fair $k$-center in general metrics, it has remained open whether this approximation guarantee is tight or could be further improved, especially since the classical unconstrained $k$-center problem admits a polynomial-time factor-$2$ approximation. We resolve this open question by proving that, assuming $\\mathsf{P} \\neq \\mathsf{NP}$, for any $\\epsilon>0$, no polynomial-time algorithm can approximate fair $k$-center to $(3-\\epsilon)$-factor.\n  Our inapproximability results hold even when only two disjoint groups are present and at least one center must be chosen from each group. Further, it extends to the canonical one-per-group setting with $k$-groups (for arbitrary $k$), where exactly one center must be selected from each group. Consequently, the factor-$3$ barrier for fair $k$-center in general metric spaces is inherent, and existing $3$-approximation algorithms are optimal up to lower-order terms even in these restricted regimes. This result stands in sharp contrast to the $k$-supplier formulation, where both the unconstrained and fair variants admit factor-$3$ approximation in polynomial time.", "date": "2026-02-18", "categories": []}
{"id": "2602.18728", "title": "Phase-Consistent Magnetic Spectral Learning for Multi-View Clustering", "abstract": "Unsupervised multi-view clustering (MVC) aims to partition data into meaningful groups by leveraging complementary information from multiple views without labels, yet a central challenge is to obtain a reliable shared structural signal to guide representation learning and cross-view alignment under view discrepancy and noise. Existing approaches often rely on magnitude-only affinities or early pseudo targets, which can be unstable when different views induce relations with comparable strengths but contradictory directional tendencies, thereby distorting the global spectral geometry and degrading clustering. In this paper, we propose \\emph{Phase-Consistent Magnetic Spectral Learning} for MVC: we explicitly model cross-view directional agreement as a phase term and combine it with a nonnegative magnitude backbone to form a complex-valued magnetic affinity, extract a stable shared spectral signal via a Hermitian magnetic Laplacian, and use it as structured self-supervision to guide unsupervised multi-view representation learning and clustering. To obtain robust inputs for spectral extraction at scale, we construct a compact shared structure with anchor-based high-order consensus modeling and apply a lightweight refinement to suppress noisy or inconsistent relations. Extensive experiments on multiple public multi-view benchmarks demonstrate that our method consistently outperforms strong baselines.", "date": "2026-02-21", "categories": []}
{"id": "2510.13887", "title": "Incomplete Multi-view Clustering via Hierarchical Semantic Alignment and Cooperative Completion", "abstract": "Incomplete multi-view data, where certain views are entirely missing for some samples, poses significant challenges for traditional multi-view clustering methods. Existing deep incomplete multi-view clustering approaches often rely on static fusion strategies or two-stage pipelines, leading to suboptimal fusion results and error propagation issues. To address these limitations, this paper proposes a novel incomplete multi-view clustering framework based on Hierarchical Semantic Alignment and Cooperative Completion (HSACC). HSACC achieves robust cross-view fusion through a dual-level semantic space design. In the low-level semantic space, consistency alignment is ensured by maximizing mutual information across views. In the high-level semantic space, adaptive view weights are dynamically assigned based on the distributional affinity between individual views and an initial fused representation, followed by weighted fusion to generate a unified global representation. Additionally, HSACC implicitly recovers missing views by projecting aligned latent representations into high-dimensional semantic spaces and jointly optimizes reconstruction and clustering objectives, enabling cooperative learning of completion and clustering. Experimental results demonstrate that HSACC significantly outperforms state-of-the-art methods on five benchmark datasets. Ablation studies validate the effectiveness of the hierarchical alignment and dynamic weighting mechanisms, while parameter analysis confirms the model's robustness to hyperparameter variations. The code is available at https://github.com/XiaojianDing/2025-NeurIPS-HSACC.", "date": "2025-10-14", "categories": []}
{"id": "2511.05983", "title": "Benchmarking of Clustering Validity Measures Revisited", "abstract": "Validation plays a crucial role in the clustering process. Many different internal validity indexes exist for the purpose of determining the best clustering solution(s) from a given collection of candidates, e.g., as produced by different algorithms or different algorithm hyper-parameters. In this study, we present a comprehensive benchmark study of 26 internal validity indexes, which includes highly popular classic indexes as well as more recently developed ones. We adopted an enhanced revision of the methodology presented in Vendramin et al. (2010), developed here to address several shortcomings of this previous work. This overall new approach consists of three complementary custom-tailored evaluation sub-methodologies, each of which has been designed to assess specific aspects of an index's behaviour while preventing potential biases of the other sub-methodologies. Each sub-methodology features two complementary measures of performance, alongside mechanisms that allow for an in-depth investigation of more complex behaviours of the internal validity indexes under study. Additionally, a new collection of 16177 datasets has been produced, paired with eight widely-used clustering algorithms, for a wider applicability scope and representation of more diverse clustering scenarios.", "date": "2025-11-08", "categories": []}
{"id": "2412.09049", "title": "Dial-In LLM: Human-Aligned LLM-in-the-loop Intent Clustering for Customer Service Dialogues", "abstract": "Discovering customer intentions is crucial for automated service agents, yet existing intent clustering methods often fall short due to their reliance on embedding distance metrics and neglect of underlying semantic structures. To address these limitations, we propose an LLM-in-the-loop (LLM-ITL) intent clustering framework, integrating the language understanding capabilities of LLMs into conventional clustering algorithms. Specifically, this paper (1) examines the effectiveness of fine-tuned LLMs in semantic coherence evaluation and intent cluster naming, achieving over 95% accuracy aligned with human judgments; (2) designs an LLM-ITL framework that facilitates the iterative discovery of coherent intent clusters and the optimal number of clusters; and (3) introduces context-aware techniques tailored for customer service dialogue. Since existing English benchmarks lack sufficient semantic diversity and intent coverage, we further present a comprehensive Chinese dialogue intent dataset comprising over 100k real customer service calls with 1,507 human-annotated clusters. The proposed approaches significantly outperform LLM-guided baselines, achieving notable improvements in clustering quality, cost efficiency, and downstream applications. Combined with several best practices, our findings highlight the prominence of LLM-in-the-loop techniques for scalable dialogue data mining.", "date": "2024-12-12", "categories": []}
{"id": "2602.13586", "title": "Interpretable clustering via optimal multiway-split decision trees", "abstract": "Clustering serves as a vital tool for uncovering latent data structures, and achieving both high accuracy and interpretability is essential. To this end, existing methods typically construct binary decision trees by solving mixed-integer nonlinear optimization problems, often leading to significant computational costs and suboptimal solutions. Furthermore, binary decision trees frequently result in excessively deep structures, which makes them difficult to interpret. To mitigate these issues, we propose an interpretable clustering method based on optimal multiway-split decision trees, formulated as a 0-1 integer linear optimization problem. This reformulation renders the optimization problem more tractable compared to existing models. A key feature of our method is the integration of a one-dimensional K-means algorithm for the discretization of continuous variables, allowing for flexible and data-driven branching. Extensive numerical experiments on publicly available real-world datasets demonstrate that our method outperforms baseline methods in terms of clustering accuracy and interpretability. Our method yields multiway-split decision trees with concise decision rules while maintaining competitive performance across various evaluation metrics.", "date": "2026-02-14", "categories": []}
{"id": "2602.13684", "title": "On the Sparsifiability of Correlation Clustering: Approximation Guarantees under Edge Sampling", "abstract": "Correlation Clustering (CC) is a fundamental unsupervised learning primitive whose strongest LP-based approximation guarantees require $\\Theta(n^3)$ triangle inequality constraints and are prohibitive at scale. We initiate the study of \\emph{sparsification--approximation trade-offs} for CC, asking how much edge information is needed to retain LP-based guarantees. We establish a structural dichotomy between pseudometric and general weighted instances. On the positive side, we prove that the VC dimension of the clustering disagreement class is exactly $n{-}1$, yielding additive $\\varepsilon$-coresets of optimal size $\\tilde{O}(n/\\varepsilon^2)$; that at most $\\binom{n}{2}$ triangle inequalities are active at any LP vertex, enabling an exact cutting-plane solver; and that a sparsified variant of LP-PIVOT, which imputes missing LP marginals via triangle inequalities, achieves a robust $\\frac{10}{3}$-approximation (up to an additive term controlled by an empirically computable imputation-quality statistic $\\overline{\\Gamma}_w$) once $\\tilde{\\Theta}(n^{3/2})$ edges are observed, a threshold we prove is sharp. On the negative side, we show via Yao's minimax principle that without pseudometric structure, any algorithm observing $o(n)$ uniformly random edges incurs an unbounded approximation ratio, demonstrating that the pseudometric condition governs not only tractability but also the robustness of CC to incomplete information.", "date": "2026-02-14", "categories": []}
{"id": "2509.03834", "title": "From Leiden to Pleasure Island: The Constant Potts Model for Community Detection as a Hedonic Game", "abstract": "Community detection is one of the fundamental problems in data science which consists of partitioning nodes into disjoint communities. We present a game-theoretic perspective on the Constant Potts Model (CPM) for partitioning networks into disjoint communities, emphasizing its efficiency, robustness, and accuracy. Efficiency: We reinterpret CPM as a potential hedonic game by decomposing its global Hamiltonian into local utility functions, where the local utility gain of each agent matches the corresponding increase in global utility. Leveraging this equivalence, we prove that local optimization of the CPM objective via better-response dynamics converges in pseudo-polynomial time to an equilibrium partition. Robustness: We introduce and relate two stability criteria: a strict criterion based on a novel notion of robustness, requiring nodes to simultaneously maximize neighbors and minimize non-neighbors within communities, and a relaxed utility function based on a weighted sum of these objectives, controlled by a resolution parameter. Accuracy: In community tracking scenarios, where initial partitions are used to bootstrap the Leiden algorithm with partial ground-truth information, our experiments reveal that robust partitions yield higher accuracy in recovering ground-truth communities.", "date": "2025-09-04", "categories": []}
{"id": "2602.11500", "title": "A Generic Framework for Fair Consensus Clustering in Streams", "abstract": "Consensus clustering seeks to combine multiple clusterings of the same dataset, potentially derived by considering various non-sensitive attributes by different agents in a multi-agent environment, into a single partitioning that best reflects the overall structure of the underlying dataset. Recent work by Chakraborty et al, introduced a fair variant under proportionate fairness and obtained a constant-factor approximation by naively selecting the best closest fair input clustering; however, their offline approach requires storing all input clusterings, which is prohibitively expensive for most large-scale applications.\n  In this paper, we initiate the study of fair consensus clustering in the streaming model, where input clusterings arrive sequentially and memory is limited. We design the first constant-factor algorithm that processes the stream while storing only a logarithmic number of inputs. En route, we introduce a new generic algorithmic framework that integrates closest fair clustering with cluster fitting, yielding improved approximation guarantees not only in the streaming setting but also when revisited offline. Furthermore, the framework is fairness-agnostic: it applies to any fairness definition for which an approximately close fair clustering can be computed efficiently. Finally, we extend our methods to the more general k-median consensus clustering problem.", "date": "2026-02-12", "categories": []}
{"id": "2602.10444", "title": "Chamfer-Linkage for Hierarchical Agglomerative Clustering", "abstract": "Hierarchical Agglomerative Clustering (HAC) is a widely-used clustering method based on repeatedly merging the closest pair of clusters, where inter-cluster distances are determined by a linkage function. Unlike many clustering methods, HAC does not optimize a single explicit global objective; clustering quality is therefore primarily evaluated empirically, and the choice of linkage function plays a crucial role in practice. However, popular classical linkages, such as single-linkage, average-linkage and Ward's method show high variability across real-world datasets and do not consistently produce high-quality clusterings in practice.\n  In this paper, we propose \\emph{Chamfer-linkage}, a novel linkage function that measures the distance between clusters using the Chamfer distance, a popular notion of distance between point-clouds in machine learning and computer vision. We argue that Chamfer-linkage satisfies desirable concept representation properties that other popular measures struggle to satisfy. Theoretically, we show that Chamfer-linkage HAC can be implemented in $O(n^2)$ time, matching the efficiency of classical linkage functions. Experimentally, we find that Chamfer-linkage consistently yields higher-quality clusterings than classical linkages such as average-linkage and Ward's method across a diverse collection of datasets. Our results establish Chamfer-linkage as a practical drop-in replacement for classical linkage functions, broadening the toolkit for hierarchical clustering in both theory and practice.", "date": "2026-02-11", "categories": []}
{"id": "2601.20680", "title": "Online Density-Based Clustering for Real-Time Narrative Evolution Monitorin", "abstract": "Automated narrative intelligence systems for social media monitoring face significant scalability challenges when relying on batch clustering methods to process continuous data streams. We investigate replacing offline HDBSCAN with online density-based clustering algorithms in a production narrative report generation pipeline that processes large volumes of multilingual social media data. While HDBSCAN effectively discovers hierarchical clusters and handles noise, its batch-only nature requires full retraining for each time window, limiting scalability and real-time adaptability. We evaluate online clustering methods with respect to cluster quality, computational efficiency, memory footprint, and integration with downstream narrative extraction. Our evaluation combines standard clustering metrics, narrative-specific measures, and human validation of cluster correctness to assess both structural quality and semantic interpretability. Experiments using sliding-window simulations on historical data from the Ukrainian information space reveal trade-offs between temporal stability and narrative coherence, with DenStream achieving the strongest overall performance. These findings bridge the gap between batch-oriented clustering approaches and the streaming requirements of large-scale narrative monitoring systems.", "date": "2026-01-28", "categories": []}
{"id": "2602.09864", "title": "Differentiable Tripartite Modularity for Clustering Heterogeneous Graphs", "abstract": "Clustering heterogeneous relational data remains a central challenge in graph learning, particularly when interactions involve more than two types of entities. While differentiable modularity objectives such as DMoN have enabled end-to-end community detection on homogeneous and bipartite graphs, extending these approaches to higher-order relational structures remains non-trivial.\n  In this work, we introduce a differentiable formulation of tripartite modularity for graphs composed of three node types connected through mediated interactions. Community structure is defined in terms of weighted co-paths across the tripartite graph, together with an exact factorized computation that avoids the explicit construction of dense third-order tensors. A structural normalization at pivot nodes is introduced to control extreme degree heterogeneity and ensure stable optimization.\n  The resulting objective can be optimized jointly with a graph neural network in an end-to-end manner, while retaining linear complexity in the number of edges. We validate the proposed framework on large-scale urban cadastral data, where it exhibits robust convergence behavior and produces spatially coherent partitions. These results highlight differentiable tripartite modularity as a generic methodological building block for unsupervised clustering of heterogeneous graphs.", "date": "2026-02-10", "categories": []}
{"id": "2602.09936", "title": "The Catastrophic Failure of The k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It", "abstract": "Lloyd's k-means algorithm is one of the most widely used clustering methods. We prove that in high-dimensional, high-noise settings, the algorithm exhibits catastrophic failure: with high probability, essentially every partition of the data is a fixed point. Consequently, Lloyd's algorithm simply returns its initial partition - even when the underlying clusters are trivially recoverable by other methods. In contrast, we prove that Hartigan's k-means algorithm does not exhibit this pathology. Our results show the stark difference between these algorithms and offer a theoretical explanation for the empirical difficulties often observed with k-means in high dimensions.", "date": "2026-02-10", "categories": []}
{"id": "2411.09979", "title": "Fully Dynamic Adversarially Robust Correlation Clustering in Polylogarithmic Update Time", "abstract": "We study the dynamic correlation clustering problem with $\\textit{adaptive}$ edge label flips. In correlation clustering, we are given a $n$-vertex complete graph whose edges are labeled either $(+)$ or $(-)$, and the goal is to minimize the total number of $(+)$ edges between clusters and the number of $(-)$ edges within clusters. We consider the dynamic setting with adversarial robustness, in which the $\\textit{adaptive}$ adversary could flip the label of an edge based on the current output of the algorithm. Our main result is a randomized algorithm that always maintains an $O(1)$-approximation to the optimal correlation clustering with $O(\\log^{2}{n})$ amortized update time. Prior to our work, no algorithm with $O(1)$-approximation and $\\text{polylog}{(n)}$ update time for the adversarially robust setting was known. We further validate our theoretical results with experiments on synthetic and real-world datasets with competitive empirical performances. Our main technical ingredient is an algorithm that maintains $\\textit{sparse-dense decomposition}$ with $\\text{polylog}{(n)}$ update time, which could be of independent interest.", "date": "2024-11-15", "categories": []}
{"id": "2502.00380", "title": "CoHiRF: Hierarchical Consensus for Interpretable Clustering Beyond Scalability Limits", "abstract": "We introduce CoHiRF (Consensus Hierarchical Random Features), a hierarchical consensus framework that enables existing clustering methods to operate beyond their usual computational and memory limits. CoHiRF is a meta-algorithm that operates exclusively on the label assignments produced by a base clustering method, without modifying its objective function, optimization procedure, or geometric assumptions. It repeatedly applies the base method to multiple low-dimensional feature views or stochastic realizations, enforces agreement through consensus, and progressively reduces the problem size via representative-based contraction. Across a diverse set of synthetic and real-world experiments involving centroid-based, kernel-based, density-based, and graph-based methods, we show that CoHiRF can improve robustness to high-dimensional noise, enhance stability under stochastic variability, and enable scalability to regimes where the base method alone is infeasible. We also provide an empirical characterization of when hierarchical consensus is beneficial, highlighting the role of reproducible label relations and their compatibility with representative-based contraction. Beyond flat partitions, CoHiRF produces an explicit Cluster Fusion Hierarchy, offering a multi-resolution and interpretable view of the clustering structure. Together, these results position hierarchical consensus as a practical and flexible tool for large-scale clustering, extending the applicability of existing methods without altering their underlying behavior.", "date": "2025-02-01", "categories": []}
{"id": "2502.09667", "title": "Summaries as Centroids for Interpretable and Scalable Text Clustering", "abstract": "We introduce k-NLPmeans and k-LLMmeans, text-clustering variants of k-means that periodically replace numeric centroids with textual summaries. The key idea, summary-as-centroid, retains k-means assignments in embedding space while producing human-readable, auditable cluster prototypes. The method is LLM-optional: k-NLPmeans uses lightweight, deterministic summarizers, enabling offline, low-cost, and stable operation; k-LLMmeans is a drop-in upgrade that uses an LLM for summaries under a fixed per-iteration budget whose cost does not grow with dataset size. We also present a mini-batch extension for real-time clustering of streaming text. Across diverse datasets, embedding models, and summarization strategies, our approach consistently outperforms classical baselines and approaches the accuracy of recent LLM-based clustering-without extensive LLM calls. Finally, we provide a case study on sequential text streams and release a StackExchange-derived benchmark for evaluating streaming text clustering.", "date": "2025-02-12", "categories": []}
{"id": "2505.22984", "title": "A Computational Approach to Improving Fairness in K-means Clustering", "abstract": "The popular K-means clustering algorithm potentially suffers from a major weakness for further analysis or interpretation. Some cluster may have disproportionately more (or fewer) points from one of the subpopulations in terms of some sensitive variable, e.g., gender or race. Such a fairness issue may cause bias and unexpected social consequences. This work attempts to improve the fairness of K-means clustering with a two-stage optimization formulation--clustering first and then adjust cluster membership of a small subset of selected data points. Two computationally efficient algorithms are proposed in identifying those data points that are expensive for fairness, with one focusing on nearest data points outside of a cluster and the other on highly 'mixed' data points. Experiments on benchmark datasets show substantial improvement on fairness with a minimal impact to clustering quality. The proposed algorithms can be easily extended to a broad class of clustering algorithms or fairness metrics.", "date": "2025-05-29", "categories": []}
{"id": "2602.07279", "title": "VertCoHiRF: Decentralized Vertical Clustering Beyond k-means", "abstract": "Vertical Federated Learning (VFL) enables collaborative analysis across parties holding complementary feature views of the same samples, yet existing approaches are largely restricted to distributed variants of $k$-means, requiring centralized coordination or the exchange of feature-dependent numerical statistics, and exhibiting limited robustness under heterogeneous views or adversarial behavior. We introduce VertCoHiRF, a fully decentralized framework for vertical federated clustering based on structural consensus across heterogeneous views, allowing each agent to apply a base clustering method adapted to its local feature space in a peer-to-peer manner. Rather than exchanging feature-dependent statistics or relying on noise injection for privacy, agents cluster their local views independently and reconcile their proposals through identifier-level consensus. Consensus is achieved via decentralized ordinal ranking to select representative medoids, progressively inducing a shared hierarchical clustering across agents. Communication is limited to sample identifiers, cluster labels, and ordinal rankings, providing privacy by design while supporting overlapping feature partitions and heterogeneous local clustering methods, and yielding an interpretable shared Cluster Fusion Hierarchy (CFH) that captures cross-view agreement at multiple resolutions.We analyze communication complexity and robustness, and experiments demonstrate competitive clustering performance in vertical federated settings.", "date": "2026-02-07", "categories": []}
{"id": "2602.08519", "title": "Bridging Academia and Industry: A Comprehensive Benchmark for Attributed Graph Clustering", "abstract": "Attributed Graph Clustering (AGC) is a fundamental unsupervised task that integrates structural topology and node attributes to uncover latent patterns in graph-structured data. Despite its significance in industrial applications such as fraud detection and user segmentation, a significant chasm persists between academic research and real-world deployment. Current evaluation protocols suffer from the small-scale, high-homophily citation datasets, non-scalable full-batch training paradigms, and a reliance on supervised metrics that fail to reflect performance in label-scarce environments. To bridge these gaps, we present PyAGC, a comprehensive, production-ready benchmark and library designed to stress-test AGC methods across diverse scales and structural properties. We unify existing methodologies into a modular Encode-Cluster-Optimize framework and, for the first time, provide memory-efficient, mini-batch implementations for a wide array of state-of-the-art AGC algorithms. Our benchmark curates 12 diverse datasets, ranging from 2.7K to 111M nodes, specifically incorporating industrial graphs with complex tabular features and low homophily. Furthermore, we advocate for a holistic evaluation protocol that mandates unsupervised structural metrics and efficiency profiling alongside traditional supervised metrics. Battle-tested in high-stakes industrial workflows at Ant Group, this benchmark offers the community a robust, reproducible, and scalable platform to advance AGC research towards realistic deployment. The code and resources are publicly available via GitHub (https://github.com/Cloudy1225/PyAGC), PyPI (https://pypi.org/project/pyagc), and Documentation (https://pyagc.readthedocs.io).", "date": "2026-02-09", "categories": []}
{"id": "2602.05690", "title": "Almost Asymptotically Optimal Active Clustering Through Pairwise Observations", "abstract": "We propose a new analysis framework for clustering $M$ items into an unknown number of $K$ distinct groups using noisy and actively collected responses. At each time step, an agent is allowed to query pairs of items and observe bandit binary feedback. If the pair of items belongs to the same (resp.\\ different) cluster, the observed feedback is $1$ with probability $p>1/2$ (resp.\\ $q<1/2$). Leveraging the ubiquitous change-of-measure technique, we establish a fundamental lower bound on the expected number of queries needed to achieve a desired confidence in the clustering accuracy, formulated as a sup-inf optimization problem. Building on this theoretical foundation, we design an asymptotically optimal algorithm in which the stopping criterion involves an empirical version of the inner infimum -- the Generalized Likelihood Ratio (GLR) statistic -- being compared to a threshold. We develop a computationally feasible variant of the GLR statistic and show that its performance gap to the lower bound can be accurately empirically estimated and remains within a constant multiple of the lower bound.", "date": "2026-02-05", "categories": []}
{"id": "2602.05749", "title": "How to Achieve the Intended Aim of Deep Clustering Now, without Deep Learning", "abstract": "Deep clustering (DC) is often quoted to have a key advantage over $k$-means clustering. Yet, this advantage is often demonstrated using image datasets only, and it is unclear whether it addresses the fundamental limitations of $k$-means clustering. Deep Embedded Clustering (DEC) learns a latent representation via an autoencoder and performs clustering based on a $k$-means-like procedure, while the optimization is conducted in an end-to-end manner. This paper investigates whether the deep-learned representation has enabled DEC to overcome the known fundamental limitations of $k$-means clustering, i.e., its inability to discover clusters of arbitrary shapes, varied sizes and densities. Our investigations on DEC have a wider implication on deep clustering methods in general. Notably, none of these methods exploit the underlying data distribution. We uncover that a non-deep learning approach achieves the intended aim of deep clustering by making use of distributional information of clusters in a dataset to effectively address these fundamental limitations.", "date": "2026-02-05", "categories": []}
{"id": "2602.03894", "title": "Vision Transformers for Zero-Shot Clustering of Animal Images: A Comparative Benchmarking Study", "abstract": "Manual labeling of animal images remains a significant bottleneck in ecological research, limiting the scale and efficiency of biodiversity monitoring efforts. This study investigates whether state-of-the-art Vision Transformer (ViT) foundation models can reduce thousands of unlabeled animal images directly to species-level clusters. We present a comprehensive benchmarking framework evaluating five ViT models combined with five dimensionality reduction techniques and four clustering algorithms, two supervised and two unsupervised, across 60 species (30 mammals and 30 birds), with each test using a random subset of 200 validated images per species. We investigate when clustering succeeds at species-level, where it fails, and whether clustering within the species-level reveals ecologically meaningful patterns such as sex, age, or phenotypic variation. Our results demonstrate near-perfect species-level clustering (V-measure: 0.958) using DINOv3 embeddings with t-SNE and supervised hierarchical clustering methods. Unsupervised approaches achieve competitive performance (0.943) while requiring no prior species knowledge, rejecting only 1.14% of images as outliers requiring expert review. We further demonstrate robustness to realistic long-tailed distributions of species and show that intentional over-clustering can reliably extract intra-specific variation including age classes, sexual dimorphism, and pelage differences. We introduce an open-source benchmarking toolkit and provide recommendations for ecologists to select appropriate methods for sorting their specific taxonomic groups and data.", "date": "2026-02-03", "categories": []}
{"id": "2411.18794", "title": "Graph Max Shift: A Hill-Climbing Method for Graph Clustering", "abstract": "We present a method for graph clustering that is analogous to gradient ascent methods previously proposed for clustering points in space. The algorithm, which can be viewed as a max-degree hill-climbing procedure on the graph, iteratively moves each node to a neighboring node of highest degree. We show that, when applied to a random geometric graph whose nodes correspond to data drawn i.i.d. from a density with Morse regularity, the method is asymptotically consistent. Here, consistency is in the sense of Fukunaga and Hostetler, meaning, with respect to the partition of the support of the density defined by the basins of attraction of the density gradient flow.", "date": "2024-11-27", "categories": []}
{"id": "2504.09970", "title": "ASIL: Augmented Structural Information Learning for Deep Graph Clustering in Hyperbolic Space", "abstract": "Graph clustering is a longstanding topic in machine learning. Recently, deep methods have achieved results but still require predefined cluster numbers K and struggle with imbalanced graphs. We study deep graph clustering without K considering realistic imbalance through structural information theory. In the literature, structural information is rarely used in deep clustering, and its classic discrete definition neglects node attributes while exhibiting prohibitive complexity. In this paper, we establish a differentiable structural information framework, generalizing the discrete formalism to the continuous realm. We design a hyperbolic model (LSEnet) to learn the neural partitioning tree in the Lorentz model. Theoretically, we demonstrate its capability in clustering without K and identifying minority clusters. Second, we refine hyperbolic representations to enhance graph semantics. Since tree contrastive learning is non-trivial and costs quadratic complexity, we advance our theory by discovering that structural entropy bounds the tree contrastive loss. Finally, we approach graph clustering through a novel augmented structural information learning (ASIL), which offers an efficient objective to integrate hyperbolic partitioning tree construction and contrastive learning. With a provable improvement in graph conductance, ASIL achieves effective debiased graph clustering in linear complexity. Extensive experiments show ASIL outperforms 20 strong baselines by an average of +12.42% in NMI on the Citeseer dataset.", "date": "2025-04-14", "categories": []}
{"id": "2512.16558", "title": "Persistent Multiscale Density-based Clustering", "abstract": "Clustering is a cornerstone of modern data analysis. Detecting clusters in exploratory data analyses (EDA) requires algorithms that make few assumptions about the data. Density-based clustering algorithms are particularly well-suited for EDA because they describe high-density regions, assuming only that a density exists. Applying density-based clustering algorithms in practice, however, requires selecting appropriate hyperparameters, which is difficult without prior knowledge of the data distribution. For example, DBSCAN requires selecting a density threshold, and HDBSCAN* relies on a minimum cluster size parameter. In this work, we propose Persistent Leaves Spatial Clustering for Applications with Noise (PLSCAN). This novel density-based clustering algorithm efficiently identifies all minimum cluster sizes for which HDBSCAN* produces stable (leaf) clusters. PLSCAN applies scale-space clustering principles and is equivalent to persistent homology on a novel metric space. We compare its performance to HDBSCAN* on several real-world datasets, demonstrating that it achieves a higher average ARI and is less sensitive to changes in the number of mutual reachability neighbours. Additionally, we compare PLSCAN's computational costs to k-Means, demonstrating competitive run-times on low-dimensional datasets. At higher dimensions, run times scale more similarly to HDBSCAN*.", "date": "2025-12-18", "categories": []}
{"id": "2601.17307", "title": "Weighted Graph Clustering via Scale Contraction and Graph Structure Learning", "abstract": "Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in graph clustering tasks faces two critical challenges. (1) The introduction of edge weights may significantly increase storage space and training time, making it essential to reduce the graph scale while preserving nodes that are beneficial for the clustering task. (2) Edge weight information may inherently contain noise that negatively impacts clustering results. However, few studies can jointly optimize clustering and edge weights, which is crucial for mitigating the negative impact of noisy edges on clustering task. To address these challenges, we propose a contractile edge-weight-aware graph clustering network. Specifically, a cluster-oriented graph contraction module is designed to reduce the graph scale while preserving important nodes. An edge-weight-aware attention network is designed to identify and weaken noisy connections. In this way, we can more easily identify and mitigate the impact of noisy edges during the clustering process, thus enhancing clustering effectiveness. We conducted extensive experiments on three real-world weighted graph datasets. In particular, our model outperforms the best baseline, demonstrating its superior performance. Furthermore, experiments also show that the proposed graph contraction module can significantly reduce training time and storage space.", "date": "2026-01-24", "categories": []}
{"id": "2602.00262", "title": "Subspace Clustering on Incomplete Data with Self-Supervised Contrastive Learning", "abstract": "Subspace clustering aims to group data points that lie in a union of low-dimensional subspaces and finds wide application in computer vision, hyperspectral imaging, and recommendation systems. However, most existing methods assume fully observed data, limiting their effectiveness in real-world scenarios with missing entries. In this paper, we propose a contrastive self-supervised framework, Contrastive Subspace Clustering (CSC), designed for clustering incomplete data. CSC generates masked views of partially observed inputs and trains a deep neural network using a SimCLR-style contrastive loss to learn invariant embeddings. These embeddings are then clustered using sparse subspace clustering. Experiments on six benchmark datasets show that CSC consistently outperforms both classical and deep learning baselines, demonstrating strong robustness to missing data and scalability to large datasets.", "date": "2026-01-30", "categories": []}
{"id": "2407.03389", "title": "A Deterministic Information Bottleneck Method for Clustering Mixed-Type Data", "abstract": "In this paper, we present an information-theoretic method for clustering mixed-type data, that is, data consisting of both continuous and categorical variables. The proposed approach extends the Information Bottleneck principle to heterogeneous data through generalised product kernels, integrating continuous, nominal, and ordinal variables within a unified optimization framework. We address the following challenges: developing a systematic bandwidth selection strategy that equalises contributions across variable types, and proposing an adaptive hyperparameter updating scheme that ensures a valid solution into a predetermined number of potentially imbalanced clusters. Through simulations on 28,800 synthetic data sets and ten publicly available benchmarks, we demonstrate that the proposed method, named DIBmix, achieves superior performance compared to four established methods (KAMILA, K-Prototypes, FAMD with K-Means, and PAM with Gower's dissimilarity). Results show DIBmix particularly excels when clusters exhibit size imbalances, data contain low or moderate cluster overlap, and categorical and continuous variables are equally represented. The method presents a significant advantage over traditional centroid-based algorithms, establishing DIBmix as a competitive and theoretically grounded alternative for mixed-type data clustering.", "date": "2024-07-03", "categories": []}
{"id": "2210.00310", "title": "Parametrized Power-Iteration Clustering for Directed Graphs", "abstract": "Vertex-level clustering for directed graphs (digraphs) remains challenging as edge directionality breaks the key assumptions underlying popular spectral methods, which also incur the overhead of eigen-decomposition. This paper proposes Parametrized Power-Iteration Clustering (ParPIC), a random-walk-based clustering method for weakly connected digraphs. This builds over the Power-Iteration Clustering paradigm, which uses the rows of the iterated diffusion operator as a data embedding. ParPIC has three important features: the use of parametrized reversible random walk operators, the automatic tuning of the diffusion time, and the efficient truncation of the final embedding, which produces low-dimensional data representations and reduces complexity. Empirical results on synthetic and real-world graphs demonstrate that ParPIC achieves competitive clustering accuracy with improved scalability relative to spectral and teleportation-based methods.", "date": "2022-10-01", "categories": []}
{"id": "2512.23471", "title": "Discovering Multi-Scale Semantic Structure in Text Corpora Using Density-Based Trees and LLM Embeddings", "abstract": "Recent advances in large language models enable documents to be represented as dense semantic embeddings, supporting similarity-based operations over large text collections. However, many web-scale systems still rely on flat clustering or predefined taxonomies, limiting insight into hierarchical topic relationships. In this paper we operationalize hierarchical density modeling on large language model embeddings in a way not previously explored. Instead of enforcing a fixed taxonomy or single clustering resolution, the method progressively relaxes local density constraints, revealing how compact semantic groups merge into broader thematic regions. The resulting tree encodes multi-scale semantic organization directly from data, making structural relationships between topics explicit. We evaluate the hierarchies on standard text benchmarks, showing that semantic alignment peaks at intermediate density levels and that abrupt transitions correspond to meaningful changes in semantic resolution. Beyond benchmarks, the approach is applied to large institutional and scientific corpora, exposing dominant fields, cross-disciplinary proximities, and emerging thematic clusters. By framing hierarchical structure as an emergent property of density in embedding spaces, this method provides an interpretable, multi-scale representation of semantic structure suitable for large, evolving text collections.", "date": "2025-12-29", "categories": []}
{"id": "2601.21160", "title": "A Federated Generalized Expectation-Maximization Algorithm for Mixture Models with an Unknown Number of Components", "abstract": "We study the problem of federated clustering when the total number of clusters $K$ across clients is unknown, and the clients have heterogeneous but potentially overlapping cluster sets in their local data. To that end, we develop FedGEM: a federated generalized expectation-maximization algorithm for the training of mixture models with an unknown number of components. Our proposed algorithm relies on each of the clients performing EM steps locally, and constructing an uncertainty set around the maximizer associated with each local component. The central server utilizes the uncertainty sets to learn potential cluster overlaps between clients, and infer the global number of clusters via closed-form computations. We perform a thorough theoretical study of our algorithm, presenting probabilistic convergence guarantees under common assumptions. Subsequently, we study the specific setting of isotropic GMMs, providing tractable, low-complexity computations to be performed by each client during each iteration of the algorithm, as well as rigorously verifying assumptions required for algorithm convergence. We perform various numerical experiments, where we empirically demonstrate that our proposed method achieves comparable performance to centralized EM, and that it outperforms various existing federated clustering methods.", "date": "2026-01-29", "categories": []}
{"id": "2601.21465", "title": "Topeax -- An Improved Clustering Topic Model with Density Peak Detection and Lexical-Semantic Term Importance", "abstract": "Text clustering is today the most popular paradigm for topic modelling, both in academia and industry. Despite clustering topic models' apparent success, we identify a number of issues in Top2Vec and BERTopic, which remain largely unsolved. Firstly, these approaches are unreliable at discovering natural clusters in corpora, due to extreme sensitivity to sample size and hyperparameters, the default values of which result in suboptimal behaviour. Secondly, when estimating term importance, BERTopic ignores the semantic distance of keywords to topic vectors, while Top2Vec ignores word counts in the corpus. This results in, on the one hand, less coherent topics due to the presence of stop words and junk words, and lack of variety and trust on the other. In this paper, I introduce a new approach, \\textbf{Topeax}, which discovers the number of clusters from peaks in density estimates, and combines lexical and semantic indices of term importance to gain high-quality topic keywords. Topeax is demonstrated to be better at both cluster recovery and cluster description than Top2Vec and BERTopic, while also exhibiting less erratic behaviour in response to changing sample size and hyperparameters.", "date": "2026-01-29", "categories": []}
{"id": "2601.19333", "title": "Metric $k$-clustering using only Weak Comparison Oracles", "abstract": "Clustering is a fundamental primitive in unsupervised learning. However, classical algorithms for $k$-clustering (such as $k$-median and $k$-means) assume access to exact pairwise distances -- an unrealistic requirement in many modern applications. We study clustering in the \\emph{Rank-model (R-model)}, where access to distances is entirely replaced by a \\emph{quadruplet oracle} that provides only relative distance comparisons. In practice, such an oracle can represent learned models or human feedback, and is expected to be noisy and entail an access cost.\n  Given a metric space with $n$ input items, we design randomized algorithms that, using only a noisy quadruplet oracle, compute a set of $O(k \\cdot \\mathsf{polylog}(n))$ centers along with a mapping from the input items to the centers such that the clustering cost of the mapping is at most constant times the optimum $k$-clustering cost. Our method achieves a query complexity of $O(n\\cdot k \\cdot \\mathsf{polylog}(n))$ for arbitrary metric spaces and improves to $O((n+k^2) \\cdot \\mathsf{polylog}(n))$ when the underlying metric has bounded doubling dimension. When the metric has bounded doubling dimension we can further improve the approximation from constant to $1+\\varepsilon$, for any arbitrarily small constant $\\varepsilon\\in(0,1)$, while preserving the same asymptotic query complexity. Our framework demonstrates how noisy, low-cost oracles, such as those derived from large language models, can be systematically integrated into scalable clustering algorithms.", "date": "2026-01-27", "categories": []}
{"id": "2601.19718", "title": "Rethinking Divisive Hierarchical Clustering from a Distributional Perspective", "abstract": "We uncover that current objective-based Divisive Hierarchical Clustering (DHC) methods produce a dendrogram that does not have three desired properties i.e., no unwarranted splitting, group similar clusters into a same subset, ground-truth correspondence. This shortcoming has their root cause in using a set-oriented bisecting assessment criterion. We show that this shortcoming can be addressed by using a distributional kernel, instead of the set-oriented criterion; and the resultant clusters achieve a new distribution-oriented objective to maximize the total similarity of all clusters (TSC). Our theoretical analysis shows that the resultant dendrogram guarantees a lower bound of TSC. The empirical evaluation shows the effectiveness of our proposed method on artificial and Spatial Transcriptomics (bioinformatics) datasets. Our proposed method successfully creates a dendrogram that is consistent with the biological regions in a Spatial Transcriptomics dataset, whereas other contenders fail.", "date": "2026-01-27", "categories": []}
{"id": "2510.19229", "title": "Brain-Inspired Perspective on Configurations: Unsupervised Similarity and Early Cognition", "abstract": "Infants discover categories, detect novelty, and adapt to new contexts without supervision-a challenge for current machine learning. We present a brain-inspired perspective on configurations, a finite-resolution clustering framework that uses a single resolution parameter and attraction-repulsion dynamics to yield hierarchical organization, novelty sensitivity, and flexible adaptation. To evaluate these properties, we introduce mheatmap, which provides proportional heatmaps and reassignment algorithm to fairly assess multi-resolution and dynamic behavior. Across datasets, configurations are competitive on standard clustering metrics, achieve 87% AUC in novelty detection, and show 35% better stability during dynamic category evolution. These results position configurations as a principled computational model of early cognitive categorization and a step toward brain-inspired AI.", "date": "2025-10-22", "categories": []}
{"id": "2601.17512", "title": "One-Shot Federated Clustering of Non-Independent Completely Distributed Data", "abstract": "Federated Learning (FL) that extracts data knowledge while protecting the privacy of multiple clients has achieved remarkable results in distributed privacy-preserving IoT systems, including smart traffic flow monitoring, smart grid load balancing, and so on. Since most data collected from edge devices are unlabeled, unsupervised Federated Clustering (FC) is becoming increasingly popular for exploring pattern knowledge from complex distributed data. However, due to the lack of label guidance, the common Non-Independent and Identically Distributed (Non-IID) issue of clients have greatly challenged FC by posing the following problems: How to fuse pattern knowledge (i.e., cluster distribution) from Non-IID clients; How are the cluster distributions among clients related; and How does this relationship connect with the global knowledge fusion? In this paper, a more tricky but overlooked phenomenon in Non-IID is revealed, which bottlenecks the clustering performance of the existing FC approaches. That is, different clients could fragment a cluster, and accordingly, a more generalized Non-IID concept, i.e., Non-ICD (Non-Independent Completely Distributed), is derived. To tackle the above FC challenges, a new framework named GOLD (Global Oriented Local Distribution Learning) is proposed. GOLD first finely explores the potential incomplete local cluster distributions of clients, then uploads the distribution summarization to the server for global fusion, and finally performs local cluster enhancement under the guidance of the global distribution. Extensive experiments, including significance tests, ablation studies, scalability evaluations, qualitative results, etc., have been conducted to show the superiority of GOLD.", "date": "2026-01-24", "categories": []}
{"id": "2601.10759", "title": "Mass Distribution versus Density Distribution in the Context of Clustering", "abstract": "This paper investigates two fundamental descriptors of data, i.e., density distribution versus mass distribution, in the context of clustering. Density distribution has been the de facto descriptor of data distribution since the introduction of statistics. We show that density distribution has its fundamental limitation -- high-density bias, irrespective of the algorithms used to perform clustering. Existing density-based clustering algorithms have employed different algorithmic means to counter the effect of the high-density bias with some success, but the fundamental limitation of using density distribution remains an obstacle to discovering clusters of arbitrary shapes, sizes and densities. Using the mass distribution as a better foundation, we propose a new algorithm which maximizes the total mass of all clusters, called mass-maximization clustering (MMC). The algorithm can be easily changed to maximize the total density of all clusters in order to examine the fundamental limitation of using density distribution versus mass distribution. The key advantage of the MMC over the density-maximization clustering is that the maximization is conducted without a bias towards dense clusters.", "date": "2026-01-14", "categories": []}
{"id": "2601.16491", "title": "Robust Categorical Data Clustering Guided by Multi-Granular Competitive Learning", "abstract": "Data set composed of categorical features is very common in big data analysis tasks. Since categorical features are usually with a limited number of qualitative possible values, the nested granular cluster effect is prevalent in the implicit discrete distance space of categorical data. That is, data objects frequently overlap in space or subspace to form small compact clusters, and similar small clusters often form larger clusters. However, the distance space cannot be well-defined like the Euclidean distance due to the qualitative categorical data values, which brings great challenges to the cluster analysis of categorical data. In view of this, we design a Multi-Granular Competitive Penalization Learning (MGCPL) algorithm to allow potential clusters to interactively tune themselves and converge in stages with different numbers of naturally compact clusters. To leverage MGCPL, we also propose a Cluster Aggregation strategy based on MGCPL Encoding (CAME) to first encode the data objects according to the learned multi-granular distributions, and then perform final clustering on the embeddings. It turns out that the proposed MGCPL-guided Categorical Data Clustering (MCDC) approach is competent in automatically exploring the nested distribution of multi-granular clusters and highly robust to categorical data sets from various domains. Benefiting from its linear time complexity, MCDC is scalable to large-scale data sets and promising in pre-partitioning data sets or compute nodes for boosting distributed computing. Extensive experiments with statistical evidence demonstrate its superiority compared to state-of-the-art counterparts on various real public data sets.", "date": "2026-01-23", "categories": []}
{"id": "2402.04794", "title": "Scalable Multi-view Clustering via Explicit Kernel Features Maps", "abstract": "The proliferation of high-dimensional data from sources such as social media, sensor networks, and online platforms has created new challenges for clustering algorithms. Multi-view clustering, which integrates complementary information from multiple data perspectives, has emerged as a powerful solution. However, existing methods often struggle with scalability and efficiency, particularly on large attributed networks. In this work, we address these limitations by leveraging explicit kernel feature maps and a non-iterative optimization strategy, enabling efficient and accurate clustering on datasets with millions of points.", "date": "2024-02-07", "categories": []}
{"id": "2505.09516", "title": "Depth-Based Local Center Clustering: A Framework for Handling Different Clustering Scenarios", "abstract": "Cluster analysis, or clustering, plays a crucial role across numerous scientific and engineering domains. Despite the wealth of clustering methods proposed over the past decades, each method is typically designed for specific scenarios and presents certain limitations in practical applications. In this paper, we propose depth-based local center clustering (DLCC). This novel method makes use of data depth, which is known to produce a center-outward ordering of sample points in a multivariate space. However, data depth typically fails to capture the multimodal characteristics of {data}, something of the utmost importance in the context of clustering. To overcome this, DLCC makes use of a local version of data depth that is based on subsets of {data}. From this, local centers can be identified as well as clusters of varying shapes. Furthermore, we propose a new internal metric based on density-based clustering to evaluate clustering performance on {non-convex clusters}. Overall, DLCC is a flexible clustering approach that seems to overcome some limitations of traditional clustering methods, thereby enhancing data analysis capabilities across a wide range of application scenarios.", "date": "2025-05-14", "categories": []}
{"id": "2512.20905", "title": "DiEC: Diffusion Embedded Clustering", "abstract": "Deep clustering methods typically rely on a single, well-defined representation for clustering. In contrast, pretrained diffusion models provide abundant and diverse multi-scale representations across network layers and noise timesteps. However, a key challenge is how to efficiently identify the most clustering-friendly representation in the layer*timestep space. To address this issue, we propose Diffusion Embedded Clustering (DiEC), an unsupervised framework that performs clustering by leveraging optimal intermediate representations from pretrained diffusion models. DiEC systematically evaluates the clusterability of representations along the trajectory of network depth and noise timesteps. Meanwhile, an unsupervised search strategy is designed for recognizing the Clustering-optimal Layer (COL) and Clustering-optimal Timestep (COT) in the layer*timestep space of pretrained diffusion models, aiming to promote clustering performance and reduce computational overhead. DiEC is fine-tuned primarily with a structure-preserving DEC-style KL-divergence objective at the fixed COL + COT, together with a random-timestep diffusion denoising objective to maintain the generative capability of the pretrained model. Without relying on augmentation-based consistency constraints or contrastive learning, DiEC achieves excellent clustering performance across multiple benchmark datasets.", "date": "2025-12-24", "categories": []}
{"id": "2505.18918", "title": "ALPCAHUS: Subspace Clustering for Heteroscedastic Data", "abstract": "Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. Various methods have been proposed to extend PCA to the union of subspace (UoS) setting for clustering data that comes from multiple subspaces like K-Subspaces (KSS). However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample. Heteroscedastic methods aim to deal with such mixed data quality. This paper develops a heteroscedastic-based subspace clustering method, named ALPCAHUS, that can estimate the sample-wise noise variances and use this information to improve the estimate of the subspace bases associated with the low-rank structure of the data. This clustering algorithm builds on K-Subspaces (KSS) principles by extending the recently proposed heteroscedastic PCA method, named LR-ALPCAH, for clusters with heteroscedastic noise in the UoS setting. Simulations and real-data experiments show the effectiveness of accounting for data heteroscedasticity compared to existing clustering algorithms. Code available at https://github.com/javiersc1/ALPCAHUS.", "date": "2025-05-25", "categories": []}
{"id": "2509.09527", "title": "Generative Diffusion Contrastive Network for Multi-View Clustering", "abstract": "In recent years, Multi-View Clustering (MVC) has been significantly advanced under the influence of deep learning. By integrating heterogeneous data from multiple views, MVC enhances clustering analysis, making multi-view fusion critical to clustering performance. However, there is a problem of low-quality data in multi-view fusion. This problem primarily arises from two reasons: 1) Certain views are contaminated by noisy data. 2) Some views suffer from missing data. This paper proposes a novel Stochastic Generative Diffusion Fusion (SGDF) method to address this problem. SGDF leverages a multiple generative mechanism for the multi-view feature of each sample. It is robust to low-quality data. Building on SGDF, we further present the Generative Diffusion Contrastive Network (GDCN). Extensive experiments show that GDCN achieves the state-of-the-art results in deep MVC tasks. The source code is publicly available at https://github.com/HackerHyper/GDCN.", "date": "2025-09-11", "categories": []}
{"id": "2512.10327", "title": "Simple Yet Effective Selective Imputation for Incomplete Multi-view Clustering", "abstract": "Incomplete Multi-view Clustering (IMC) has emerged as a significant challenge in multi-view learning. A predominant line for IMC is data imputation; however, indiscriminate imputation can result in unreliable content. Recently, researchers have proposed selective imputation methods that use a post-imputation assessment strategy: (1) impute all or some missing values, and (2) evaluate their quality through clustering tasks. We observe that this strategy incurs substantial computational complexity and is heavily dependent on the performance of the clustering model. To address these challenges, we first introduce the concept of pre-imputation assessment. We propose an Implicit Informativeness-based Selective Imputation (SI$^3$) method for incomplete multi-view clustering, which explicitly addresses the trade-off between imputation utility and imputation risk. SI$^3$ evaluates the imputation-relevant informativeness of each missing position in a training-free manner, and selectively imputes data only when sufficient informative support is available. Under a multi-view generative assumption, SI$^3$ further integrates selective imputation into a variational inference framework, enabling uncertainty-aware imputation at the latent distribution level and robust multi-view fusion. Compared with existing selective imputation strategies, SI$^3$ is lightweight, data-driven, and model-agnostic, and can be seamlessly incorporated into existing incomplete multi-view clustering frameworks as a plug-in strategy. Extensive experiments on multiple benchmark datasets demonstrate that SI$^3$ consistently outperforms both imputation-based and imputation-free methods, particularly under challenging unbalanced missing scenarios.", "date": "2025-12-11", "categories": []}
{"id": "2601.12903", "title": "Deep Temporal Graph Clustering: A Comprehensive Benchmark and Datasets", "abstract": "Temporal Graph Clustering (TGC) is a new task with little attention, focusing on node clustering in temporal graphs. Compared with existing static graph clustering, it can find the balance between time requirement and space requirement (Time-Space Balance) through the interaction sequence-based batch-processing pattern. However, there are two major challenges that hinder the development of TGC, i.e., inapplicable clustering techniques and inapplicable datasets. To address these challenges, we propose a comprehensive benchmark, called BenchTGC. Specially, we design a BenchTGC Framework to illustrate the paradigm of temporal graph clustering and improve existing clustering techniques to fit temporal graphs. In addition, we also discuss problems with public temporal graph datasets and develop multiple datasets suitable for TGC task, called BenchTGC Datasets. According to extensive experiments, we not only verify the advantages of BenchTGC, but also demonstrate the necessity and importance of TGC task. We wish to point out that the dynamically changing and complex scenarios in real world are the foundation of temporal graph clustering. The code and data is available at: https://github.com/MGitHubL/BenchTGC.", "date": "2026-01-19", "categories": []}
{"id": "2601.13251", "title": "Beyond Cosine Similarity: Taming Semantic Drift and Antonym Intrusion in a 15-Million Node Turkish Synonym Graph", "abstract": "Neural embeddings have a notorious blind spot: they can't reliably tell synonyms apart from antonyms. Consequently, increasing similarity thresholds often fails to prevent opposites from being grouped together. We've built a large-scale semantic clustering system specifically designed to tackle this problem head on. Our pipeline chews through 15 million lexical items, evaluates a massive 520 million potential relationships, and ultimately generates 2.9 million high-precision semantic clusters. The system makes three primary contributions. First, we introduce a labeled dataset of 843,000 concept pairs spanning synonymy, antonymy, and co-hyponymy, constructed via Gemini 2.5-Flash LLM augmentation and verified using human-curated dictionary resources. Second, we propose a specialized three-way semantic relation discriminator that achieves 90% macro-F1, enabling robust disambiguation beyond raw embedding similarity. Third, we introduce a novel soft-to-hard clustering algorithm that mitigates semantic drift preventing erroneous transitive chains (e.g., hot -> spicy -> pain -> depression) while simultaneously resolving polysemy. Our approach employs a topology-aware two-stage expansion-pruning procedure with topological voting, ensuring that each term is assigned to exactly one semantically coherent cluster. The resulting resource enables high-precision semantic search and retrieval-augmented generation, particularly for morphologically rich and low-resource languages where existing synonym databases remain sparse.", "date": "2026-01-19", "categories": []}
{"id": "2601.11118", "title": "Optimized Algorithms for Text Clustering with LLM-Generated Constraints", "abstract": "Clustering is a fundamental tool that has garnered significant interest across a wide range of applications including text analysis. To improve clustering accuracy, many researchers have incorporated background knowledge, typically in the form of must-link and cannot-link constraints, to guide the clustering process. With the recent advent of large language models (LLMs), there is growing interest in improving clustering quality through LLM-based automatic constraint generation. In this paper, we propose a novel constraint-generation approach that reduces resource consumption by generating constraint sets rather than using traditional pairwise constraints. This approach improves both query efficiency and constraint accuracy compared to state-of-the-art methods. We further introduce a constrained clustering algorithm tailored to the characteristics of LLM-generated constraints. Our method incorporates a confidence threshold and a penalty mechanism to address potentially inaccurate constraints. We evaluate our approach on five text datasets, considering both the cost of constraint generation and the overall clustering performance. The results show that our method achieves clustering accuracy comparable to the state-of-the-art algorithms while reducing the number of LLM queries by more than 20 times.", "date": "2026-01-16", "categories": []}
{"id": "2601.11160", "title": "Clustering High-dimensional Data: Balancing Abstraction and Representation Tutorial at AAAI 2026", "abstract": "How to find a natural grouping of a large real data set? Clustering requires a balance between abstraction and representation. To identify clusters, we need to abstract from superfluous details of individual objects. But we also need a rich representation that emphasizes the key features shared by groups of objects that distinguish them from other groups of objects.\n  Each clustering algorithm implements a different trade-off between abstraction and representation. Classical K-means implements a high level of abstraction - details are simply averaged out - combined with a very simple representation - all clusters are Gaussians in the original data space. We will see how approaches to subspace and deep clustering support high-dimensional and complex data by allowing richer representations. However, with increasing representational expressiveness comes the need to explicitly enforce abstraction in the objective function to ensure that the resulting method performs clustering and not just representation learning. We will see how current deep clustering methods define and enforce abstraction through centroid-based and density-based clustering losses. Balancing the conflicting goals of abstraction and representation is challenging. Ideas from subspace clustering help by learning one latent space for the information that is relevant to clustering and another latent space to capture all other information in the data.\n  The tutorial ends with an outlook on future research in clustering. Future methods will more adaptively balance abstraction and representation to improve performance, energy efficiency and interpretability. By automatically finding the sweet spot between abstraction and representation, the human brain is very good at clustering and other related tasks such as single-shot learning. So, there is still much room for improvement.", "date": "2026-01-16", "categories": []}
{"id": "2601.09162", "title": "Efficient Clustering in Stochastic Bandits", "abstract": "We study the Bandit Clustering (BC) problem under the fixed confidence setting, where the objective is to group a collection of data sequences (arms) into clusters through sequential sampling from adaptively selected arms at each time step while ensuring a fixed error probability at the stopping time. We consider a setting where arms in a cluster may have different distributions. Unlike existing results in this setting, which assume Gaussian-distributed arms, we study a broader class of vector-parametric distributions that satisfy mild regularity conditions. Existing asymptotically optimal BC algorithms require solving an optimization problem as part of their sampling rule at each step, which is computationally costly. We propose an Efficient Bandit Clustering algorithm (EBC), which, instead of solving the full optimization problem, takes a single step toward the optimal value at each time step, making it computationally efficient while remaining asymptotically optimal. We also propose a heuristic variant of EBC, called EBC-H, which further simplifies the sampling rule, with arm selection based on quantities computed as part of the stopping rule. We highlight the computational efficiency of EBC and EBC-H by comparing their per-sample run time with that of existing algorithms. The asymptotic optimality of EBC is supported through simulations on the synthetic datasets. Through simulations on both synthetic and real-world datasets, we show the performance gain of EBC and EBC-H over existing approaches.", "date": "2026-01-14", "categories": []}
{"id": "2601.08781", "title": "Fast and explainable clustering in the Manhattan and Tanimoto distance", "abstract": "The CLASSIX algorithm is a fast and explainable approach to data clustering. In its original form, this algorithm exploits the sorting of the data points by their first principal component to truncate the search for nearby data points, with nearness being defined in terms of the Euclidean distance. Here we extend CLASSIX to other distance metrics, including the Manhattan distance and the Tanimoto distance. Instead of principal components, we use an appropriate norm of the data vectors as the sorting criterion, combined with the triangle inequality for search termination. In the case of Tanimoto distance, a provably sharper intersection inequality is used to further boost the performance of the new algorithm. On a real-world chemical fingerprint benchmark, CLASSIX Tanimoto is about 30 times faster than the Taylor--Butina algorithm, and about 80 times faster than DBSCAN, while computing higher-quality clusters in both cases.", "date": "2026-01-13", "categories": []}
{"id": "2408.10084", "title": "TANGO: Clustering with Typicality-Aware Nonlocal Mode-Seeking and Graph-Cut Optimization", "abstract": "Density-based mode-seeking methods generate a \\emph{density-ascending dependency} from low-density points towards higher-density neighbors. Current mode-seeking methods identify modes by breaking some dependency connections, but relying heavily on local data characteristics, requiring case-by-case threshold settings or human intervention to be effective for different datasets. To address this issue, we introduce a novel concept called \\emph{typicality}, by exploring the \\emph{locally defined} dependency from a \\emph{global} perspective, to quantify how confident a point would be a mode. We devise an algorithm that effectively and efficiently identifies modes with the help of the global-view typicality. To implement and validate our idea, we design a clustering method called TANGO, which not only leverages typicality to detect modes, but also utilizes graph-cut with an improved \\emph{path-based similarity} to aggregate data into the final clusters. Moreover, this paper also provides some theoretical analysis on the proposed algorithm. Experimental results on several synthetic and extensive real-world datasets demonstrate the effectiveness and superiority of TANGO. The code is available at https://github.com/SWJTU-ML/TANGO_code.", "date": "2024-08-19", "categories": []}
{"id": "2510.06747", "title": "LLMs Enable Bag-of-Texts Representations for Short-Text Clustering", "abstract": "In this paper, we propose a training-free method for unsupervised short text clustering that relies less on careful selection of embedders than other methods. In customer-facing chatbots, companies are dealing with large amounts of user utterances that need to be clustered according to their intent. In these settings, no labeled data is typically available, and the number of clusters is not known. Recent approaches to short-text clustering in label-free settings incorporate LLM output to refine existing embeddings. While LLMs can identify similar texts effectively, the resulting similarities may not be directly represented by distances in the dense vector space, as they depend on the original embedding. We therefore propose a method for transforming LLM judgments directly into a bag-of-texts representation in which texts are initialized to be equidistant, without assuming any prior distance relationships. Our method achieves comparable or superior results to state-of-the-art methods, but without embeddings optimization or assuming prior knowledge of clusters or labels. Experiments on diverse datasets and smaller LLMs show that our method is model agnostic and can be applied to any embedder, with relatively small LLMs, and different clustering methods. We also show how our method scales to large datasets, reducing the computational cost of the LLM use. The flexibility and scalability of our method make it more aligned with real-world training-free scenarios than existing clustering methods.", "date": "2025-10-08", "categories": []}
{"id": "2601.06221", "title": "LDTC: Lifelong deep temporal clustering for multivariate time series", "abstract": "Clustering temporal and dynamically changing multivariate time series from real-world fields, called temporal clustering for short, has been a major challenge due to inherent complexities. Although several deep temporal clustering algorithms have demonstrated a strong advantage over traditional methods in terms of model learning and clustering results, the accuracy of the few algorithms are not satisfactory. None of the existing algorithms can continuously learn new tasks and deal with the dynamic data effectively and efficiently in the sequential tasks learning. To bridge the gap and tackle these issues, this paper proposes a novel algorithm \\textbf{L}ifelong \\textbf{D}eep \\textbf{T}emporal \\textbf{C}lustering (\\textbf{LDTC}), which effectively integrates dimensionality reduction and temporal clustering into an end-to-end deep unsupervised learning framework. Using a specifically designed autoencoder and jointly optimizing for both the latent representation and clustering objective, the LDTC can achieve high-quality clustering results. Moreover, unlike any previous work, the LDTC is uniquely equipped with the fully dynamic model expansion and rehearsal-based techniques to effectively learn new tasks and to tackle the dynamic data in the sequential tasks learning without the catastrophic forgetting or degradation of the model accuracy. Experiments on seven real-world multivariate time series datasets show that the LDTC is a promising method for dealing with temporal clustering issues effectively and efficiently.", "date": "2026-01-09", "categories": []}
{"id": "2601.06404", "title": "One-Shot Hierarchical Federated Clustering", "abstract": "Driven by the growth of Web-scale decentralized services, Federated Clustering (FC) aims to extract knowledge from heterogeneous clients in an unsupervised manner while preserving the clients' privacy, which has emerged as a significant challenge due to the lack of label guidance and the Non-Independent and Identically Distributed (non-IID) nature of clients. In real scenarios such as personalized recommendation and cross-device user profiling, the global cluster may be fragmented and distributed among different clients, and the clusters may exist at different granularities or even nested. Although Hierarchical Clustering (HC) is considered promising for exploring such distributions, the sophisticated recursive clustering process makes it more computationally expensive and vulnerable to privacy exposure, thus relatively unexplored under the federated learning scenario. This paper introduces an efficient one-shot hierarchical FC framework that performs client-end distribution exploration and server-end distribution aggregation through one-way prototype-level communication from clients to the server. A fine partition mechanism is developed to generate successive clusterlets to describe the complex landscape of the clients' clusters. Then, a multi-granular learning mechanism on the server is proposed to fuse the clusterlets, even when they have inconsistent granularities generated from different clients. It turns out that the complex cluster distributions across clients can be efficiently explored, and extensive experiments comparing state-of-the-art methods on ten public datasets demonstrate the superiority of the proposed method.", "date": "2026-01-10", "categories": []}
{"id": "2601.07535", "title": "Nonparametric Kernel Clustering with Bandit Feedback", "abstract": "Clustering with bandit feedback refers to the problem of partitioning a set of items, where the clustering algorithm can sequentially query the items to receive noisy observations. The problem is formally posed as the task of partitioning the arms of an N-armed stochastic bandit according to their underlying distributions, grouping two arms together if and only if they share the same distribution, using samples collected sequentially and adaptively. This setting has gained attention in recent years due to its applicability in recommendation systems and crowdsourcing. Existing works on clustering with bandit feedback rely on a strong assumption that the underlying distributions are sub-Gaussian. As a consequence, the existing methods mainly cover settings with linearly-separable clusters, which has little practical relevance. We introduce a framework of ``nonparametric clustering with bandit feedback'', where the underlying arm distributions are not constrained to any parametric, and hence, it is applicable for active clustering of real-world datasets. We adopt a kernel-based approach, which allows us to reformulate the nonparametric problem as the task of clustering the arms according to their kernel mean embeddings in a reproducing kernel Hilbert space (RKHS). Building on this formulation, we introduce the KABC algorithm with theoretical correctness guarantees and analyze its sampling budget. We introduce a notion of signal-to-noise ratio for this problem that depends on the maximum mean discrepancy (MMD) between the arm distributions and on their variance in the RKHS. Our algorithm is adaptive to this unknown quantity: it does not require it as an input yet achieves instance-dependent guarantees.", "date": "2026-01-12", "categories": []}
{"id": "2601.07550", "title": "TFEC: Multivariate Time-Series Clustering via Temporal-Frequency Enhanced Contrastive Learning", "abstract": "Multivariate Time-Series (MTS) clustering is crucial for signal processing and data analysis. Although deep learning approaches, particularly those leveraging Contrastive Learning (CL), are prominent for MTS representation, existing CL-based models face two key limitations: 1) neglecting clustering information during positive/negative sample pair construction, and 2) introducing unreasonable inductive biases, e.g., destroying time dependence and periodicity through augmentation strategies, compromising representation quality. This paper, therefore, proposes a Temporal-Frequency Enhanced Contrastive (TFEC) learning framework. To preserve temporal structure while generating low-distortion representations, a temporal-frequency Co-EnHancement (CoEH) mechanism is introduced. Accordingly, a synergistic dual-path representation and cluster distribution learning framework is designed to jointly optimize cluster structure and representation fidelity. Experiments on six real-world benchmark datasets demonstrate TFEC's superiority, achieving 4.48% average NMI gains over SOTA methods, with ablation studies validating the design. The code of the paper is available at: https://github.com/yueliangy/TFEC.", "date": "2026-01-12", "categories": []}
{"id": "2601.04388", "title": "LLM-Guided Lifecycle-Aware Clustering of Multi-Turn Customer Support Conversations", "abstract": "Clustering customer chat data is vital for cloud providers handling multi service queries. Traditional methods struggle with overlapping concerns and create broad, static clusters that degrade over time. Reclustering disrupts continuity, making issue tracking difficult. We propose an adaptive system that segments multi turn chats into service specific concerns and incrementally refines clusters as new issues arise. Cluster quality is tracked via DaviesBouldin Index and Silhouette Scores, with LLM based splitting applied only to degraded clusters. Our method improves Silhouette Scores by over 100\\% and reduces DBI by 65.6\\% compared to baselines, enabling scalable, real time analytics without full reclustering.", "date": "2026-01-07", "categories": []}
{"id": "2512.22612", "title": "Enhancing Noise Resilience in Face Clustering via Sparse Differential Transformer", "abstract": "The method used to measure relationships between face embeddings plays a crucial role in determining the performance of face clustering. Existing methods employ the Jaccard similarity coefficient instead of the cosine distance to enhance the measurement accuracy. However, these methods introduce too many irrelevant nodes, producing Jaccard coefficients with limited discriminative power and adversely affecting clustering performance. To address this issue, we propose a prediction-driven Top-K Jaccard similarity coefficient that enhances the purity of neighboring nodes, thereby improving the reliability of similarity measurements. Nevertheless, accurately predicting the optimal number of neighbors (Top-K) remains challenging, leading to suboptimal clustering results. To overcome this limitation, we develop a Transformer-based prediction model that examines the relationships between the central node and its neighboring nodes near the Top-K to further enhance the reliability of similarity estimation. However, vanilla Transformer, when applied to predict relationships between nodes, often introduces noise due to their overemphasis on irrelevant feature relationships. To address these challenges, we propose a Sparse Differential Transformer (SDT), instead of the vanilla Transformer, to eliminate noise and enhance the model's anti-noise capabilities. Extensive experiments on multiple datasets, such as MS-Celeb-1M, demonstrate that our approach achieves state-of-the-art (SOTA) performance, outperforming existing methods and providing a more robust solution for face clustering.", "date": "2025-12-27", "categories": []}
{"id": "2601.01127", "title": "Wittgenstein's Family Resemblance Clustering Algorithm", "abstract": "This paper, introducing a novel method in philomatics, draws on Wittgenstein's concept of family resemblance from analytic philosophy to develop a clustering algorithm for machine learning. According to Wittgenstein's Philosophical Investigations (1953), family resemblance holds that members of a concept or category are connected by overlapping similarities rather than a single defining property. Consequently, a family of entities forms a chain of items sharing overlapping traits. This philosophical idea naturally lends itself to a graph-based approach in machine learning. Accordingly, we propose the Wittgenstein's Family Resemblance (WFR) clustering algorithm and its kernel variant, kernel WFR. This algorithm computes resemblance scores between neighboring data instances, and after thresholding these scores, a resemblance graph is constructed. The connected components of this graph define the resulting clusters. Simulations on benchmark datasets demonstrate that WFR is an effective nonlinear clustering algorithm that does not require prior knowledge of the number of clusters or assumptions about their shapes.", "date": "2026-01-03", "categories": []}
{"id": "2506.10244", "title": "A new type of federated clustering: A non-model-sharing approach", "abstract": "In recent years, the growing need to leverage sensitive data across institutions has led to increased attention on federated learning (FL), a decentralized machine learning paradigm that enables model training without sharing raw data. However, existing FL-based clustering methods, known as federated clustering, typically assume simple data partitioning scenarios such as horizontal or vertical splits, and cannot handle more complex distributed structures. This study proposes data collaboration clustering (DC-Clustering), a novel federated clustering method that supports clustering over complex data partitioning scenarios where horizontal and vertical splits coexist. In DC-Clustering, each institution shares only intermediate representations instead of raw data, ensuring privacy preservation while enabling collaborative clustering. The method allows flexible selection between k-means and spectral clustering, and achieves final results with a single round of communication with the central server. We conducted extensive experiments using synthetic and open benchmark datasets. The results show that our method achieves clustering performance comparable to centralized clustering where all data are pooled. DC-Clustering addresses an important gap in current FL research by enabling effective knowledge discovery from distributed heterogeneous data. Its practical properties -- privacy preservation, communication efficiency, and flexibility -- make it a promising tool for privacy-sensitive domains such as healthcare and finance.", "date": "2025-06-11", "categories": []}
{"id": "2601.02656", "title": "Statistical Inference for Fuzzy Clustering", "abstract": "Clustering is a central tool in biomedical research for discovering heterogeneous patient subpopulations, where group boundaries are often diffuse rather than sharply separated. Traditional methods produce hard partitions, whereas soft clustering methods such as fuzzy $c$-means (FCM) allow mixed memberships and better capture uncertainty and gradual transitions. Despite the widespread use of FCM, principled statistical inference for fuzzy clustering remains limited.\n  We develop a new framework for weighted fuzzy $c$-means (WFCM) for settings with potential cluster size imbalance. Cluster-specific weights rebalance the classical FCM criterion so that smaller clusters are not overwhelmed by dominant groups, and the weighted objective induces a normalized density model with scale parameter $\\sigma$ and fuzziness parameter $m$. Estimation is performed via a blockwise majorize--minimize (MM) procedure that alternates closed-form membership and centroid updates with likelihood-based updates of $(\\sigma,\\bw)$. The intractable normalizing constant is approximated by importance sampling using a data-adaptive Gaussian mixture proposal. We further provide likelihood ratio tests for comparing cluster centers and bootstrap-based confidence intervals.\n  We establish consistency and asymptotic normality of the maximum likelihood estimator, validate the method through simulations, and illustrate it using single-cell RNA-seq and Alzheimer disease Neuroimaging Initiative (ADNI) data. These applications demonstrate stable uncertainty quantification and biologically meaningful soft memberships, ranging from well-separated cell populations under imbalance to a graded AD versus non-AD continuum consistent with disease progression.", "date": "2026-01-06", "categories": []}
{"id": "2601.03237", "title": "PET-TURTLE: Deep Unsupervised Support Vector Machines for Imbalanced Data Clusters", "abstract": "Foundation vision, audio, and language models enable zero-shot performance on downstream tasks via their latent representations. Recently, unsupervised learning of data group structure with deep learning methods has gained popularity. TURTLE, a state of the art deep clustering algorithm, uncovers data labeling without supervision by alternating label and hyperplane updates, maximizing the hyperplane margin, in a similar fashion to support vector machines (SVMs). However, TURTLE assumes clusters are balanced; when data is imbalanced, it yields non-ideal hyperplanes that cause higher clustering error. We propose PET-TURTLE, which generalizes the cost function to handle imbalanced data distributions by a power law prior. Additionally, by introducing sparse logits in the labeling process, PET-TURTLE optimizes a simpler search space that in turn improves accuracy for balanced datasets. Experiments on synthetic and real data show that PET-TURTLE improves accuracy for imbalanced sources, prevents over-prediction of minority clusters, and enhances overall clustering.", "date": "2026-01-06", "categories": []}
{"id": "2601.00963", "title": "Deep Clustering with Associative Memories", "abstract": "Deep clustering - joint representation learning and latent space clustering - is a well studied problem especially in computer vision and text processing under the deep learning framework. While the representation learning is generally differentiable, clustering is an inherently discrete optimization task, requiring various approximations and regularizations to fit in a standard differentiable pipeline. This leads to a somewhat disjointed representation learning and clustering. In this work, we propose a novel loss function utilizing energy-based dynamics via Associative Memories to formulate a new deep clustering method, DCAM, which ties together the representation learning and clustering aspects more intricately in a single objective. Our experiments showcase the advantage of DCAM, producing improved clustering quality for various architecture choices (convolutional, residual or fully-connected) and data modalities (images or text).", "date": "2026-01-02", "categories": []}
{"id": "2410.21745", "title": "RDSA: A Robust Deep Graph Clustering Framework via Dual Soft Assignment", "abstract": "Graph clustering is an essential aspect of network analysis that involves grouping nodes into separate clusters. Recent developments in deep learning have resulted in graph clustering, which has proven effective in many applications. Nonetheless, these methods often encounter difficulties when dealing with real-world graphs, particularly in the presence of noisy edges. Additionally, many denoising graph clustering methods tend to suffer from lower performance, training instability, and challenges in scaling to large datasets compared to non-denoised models. To tackle these issues, we introduce a new framework called the Robust Deep Graph Clustering Framework via Dual Soft Assignment (RDSA). RDSA consists of three key components: (i) a node embedding module that effectively integrates the graph's topological features and node attributes; (ii) a structure-based soft assignment module that improves graph modularity by utilizing an affinity matrix for node assignments; and (iii) a node-based soft assignment module that identifies community landmarks and refines node assignments to enhance the model's robustness. We assess RDSA on various real-world datasets, demonstrating its superior performance relative to existing state-of-the-art methods. Our findings indicate that RDSA provides robust clustering across different graph types, excelling in clustering effectiveness and robustness, including adaptability to noise, stability, and scalability.", "date": "2024-10-29", "categories": []}
{"id": "2509.16101", "title": "Personalized Federated Heat-Kernel Enhanced Multi-View Clustering via Advanced Tensor Decomposition Techniques", "abstract": "This paper introduces mathematical frameworks that address the challenges of multi-view clustering in federated learning environments. The objective is to integrate optimization techniques based on new objective functions employing heat-kernel coefficients to replace conventional distance metrics with quantum-inspired measures. The proposed frameworks utilize advanced tensor decomposition methods, specifically, PARAFAC2 and Tucker decomposition to efficiently represent high-dimensional, multi-view data while preserving inter-view relationships. The research has yielded the development of four novel algorithms, an efficient federated kernel multi-view clustering (E-FKMVC) model, FedHK-PARAFAC2, FedHK-Tucker, and FedHK-MVC-Person with PARAFAC2 Decomposition (Personalized FedHK-PARAFAC2). The primary objective of these algorithms is to enhance the efficacy of clustering processes while ensuring the confidentiality and efficient communication in federated learning environments. Theoretical analyses of convergence guarantees, privacy bounds, and complexity are provided to validate the effectiveness of the proposed methods. In essence, this paper makes a significant academic contribution to the field of federated multi-view clustering through its innovative integration of mathematical modeling and algorithm design. This approach addresses the critical challenges of data heterogeneity and privacy concerns, paving the way for enhanced data management and analytics in various contexts.", "date": "2025-09-19", "categories": []}
{"id": "2512.23766", "title": "A Granular Grassmannian Clustering Framework via the Schubert Variety of Best Fit", "abstract": "In many classification and clustering tasks, it is useful to compute a geometric representative for a dataset or a cluster, such as a mean or median. When datasets are represented by subspaces, these representatives become points on the Grassmann or flag manifold, with distances induced by their geometry, often via principal angles. We introduce a subspace clustering algorithm that replaces subspace means with a trainable prototype defined as a Schubert Variety of Best Fit (SVBF) - a subspace that comes as close as possible to intersecting each cluster member in at least one fixed direction. Integrated in the Linde-Buzo-Grey (LBG) pipeline, this SVBF-LBG scheme yields improved cluster purity on synthetic, image, spectral, and video action data, while retaining the mathematical structure required for downstream analysis.", "date": "2025-12-29", "categories": []}
{"id": "2512.21434", "title": "Scalable Deep Subspace Clustering Network", "abstract": "Subspace clustering methods face inherent scalability limits due to the $O(n^3)$ cost (with $n$ denoting the number of data samples) of constructing full $n\\times n$ affinities and performing spectral decomposition. While deep learning-based approaches improve feature extraction, they maintain this computational bottleneck through exhaustive pairwise similarity computations. We propose SDSNet (Scalable Deep Subspace Network), a deep subspace clustering framework that achieves $\\mathcal{O}(n)$ complexity through (1) landmark-based approximation, avoiding full affinity matrices, (2) joint optimization of auto-encoder reconstruction with self-expression objectives, and (3) direct spectral clustering on factorized representations. The framework combines convolutional auto-encoders with subspace-preserving constraints. Experimental results demonstrate that SDSNet achieves comparable clustering quality to state-of-the-art methods with significantly improved computational efficiency.", "date": "2025-12-24", "categories": []}
{"id": "2512.21516", "title": "Global-Graph Guided and Local-Graph Weighted Contrastive Learning for Unified Clustering on Incomplete and Noise Multi-View Data", "abstract": "Recently, contrastive learning (CL) plays an important role in exploring complementary information for multi-view clustering (MVC) and has attracted increasing attention. Nevertheless, real-world multi-view data suffer from data incompleteness or noise, resulting in rare-paired samples or mis-paired samples which significantly challenges the effectiveness of CL-based MVC. That is, rare-paired issue prevents MVC from extracting sufficient multi-view complementary information, and mis-paired issue causes contrastive learning to optimize the model in the wrong direction. To address these issues, we propose a unified CL-based MVC framework for enhancing clustering effectiveness on incomplete and noise multi-view data. First, to overcome the rare-paired issue, we design a global-graph guided contrastive learning, where all view samples construct a global-view affinity graph to form new sample pairs for fully exploring complementary information. Second, to mitigate the mis-paired issue, we propose a local-graph weighted contrastive learning, which leverages local neighbors to generate pair-wise weights to adaptively strength or weaken the pair-wise contrastive learning. Our method is imputation-free and can be integrated into a unified global-local graph-guided contrastive learning framework. Extensive experiments on both incomplete and noise settings of multi-view data demonstrate that our method achieves superior performance compared with state-of-the-art approaches.", "date": "2025-12-25", "categories": []}
{"id": "2512.21960", "title": "Modeling high dimensional point clouds with the spherical cluster model", "abstract": "A parametric cluster model is a statistical model providing geometric insights onto the points defining a cluster. The {\\em spherical cluster model} (SC) approximates a finite point set $P\\subset \\mathbb{R}^d$ by a sphere $S(c,r)$ as follows. Taking $r$ as a fraction $\\eta\\in(0,1)$ (hyper-parameter) of the std deviation of distances between the center $c$ and the data points, the cost of the SC model is the sum over all data points lying outside the sphere $S$ of their power distance with respect to $S$. The center $c$ of the SC model is the point minimizing this cost. Note that $\\eta=0$ yields the celebrated center of mass used in KMeans clustering. We make three contributions.\n  First, we show fitting a spherical cluster yields a strictly convex but not smooth combinatorial optimization problem. Second, we present an exact solver using the Clarke gradient on a suitable stratified cell complex defined from an arrangement of hyper-spheres. Finally, we present experiments on a variety of datasets ranging in dimension from $d=9$ to $d=10,000$, with two main observations. First, the exact algorithm is orders of magnitude faster than BFGS based heuristics for datasets of small/intermediate dimension and small values of $\\eta$, and for high dimensional datasets (say $d>100$) whatever the value of $\\eta$. Second, the center of the SC model behave as a parameterized high-dimensional median.\n  The SC model is of direct interest for high dimensional multivariate data analysis, and the application to the design of mixtures of SC will be reported in a companion paper.", "date": "2025-12-26", "categories": []}
{"id": "2402.02162", "title": "A Bayesian cluster validity index", "abstract": "Selecting the appropriate number of clusters is a critical step in applying clustering algorithms. To assist in this process, various cluster validity indices (CVIs) have been developed. These indices are designed to identify the optimal number of clusters within a dataset. However, users may not always seek the absolute optimal number of clusters but rather a secondary option that better aligns with their specific applications. This realization has led us to introduce a Bayesian cluster validity index (BCVI), which builds upon existing indices. The BCVI utilizes either Dirichlet or generalized Dirichlet priors, resulting in the same posterior distribution. We evaluate our BCVI using the Wiroonsri index for hard clustering and the Wiroonsri-Preedasawakul index for soft clustering as underlying indices. We compare the performance of our proposed BCVI with that of the original underlying indices and several other existing CVIs, including Davies-Bouldin, Starczewski, Xie-Beni, and KWON2 indices. Our BCVI offers clear advantages in situations where user expertise is valuable, allowing users to specify their desired range for the final number of clusters. To illustrate this, we conduct experiments classified into three different scenarios. Additionally, we showcase the practical applicability of our approach through real-world datasets, such as MRI brain tumor images. These tools will be published as a new R package 'BayesCVI'.", "date": "2024-02-03", "categories": []}
{"id": "2512.19772", "title": "A K-Means, Ward and DBSCAN repeatability study", "abstract": "Reproducibility is essential in machine learning because it ensures that a model or experiment yields the same scientific conclusion. For specific algorithms repeatability with bitwise identical results is also a key for scientific integrity because it allows debugging. We decomposed several very popular clustering algorithms: K-Means, DBSCAN and Ward into their fundamental steps, and we identify the conditions required to achieve repeatability at each stage. We use an implementation example with the Python library scikit-learn to examine the repeatable aspects of each method. Our results reveal inconsistent results with K-Means when the number of OpenMP threads exceeds two. This work aims to raise awareness of this issue among both users and developers, encouraging further investigation and potential fixes.", "date": "2025-12-22", "categories": []}
{"id": "2502.04226", "title": "Keep It Light! Simplifying Image Clustering Via Text-Free Adapters", "abstract": "In the era of pre-trained models, effective classification can often be achieved using simple linear probing or lightweight readout layers. In contrast, many competitive clustering pipelines have a multi-modal design, leveraging large language models (LLMs) or other text encoders, and text-image pairs, which are often unavailable in real-world downstream applications. Additionally, such frameworks are generally complicated to train and require substantial computational resources, making widespread adoption challenging. In this work, we show that in deep clustering, competitive performance with more complex state-of-the-art methods can be achieved using a text-free and highly simplified training pipeline. In particular, our approach, Simple Clustering via Pre-trained models (SCP), trains only a small cluster head while leveraging pre-trained vision model feature representations and positive data pairs. Experiments on benchmark datasets, including CIFAR-10, CIFAR-20, CIFAR-100, STL-10, ImageNet-10, and ImageNet-Dogs, demonstrate that SCP achieves highly competitive performance. Furthermore, we provide a theoretical result explaining why, at least under ideal conditions, additional text-based embeddings may not be necessary to achieve strong clustering performance in vision.", "date": "2025-02-06", "categories": []}
{"id": "2512.15396", "title": "SMART: Semantic Matching Contrastive Learning for Partially View-Aligned Clustering", "abstract": "Multi-view clustering has been empirically shown to improve learning performance by leveraging the inherent complementary information across multiple views of data. However, in real-world scenarios, collecting strictly aligned views is challenging, and learning from both aligned and unaligned data becomes a more practical solution. Partially View-aligned Clustering aims to learn correspondences between misaligned view samples to better exploit the potential consistency and complementarity across views, including both aligned and unaligned data. However, most existing PVC methods fail to leverage unaligned data to capture the shared semantics among samples from the same cluster. Moreover, the inherent heterogeneity of multi-view data induces distributional shifts in representations, leading to inaccuracies in establishing meaningful correspondences between cross-view latent features and, consequently, impairing learning effectiveness. To address these challenges, we propose a Semantic MAtching contRasTive learning model (SMART) for PVC. The main idea of our approach is to alleviate the influence of cross-view distributional shifts, thereby facilitating semantic matching contrastive learning to fully exploit semantic relationships in both aligned and unaligned data. Extensive experiments on eight benchmark datasets demonstrate that our method consistently outperforms existing approaches on the PVC problem.", "date": "2025-12-17", "categories": []}
{"id": "2512.19654", "title": "Clustering with Label Consistency", "abstract": "Designing efficient, effective, and consistent metric clustering algorithms is a significant challenge attracting growing attention. Traditional approaches focus on the stability of cluster centers; unfortunately, this neglects the real-world need for stable point labels, i.e., stable assignments of points to named sets (clusters). In this paper, we address this gap by initiating the study of label-consistent metric clustering. We first introduce a new notion of consistency, measuring the label distance between two consecutive solutions. Then, armed with this new definition, we design new consistent approximation algorithms for the classical $k$-center and $k$-median problems.", "date": "2025-12-22", "categories": []}
{"id": "2412.09832", "title": "Multivariate Time Series Clustering for Environmental State Characterization of Ground-Based Gravitational-Wave Detectors", "abstract": "Gravitational-wave observatories like LIGO are large-scale, terrestrial instruments housed in infrastructure that spans a multi-kilometer geographic area and which must be actively controlled to maintain operational stability for long observation periods. Despite exquisite seismic isolation, they remain susceptible to seismic noise and other terrestrial disturbances that can couple undesirable vibrations into the instrumental infrastructure, potentially leading to control instabilities or noise artifacts in the detector output. It is, therefore, critical to characterize the seismic state of these observatories to identify a set of temporal patterns that can inform the detector operators in day-to-day monitoring and diagnostics. On a day-to-day basis, the operators monitor several seismically relevant data streams to diagnose operational instabilities and sources of noise using some simple empirically-determined thresholds. It can be untenable for a human operator to monitor multiple data streams in this manual fashion and thus a distillation of these data-streams into a more human-friendly format is sought. In this paper, we present an end-to-end machine learning pipeline for features-based multivariate time series clustering to achieve this goal and to provide actionable insights to the detector operators by correlating found clusters with events of interest in the detector.", "date": "2024-12-13", "categories": []}
{"id": "2410.07858", "title": "From Logits to Hierarchies: Hierarchical Clustering made Simple", "abstract": "The hierarchical structure inherent in many real-world datasets makes the modeling of such hierarchies a crucial objective in both unsupervised and supervised machine learning. While recent advancements have introduced deep architectures specifically designed for hierarchical clustering, we adopt a critical perspective on this line of research. Our findings reveal that these methods face significant limitations in scalability and performance when applied to realistic datasets. Given these findings, we present an alternative approach and introduce a lightweight method that builds on pre-trained non-hierarchical clustering models. Remarkably, our approach outperforms specialized deep models for hierarchical clustering, and it is broadly applicable to any pre-trained clustering model that outputs logits, without requiring any fine-tuning. To highlight the generality of our approach, we extend its application to a supervised setting, demonstrating its ability to recover meaningful hierarchies from a pre-trained ImageNet classifier. Our results establish a practical and effective alternative to existing deep hierarchical clustering methods, with significant advantages in efficiency, scalability and performance.", "date": "2024-10-10", "categories": []}
{"id": "2512.00904", "title": "Hierarchical Semantic Alignment for Image Clustering", "abstract": "Image clustering is a classic problem in computer vision, which categorizes images into different groups. Recent studies utilize nouns as external semantic knowledge to improve clustering performance. However, these methods often overlook the inherent ambiguity of nouns, which can distort semantic representations and degrade clustering quality. To address this issue, we propose a hierarChical semAntic alignmEnt method for image clustering, dubbed CAE, which improves clustering performance in a training-free manner. In our approach, we incorporate two complementary types of textual semantics: caption-level descriptions, which convey fine-grained attributes of image content, and noun-level concepts, which represent high-level object categories. We first select relevant nouns from WordNet and descriptions from caption datasets to construct a semantic space aligned with image features. Then, we align image features with selected nouns and captions via optimal transport to obtain a more discriminative semantic space. Finally, we combine the enhanced semantic and image features to perform clustering. Extensive experiments across 8 datasets demonstrate the effectiveness of our method, notably surpassing the state-of-the-art training-free approach with a 4.2% improvement in accuracy and a 2.9% improvement in adjusted rand index (ARI) on the ImageNet-1K dataset.", "date": "2025-11-30", "categories": []}
{"id": "2512.15210", "title": "Label-consistent clustering for evolving data", "abstract": "Data analysis often involves an iterative process, where solutions must be continuously refined in response to new data. Typically, as new data becomes available, an existing solution must be updated to incorporate the latest information. In addition to seeking a high-quality solution for the task at hand, it is also crucial to ensure consistency by minimizing drastic changes from previous solutions. Applying this approach across many iterations, ensures that the solution evolves gradually and smoothly.\n  In this paper, we study the above problem in the context of clustering, specifically focusing on the $k$-center problem. More precisely, we study the following problem: Given a set of points $X$, parameters $k$ and $b$, and a prior clustering solution $H$ for $X$, our goal is to compute a new solution $C$ for $X$, consisting of $k$ centers, which minimizes the clustering cost while introducing at most $b$ changes from $H$. We refer to this problem as label-consistent $k$-center, and we propose two constant-factor approximation algorithms for it. We complement our theoretical findings with an experimental evaluation demonstrating the effectiveness of our methods on real-world datasets.", "date": "2025-12-17", "categories": []}
{"id": "2504.21808", "title": "Stable Trajectory Clustering: An Efficient Split and Merge Algorithm", "abstract": "Clustering algorithms fundamentally group data points by characteristics to identify patterns. Over the past two decades, researchers have extended these methods to analyze trajectories of humans, animals, and vehicles, studying their behavior and movement across applications. \\noindent This paper presents whole-trajectory clustering and sub-trajectory clustering algorithms based on DBSCAN line segment clustering, which encompasses two key events: split and merge of line segments. The events are utilized to capture object movement history based on the average Euclidean distance between line segments.\n  In this framework, whole-trajectory clustering considers entire entities' trajectories, whereas sub-trajectory clustering employs a sliding window model to identify local similarity patterns. Many existing trajectory clustering algorithms respond to temporary anomalies in data by splitting trajectories, which often obscures otherwise consistent clustering patterns and leads to less reliable insights. To address this, we introduce the stable trajectory clustering algorithm, which leverages the mean absolute deviation concept to demonstrate that selective omission of transient deviations not only preserves the integrity of clusters but also improves their stability and interpretability. We evaluate all proposed algorithms on real trajectory datasets to illustrate their effectiveness and sensitivity to parameter variations.", "date": "2025-04-30", "categories": []}
{"id": "2512.11448", "title": "Hyperbolic Gaussian Blurring Mean Shift: A Statistical Mode-Seeking Framework for Clustering in Curved Spaces", "abstract": "Clustering is a fundamental unsupervised learning task for uncovering patterns in data. While Gaussian Blurring Mean Shift (GBMS) has proven effective for identifying arbitrarily shaped clusters in Euclidean space, it struggles with datasets exhibiting hierarchical or tree-like structures. In this work, we introduce HypeGBMS, a novel extension of GBMS to hyperbolic space. Our method replaces Euclidean computations with hyperbolic distances and employs M\\\"obius-weighted means to ensure that all updates remain consistent with the geometry of the space. HypeGBMS effectively captures latent hierarchies while retaining the density-seeking behavior of GBMS. We provide theoretical insights into convergence and computational complexity, along with empirical results that demonstrate improved clustering quality in hierarchical datasets. This work bridges classical mean-shift clustering and hyperbolic representation learning, offering a principled approach to density-based clustering in curved spaces. Extensive experimental evaluations on $11$ real-world datasets demonstrate that HypeGBMS significantly outperforms conventional mean-shift clustering methods in non-Euclidean settings, underscoring its robustness and effectiveness.", "date": "2025-12-12", "categories": []}
{"id": "2412.00173", "title": "Enhanced Spatial Clustering of Single-Molecule Localizations with Graph Neural Networks", "abstract": "Single-molecule localization microscopy generates point clouds corresponding to fluorophore localizations. Spatial cluster identification and analysis of these point clouds are crucial for extracting insights about molecular organization. However, this task becomes challenging in the presence of localization noise, high point density, or complex biological structures. Here, we introduce MIRO (Multifunctional Integration through Relational Optimization), an algorithm that uses recurrent graph neural networks to transform the point clouds in order to improve clustering efficiency when applying conventional clustering techniques. We show that MIRO supports simultaneous processing of clusters of different shapes and at multiple scales, demonstrating improved performance across varied datasets. Our comprehensive evaluation demonstrates MIRO's transformative potential for single-molecule localization applications, showcasing its capability to revolutionize cluster analysis and provide accurate, reliable details of molecular architecture. In addition, MIRO's robust clustering capabilities hold promise for applications in various fields such as neuroscience, for the analysis of neural connectivity patterns, and environmental science, for studying spatial distributions of ecological data.", "date": "2024-11-29", "categories": []}
{"id": "2503.00127", "title": "Internal Evaluation of Density-Based Clusterings with Noise", "abstract": "Being able to evaluate the quality of a clustering result even in the absence of ground truth cluster labels is fundamental for research in data mining. However, most cluster validation indices (CVIs) do not capture noise assignments by density-based clustering methods like DBSCAN or HDBSCAN, even though the ability to correctly determine noise is crucial for successful clustering. In this paper, we propose DISCO, a Density-based Internal Score for Clusterings with nOise, the first CVI to explicitly assess the quality of noise assignments rather than merely counting them. DISCO is based on the established idea of the Silhouette Coefficient, but adopts density-connectivity to evaluate clusters of arbitrary shapes, and proposes explicit noise evaluation: it rewards correctly assigned noise labels and penalizes noise labels where a cluster label would have been more appropriate. The pointwise definition of DISCO allows for the seamless integration of noise evaluation into the final clustering evaluation, while also enabling explainable evaluations of the clustered data. In contrast to most state-of-the-art, DISCO is well-defined and also covers edge cases that regularly appear as output from clustering algorithms, such as singleton clusters or a single cluster plus noise.", "date": "2025-02-28", "categories": []}
{"id": "2402.03587", "title": "Information-Theoretic Active Correlation Clustering", "abstract": "Correlation clustering is a flexible framework for partitioning data based solely on pairwise similarity or dissimilarity information, without requiring the number of clusters as input. However, in many practical scenarios, these pairwise similarities are not available a priori and must be obtained through costly measurements or human feedback. This motivates the use of active learning to query only the most informative pairwise comparisons, enabling effective clustering under budget constraints. In this work, we develop a principled active learning approach for correlation clustering by introducing several information-theoretic acquisition functions that prioritize queries based on entropy and expected information gain. These strategies aim to reduce uncertainty about the clustering structure as efficiently as possible. We evaluate our methods across a range of synthetic and real-world settings and show that they significantly outperform existing baselines in terms of clustering accuracy and query efficiency. Our results highlight the benefits of combining active learning with correlation clustering in settings where similarity information is costly or limited.", "date": "2024-02-05", "categories": []}
{"id": "2506.23776", "title": "Model-driven Stochastic Trace Clustering", "abstract": "Process discovery algorithms automatically extract process models from event logs, but high variability often results in complex and hard-to-understand models. To mitigate this issue, trace clustering techniques group process executions into clusters, each represented by a simpler and more understandable process model. Model-driven trace clustering improves on this by assigning traces to clusters based on their conformity to cluster-specific process models. However, most existing clustering techniques rely on either no process model discovery, or non-stochastic models, neglecting the frequency or probability of activities and transitions, thereby limiting their capability to capture real-world execution dynamics. We propose a novel model-driven trace clustering method that optimizes stochastic process models within each cluster. Our approach uses entropic relevance, a stochastic conformance metric based on directly-follows probabilities, to guide trace assignment. This allows clustering decisions to consider both structural alignment with a cluster's process model and the likelihood that a trace originates from a given stochastic process model. The method is computationally efficient, scales linearly with input size, and improves model interpretability by producing clusters with clearer control-flow patterns. Extensive experiments on public real-life datasets demonstrate that while our method yields superior stochastic coherence and graph simplicity, traditional fitness metrics reveal a trade-off, highlighting the specific utility of our approach for stochastic process analysis.", "date": "2025-06-30", "categories": []}
{"id": "2512.00368", "title": "THCRL: Trusted Hierarchical Contrastive Representation Learning for Multi-View Clustering", "abstract": "Multi-View Clustering (MVC) has garnered increasing attention in recent years. It is capable of partitioning data samples into distinct groups by learning a consensus representation. However, a significant challenge remains: the problem of untrustworthy fusion. This problem primarily arises from two key factors: 1) Existing methods often ignore the presence of inherent noise within individual views; 2) In traditional MVC methods using Contrastive Learning (CL), similarity computations typically rely on different views of the same instance, while neglecting the structural information from nearest neighbors within the same cluster. Consequently, this leads to the wrong direction for multi-view fusion. To address this problem, we present a novel Trusted Hierarchical Contrastive Representation Learning (THCRL). It consists of two key modules. Specifically, we propose the Deep Symmetry Hierarchical Fusion (DSHF) module, which leverages the UNet architecture integrated with multiple denoising mechanisms to achieve trustworthy fusion of multi-view data. Furthermore, we present the Average K-Nearest Neighbors Contrastive Learning (AKCL) module to align the fused representation with the view-specific representation. Unlike conventional strategies, AKCL enhances representation similarity among samples belonging to the same cluster, rather than merely focusing on the same sample across views, thereby reinforcing the confidence of the fused representation. Extensive experiments demonstrate that THCRL achieves the state-of-the-art performance in deep MVC tasks.", "date": "2025-11-29", "categories": []}
{"id": "2512.09402", "title": "Wasserstein-Aligned Hyperbolic Multi-View Clustering", "abstract": "Multi-view clustering (MVC) aims to uncover the latent structure of multi-view data by learning view-common and view-specific information. Although recent studies have explored hyperbolic representations for better tackling the representation gap between different views, they focus primarily on instance-level alignment and neglect global semantic consistency, rendering them vulnerable to view-specific information (\\textit{e.g.}, noise and cross-view discrepancies). To this end, this paper proposes a novel Wasserstein-Aligned Hyperbolic (WAH) framework for multi-view clustering. Specifically, our method exploits a view-specific hyperbolic encoder for each view to embed features into the Lorentz manifold for hierarchical semantic modeling. Whereafter, a global semantic loss based on the hyperbolic sliced-Wasserstein distance is introduced to align manifold distributions across views. This is followed by soft cluster assignments to encourage cross-view semantic consistency. Extensive experiments on multiple benchmarking datasets show that our method can achieve SOTA clustering performance.", "date": "2025-12-10", "categories": []}
{"id": "2512.06211", "title": "A Broader View on Clustering under Cluster-Aware Norm Objectives", "abstract": "We revisit the $(f,g)$-clustering problem that we introduced in a recent work [SODA'25], and which subsumes fundamental clustering problems such as $k$-Center, $k$-Median, Min-Sum of Radii, and Min-Load $k$-Clustering. This problem assigns each of the $k$ clusters a cost determined by the monotone, symmetric norm $f$ applied to the vector distances in the cluster, and aims at minimizing the norm $g$ applied to the vector of cluster costs. Previously, we focused on certain special cases for which we designed constant-factor approximation algorithms. Our bounds for more general settings left, however, large gaps to the known bounds for the basic problems they capture.\n  In this work, we provide a clearer picture of the approximability of these more general settings. First, we design an $O(\\log^2 n)$-approximation algorithm for $(f, L_{1})$-clustering for any $f$. This improves upon our previous $\\widetilde{O}(\\sqrt{n})$-approximation. Second, we provide an $O(k)$-approximation for the general $(f,g)$-clustering problem, which improves upon our previous $\\widetilde{O}(\\sqrt{kn})$-approximation algorithm and matches the best-known upper bound for Min-Load $k$-Clustering.\n  We then design an approximation algorithm for $(f,g)$-clustering that interpolates, up to polylog factors, between the best known bounds for $k$-Center, $k$-Median, Min-Sum of Radii, Min-Load $k$-Clustering, (Top, $L_{1}$)-clustering, and $(L_{\\infty},g)$-clustering based on a newly defined parameter of $f$ and $g$.", "date": "2025-12-05", "categories": []}
{"id": "2512.07879", "title": "Nonnegative Matrix Factorization through Cone Collapse", "abstract": "Nonnegative matrix factorization (NMF) is a widely used tool for learning parts-based, low-dimensional representations of nonnegative data, with applications in vision, text, and bioinformatics. In clustering applications, orthogonal NMF (ONMF) variants further impose (approximate) orthogonality on the representation matrix so that its rows behave like soft cluster indicators. Existing algorithms, however, are typically derived from optimization viewpoints and do not explicitly exploit the conic geometry induced by NMF: data points lie in a convex cone whose extreme rays encode fundamental directions or \"topics\". In this work we revisit NMF from this geometric perspective and propose Cone Collapse, an algorithm that starts from the full nonnegative orthant and iteratively shrinks it toward the minimal cone generated by the data. We prove that, under mild assumptions on the data, Cone Collapse terminates in finitely many steps and recovers the minimal generating cone of $\\mathbf{X}^\\top$ . Building on this basis, we then derive a cone-aware orthogonal NMF model (CC-NMF) by applying uni-orthogonal NMF to the recovered extreme rays. Across 16 benchmark gene-expression, text, and image datasets, CC-NMF consistently matches or outperforms strong NMF baselines-including multiplicative updates, ANLS, projective NMF, ONMF, and sparse NMF-in terms of clustering purity. These results demonstrate that explicitly recovering the data cone can yield both theoretically grounded and empirically strong NMF-based clustering methods.", "date": "2025-11-27", "categories": []}
{"id": "2511.17008", "title": "Mask the Redundancy: Evolving Masking Representation Learning for Multivariate Time-Series Clustering", "abstract": "Multivariate Time-Series (MTS) clustering discovers intrinsic grouping patterns of temporal data samples. Although time-series provide rich discriminative information, they also contain substantial redundancy, such as steady-state machine operation records and zero-output periods of solar power generation. Such redundancy diminishes the attention given to discriminative timestamps in representation learning, thus leading to performance bottlenecks in MTS clustering. Masking has been widely adopted to enhance the MTS representation, where temporal reconstruction tasks are designed to capture critical information from MTS. However, most existing masking strategies appear to be standalone preprocessing steps, isolated from the learning process, which hinders dynamic adaptation to the importance of clustering-critical timestamps. Accordingly, this paper proposes the Evolving-masked MTS Clustering (EMTC) method, whose model architecture comprises Importance-aware Variate-wise Masking (IVM) and Multi-Endogenous Views (MEV) generation modules. IVM adaptively guides the model in learning more discriminative representations for clustering, while the reconstruction and cluster-guided contrastive learning pathways enhance and connect the representation learning to clustering tasks. Extensive experiments on 15 benchmark datasets demonstrate the superiority of EMTC over eight SOTA methods, where the EMTC achieves an average improvement of 4.85% in F1-Score over the strongest baselines.", "date": "2025-11-21", "categories": []}
{"id": "2511.17983", "title": "An Adaptive Resonance Theory-based Topological Clustering Algorithm with a Self-Adjusting Vigilance Parameter", "abstract": "Clustering in stationary and nonstationary settings, where data distributions remain static or evolve over time, requires models that can adapt to distributional shifts while preserving previously learned cluster structures. This paper proposes an Adaptive Resonance Theory (ART)-based topological clustering algorithm that autonomously adjusts its recalculation interval and vigilance threshold through a diversity-driven adaptation mechanism. This mechanism enables hyperparameter-free learning that maintains cluster stability and continuity in dynamic environments. Experiments on 24 real-world datasets demonstrate that the proposed algorithm outperforms state-of-the-art methods in both clustering performance and continual learning capability. These results highlight the effectiveness of the proposed parameter adaptation in mitigating catastrophic forgetting and maintaining consistent clustering in evolving data streams. Source code is available at https://github.com/Masuyama-lab/IDAT", "date": "2025-11-22", "categories": []}
{"id": "2512.05169", "title": "Advanced Unsupervised Learning: A Comprehensive Overview of Multi-View Clustering Techniques", "abstract": "Machine learning techniques face numerous challenges to achieve optimal performance. These include computational constraints, the limitations of single-view learning algorithms and the complexity of processing large datasets from different domains, sources or views. In this context, multi-view clustering (MVC), a class of unsupervised multi-view learning, emerges as a powerful approach to overcome these challenges. MVC compensates for the shortcomings of single-view methods and provides a richer data representation and effective solutions for a variety of unsupervised learning tasks. In contrast to traditional single-view approaches, the semantically rich nature of multi-view data increases its practical utility despite its inherent complexity. This survey makes a threefold contribution: (1) a systematic categorization of multi-view clustering methods into well-defined groups, including co-training, co-regularization, subspace, deep learning, kernel-based, anchor-based, and graph-based strategies; (2) an in-depth analysis of their respective strengths, weaknesses, and practical challenges, such as scalability and incomplete data; and (3) a forward-looking discussion of emerging trends, interdisciplinary applications, and future directions in MVC research. This study represents an extensive workload, encompassing the review of over 140 foundational and recent publications, the development of comparative insights on integration strategies such as early fusion, late fusion, and joint learning, and the structured investigation of practical use cases in the areas of healthcare, multimedia, and social network analysis. By integrating these efforts, this work aims to fill existing gaps in MVC research and provide actionable insights for the advancement of the field.", "date": "2025-12-04", "categories": []}
{"id": "2512.05926", "title": "BalLOT: Balanced $k$-means clustering with optimal transport", "abstract": "We consider the fundamental problem of balanced $k$-means clustering. In particular, we introduce an optimal transport approach to alternating minimization called BalLOT, and we show that it delivers a fast and effective solution to this problem. We establish this with a variety of numerical experiments before proving several theoretical guarantees. First, we prove that for generic data, BalLOT produces integral couplings at each step. Next, we perform a landscape analysis to provide theoretical guarantees for both exact and partial recoveries of planted clusters under the stochastic ball model. Finally, we propose initialization schemes that achieve one-step recovery of planted clusters.", "date": "2025-12-05", "categories": []}
{"id": "2501.13820", "title": "Consistent spectral clustering in sparse tensor block models", "abstract": "High-order clustering aims to classify objects in multiway datasets that are prevalent in various fields such as bioinformatics, recommendation systems, and social network analysis. Such data are often sparse and high-dimensional, posing significant statistical and computational challenges. This paper introduces a tensor block model specifically designed for sparse integer-valued data tensors. We propose a simple spectral clustering algorithm augmented with a trimming step to mitigate noise fluctuations, and identify a density threshold that ensures the algorithm's consistency. Our approach models sparsity using a sub-Poisson noise concentration framework, accommodating heavier than sub-Gaussian tails. Remarkably, this natural class of tensor block models is closed under aggregation across arbitrary modes. Consequently, we obtain a comprehensive framework for evaluating the tradeoff between signal loss and noise reduction incurred by aggregating data. The analysis is based on a novel concentration bound for sparse random Gram matrices. The theoretical findings are illustrated through numerical experiments.", "date": "2025-01-23", "categories": []}
{"id": "2512.04350", "title": "ClusterFusion: Hybrid Clustering with Embedding Guidance and LLM Adaptation", "abstract": "Text clustering is a fundamental task in natural language processing, yet traditional clustering algorithms with pre-trained embeddings often struggle in domain-specific contexts without costly fine-tuning. Large language models (LLMs) provide strong contextual reasoning, yet prior work mainly uses them as auxiliary modules to refine embeddings or adjust cluster boundaries. We propose ClusterFusion, a hybrid framework that instead treats the LLM as the clustering core, guided by lightweight embedding methods. The framework proceeds in three stages: embedding-guided subset partition, LLM-driven topic summarization, and LLM-based topic assignment. This design enables direct incorporation of domain knowledge and user preferences, fully leveraging the contextual adaptability of LLMs. Experiments on three public benchmarks and two new domain-specific datasets demonstrate that ClusterFusion not only achieves state-of-the-art performance on standard tasks but also delivers substantial gains in specialized domains. To support future work, we release our newly constructed dataset and results on all benchmarks.", "date": "2025-12-04", "categories": []}
{"id": "2507.08243", "title": "CoreSPECT: Enhancing Clustering Algorithms via an Interplay of Density and Geometry", "abstract": "In this paper, we provide a novel perspective on the underlying structure of real-world data with ground-truth clusters via characterization of an abundantly observed yet often overlooked density-geometry correlation, that manifests itself as a multi-layered manifold structure.\n  We leverage this correlation to design CoreSPECT (Core Space Projection based Enhancement of Clustering Techniques), a general framework that improves the performance of generic clustering algorithms. Our framework boosts the performance of clustering algorithms by applying them to strategically selected regions, then extending the partial partition to a complete partition for the dataset using a novel neighborhood graph based multi-layer propagation procedure.\n  We provide initial theoretical support of the functionality of our framework under the assumption of our model, and then provide large-scale real-world experiments on 19 datasets that include standard image datasets as well as genomics datasets.\n  We observe two notable improvements. First, CoreSPECT improves the NMI of K-Means by 20% on average, making it competitive to (and in some cases surpassing) the state-of-the-art manifold-based clustering algorithms, while being orders of magnitude faster.\n  Secondly, our framework boosts the NMI of HDBSCAN by more than 100% on average, making it competitive to the state-of-the-art in several cases without requiring the true number of clusters and hyper-parameter tuning. The overall ARI improvements are higher.", "date": "2025-07-11", "categories": []}
{"id": "2512.03069", "title": "Hierarchical clustering of complex energy systems using pretopology", "abstract": "This article attempts answering the following problematic: How to model and classify energy consumption profiles over a large distributed territory to optimize the management of buildings' consumption?\n  Doing case-by-case in depth auditing of thousands of buildings would require a massive amount of time and money as well as a significant number of qualified people. Thus, an automated method must be developed to establish a relevant and effective recommendations system.\n  To answer this problematic, pretopology is used to model the sites' consumption profiles and a multi-criterion hierarchical classification algorithm, using the properties of pretopological space, has been developed in a Python library.\n  To evaluate the results, three data sets are used: A generated set of dots of various sizes in a 2D space, a generated set of time series and a set of consumption time series of 400 real consumption sites from a French Energy company.\n  On the point data set, the algorithm is able to identify the clusters of points using their position in space and their size as parameter. On the generated time series, the algorithm is able to identify the time series clusters using Pearson's correlation with an Adjusted Rand Index (ARI) of 1.", "date": "2025-11-27", "categories": []}
{"id": "2512.03070", "title": "Mixed Data Clustering Survey and Challenges", "abstract": "The advent of the big data paradigm has transformed how industries manage and analyze information, ushering in an era of unprecedented data volume, velocity, and variety. Within this landscape, mixed-data clustering has become a critical challenge, requiring innovative methods that can effectively exploit heterogeneous data types, including numerical and categorical variables. Traditional clustering techniques, typically designed for homogeneous datasets, often struggle to capture the additional complexity introduced by mixed data, underscoring the need for approaches specifically tailored to this setting. Hierarchical and explainable algorithms are particularly valuable in this context, as they provide structured, interpretable clustering results that support informed decision-making. This paper introduces a clustering method grounded in pretopological spaces. In addition, benchmarking against classical numerical clustering algorithms and existing pretopological approaches yields insights into the performance and effectiveness of the proposed method within the big data paradigm.", "date": "2025-11-27", "categories": []}
{"id": "2512.03071", "title": "PretopoMD: Pretopology-based Mixed Data Hierarchical Clustering", "abstract": "This article presents a novel pretopology-based algorithm designed to address the challenges of clustering mixed data without the need for dimensionality reduction. Leveraging Disjunctive Normal Form, our approach formulates customizable logical rules and adjustable hyperparameters that allow for user-defined hierarchical cluster construction and facilitate tailored solutions for heterogeneous datasets. Through hierarchical dendrogram analysis and comparative clustering metrics, our method demonstrates superior performance by accurately and interpretably delineating clusters directly from raw data, thus preserving data integrity. Empirical findings highlight the algorithm's robustness in constructing meaningful clusters and reveal its potential in overcoming issues related to clustered data explainability. The novelty of this work lies in its departure from traditional dimensionality reduction techniques and its innovative use of logical rules that enhance both cluster formation and clarity, thereby contributing a significant advancement to the discourse on clustering mixed data.", "date": "2025-11-27", "categories": []}
{"id": "2512.03718", "title": "Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity", "abstract": "We study the computational problem of computing a fair means clustering of discrete vectors, which admits an equivalent formulation as editing a colored matrix into one with few distinct color-balanced rows by changing at most $k$ values. While NP-hard in both the fairness-oblivious and the fair settings, the problem is well-known to admit a fixed-parameter algorithm in the former ``vanilla'' setting. As our first contribution, we exclude an analogous algorithm even for highly restricted fair means clustering instances. We then proceed to obtain a full complexity landscape of the problem, and establish tractability results which capture three means of circumventing our obtained lower bound: placing additional constraints on the problem instances, fixed-parameter approximation, or using an alternative parameterization targeting tree-like matrices.", "date": "2025-12-03", "categories": []}
{"id": "2512.02471", "title": "scCluBench: Comprehensive Benchmarking of Clustering Algorithms for Single-Cell RNA Sequencing", "abstract": "Cell clustering is crucial for uncovering cellular heterogeneity in single-cell RNA sequencing (scRNA-seq) data by identifying cell types and marker genes. Despite its importance, benchmarks for scRNA-seq clustering methods remain fragmented, often lacking standardized protocols and failing to incorporate recent advances in artificial intelligence. To fill these gaps, we present scCluBench, a comprehensive benchmark of clustering algorithms for scRNA-seq data. First, scCluBench provides 36 scRNA-seq datasets collected from diverse public sources, covering multiple tissues, which are uniformly processed and standardized to ensure consistency for systematic evaluation and downstream analyses. To evaluate performance, we collect and reproduce a range of scRNA-seq clustering methods, including traditional, deep learning-based, graph-based, and biological foundation models. We comprehensively evaluate each method both quantitatively and qualitatively, using core performance metrics as well as visualization analyses. Furthermore, we construct representative downstream biological tasks, such as marker gene identification and cell type annotation, to further assess the practical utility. scCluBench then investigates the performance differences and applicability boundaries of various clustering models across diverse analytical tasks, systematically assessing their robustness and scalability in real-world scenarios. Overall, scCluBench offers a standardized and user-friendly benchmark for scRNA-seq clustering, with curated datasets, unified evaluation protocols, and transparent analyses, facilitating informed method selection and providing valuable insights into model generalizability and application scope.", "date": "2025-12-02", "categories": []}
{"id": "2403.04322", "title": "Memetic Differential Evolution Methods for Semi-Supervised Clustering", "abstract": "In this paper, we propose an extension for semi-supervised Minimum Sum-of-Squares Clustering (MSSC) problems of MDEClust, a memetic framework based on the Differential Evolution paradigm for unsupervised clustering. In semi-supervised MSSC, background knowledge is available in the form of (instance-level) \"must-link\" and \"cannot-link\" constraints, each of which indicating if two dataset points should be associated to the same or to a different cluster, respectively. The presence of such constraints makes the problem at least as hard as its unsupervised version and, as a consequence, some framework operations need to be carefully designed to handle this additional complexity: for instance, it is no more true that each point is associated to its nearest cluster center. As far as we know, our new framework, called S-MDEClust, represents the first memetic methodology designed to generate a (hopefully) optimal feasible solution for semi-supervised MSSC problems. Results of thorough computational experiments on a set of well-known as well as synthetic datasets show the effectiveness and efficiency of our proposal.", "date": "2024-03-07", "categories": []}
{"id": "2509.15844", "title": "FedHK-MVFC: Federated Heat Kernel Multi-View Clustering", "abstract": "In the realm of distributed artificial intelligence (AI) and privacy-focused medical applications, this paper proposes a multi-view clustering framework that links quantum field theory with federated healthcare analytics. The method uses heat kernel coefficients from spectral analysis to convert Euclidean distances into geometry-aware similarity measures that capture the structure of diverse medical data. The framework is presented through the heat kernel distance (HKD) transformation, which has convergence guarantees. Two algorithms have been developed: The first, Heat Kernel-Enhanced Multi-View Fuzzy Clustering (HK-MVFC), is used for central analysis. The second, Federated Heat Kernel Multi-View Fuzzy Clustering (FedHK-MVFC), is used for secure, privacy-preserving learning across hospitals. FedHK-MVFC uses differential privacy and secure aggregation to enable HIPAA-compliant collaboration. Tests on synthetic cardiovascular patient datasets demonstrate increased clustering accuracy, reduced communication, and retained efficiency compared to centralized methods. After being validated on 10,000 synthetic patient records across two hospitals, the methods proved useful for collaborative phenotyping involving electrocardiogram (ECG) data, cardiac imaging data, and behavioral data. The proposed methods' theoretical contributions include update rules with proven convergence, adaptive view weighting, and privacy-preserving protocols. These contributions establish a new standard for geometry-aware federated learning in healthcare, translating advanced mathematics into practical solutions for analyzing sensitive medical data while ensuring rigor and clinical relevance.", "date": "2025-09-19", "categories": []}
{"id": "2512.00524", "title": "Hyperbolic Continuous Structural Entropy for Hierarchical Clustering", "abstract": "Hierarchical clustering is a fundamental machine-learning technique for grouping data points into dendrograms. However, existing hierarchical clustering methods encounter two primary challenges: 1) Most methods specify dendrograms without a global objective. 2) Graph-based methods often neglect the significance of graph structure, optimizing objectives on complete or static predefined graphs. In this work, we propose Hyperbolic Continuous Structural Entropy neural networks, namely HypCSE, for structure-enhanced continuous hierarchical clustering. Our key idea is to map data points in the hyperbolic space and minimize the relaxed continuous structural entropy (SE) on structure-enhanced graphs. Specifically, we encode graph vertices in hyperbolic space using hyperbolic graph neural networks and minimize approximate SE defined on graph embeddings. To make the SE objective differentiable for optimization, we reformulate it into a function using the lowest common ancestor (LCA) on trees and then relax it into continuous SE (CSE) by the analogy of hyperbolic graph embeddings and partitioning trees. To ensure a graph structure that effectively captures the hierarchy of data points for CSE calculation, we employ a graph structure learning (GSL) strategy that updates the graph structure during training. Extensive experiments on seven datasets demonstrate the superior performance of HypCSE.", "date": "2025-11-29", "categories": []}
{"id": "2512.00725", "title": "ESMC: MLLM-Based Embedding Selection for Explainable Multiple Clustering", "abstract": "Typical deep clustering methods, while achieving notable progress, can only provide one clustering result per dataset. This limitation arises from their assumption of a fixed underlying data distribution, which may fail to meet user needs and provide unsatisfactory clustering outcomes. Our work investigates how multi-modal large language models (MLLMs) can be leveraged to achieve user-driven clustering, emphasizing their adaptability to user-specified semantic requirements. However, directly using MLLM output for clustering has risks for producing unstructured and generic image descriptions instead of feature-specific and concrete ones. To address these issues, our method first discovers that MLLMs' hidden states of text tokens are strongly related to the corresponding features, and leverages these embeddings to perform clusterings from any user-defined criteria. We also employ a lightweight clustering head augmented with pseudo-label learning, significantly enhancing clustering accuracy. Extensive experiments demonstrate its competitive performance on diverse datasets and metrics.", "date": "2025-11-30", "categories": []}
{"id": "2512.00849", "title": "Topological Federated Clustering via Gravitational Potential Fields under Local Differential Privacy", "abstract": "Clustering non-independent and identically distributed (non-IID) data under local differential privacy (LDP) in federated settings presents a critical challenge: preserving privacy while maintaining accuracy without iterative communication. Existing one-shot methods rely on unstable pairwise centroid distances or neighborhood rankings, degrading severely under strong LDP noise and data heterogeneity. We present Gravitational Federated Clustering (GFC), a novel approach to privacy-preserving federated clustering that overcomes the limitations of distance-based methods under varying LDP. Addressing the critical challenge of clustering non-IID data with diverse privacy guarantees, GFC transforms privatized client centroids into a global gravitational potential field where true cluster centers emerge as topologically persistent singularities. Our framework introduces two key innovations: (1) a client-side compactness-aware perturbation mechanism that encodes local cluster geometry as \"mass\" values, and (2) a server-side topological aggregation phase that extracts stable centroids through persistent homology analysis of the potential field's superlevel sets. Theoretically, we establish a closed-form bound between the privacy budget $\\epsilon$ and centroid estimation error, proving the potential field's Lipschitz smoothing properties exponentially suppress noise in high-density regions. Empirically, GFC outperforms state-of-the-art methods on ten benchmarks, especially under strong LDP constraints ($\\epsilon < 1$), while maintaining comparable performance at lower privacy budgets. By reformulating federated clustering as a topological persistence problem in a synthetic physics-inspired space, GFC achieves unprecedented privacy-accuracy trade-offs without iterative communication, providing a new perspective for privacy-preserving distributed learning.", "date": "2025-11-30", "categories": []}
{"id": "2512.00979", "title": "An Approach to Variable Clustering: K-means in Transposed Data and its Relationship with Principal Component Analysis", "abstract": "Principal Component Analysis (PCA) and K-means constitute fundamental techniques in multivariate analysis. Although they are frequently applied independently or sequentially to cluster observations, the relationship between them, especially when K-means is used to cluster variables rather than observations, has been scarcely explored. This study seeks to address this gap by proposing an innovative method that analyzes the relationship between clusters of variables obtained by applying K-means on transposed data and the principal components of PCA. Our approach involves applying PCA to the original data and K-means to the transposed data set, where the original variables are converted into observations. The contribution of each variable cluster to each principal component is then quantified using measures based on variable loadings. This process provides a tool to explore and understand the clustering of variables and how such clusters contribute to the principal dimensions of variation identified by PCA.", "date": "2025-11-30", "categories": []}
{"id": "2512.01150", "title": "Dynamic Algorithm for Explainable k-medians Clustering under lp Norm", "abstract": "We study the problem of explainable k-medians clustering introduced by Dasgupta, Frost, Moshkovitz, and Rashtchian (2020). In this problem, the goal is to construct a threshold decision tree that partitions data into k clusters while minimizing the k-medians objective. These trees are interpretable because each internal node makes a simple decision by thresholding a single feature, allowing users to trace and understand how each point is assigned to a cluster. We present the first algorithm for explainable k-medians under lp norm for every finite p >= 1. Our algorithm achieves an O(p(log k)^{1 + 1/p - 1/p^2}) approximation to the optimal k-medians cost for any p >= 1. Previously, algorithms were known only for p = 1 and p = 2. For p = 2, our algorithm improves upon the existing bound of O(log^{3/2}k), and for p = 1, it matches the tight bound of log k + O(1) up to a multiplicative O(log log k) factor. We show how to implement our algorithm in a dynamic setting. The dynamic algorithm maintains an explainable clustering under a sequence of insertions and deletions, with amortized update time O(d log^3 k) and O(log k) recourse, making it suitable for large-scale and evolving datasets.", "date": "2025-12-01", "categories": []}
{"id": "2503.07995", "title": "Almost Linear Time Consistent Mode Estimation and Quick Shift Clustering", "abstract": "In this paper, we propose a method for density-based clustering in high-dimensional spaces that combines Locality-Sensitive Hashing (LSH) with the Quick Shift algorithm. The Quick Shift algorithm, known for its hierarchical clustering capabilities, is extended by integrating approximate Kernel Density Estimation (KDE) using LSH to provide efficient density estimates. The proposed approach achieves almost linear time complexity while preserving the consistency of density-based clustering.", "date": "2025-03-11", "categories": []}
{"id": "2506.18396", "title": "ADNF-Clustering: An Adaptive and Dynamic Neuro-Fuzzy Clustering for Leukemia Prediction", "abstract": "Leukemia diagnosis and monitoring rely increasingly on high-throughput image data, yet conventional clustering methods lack the flexibility to accommodate evolving cellular patterns and quantify uncertainty in real time. We introduce Adaptive and Dynamic Neuro-Fuzzy Clustering, a novel streaming-capable framework that combines Convolutional Neural Network-based feature extraction with an online fuzzy clustering engine. ADNF initializes soft partitions via Fuzzy C-Means, then continuously updates micro-cluster centers, densities, and fuzziness parameters using a Fuzzy Temporal Index (FTI) that measures entropy evolution. A topology refinement stage performs density-weighted merging and entropy-guided splitting to guard against over- and under-segmentation. On the C-NMC leukemia microscopy dataset, our tool achieves a silhouette score of 0.51, demonstrating superior cohesion and separation over static baselines. The method's adaptive uncertainty modeling and label-free operation hold immediate potential for integration within the INFANT pediatric oncology network, enabling scalable, up-to-date support for personalized leukemia management.", "date": "2025-06-23", "categories": []}
{"id": "2508.17150", "title": "SACA: Selective Attention-Based Clustering Algorithm", "abstract": "Clustering algorithms are fundamental tools across many fields, with density-based methods offering particular advantages in identifying arbitrarily shaped clusters and handling noise. However, their effectiveness is often limited by the requirement of critical parameter tuning by users, which typically requires significant domain expertise. This paper introduces a novel density-based clustering algorithm loosely inspired by the concept of selective attention, designed to minimize reliance on parameter tuning for most applications. The proposed method computes an adaptive threshold to exclude sparsely distributed points and outliers, constructs an initial cluster framework, and subsequently reintegrates the filtered points to refine the final results. Extensive experiments on diverse benchmark datasets demonstrate the robustness, accuracy, and ease of use of the proposed approach, establishing it as a powerful alternative to conventional density-based clustering techniques.", "date": "2025-08-23", "categories": []}
{"id": "2511.23261", "title": "An Improved and Generalised Analysis for Spectral Clustering", "abstract": "We revisit the theoretical performances of Spectral Clustering, a classical algorithm for graph partitioning that relies on the eigenvectors of a matrix representation of the graph. Informally, we show that Spectral Clustering works well as long as the smallest eigenvalues appear in groups well separated from the rest of the matrix representation's spectrum. This arises, for example, whenever there exists a hierarchy of clusters at different scales, a regime not captured by previous analyses. Our results are very general and can be applied beyond the traditional graph Laplacian. In particular, we study Hermitian representations of digraphs and show Spectral Clustering can recover partitions where edges between clusters are oriented mostly in the same direction. This has applications in, for example, the analysis of trophic levels in ecological networks. We demonstrate that our results accurately predict the performances of Spectral Clustering on synthetic and real-world data sets.", "date": "2025-11-28", "categories": []}
{"id": "2511.21193", "title": "You Can Trust Your Clustering Model: A Parameter-free Self-Boosting Plug-in for Deep Clustering", "abstract": "Recent deep clustering models have produced impressive clustering performance. However, a common issue with existing methods is the disparity between global and local feature structures. While local structures typically show strong consistency and compactness within class samples, global features often present intertwined boundaries and poorly separated clusters. Motivated by this observation, we propose DCBoost, a parameter-free plug-in designed to enhance the global feature structures of current deep clustering models. By harnessing reliable local structural cues, our method aims to elevate clustering performance effectively. Specifically, we first identify high-confidence samples through adaptive $k$-nearest neighbors-based consistency filtering, aiming to select a sufficient number of samples with high label reliability to serve as trustworthy anchors for self-supervision. Subsequently, these samples are utilized to compute a discriminative loss, which promotes both intra-class compactness and inter-class separability, to guide network optimization. Extensive experiments across various benchmark datasets showcase that our DCBoost significantly improves the clustering performance of diverse existing deep clustering models. Notably, our method improves the performance of current state-of-the-art baselines (e.g., ProPos) by more than 3% and amplifies the silhouette coefficient by over $7\\times$. Code is available at <https://github.com/l-h-y168/DCBoost>.", "date": "2025-11-26", "categories": []}
{"id": "2511.19350", "title": "Scalable Parameter-Light Spectral Method for Clustering Short Text Embeddings with a Cohesion-Based Evaluation Metric", "abstract": "Clustering short text embeddings is a foundational task in natural language processing, yet remains challenging due to the need to specify the number of clusters in advance. We introduce a scalable spectral method that estimates the number of clusters directly from the structure of the Laplacian eigenspectrum, constructed using cosine similarities and guided by an adaptive sampling strategy. This sampling approach enables our estimator to efficiently scale to large datasets without sacrificing reliability. To support intrinsic evaluation of cluster quality without ground-truth labels, we propose the Cohesion Ratio, a simple and interpretable evaluation metric that quantifies how much intra-cluster similarity exceeds the global similarity background. It has an information-theoretic motivation inspired by mutual information, and in our experiments it correlates closely with extrinsic measures such as normalized mutual information and homogeneity. Extensive experiments on six short-text datasets and four modern embedding models show that standard algorithms like K-Means and HAC, when guided by our estimator, significantly outperform popular parameter-light methods such as HDBSCAN, OPTICS, and Leiden. These results demonstrate the practical value of our spectral estimator and Cohesion Ratio for unsupervised organization and evaluation of short text data. Implementation of our estimator of k and Cohesion Ratio, along with code for reproducing the experiments, is available at https://anonymous.4open.science/r/towards_clustering-0C2E.", "date": "2025-11-24", "categories": []}
{"id": "2511.19755", "title": "Clustering Approaches for Mixed-Type Data: A Comparative Study", "abstract": "Clustering is widely used in unsupervised learning to find homogeneous groups of observations within a dataset. However, clustering mixed-type data remains a challenge, as few existing approaches are suited for this task. This study presents the state-of-the-art of these approaches and compares them using various simulation models. The compared methods include the distance-based approaches k-prototypes, PDQ, and convex k-means, and the probabilistic methods KAy-means for MIxed LArge data (KAMILA), the mixture of Bayesian networks (MBNs), and latent class model (LCM). The aim is to provide insights into the behavior of different methods across a wide range of scenarios by varying some experimental factors such as the number of clusters, cluster overlap, sample size, dimension, proportion of continuous variables in the dataset, and clusters' distribution. The degree of cluster overlap and the proportion of continuous variables in the dataset and the sample size have a significant impact on the observed performances. When strong interactions exist between variables alongside an explicit dependence on cluster membership, none of the evaluated methods demonstrated satisfactory performance. In our experiments KAMILA, LCM, and k-prototypes exhibited the best performance, with respect to the adjusted rand index (ARI). All the methods are available in R.", "date": "2025-11-24", "categories": []}
{"id": "2511.20030", "title": "Cross-Contrastive Clustering for Multimodal Attributed Graphs with Dual Graph Filtering", "abstract": "Multimodal Attributed Graphs (MMAGs) are an expressive data model for representing the complex interconnections among entities that associate attributes from multiple data modalities (text, images, etc.). Clustering over such data finds numerous practical applications in real scenarios, including social community detection, medical data analytics, etc. However, as revealed by our empirical studies, existing multi-view clustering solutions largely rely on the high correlation between attributes across various views and overlook the unique characteristics (e.g., low modality-wise correlation and intense feature-wise noise) of multimodal attributes output by large pre-trained language and vision models in MMAGs, leading to suboptimal clustering performance.\n  Inspired by foregoing empirical observations and our theoretical analyses with graph signal processing, we propose the Dual Graph Filtering (DGF) scheme, which innovatively incorporates a feature-wise denoising component into node representation learning, thereby effectively overcoming the limitations of traditional graph filters adopted in the extant multi-view graph clustering approaches. On top of that, DGF includes a tri-cross contrastive training strategy that employs instance-level contrastive learning across modalities, neighborhoods, and communities for learning robust and discriminative node representations. Our comprehensive experiments on eight benchmark MMAG datasets exhibit that DGF is able to outperform a wide range of state-of-the-art baselines consistently and significantly in terms of clustering quality measured against ground-truth labels.", "date": "2025-11-25", "categories": []}
{"id": "2303.08582", "title": "High-dimensional multi-view clustering methods", "abstract": "Multi-view clustering has been widely used in recent years in comparison to single-view clustering, for clear reasons, as it offers more insights into the data, which has brought with it some challenges, such as how to combine these views or features. Most of recent work in this field focuses mainly on tensor representation instead of treating the data as simple matrices. This permits to deal with the high-order correlation between the data which the based matrix approach struggles to capture. Accordingly, we will examine and compare these approaches, particularly in two categories, namely graph-based clustering and subspace-based clustering. We will conduct and report experiments of the main clustering methods over a benchmark datasets.", "date": "2023-03-14", "categories": []}
{"id": "2306.00833", "title": "When Does Bottom-up Beat Top-down in Hierarchical Community Detection?", "abstract": "Hierarchical clustering of networks consists in finding a tree of communities, such that lower levels of the hierarchy reveal finer-grained community structures. There are two main classes of algorithms tackling this problem. Divisive (top-down) algorithms recursively partition the nodes into two communities, until a stopping rule indicates that no further split is needed. In contrast, agglomerative (bottom-up) algorithms first identify the smallest community structure and then repeatedly merge the communities using a linkage method. In this article, we establish theoretical guarantees for the recovery of the hierarchical tree and community structure of a Hierarchical Stochastic Block Model by a bottom-up algorithm. We also establish that this bottom-up algorithm attains the information-theoretic threshold for exact recovery at intermediate levels of the hierarchy. Notably, these recovery conditions are less restrictive compared to those existing for top-down algorithms. This shows that bottom-up algorithms extend the feasible region for achieving exact recovery at intermediate levels. Numerical experiments on both synthetic and real data sets confirm the superiority of bottom-up algorithms over top-down algorithms. We also observe that top-down algorithms can produce dendrograms with inversions. These findings contribute to a better understanding of hierarchical clustering techniques and their applications in network analysis.", "date": "2023-06-01", "categories": []}
{"id": "2511.17631", "title": "Enhanced Federated Deep Multi-View Clustering under Uncertainty Scenario", "abstract": "Traditional Federated Multi-View Clustering assumes uniform views across clients, yet practical deployments reveal heterogeneous view completeness with prevalent incomplete, redundant, or corrupted data. While recent approaches model view heterogeneity, they neglect semantic conflicts from dynamic view combinations, failing to address dual uncertainties: view uncertainty (semantic inconsistency from arbitrary view pairings) and aggregation uncertainty (divergent client updates with imbalanced contributions). To address these, we propose a novel Enhanced Federated Deep Multi-View Clustering framework: first align local semantics, hierarchical contrastive fusion within clients resolves view uncertainty by eliminating semantic conflicts; a view adaptive drift module mitigates aggregation uncertainty through global-local prototype contrast that dynamically corrects parameter deviations; and a balanced aggregation mechanism coordinates client updates. Experimental results demonstrate that EFDMVC achieves superior robustness against heterogeneous uncertain views across multiple benchmark datasets, consistently outperforming all state-of-the-art baselines in comprehensive evaluations.", "date": "2025-11-19", "categories": []}
{"id": "2511.17823", "title": "A novel k-means clustering approach using two distance measures for Gaussian data", "abstract": "Clustering algorithms have long been the topic of research, representing the more popular side of unsupervised learning. Since clustering analysis is one of the best ways to find some clarity and structure within raw data, this paper explores a novel approach to \\textit{k}-means clustering. Here we present a \\textit{k}-means clustering algorithm that takes both the within cluster distance (WCD) and the inter cluster distance (ICD) as the distance metric to cluster the data into \\emph{k} clusters pre-determined by the Calinski-Harabasz criterion in order to provide a more robust output for the clustering analysis. The idea with this approach is that by including both the measurement metrics, the convergence of the data into their clusters becomes solidified and more robust. We run the algorithm with some synthetically produced data and also some benchmark data sets obtained from the UCI repository. The results show that the convergence of the data into their respective clusters is more accurate by using both WCD and ICD measurement metrics. The algorithm is also better at clustering the outliers into their true clusters as opposed to the traditional \\textit{k} means method. We also address some interesting possible research topics that reveal themselves as we answer the questions we initially set out to address.", "date": "2025-11-21", "categories": []}
{"id": "2511.18056", "title": "Hierarchical Linkage Clustering Beyond Binary Trees and Ultrametrics", "abstract": "Hierarchical clustering seeks to uncover nested structures in data by constructing a tree of clusters, where deeper levels reveal finer-grained relationships. Traditional methods, including linkage approaches, face three major limitations: (i) they always return a hierarchy, even if none exists, (ii) they are restricted to binary trees, even if the true hierarchy is non-binary, and (iii) they are highly sensitive to the choice of linkage function. In this paper, we address these issues by introducing the notion of a valid hierarchy and defining a partial order over the set of valid hierarchies. We prove the existence of a finest valid hierarchy, that is, the hierarchy that encodes the maximum information consistent with the similarity structure of the data set. In particular, the finest valid hierarchy is not constrained to binary structures and, when no hierarchical relationships exist, collapses to a star tree. We propose a simple two-step algorithm that first constructs a binary tree via a linkage method and then prunes it to enforce validity. We establish necessary and sufficient conditions on the linkage function under which this procedure exactly recovers the finest valid hierarchy, and we show that all linkage functions satisfying these conditions yield the same hierarchy after pruning. Notably, classical linkage rules such as single, complete, and average satisfy these conditions, whereas Ward's linkage fails to do so.", "date": "2025-11-22", "categories": []}
{"id": "2511.18992", "title": "Classification EM-PCA for clustering and embedding", "abstract": "The mixture model is undoubtedly one of the greatest contributions to clustering. For continuous data, Gaussian models are often used and the Expectation-Maximization (EM) algorithm is particularly suitable for estimating parameters from which clustering is inferred. If these models are particularly popular in various domains including image clustering, they however suffer from the dimensionality and also from the slowness of convergence of the EM algorithm. However, the Classification EM (CEM) algorithm, a classifying version, offers a fast convergence solution while dimensionality reduction still remains a challenge. Thus we propose in this paper an algorithm combining simultaneously and non-sequentially the two tasks --Data embedding and Clustering-- relying on Principal Component Analysis (PCA) and CEM. We demonstrate the interest of such approach in terms of clustering and data embedding. We also establish different connections with other clustering approaches.", "date": "2025-11-24", "categories": []}
{"id": "2511.19107", "title": "The Core in Max-Loss Non-Centroid Clustering Can Be Empty", "abstract": "We study core stability in non-centroid clustering under the max-loss objective, where each agent's loss is the maximum distance to other members of their cluster. We prove that for all $k\\geq 3$ there exist metric instances with $n\\ge 9$ agents, with $n$ divisible by $k$, for which no clustering lies in the $\\alpha$-core for any $\\alpha<2^{\\frac{1}{5}}\\sim 1.148$. The bound is tight for our construction. Using a computer-aided proof, we also identify a two-dimensional Euclidean point set whose associated lower bound is slightly smaller than that of our general construction. This is, to our knowledge, the first impossibility result showing that the core can be empty in non-centroid clustering under the max-loss objective.", "date": "2025-11-24", "categories": []}
{"id": "2511.17219", "title": "DelTriC: A Novel Clustering Method with Accurate Outlier", "abstract": "The paper introduces DelTriC (Delaunay Triangulation Clustering), a clustering algorithm which integrates PCA/UMAP-based projection, Delaunay triangulation, and a novel back-projection mechanism to form clusters in the original high-dimensional space. DelTriC decouples neighborhood construction from decision-making by first triangulating in a low-dimensional proxy to index local adjacency, and then back-projecting to the original space to perform robust edge pruning, merging, and anomaly detection. DelTriC can outperform traditional methods such as k-means, DBSCAN, and HDBSCAN in many scenarios; it is both scalable and accurate, and it also significantly improves outlier detection.", "date": "2025-11-21", "categories": []}
{"id": "2312.11157", "title": "A low-rank non-convex norm method for multiview graph clustering", "abstract": "This study introduces a novel technique for multi-view clustering known as the \"Consensus Graph-Based Multi-View Clustering Method Using Low-Rank Non-Convex Norm\" (CGMVC-NC). Multi-view clustering is a challenging task in machine learning as it requires the integration of information from multiple data sources or views to cluster data points accurately. The suggested approach makes use of the structural characteristics of multi-view data tensors, introducing a non-convex tensor norm to identify correlations between these views. In contrast to conventional methods, this approach demonstrates superior clustering accuracy across several benchmark datasets. Despite the non-convex nature of the tensor norm used, the proposed method remains amenable to efficient optimization using existing algorithms. The approach provides a valuable tool for multi-view data analysis and has the potential to enhance our understanding of complex systems in various fields. Further research can explore the application of this method to other types of data and extend it to other machine-learning tasks.", "date": "2023-12-18", "categories": []}
{"id": "2506.09920", "title": "Structural-Spectral Graph Convolution with Evidential Edge Learning for Hyperspectral Image Clustering", "abstract": "Hyperspectral image (HSI) clustering groups pixels into clusters without labeled data, which is an important yet challenging task. For large-scale HSIs, most methods rely on superpixel segmentation and perform superpixel-level clustering based on graph neural networks (GNNs). However, existing GNNs cannot fully exploit the spectral information of the input HSI, and the inaccurate superpixel topological graph may lead to the confusion of different class semantics during information aggregation. To address these challenges, we first propose a structural-spectral graph convolutional operator (SSGCO) tailored for graph-structured HSI superpixels to improve their representation quality through the co-extraction of spatial and spectral features. Second, we propose an evidence-guided adaptive edge learning (EGAEL) module that adaptively predicts and refines edge weights in the superpixel topological graph. We integrate the proposed method into a contrastive learning framework to achieve clustering, where representation learning and clustering are simultaneously conducted. Experiments demonstrate that the proposed method improves clustering accuracy by 2.61%, 6.06%, 4.96% and 3.15% over the best compared methods on four HSI datasets. Our code is available at https://github.com/jhqi/SSGCO-EGAEL.", "date": "2025-06-11", "categories": []}
{"id": "2511.12564", "title": "Linear time small coresets for k-mean clustering of segments with applications", "abstract": "We study the $k$-means problem for a set $\\mathcal{S} \\subseteq \\mathbb{R}^d$ of $n$ segments, aiming to find $k$ centers $X \\subseteq \\mathbb{R}^d$ that minimize\n  $D(\\mathcal{S},X) := \\sum_{S \\in \\mathcal{S}} \\min_{x \\in X} D(S,x)$, where $D(S,x) := \\int_{p \\in S} |p - x| dp$\n  measures the total distance from each point along a segment to a center. Variants of this problem include handling outliers, employing alternative distance functions such as M-estimators, weighting distances to achieve balanced clustering, or enforcing unique cluster assignments. For any $\\varepsilon > 0$, an $\\varepsilon$-coreset is a weighted subset $C \\subseteq \\mathbb{R}^d$ that approximates $D(\\mathcal{S},X)$ within a factor of $1 \\pm \\varepsilon$ for any set of $k$ centers, enabling efficient streaming, distributed, or parallel computation. We propose the first coreset construction that provably handles arbitrary input segments. For constant $k$ and $\\varepsilon$, it produces a coreset of size $O(\\log^2 n)$ computable in $O(nd)$ time. Experiments, including a real-time video tracking application, demonstrate substantial speedups with minimal loss in clustering accuracy, confirming both the practical efficiency and theoretical guarantees of our method.", "date": "2025-11-16", "categories": []}
{"id": "2511.16213", "title": "Unsupervised Image Classification with Adaptive Nearest Neighbor Selection and Cluster Ensembles", "abstract": "Unsupervised image classification, or image clustering, aims to group unlabeled images into semantically meaningful categories. Early methods integrated representation learning and clustering within an iterative framework. However, the rise of foundational models have recently shifted focus solely to clustering, bypassing the representation learning step. In this work, we build upon a recent multi-head clustering approach by introducing adaptive nearest neighbor selection and cluster ensembling strategies to improve clustering performance. Our method, \"Image Clustering through Cluster Ensembles\" (ICCE), begins with a clustering stage, where we train multiple clustering heads on a frozen backbone, producing diverse image clusterings. We then employ a cluster ensembling technique to consolidate these potentially conflicting results into a unified consensus clustering. Finally, we train an image classifier using the consensus clustering result as pseudo-labels. ICCE achieves state-of-the-art performance on ten image classification benchmarks, achieving 99.3% accuracy on CIFAR10, 89% on CIFAR100, and 70.4% on ImageNet datasets, narrowing the performance gap with supervised methods. To the best of our knowledge, ICCE is the first fully unsupervised image classification method to exceed 70% accuracy on ImageNet.", "date": "2025-11-20", "categories": []}
{"id": "2511.14784", "title": "Convex Clustering Redefined: Robust Learning with the Median of Means Estimator", "abstract": "Clustering approaches that utilize convex loss functions have recently attracted growing interest in the formation of compact data clusters. Although classical methods like k-means and its wide family of variants are still widely used, all of them require the number of clusters k to be supplied as input, and many are notably sensitive to initialization. Convex clustering provides a more stable alternative by formulating the clustering task as a convex optimization problem, ensuring a unique global solution. However, it faces challenges in handling high-dimensional data, especially in the presence of noise and outliers. Additionally, strong fusion regularization, controlled by the tuning parameter, can hinder effective cluster formation within a convex clustering framework. To overcome these challenges, we introduce a robust approach that integrates convex clustering with the Median of Means (MoM) estimator, thus developing an outlier-resistant and efficient clustering framework that does not necessitate prior knowledge of the number of clusters. By leveraging the robustness of MoM alongside the stability of convex clustering, our method enhances both performance and efficiency, especially on large-scale datasets. Theoretical analysis demonstrates weak consistency under specific conditions, while experiments on synthetic and real-world datasets validate the method's superior performance compared to existing approaches.", "date": "2025-11-12", "categories": []}
{"id": "2501.02036", "title": "Deep Clustering via Gradual Community Detection", "abstract": "Deep clustering is an essential task in modern artificial intelligence, aiming to partition a set of data samples into a given number of homogeneous groups (i.e., clusters). Recent studies have proposed increasingly advanced deep neural networks and training strategies for deep clustering, effectively improving performance. However, deep clustering generally remains challenging due to the inadequacy of supervision signals. Building upon the existing representation learning backbones, this paper proposes a novel clustering strategy of gradual community detection. It initializes clustering by partitioning samples into many pseudo-communities and then gradually expands clusters by community merging. Compared with the existing clustering strategies, community detection factors in the new perspective of cluster network analysis in the clustering process. The new perspective can effectively leverage global structural characteristics to enhance cluster pseudo-label purity, which is critical to the performance of self-supervision. We have implemented the proposed approach based on the popular backbones and evaluated its efficacy on benchmark image datasets. Our extensive experiments have shown that the proposed clustering strategy can effectively improve the SOTA performance. Our ablation study also demonstrates that the new network perspective can effectively improve community pseudo-label purity, resulting in improved self-supervision.", "date": "2025-01-03", "categories": []}
{"id": "2510.22540", "title": "qc-kmeans: A Quantum Compressive K-Means Algorithm for NISQ Devices", "abstract": "Clustering on NISQ hardware is constrained by data loading and limited qubits. We present \\textbf{qc-kmeans}, a hybrid compressive $k$-means that summarizes a dataset with a constant-size Fourier-feature sketch and selects centroids by solving small per-group QUBOs with shallow QAOA circuits. The QFF sketch estimator is unbiased with mean-squared error $O(\\varepsilon^2)$ for $B,S=\\Theta(\\varepsilon^{-2})$, and the peak-qubit requirement $q_{\\text{peak}}=\\max\\{D,\\lceil \\log_2 B\\rceil + 1\\}$ does not scale with the number of samples. A refinement step with elitist retention ensures non-increasing surrogate cost. In Qiskit Aer simulations (depth $p{=}1$), the method ran with $\\le 9$ qubits on low-dimensional synthetic benchmarks and achieved competitive sum-of-squared errors relative to quantum baselines; runtimes are not directly comparable. On nine real datasets (up to $4.3\\times 10^5$ points), the pipeline maintained constant peak-qubit usage in simulation. Under IBM noise models, accuracy was similar to the idealized setting. Overall, qc-kmeans offers a NISQ-oriented formulation with shallow, bounded-width circuits and competitive clustering quality in simulation.", "date": "2025-10-26", "categories": []}
{"id": "2511.13444", "title": "Discovering Operational Patterns Using Image-Based Convolutional Clustering and Composite Evaluation: A Case Study in Foundry Melting Processes", "abstract": "Industrial process monitoring increasingly relies on sensor-generated time-series data, yet the lack of labels, high variability, and operational noise make it difficult to extract meaningful patterns using conventional methods. Existing clustering techniques either rely on fixed distance metrics or deep models designed for static data, limiting their ability to handle dynamic, unstructured industrial sequences. Addressing this gap, this paper proposes a novel framework for unsupervised discovery of operational modes in univariate time-series data using image-based convolutional clustering with composite internal evaluation. The proposed framework improves upon existing approaches in three ways: (1) raw time-series sequences are transformed into grayscale matrix representations via overlapping sliding windows, allowing effective feature extraction using a deep convolutional autoencoder; (2) the framework integrates both soft and hard clustering outputs and refines the selection through a two-stage strategy; and (3) clustering performance is objectively evaluated by a newly developed composite score, S_eva, which combines normalized Silhouette, Calinski-Harabasz, and Davies-Bouldin indices. Applied to over 3900 furnace melting operations from a Nordic foundry, the method identifies seven explainable operational patterns, revealing significant differences in energy consumption, thermal dynamics, and production duration. Compared to classical and deep clustering baselines, the proposed approach achieves superior overall performance, greater robustness, and domain-aligned explainability. The framework addresses key challenges in unsupervised time-series analysis, such as sequence irregularity, overlapping modes, and metric inconsistency, and provides a generalizable solution for data-driven diagnostics and energy optimization in industrial systems.", "date": "2025-11-17", "categories": []}
{"id": "2511.13561", "title": "RAC-DMVC: Reliability-Aware Contrastive Deep Multi-View Clustering under Multi-Source Noise", "abstract": "Multi-view clustering (MVC), which aims to separate the multi-view data into distinct clusters in an unsupervised manner, is a fundamental yet challenging task. To enhance its applicability in real-world scenarios, this paper addresses a more challenging task: MVC under multi-source noises, including missing noise and observation noise. To this end, we propose a novel framework, Reliability-Aware Contrastive Deep Multi-View Clustering (RAC-DMVC), which constructs a reliability graph to guide robust representation learning under noisy environments. Specifically, to address observation noise, we introduce a cross-view reconstruction to enhances robustness at the data level, and a reliability-aware noise contrastive learning to mitigates bias in positive and negative pairs selection caused by noisy representations. To handle missing noise, we design a dual-attention imputation to capture shared information across views while preserving view-specific features. In addition, a self-supervised cluster distillation module further refines the learned representations and improves the clustering performance. Extensive experiments on five benchmark datasets demonstrate that RAC-DMVC outperforms SOTA methods on multiple evaluation metrics and maintains excellent performance under varying ratios of noise.", "date": "2025-11-17", "categories": []}
{"id": "2511.13705", "title": "Rare Genomic Subtype Discovery from RNA-seq via Autoencoder Embeddings and Stability-Aware Clustering", "abstract": "Unsupervised learning on high-dimensional RNA-seq data can reveal molecular subtypes beyond standard labels. We combine an autoencoder-based representation with clustering and stability analysis to search for rare but reproducible genomic subtypes. On the UCI \"Gene Expression Cancer RNA-Seq\" dataset (801 samples, 20,531 genes; BRCA, COAD, KIRC, LUAD, PRAD), a pan-cancer analysis shows clusters aligning almost perfectly with tissue of origin (Cramer's V = 0.887), serving as a negative control. We therefore reframe the problem within KIRC (n = 146): we select the top 2,000 highly variable genes, standardize them, train a feed-forward autoencoder (128-dimensional latent space), and run k-means for k = 2-10. While global indices favor small k, scanning k with a pre-specified discovery rule (rare < 10 percent and stable with Jaccard >= 0.60 across 20 seeds after Hungarian alignment) yields a simple solution at k = 5 (silhouette = 0.129, DBI = 2.045) with a rare cluster C0 (6.85 percent of patients) that is highly stable (Jaccard = 0.787). Cluster-vs-rest differential expression (Welch's t-test, Benjamini-Hochberg FDR) identifies coherent markers. Overall, pan-cancer clustering is dominated by tissue of origin, whereas a stability-aware within-cancer approach reveals a rare, reproducible KIRC subtype.", "date": "2025-11-17", "categories": []}
{"id": "2511.10915", "title": "Towards Federated Clustering: A Client-wise Private Graph Aggregation Framework", "abstract": "Federated clustering addresses the critical challenge of extracting patterns from decentralized, unlabeled data. However, it is hampered by the flaw that current approaches are forced to accept a compromise between performance and privacy: \\textit{transmitting embedding representations risks sensitive data leakage, while sharing only abstract cluster prototypes leads to diminished model accuracy}. To resolve this dilemma, we propose Structural Privacy-Preserving Federated Graph Clustering (SPP-FGC), a novel algorithm that innovatively leverages local structural graphs as the primary medium for privacy-preserving knowledge sharing, thus moving beyond the limitations of conventional techniques. Our framework operates on a clear client-server logic; on the client-side, each participant constructs a private structural graph that captures intrinsic data relationships, which the server then securely aggregates and aligns to form a comprehensive global graph from which a unified clustering structure is derived. The framework offers two distinct modes to suit different needs. SPP-FGC is designed as an efficient one-shot method that completes its task in a single communication round, ideal for rapid analysis. For more complex, unstructured data like images, SPP-FGC+ employs an iterative process where clients and the server collaboratively refine feature representations to achieve superior downstream performance. Extensive experiments demonstrate that our framework achieves state-of-the-art performance, improving clustering accuracy by up to 10\\% (NMI) over federated baselines while maintaining provable privacy guarantees.", "date": "2025-11-14", "categories": []}
{"id": "2511.11181", "title": "Dynamic Deep Graph Learning for Incomplete Multi-View Clustering with Masked Graph Reconstruction Loss", "abstract": "The prevalence of real-world multi-view data makes incomplete multi-view clustering (IMVC) a crucial research. The rapid development of Graph Neural Networks (GNNs) has established them as one of the mainstream approaches for multi-view clustering. Despite significant progress in GNNs-based IMVC, some challenges remain: (1) Most methods rely on the K-Nearest Neighbors (KNN) algorithm to construct static graphs from raw data, which introduces noise and diminishes the robustness of the graph topology. (2) Existing methods typically utilize the Mean Squared Error (MSE) loss between the reconstructed graph and the sparse adjacency graph directly as the graph reconstruction loss, leading to substantial gradient noise during optimization. To address these issues, we propose a novel \\textbf{D}ynamic Deep \\textbf{G}raph Learning for \\textbf{I}ncomplete \\textbf{M}ulti-\\textbf{V}iew \\textbf{C}lustering with \\textbf{M}asked Graph Reconstruction Loss (DGIMVCM). Firstly, we construct a missing-robust global graph from the raw data. A graph convolutional embedding layer is then designed to extract primary features and refined dynamic view-specific graph structures, leveraging the global graph for imputation of missing views. This process is complemented by graph structure contrastive learning, which identifies consistency among view-specific graph structures. Secondly, a graph self-attention encoder is introduced to extract high-level representations based on the imputed primary features and view-specific graphs, and is optimized with a masked graph reconstruction loss to mitigate gradient noise during optimization. Finally, a clustering module is constructed and optimized through a pseudo-label self-supervised training mechanism. Extensive experiments on multiple datasets validate the effectiveness and superiority of DGIMVCM.", "date": "2025-11-14", "categories": []}
{"id": "2511.11539", "title": "Generalizing Fair Clustering to Multiple Groups: Algorithms and Applications", "abstract": "Clustering is a fundamental task in machine learning and data analysis, but it frequently fails to provide fair representation for various marginalized communities defined by multiple protected attributes -- a shortcoming often caused by biases in the training data. As a result, there is a growing need to enhance the fairness of clustering outcomes, ideally by making minimal modifications, possibly as a post-processing step after conventional clustering. Recently, Chakraborty et al. [COLT'25] initiated the study of \\emph{closest fair clustering}, though in a restricted scenario where data points belong to only two groups. In practice, however, data points are typically characterized by many groups, reflecting diverse protected attributes such as age, ethnicity, gender, etc.\n  In this work, we generalize the study of the \\emph{closest fair clustering} problem to settings with an arbitrary number (more than two) of groups. We begin by showing that the problem is NP-hard even when all groups are of equal size -- a stark contrast with the two-group case, for which an exact algorithm exists. Next, we propose near-linear time approximation algorithms that efficiently handle arbitrary-sized multiple groups, thereby answering an open question posed by Chakraborty et al. [COLT'25].\n  Leveraging our closest fair clustering algorithms, we further achieve improved approximation guarantees for the \\emph{fair correlation clustering} problem, advancing the state-of-the-art results established by Ahmadian et al. [AISTATS'20] and Ahmadi et al. [2020]. Additionally, we are the first to provide approximation algorithms for the \\emph{fair consensus clustering} problem involving multiple (more than two) groups, thus addressing another open direction highlighted by Chakraborty et al. [COLT'25].", "date": "2025-11-14", "categories": []}
{"id": "2503.06066", "title": "Multi-view Spectral Clustering on the Grassmannian Manifold With Hypergraph Representation", "abstract": "Graph-based multi-view spectral clustering methods have achieved notable progress recently, yet they often fall short in either oversimplifying pairwise relationships or struggling with inefficient spectral decompositions in high-dimensional Euclidean spaces. In this paper, we introduce a novel approach that begins to generate hypergraphs by leveraging sparse representation learning from data points. Based on the generated hypergraph, we propose an optimization function with orthogonality constraints for multi-view hypergraph spectral clustering, which incorporates spectral clustering for each view and ensures consistency across different views. In Euclidean space, solving the orthogonality-constrained optimization problem may yield local maxima and approximation errors. Innovately, we transform this problem into an unconstrained form on the Grassmannian manifold. Finally, we devise an alternating iterative Riemannian optimization algorithm to solve the problem. To validate the effectiveness of the proposed algorithm, we test it on four real-world multi-view datasets and compare its performance with seven state-of-the-art multi-view clustering algorithms. The experimental results demonstrate that our method outperforms the baselines in terms of clustering performance due to its superior low-dimensional and resilient feature representation.", "date": "2025-03-08", "categories": []}
{"id": "2511.09889", "title": "A General Anchor-Based Framework for Scalable Fair Clustering", "abstract": "Fair clustering is crucial for mitigating bias in unsupervised learning, yet existing algorithms often suffer from quadratic or super-quadratic computational complexity, rendering them impractical for large-scale datasets. To bridge this gap, we introduce the Anchor-based Fair Clustering Framework (AFCF), a novel, general, and plug-and-play framework that empowers arbitrary fair clustering algorithms with linear-time scalability. Our approach first selects a small but representative set of anchors using a novel fair sampling strategy. Then, any off-the-shelf fair clustering algorithm can be applied to this small anchor set. The core of our framework lies in a novel anchor graph construction module, where we formulate an optimization problem to propagate labels while preserving fairness. This is achieved through a carefully designed group-label joint constraint, which we prove theoretically ensures that the fairness of the final clustering on the entire dataset matches that of the anchor clustering. We solve this optimization efficiently using an ADMM-based algorithm. Extensive experiments on multiple large-scale benchmarks demonstrate that AFCF drastically accelerates state-of-the-art methods, which reduces computational time by orders of magnitude while maintaining strong clustering performance and fairness guarantees.", "date": "2025-11-13", "categories": []}
{"id": "2511.10392", "title": "Enhancing Kernel Power K-means: Scalable and Robust Clustering with Random Fourier Features and Possibilistic Method", "abstract": "Kernel power $k$-means (KPKM) leverages a family of means to mitigate local minima issues in kernel $k$-means. However, KPKM faces two key limitations: (1) the computational burden of the full kernel matrix restricts its use on extensive data, and (2) the lack of authentic centroid-sample assignment learning reduces its noise robustness. To overcome these challenges, we propose RFF-KPKM, introducing the first approximation theory for applying random Fourier features (RFF) to KPKM. RFF-KPKM employs RFF to generate efficient, low-dimensional feature maps, bypassing the need for the whole kernel matrix. Crucially, we are the first to establish strong theoretical guarantees for this combination: (1) an excess risk bound of $\\mathcal{O}(\\sqrt{k^3/n})$, (2) strong consistency with membership values, and (3) a $(1+\\varepsilon)$ relative error bound achievable using the RFF of dimension $\\mathrm{poly}(\\varepsilon^{-1}\\log k)$. Furthermore, to improve robustness and the ability to learn multiple kernels, we propose IP-RFF-MKPKM, an improved possibilistic RFF-based multiple kernel power $k$-means. IP-RFF-MKPKM ensures the scalability of MKPKM via RFF and refines cluster assignments by combining the merits of the possibilistic membership and fuzzy membership. Experiments on large-scale datasets demonstrate the superior efficiency and clustering accuracy of the proposed methods compared to the state-of-the-art alternatives.", "date": "2025-11-13", "categories": []}
{"id": "2502.14018", "title": "Ultrametric Cluster Hierarchies: I Want 'em All!", "abstract": "Hierarchical clustering is a powerful tool for exploratory data analysis, organizing data into a tree of clusterings from which a partition can be chosen. This paper generalizes these ideas by proving that, for any reasonable hierarchy, one can optimally solve any center-based clustering objective over it (such as $k$-means). Moreover, these solutions can be found exceedingly quickly and are themselves necessarily hierarchical. Thus, given a cluster tree, we show that one can quickly access a plethora of new, equally meaningful hierarchies. Just as in standard hierarchical clustering, one can then choose any desired partition from these new hierarchies. We conclude by verifying the utility of our proposed techniques across datasets, hierarchies, and partitioning schemes.", "date": "2025-02-19", "categories": []}
{"id": "2511.08993", "title": "Fast $k$-means clustering in Riemannian manifolds via Fr\\'{e}chet maps: Applications to large-dimensional SPD matrices", "abstract": "We introduce a novel, efficient framework for clustering data on high-dimensional, non-Euclidean manifolds that overcomes the computational challenges associated with standard intrinsic methods. The key innovation is the use of the $p$-Fr\\'{e}chet map $F^p : \\mathcal{M} \\to \\mathbb{R}^\\ell$ -- defined on a generic metric space $\\mathcal{M}$ -- which embeds the manifold data into a lower-dimensional Euclidean space $\\mathbb{R}^\\ell$ using a set of reference points $\\{r_i\\}_{i=1}^\\ell$, $r_i \\in \\mathcal{M}$. Once embedded, we can efficiently and accurately apply standard Euclidean clustering techniques such as k-means. We rigorously analyze the mathematical properties of $F^p$ in the Euclidean space and the challenging manifold of $n \\times n$ symmetric positive definite matrices $\\mathit{SPD}(n)$. Extensive numerical experiments using synthetic and real $\\mathit{SPD}(n)$ data demonstrate significant performance gains: our method reduces runtime by up to two orders of magnitude compared to intrinsic manifold-based approaches, all while maintaining high clustering accuracy, including scenarios where existing alternative methods struggle or fail.", "date": "2025-11-12", "categories": []}
{"id": "2511.09049", "title": "Break the Tie: Learning Cluster-Customized Category Relationships for Categorical Data Clustering", "abstract": "Categorical attributes with qualitative values are ubiquitous in cluster analysis of real datasets. Unlike the Euclidean distance of numerical attributes, the categorical attributes lack well-defined relationships of their possible values (also called categories interchangeably), which hampers the exploration of compact categorical data clusters. Although most attempts are made for developing appropriate distance metrics, they typically assume a fixed topological relationship between categories when learning distance metrics, which limits their adaptability to varying cluster structures and often leads to suboptimal clustering performance. This paper, therefore, breaks the intrinsic relationship tie of attribute categories and learns customized distance metrics suitable for flexibly and accurately revealing various cluster distributions. As a result, the fitting ability of the clustering algorithm is significantly enhanced, benefiting from the learnable category relationships. Moreover, the learned category relationships are proved to be Euclidean distance metric-compatible, enabling a seamless extension to mixed datasets that include both numerical and categorical attributes. Comparative experiments on 12 real benchmark datasets with significance tests show the superior clustering accuracy of the proposed method with an average ranking of 1.25, which is significantly higher than the 5.21 ranking of the current best-performing method.", "date": "2025-11-12", "categories": []}
{"id": "2511.09202", "title": "Stochastic Mean-Shift Clustering", "abstract": "We present a stochastic version of the mean-shift clustering algorithm. In this stochastic version a randomly chosen sequence of data points move according to partial gradient ascent steps of the objective function. Theoretical results illustrating the convergence of the proposed approach, and its relative performances is evaluated on synthesized 2-dimensional samples generated by a Gaussian mixture distribution and compared with state-of-the-art methods. It can be observed that in most cases the stochastic mean-shift clustering outperforms the standard mean-shift. We also illustrate as a practical application the use of the presented method for speaker clustering.", "date": "2025-11-12", "categories": []}
{"id": "2509.14544", "title": "Association and Consolidation: Evolutionary Memory-Enhanced Incremental Multi-View Clustering", "abstract": "Incremental multi-view clustering aims to achieve stable clustering results while addressing the stability-plasticity dilemma (SPD) in view-incremental scenarios. The core challenge is that the model must have enough plasticity to quickly adapt to new data, while maintaining sufficient stability to consolidate long-term knowledge. To address this challenge, we propose a novel Evolutionary Memory-Enhanced Incremental Multi-View Clustering (EMIMC), inspired by the memory regulation mechanisms of the human brain. Specifically, we design a rapid association module to establish connections between new and historical views, thereby ensuring the plasticity required for learning new knowledge. Second, a cognitive forgetting module with a decay mechanism is introduced. By dynamically adjusting the contribution of the historical view to optimize knowledge integration. Finally, we propose a knowledge consolidation module to progressively refine short-term knowledge into stable long-term memory using temporal tensors, thereby ensuring model stability. By integrating these modules, EMIMC achieves strong knowledge retention capabilities in scenarios with growing views. Extensive experiments demonstrate that EMIMC exhibits remarkable advantages over existing state-of-the-art methods.", "date": "2025-09-18", "categories": []}
{"id": "2511.05554", "title": "MCFCN: Multi-View Clustering via a Fusion-Consensus Graph Convolutional Network", "abstract": "Existing Multi-view Clustering (MVC) methods based on subspace learning focus on consensus representation learning while neglecting the inherent topological structure of data. Despite the integration of Graph Neural Networks (GNNs) into MVC, their input graph structures remain susceptible to noise interference. Methods based on Multi-view Graph Refinement (MGRC) also have limitations such as insufficient consideration of cross-view consistency, difficulty in handling hard-to-distinguish samples in the feature space, and disjointed optimization processes caused by graph construction algorithms. To address these issues, a Multi-View Clustering method via a Fusion-Consensus Graph Convolutional Network (MCFCN) is proposed. The network learns the consensus graph of multi-view data in an end-to-end manner and learns effective consensus representations through a view feature fusion model and a Unified Graph Structure Adapter (UGA). It designs Similarity Matrix Alignment Loss (SMAL) and Feature Representation Alignment Loss (FRAL). With the guidance of consensus, it optimizes view-specific graphs, preserves cross-view topological consistency, promotes the construction of intra-class edges, and realizes effective consensus representation learning with the help of GCN to improve clustering performance. MCFCN demonstrates state-of-the-art performance on eight multi-view benchmark datasets, and its effectiveness is verified by extensive qualitative and quantitative implementations. The code will be provided at https://github.com/texttao/MCFCN.", "date": "2025-11-03", "categories": []}
{"id": "2511.07274", "title": "Multi-modal Dynamic Proxy Learning for Personalized Multiple Clustering", "abstract": "Multiple clustering aims to discover diverse latent structures from different perspectives, yet existing methods generate exhaustive clusterings without discerning user interest, necessitating laborious manual screening. Current multi-modal solutions suffer from static semantic rigidity: predefined candidate words fail to adapt to dataset-specific concepts, and fixed fusion strategies ignore evolving feature interactions. To overcome these limitations, we propose Multi-DProxy, a novel multi-modal dynamic proxy learning framework that leverages cross-modal alignment through learnable textual proxies. Multi-DProxy introduces 1) gated cross-modal fusion that synthesizes discriminative joint representations by adaptively modeling feature interactions. 2) dual-constraint proxy optimization where user interest constraints enforce semantic consistency with domain concepts while concept constraints employ hard example mining to enhance cluster discrimination. 3) dynamic candidate management that refines textual proxies through iterative clustering feedback. Therefore, Multi-DProxy not only effectively captures a user's interest through proxies but also enables the identification of relevant clusterings with greater precision. Extensive experiments demonstrate state-of-the-art performance with significant improvements over existing methods across a broad set of multi-clustering benchmarks.", "date": "2025-11-10", "categories": []}
{"id": "2511.05462", "title": "SiamMM: A Mixture Model Perspective on Deep Unsupervised Learning", "abstract": "Recent studies have demonstrated the effectiveness of clustering-based approaches for self-supervised and unsupervised learning. However, the application of clustering is often heuristic, and the optimal methodology remains unclear. In this work, we establish connections between these unsupervised clustering methods and classical mixture models from statistics. Through this framework, we demonstrate significant enhancements to these clustering methods, leading to the development of a novel model named SiamMM. Our method attains state-of-the-art performance across various self-supervised learning benchmarks. Inspection of the learned clusters reveals a strong resemblance to unseen ground truth labels, uncovering potential instances of mislabeling.", "date": "2025-11-07", "categories": []}
{"id": "2306.00011", "title": "DeepVAT: A Self-Supervised Technique for Cluster Assessment in Image Datasets", "abstract": "Estimating the number of clusters and cluster structures in unlabeled, complex, and high-dimensional datasets (like images) is challenging for traditional clustering algorithms. In recent years, a matrix reordering-based algorithm called Visual Assessment of Tendency (VAT), and its variants have attracted many researchers from various domains to estimate the number of clusters and inherent cluster structure present in the data. However, these algorithms face significant challenges when dealing with image data as they fail to effectively capture the crucial features inherent in images. To overcome these limitations, we propose a deep-learning-based framework that enables the assessment of cluster structure in complex image datasets. Our approach utilizes a self-supervised deep neural network to generate representative embeddings for the data. These embeddings are then reduced to 2-dimension using t-distributed Stochastic Neighbour Embedding (t-SNE) and inputted into VAT based algorithms to estimate the underlying cluster structure. Importantly, our framework does not rely on any prior knowledge of the number of clusters. Our proposed approach demonstrates superior performance compared to state-of-the-art VAT family algorithms and two other deep clustering algorithms on four benchmark image datasets, namely MNIST, FMNIST, CIFAR-10, and INTEL.", "date": "2023-05-29", "categories": []}
{"id": "2410.07786", "title": "Orthogonal Nonnegative Matrix Factorization with the Kullback-Leibler divergence", "abstract": "Orthogonal nonnegative matrix factorization (ONMF) has become a standard approach for clustering. As far as we know, most works on ONMF rely on the Frobenius norm to assess the quality of the approximation. This paper presents a new model and algorithm for ONMF that minimizes the Kullback-Leibler (KL) divergence. As opposed to the Frobenius norm which assumes Gaussian noise, the KL divergence is the maximum likelihood estimator for Poisson-distributed data, which can model better sparse vectors of word counts in document data sets and photo counting processes in imaging. We develop an algorithm based on alternating optimization, KL-ONMF, and show that it performs favorably with the Frobenius-norm based ONMF for document classification and hyperspectral image unmixing.", "date": "2024-10-10", "categories": []}
{"id": "2505.19093", "title": "A Unified Framework for Variable Selection in Model-Based Clustering with Missing Not at Random", "abstract": "Model-based clustering integrated with variable selection is a powerful tool for uncovering latent structures within complex data. However, its effectiveness is often hindered by challenges such as identifying relevant variables that define heterogeneous subgroups and handling data that are missing not at random, a prevalent issue in fields like transcriptomics. While several notable methods have been proposed to address these problems, they typically tackle each issue in isolation, thereby limiting their flexibility and adaptability. This paper introduces a unified framework designed to address these challenges simultaneously. Our approach incorporates a data-driven penalty matrix into penalized clustering to enable more flexible variable selection, along with a mechanism that explicitly models the relationship between missingness and latent class membership. We demonstrate that, under certain regularity conditions, the proposed framework achieves both asymptotic consistency and selection consistency, even in the presence of missing data. This unified strategy significantly enhances the capability and efficiency of model-based clustering, advancing methodologies for identifying informative variables that define homogeneous subgroups in the presence of complex missing data patterns. The performance of the framework, including its computational efficiency, is evaluated through simulations and demonstrated using both synthetic and real-world transcriptomic datasets.", "date": "2025-05-25", "categories": []}
{"id": "2511.01945", "title": "Learning a Distance for the Clustering of Patients with Amyotrophic Lateral Sclerosis", "abstract": "Amyotrophic lateral sclerosis (ALS) is a severe disease with a typical survival of 3-5 years after symptom onset. Current treatments offer only limited life extension, and the variability in patient responses highlights the need for personalized care. However, research is hindered by small, heterogeneous cohorts, sparse longitudinal data, and the lack of a clear definition for clinically meaningful patient clusters. Existing clustering methods remain limited in both scope and number. To address this, we propose a clustering approach that groups sequences using a disease progression declarative score. Our approach integrates medical expertise through multiple descriptive variables, investigating several distance measures combining such variables, both by reusing off-the-shelf distances and employing a weak-supervised learning method. We pair these distances with clustering methods and benchmark them against state-of-the-art techniques. The evaluation of our approach on a dataset of 353 ALS patients from the University Hospital of Tours, shows that our method outperforms state-of-the-art methods in survival analysis while achieving comparable silhouette scores. In addition, the learned distances enhance the relevance and interpretability of results for medical experts.", "date": "2025-11-03", "categories": []}
{"id": "2501.13451", "title": "Deep Modularity Networks with Diversity-Preserving Regularization", "abstract": "Graph clustering plays a crucial role in graph representation learning but often faces challenges in achieving feature-space diversity. While Deep Modularity Networks (DMoN) leverage modularity maximization and collapse regularization to ensure structural separation, they lack explicit mechanisms for feature-space separation, assignment dispersion, and assignment-confidence control. We address this limitation by proposing Deep Modularity Networks with Diversity-Preserving Regularization (DMoN-DPR), which introduces three novel regularization terms: distance-based for inter-cluster separation, variance-based for per-cluster assignment dispersion, and an assignment-entropy penalty with a small positive weight, encouraging more confident assignments gradually. Our method significantly enhances label-based clustering metrics on feature-rich benchmark datasets (paired two-tailed t-test, $p\\leq0.05$), demonstrating the effectiveness of incorporating diversity-preserving regularizations in creating meaningful and interpretable clusters.", "date": "2025-01-23", "categories": []}
{"id": "2506.21291", "title": "Improved seeding strategies for k-means and k-GMM", "abstract": "We revisit the randomized seeding techniques for k-means clustering and k-GMM (Gaussian Mixture model fitting with Expectation-Maximization), formalizing their three key ingredients: the metric used for seed sampling, the number of candidate seeds, and the metric used for seed selection. This analysis yields novel families of initialization methods exploiting a lookahead principle--conditioning the seed selection to an enhanced coherence with the final metric used to assess the algorithm, and a multipass strategy to tame down the effect of randomization.\n  Experiments show a consistent constant factor improvement over classical contenders in terms of the final metric (SSE for k-means, log-likelihood for k-GMM), at a modest overhead. In particular, for k-means, our methods improve on the recently designed multi-swap strategy, which was the first one to outperform the greedy k-means++ seeding.\n  Our experimental analysis also shed light on subtle properties of k-means often overlooked, including the (lack of) correlations between the SSE upon seeding and the final SSE, the variance reduction phenomena observed in iterative seeding methods, and the sensitivity of the final SSE to the pool size for greedy methods.\n  Practically, our most effective seeding methods are strong candidates to become one of the--if not the--standard techniques. From a theoretical perspective, our formalization of seeding opens the door to a new line of analytical approaches.", "date": "2025-06-26", "categories": []}
{"id": "2511.00071", "title": "Wavelet-Based Feature Extraction and Unsupervised Clustering for Parity Detection: A Feature Engineering Perspective", "abstract": "This paper explores a deliberately over-engineered approach to the classical problem of parity detection -- determining whether a number is odd or even -- by combining wavelet-based feature extraction with unsupervised clustering. Instead of relying on modular arithmetic, integers are transformed into wavelet-domain representations, from which multi-scale statistical features are extracted and clustered using the k-means algorithm. The resulting feature space reveals meaningful structural differences between odd and even numbers, achieving a classification accuracy of approximately 69.67% without any label supervision. These results suggest that classical signal-processing techniques, originally designed for continuous data, can uncover latent structure even in purely discrete symbolic domains. Beyond parity detection, the study provides an illustrative perspective on how feature engineering and clustering may be repurposed for unconventional machine learning problems, potentially bridging symbolic reasoning and feature-based learning.", "date": "2025-10-29", "categories": []}
{"id": "2511.00885", "title": "SpEx: A Spectral Approach to Explainable Clustering", "abstract": "Explainable clustering by axis-aligned decision trees was introduced by Moshkovitz et al. (2020) and has gained considerable interest. Prior work has focused on minimizing the price of explainability for specific clustering objectives, lacking a general method to fit an explanation tree to any given clustering, without restrictions. In this work, we propose a new and generic approach to explainable clustering, based on spectral graph partitioning. With it, we design an explainable clustering algorithm that can fit an explanation tree to any given non-explainable clustering, or directly to the dataset itself. Moreover, we show that prior algorithms can also be interpreted as graph partitioning, through a generalized framework due to Trevisan (2013) wherein cuts are optimized in two graphs simultaneously. Our experiments show the favorable performance of our method compared to baselines on a range of datasets.", "date": "2025-11-02", "categories": []}
{"id": "2306.09977", "title": "Adversarially robust clustering with optimality guarantees", "abstract": "We consider the problem of clustering data points coming from sub-Gaussian mixtures. Existing methods that provably achieve the optimal mislabeling error, such as the Lloyd algorithm, are usually vulnerable to outliers. In contrast, clustering methods seemingly robust to adversarial perturbations are not known to satisfy the optimal statistical guarantees. We propose a simple robust algorithm based on the coordinatewise median that obtains the optimal mislabeling rate even when we allow adversarial outliers to be present. Our algorithm achieves the optimal error rate in constant iterations when a weak initialization condition is satisfied. In the absence of outliers, in fixed dimensions, our theoretical guarantees are similar to that of the Lloyd algorithm. Extensive experiments on various simulated and public datasets are conducted to support the theoretical guarantees of our method.", "date": "2023-06-16", "categories": []}
{"id": "2510.27136", "title": "FairAD: Computationally Efficient Fair Graph Clustering via Algebraic Distance", "abstract": "Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in graph clustering. Fair graph clustering aims to partition the set of nodes in a graph into $k$ disjoint clusters such that the proportion of each protected group within each cluster is consistent with the proportion of that group in the entire dataset. It is, however, computationally challenging to incorporate fairness constraints into existing graph clustering algorithms, particularly for large graphs. To address this problem, we propose FairAD, a computationally efficient fair graph clustering method. It first constructs a new affinity matrix based on the notion of algebraic distance such that fairness constraints are imposed. A graph coarsening process is then performed on this affinity matrix to find representative nodes that correspond to $k$ clusters. Finally, a constrained minimization problem is solved to obtain the solution of fair clustering. Experiment results on the modified stochastic block model and six public datasets show that FairAD can achieve fair clustering while being up to 40 times faster compared to state-of-the-art fair graph clustering algorithms.", "date": "2025-10-31", "categories": []}
{"id": "2407.11217", "title": "Faster and Simpler Greedy Algorithm for $k$-Median and $k$-Means", "abstract": "Clustering problems such as $k$-means and $k$-median are staples of unsupervised learning, and many algorithmic techniques have been developed to tackle their numerous aspects.\n  In this paper, we focus on the class of greedy approximation algorithm, that attracted less attention than local-search or primal-dual counterparts. In particular, we study the recursive greedy algorithm developed by Mettu and Plaxton [SIAM J. Comp 2003]. We provide a simplification of the algorithm, allowing for faster implementation, in graph metrics or in Euclidean space, where our algorithm matches or improves the state-of-the-art.", "date": "2024-07-15", "categories": []}
{"id": "2412.15695", "title": "Hypergraph clustering using Ricci curvature: an edge transport perspective", "abstract": "In this paper, we introduce a novel method for extending Ricci flow to hypergraphs by defining probability measures on the edges and transporting them on the line expansion. This approach yields a new weighting on the edges, which proves particularly effective for community detection. We extensively compare this method with a similar notion of Ricci flow defined on the clique expansion, demonstrating its enhanced sensitivity to the hypergraph structure, especially in the presence of large hyperedges. The two methods are complementary and together form a powerful and highly interpretable framework for community detection in hypergraphs.", "date": "2024-12-20", "categories": []}
{"id": "2507.19085", "title": "Clustering-Oriented Generative Attribute Graph Imputation", "abstract": "Attribute-missing graph clustering has emerged as a significant unsupervised task, where only attribute vectors of partial nodes are available and the graph structure is intact. The related models generally follow the two-step paradigm of imputation and refinement. However, most imputation approaches fail to capture class-relevant semantic information, leading to sub-optimal imputation for clustering. Moreover, existing refinement strategies optimize the learned embedding through graph reconstruction, while neglecting the fact that some attributes are uncorrelated with the graph. To remedy the problems, we establish the Clustering-oriented Generative Imputation with reliable Refinement (CGIR) model. Concretely, the subcluster distributions are estimated to reveal the class-specific characteristics precisely, and constrain the sampling space of the generative adversarial module, such that the imputation nodes are impelled to align with the correct clusters. Afterwards, multiple subclusters are merged to guide the proposed edge attention network, which identifies the edge-wise attributes for each class, so as to avoid the redundant attributes in graph reconstruction from disturbing the refinement of overall embedding. To sum up, CGIR splits attribute-missing graph clustering into the search and mergence of subclusters, which guides to implement node imputation and refinement within a unified framework. Extensive experiments prove the advantages of CGIR over state-of-the-art competitors.", "date": "2025-07-25", "categories": []}
{"id": "2505.13071", "title": "OmniFC: Rethinking Federated Clustering via Lossless and Secure Distance Reconstruction", "abstract": "Federated clustering (FC) aims to discover global cluster structures across decentralized clients without sharing raw data, making privacy preservation a fundamental requirement. There are two critical challenges: (1) privacy leakage during collaboration, and (2) robustness degradation due to aggregation of proxy information from non-independent and identically distributed (Non-IID) local data, leading to inaccurate or inconsistent global clustering. Existing solutions typically rely on model-specific local proxies, which are sensitive to data heterogeneity and inherit inductive biases from their centralized counterparts, thus limiting robustness and generality. We propose Omni Federated Clustering (OmniFC), a unified and model-agnostic framework. Leveraging Lagrange coded computing, our method enables clients to share only encoded data, allowing exact reconstruction of the global distance matrix--a fundamental representation of sample relationships--without leaking private information, even under client collusion. This construction is naturally resilient to Non-IID data distributions. This approach decouples FC from model-specific proxies, providing a unified extension mechanism applicable to diverse centralized clustering methods. Theoretical analysis confirms both reconstruction fidelity and privacy guarantees, while comprehensive experiments demonstrate OmniFC's superior robustness, effectiveness, and generality across various benchmarks compared to state-of-the-art methods. Code will be released.", "date": "2025-05-19", "categories": []}
{"id": "2506.12116", "title": "Unsupervised Document and Template Clustering using Multimodal Embeddings", "abstract": "We study unsupervised clustering of documents at both the category and template levels using frozen multimodal encoders and classical clustering algorithms. We systematize a model-agnostic pipeline that (i) projects heterogeneous last-layer states from text-layout-vision encoders into token-type-aware document vectors and (ii) performs clustering with centroid- or density-based methods, including an HDBSCAN + $k$-NN assignment to eliminate unlabeled points. We evaluate eight encoders (text-only, layout-aware, vision-only, and vision-language) with $k$-Means, DBSCAN, HDBSCAN + $k$-NN, and BIRCH on five corpora spanning clean synthetic invoices, their heavily degraded print-and-scan counterparts, scanned receipts, and real identity and certificate documents. The study reveals modality-specific failure modes and a robustness-accuracy trade-off, with vision features nearly solving template discovery on clean pages while text dominates under covariate shift, and fused encoders offering the best balance. We detail a reproducible, oracle-free tuning protocol and the curated evaluation settings to guide future work on unsupervised document organization.", "date": "2025-06-13", "categories": []}
{"id": "2510.22519", "title": "A Scalable Global Optimization Algorithm For Constrained Clustering", "abstract": "Constrained clustering leverages limited domain knowledge to improve clustering performance and interpretability, but incorporating pairwise must-link and cannot-link constraints is an NP-hard challenge, making global optimization intractable. Existing mixed-integer optimization methods are confined to small-scale datasets, limiting their utility. We propose Sample-Driven Constrained Group-Based Branch-and-Bound (SDC-GBB), a decomposable branch-and-bound (BB) framework that collapses must-linked samples into centroid-based pseudo-samples and prunes cannot-link through geometric rules, while preserving convergence and guaranteeing global optimality. By integrating grouped-sample Lagrangian decomposition and geometric elimination rules for efficient lower and upper bounds, the algorithm attains highly scalable pairwise k-Means constrained clustering via parallelism. Experimental results show that our approach handles datasets with 200,000 samples with cannot-link constraints and 1,500,000 samples with must-link constraints, which is 200 - 1500 times larger than the current state-of-the-art under comparable constraint settings, while reaching an optimality gap of less than 3%. In providing deterministic global guarantees, our method also avoids the search failures that off-the-shelf heuristics often encounter on large datasets.", "date": "2025-10-26", "categories": []}
{"id": "2510.23259", "title": "GCAO: Group-driven Clustering via Gravitational Attraction and Optimization", "abstract": "Traditional clustering algorithms often struggle with high-dimensional and non-uniformly distributed data, where low-density boundary samples are easily disturbed by neighboring clusters, leading to unstable and distorted clustering results. To address this issue, we propose a Group-driven Clustering via Gravitational Attraction and Optimization (GCAO) algorithm. GCAO introduces a group-level optimization mechanism that aggregates low-density boundary points into collaboratively moving groups, replacing the traditional point-based contraction process. By combining local density estimation with neighborhood topology, GCAO constructs effective gravitational interactions between groups and their surroundings, enhancing boundary clarity and structural consistency. Using groups as basic motion units, a gravitational contraction strategy ensures globally stable and directionally consistent convergence. Experiments on multiple high-dimensional datasets demonstrate that GCAO outperforms 11 representative clustering methods, achieving average improvements of 37.13%, 52.08%, 44.98%, and 38.81% in NMI, ARI, Homogeneity, and ACC, respectively, while maintaining competitive efficiency and scalability. These results highlight GCAO's superiority in preserving cluster integrity, enhancing boundary separability, and ensuring robust performance on complex data distributions.", "date": "2025-10-27", "categories": []}
{"id": "2510.23438", "title": "Coresets for Clustering Under Stochastic Noise", "abstract": "We study the problem of constructing coresets for $(k, z)$-clustering when the input dataset is corrupted by stochastic noise drawn from a known distribution. In this setting, evaluating the quality of a coreset is inherently challenging, as the true underlying dataset is unobserved. To address this, we investigate coreset construction using surrogate error metrics that are tractable and provably related to the true clustering cost. We analyze a traditional metric from prior work and introduce a new error metric that more closely aligns with the true cost. Although our metric is defined independently of the noise distribution, it enables approximation guarantees that scale with the noise level. We design a coreset construction algorithm based on this metric and show that, under mild assumptions on the data and noise, enforcing an $\\varepsilon$-bound under our metric yields smaller coresets and tighter guarantees on the true clustering cost than those obtained via classical metrics. In particular, we prove that the coreset size can improve by a factor of up to $\\mathrm{poly}(k)$, where $n$ is the dataset size. Experiments on real-world datasets support our theoretical findings and demonstrate the practical advantages of our approach.", "date": "2025-10-27", "categories": []}
{"id": "2505.10704", "title": "ZEUS: Zero-shot Embeddings for Unsupervised Separation of Tabular Data", "abstract": "Clustering tabular data remains a significant open challenge in data analysis and machine learning. Unlike for image data, similarity between tabular records often varies across datasets, making the definition of clusters highly dataset-dependent. Furthermore, the absence of supervised signals complicates hyperparameter tuning in deep learning clustering methods, frequently resulting in unstable performance. To address these issues and reduce the need for per-dataset tuning, we adopt an emerging approach in deep learning: zero-shot learning. We propose ZEUS, a self-contained model capable of clustering new datasets without any additional training or fine-tuning. It operates by decomposing complex datasets into meaningful components that can then be clustered effectively. Thanks to pre-training on synthetic datasets generated from a latent-variable prior, it generalizes across various datasets without requiring user intervention. To the best of our knowledge, ZEUS is the first zero-shot method capable of generating embeddings for tabular data in a fully unsupervised manner. Experimental results demonstrate that it performs on par with or better than traditional clustering algorithms and recent deep learning-based methods, while being significantly faster and more user-friendly.", "date": "2025-05-15", "categories": []}
{"id": "2510.21669", "title": "Optimal Graph Clustering without Edge Density Signals", "abstract": "This paper establishes the theoretical limits of graph clustering under the Popularity-Adjusted Block Model (PABM), addressing limitations of existing models. In contrast to the Stochastic Block Model (SBM), which assumes uniform vertex degrees, and to the Degree-Corrected Block Model (DCBM), which applies uniform degree corrections across clusters, PABM introduces separate popularity parameters for intra- and inter-cluster connections. Our main contribution is the characterization of the optimal error rate for clustering under PABM, which provides novel insights on clustering hardness: we demonstrate that unlike SBM and DCBM, cluster recovery remains possible in PABM even when traditional edge-density signals vanish, provided intra- and inter-cluster popularity coefficients differ. This highlights a dimension of degree heterogeneity captured by PABM but overlooked by DCBM: local differences in connectivity patterns can enhance cluster separability independently of global edge densities. Finally, because PABM exhibits a richer structure, its expected adjacency matrix has rank between $k$ and $k^2$, where $k$ is the number of clusters. As a result, spectral embeddings based on the top $k$ eigenvectors may fail to capture important structural information. Our numerical experiments on both synthetic and real datasets confirm that spectral clustering algorithms incorporating $k^2$ eigenvectors outperform traditional spectral approaches.", "date": "2025-10-24", "categories": []}
{"id": "2505.09131", "title": "Fair Clustering via Alignment", "abstract": "Algorithmic fairness in clustering aims to balance the proportions of instances assigned to each cluster with respect to a given sensitive attribute. While recently developed fair clustering algorithms optimize clustering objectives under specific fairness constraints, their inherent complexity or approximation often results in suboptimal clustering utility or numerical instability in practice. To resolve these limitations, we propose a new fair clustering algorithm based on a novel decomposition of the fair $K$-means clustering objective function. The proposed algorithm, called Fair Clustering via Alignment (FCA), operates by alternately (i) finding a joint probability distribution to align the data from different protected groups, and (ii) optimizing cluster centers in the aligned space. A key advantage of FCA is that it theoretically guarantees approximately optimal clustering utility for any given fairness level without complex constraints, thereby enabling high-utility fair clustering in practice. Experiments show that FCA outperforms existing methods by (i) attaining a superior trade-off between fairness level and clustering utility, and (ii) achieving near-perfect fairness without numerical instability.", "date": "2025-05-14", "categories": []}
{"id": "2510.20077", "title": "Data-Adaptive Transformed Bilateral Tensor Low-Rank Representation for Clustering", "abstract": "Tensor low-rank representation (TLRR) has demonstrated significant success in image clustering. However, most existing methods rely on fixed transformations and suffer from poor robustness to noise. In this paper, we propose a novel transformed bilateral tensor low-rank representation model called TBTLRR, which introduces a data-adaptive tensor nuclear norm by learning arbitrary unitary transforms, allowing for more effective capture of global correlations. In addition, by leveraging the bilateral structure of latent tensor data, TBTLRR is able to exploit local correlations between image samples and features. Furthermore, TBTLRR integrates the $\\ell_{1/2}$-norm and Frobenius norm regularization terms for better dealing with complex noise in real-world scenarios. To solve the proposed nonconvex model, we develop an efficient optimization algorithm inspired by the alternating direction method of multipliers (ADMM) and provide theoretical convergence. Extensive experiments validate its superiority over the state-of-the-art methods in clustering. The code will be available at https://github.com/xianchaoxiu/TBTLRR.", "date": "2025-10-22", "categories": []}
{"id": "2510.20431", "title": "Partial Optimality in Cubic Correlation Clustering for General Graphs", "abstract": "The higher-order correlation clustering problem for a graph $G$ and costs associated with cliques of $G$ consists in finding a clustering of $G$ so as to minimize the sum of the costs of those cliques whose nodes all belong to the same cluster. To tackle this NP-hard problem in practice, local search heuristics have been proposed and studied in the context of applications. Here, we establish partial optimality conditions for cubic correlation clustering, i.e., for the special case of at most 3-cliques. We define and implement algorithms for deciding these conditions and examine their effectiveness numerically, on two data sets.", "date": "2025-10-23", "categories": []}
{"id": "2510.19248", "title": "Mixing Configurations for Downstream Prediction", "abstract": "Humans possess an innate ability to group objects by similarity, a cognitive mechanism that clustering algorithms aim to emulate. Recent advances in community detection have enabled the discovery of configurations -- valid hierarchical clusterings across multiple resolution scales -- without requiring labeled data. In this paper, we formally characterize these configurations and identify similar emergent structures in register tokens within Vision Transformers. Unlike register tokens, configurations exhibit lower redundancy and eliminate the need for ad hoc selection. They can be learned through unsupervised or self-supervised methods, yet their selection or composition remains specific to the downstream task and input. Building on these insights, we introduce GraMixC, a plug-and-play module that extracts configurations, aligns them using our Reverse Merge/Split (RMS) technique, and fuses them via attention heads before forwarding them to any downstream predictor. On the DSN1 16S rRNA cultivation-media prediction task, GraMixC improves the R2 score from 0.6 to 0.9 across multiple methods, setting a new state of the art. We further validate GraMixC on standard tabular benchmarks, where it consistently outperforms single-resolution and static-feature baselines.", "date": "2025-10-22", "categories": []}
{"id": "2510.19306", "title": "Topology of Currencies: Persistent Homology for FX Co-movements: A Comparative Clustering Study", "abstract": "This study investigates whether Topological Data Analysis (TDA) can provide additional insights beyond traditional statistical methods in clustering currency behaviours. We focus on the foreign exchange (FX) market, which is a complex system often exhibiting non-linear and high-dimensional dynamics that classical techniques may not fully capture. We compare clustering results based on TDA-derived features versus classical statistical features using monthly logarithmic returns of 13 major currency exchange rates (all against the euro). Two widely-used clustering algorithms, \\(k\\)-means and Hierarchical clustering, are applied on both types of features, and cluster quality is evaluated via the Silhouette score and the Calinski-Harabasz index. Our findings show that TDA-based feature clustering produces more compact and well-separated clusters than clustering on traditional statistical features, particularly achieving substantially higher Calinski-Harabasz scores. However, all clustering approaches yield modest Silhouette scores, underscoring the inherent difficulty of grouping FX time series. The differing cluster compositions under TDA vs. classical features suggest that TDA captures structural patterns in currency co-movements that conventional methods might overlook. These results highlight TDA as a valuable complementary tool for analysing financial time series, with potential applications in risk management where understanding structural co-movements is crucial.", "date": "2025-10-22", "categories": []}
{"id": "2510.18004", "title": "Attention-Guided Deep Adversarial Temporal Subspace Clustering (A-DATSC) Model for multivariate spatiotemporal data", "abstract": "Deep subspace clustering models are vital for applications such as snowmelt detection, sea ice tracking, crop health monitoring, infectious disease modeling, network load prediction, and land-use planning, where multivariate spatiotemporal data exhibit complex temporal dependencies and reside on multiple nonlinear manifolds beyond the capability of traditional clustering methods. These models project data into a latent space where samples lie in linear subspaces and exploit the self-expressiveness property to uncover intrinsic relationships. Despite their success, existing methods face major limitations: they use shallow autoencoders that ignore clustering errors, emphasize global features while neglecting local structure, fail to model long-range dependencies and positional information, and are rarely applied to 4D spatiotemporal data. To address these issues, we propose A-DATSC (Attention-Guided Deep Adversarial Temporal Subspace Clustering), a model combining a deep subspace clustering generator and a quality-verifying discriminator. The generator, inspired by U-Net, preserves spatial and temporal integrity through stacked TimeDistributed ConvLSTM2D layers, reducing parameters and enhancing generalization. A graph attention transformer based self-expressive network captures local spatial relationships, global dependencies, and both short- and long-range correlations. Experiments on three real-world multivariate spatiotemporal datasets show that A-DATSC achieves substantially superior clustering performance compared to state-of-the-art deep subspace clustering models.", "date": "2025-10-20", "categories": []}
{"id": "2412.04781", "title": "DPGIIL: Dirichlet Process-Deep Generative Model-Integrated Incremental Learning for Clustering in Transmissibility-based Online Structural Anomaly Detection", "abstract": "Clustering based on vibration responses, such as transmissibility functions (TFs), is promising in structural anomaly detection. However, most existing methods struggle to determine the optimal cluster number, handle high-dimensional streaming data, and rely heavily on manually engineered features due to their shallow structures. To address these issues, this work proposes a novel clustering framework, referred to as Dirichlet process-deep generative model-integrated incremental learning (DPGIIL), for online structural anomaly detection, which combines the advantages of deep generative models (DGMs) in representation learning and the Dirichlet process mixture model (DPMM) in identifying distinct patterns in observed data. Within the context of variational Bayesian inference, a lower bound on the log marginal likelihood of DPGIIL, tighter than the evidence lower bound, is derived analytically, which enables the joint optimization of DGM and DPMM parameters, thereby allowing the DPMM to regularize the DGM's feature extraction process. Additionally, a greedy split-merge scheme-based coordinate ascent variational inference method is devised to accelerate the optimization. The summary statistics of the DPMM, along with the network parameters, are used to retain information about previous data for incremental learning. For online structural anomaly detection, DPGIIL can not only detect anomalies by dynamically assigning incoming data to new clusters but also indicate different structural states using distinct clusters, thereby providing additional information about the operating conditions of the monitored structure compared to traditional anomaly detectors. Three case studies demonstrate the dynamic adaptability of the proposed method and show that it outperforms some state-of-the-art approaches in both structural anomaly detection and clustering.", "date": "2024-12-06", "categories": []}
{"id": "2507.20840", "title": "Towards Explainable Deep Clustering for Time Series Data", "abstract": "Deep clustering uncovers hidden patterns and groups in complex time series data, yet its opaque decision-making limits use in safety-critical settings. This survey offers a structured overview of explainable deep clustering for time series, collecting current methods and their real-world applications. We thoroughly discuss and compare peer-reviewed and preprint papers through application domains across healthcare, finance, IoT, and climate science. Our analysis reveals that most work relies on autoencoder and attention architectures, with limited support for streaming, irregularly sampled, or privacy-preserved series, and interpretability is still primarily treated as an add-on. To push the field forward, we outline six research opportunities: (1) combining complex networks with built-in interpretability; (2) setting up clear, faithfulness-focused evaluation metrics for unsupervised explanations; (3) building explainers that adapt to live data streams; (4) crafting explanations tailored to specific domains; (5) adding human-in-the-loop methods that refine clusters and explanations together; and (6) improving our understanding of how time series clustering models work internally. By making interpretability a primary design goal rather than an afterthought, we propose the groundwork for the next generation of trustworthy deep clustering time series analytics.", "date": "2025-07-28", "categories": []}
{"id": "2510.15986", "title": "User Profiles of Sleep Disorder Sufferers: Towards Explainable Clustering and Differential Variable Analysis", "abstract": "Sleep disorders have a major impact on patients' health and quality of life, but their diagnosis remains complex due to the diversity of symptoms. Today, technological advances, combined with medical data analysis, are opening new perspectives for a better understanding of these disorders. In particular, explainable artificial intelligence (XAI) aims to make AI model decisions understandable and interpretable for users. In this study, we propose a clustering-based method to group patients according to different sleep disorder profiles. By integrating an explainable approach, we identify the key factors influencing these pathologies. An experiment on anonymized real data illustrates the effectiveness and relevance of our approach.", "date": "2025-10-13", "categories": []}
{"id": "2510.15076", "title": "Online Correlation Clustering: Simultaneously Optimizing All $\\ell_p$-norms", "abstract": "The $\\ell_p$-norm objectives for correlation clustering present a fundamental trade-off between minimizing total disagreements (the $\\ell_1$-norm) and ensuring fairness to individual nodes (the $\\ell_\\infty$-norm). Surprisingly, in the offline setting it is possible to simultaneously approximate all $\\ell_p$-norms with a single clustering. Can this powerful guarantee be achieved in an online setting? This paper provides the first affirmative answer. We present a single algorithm for the online-with-a-sample (AOS) model that, given a small constant fraction of the input as a sample, produces one clustering that is simultaneously $O(\\log^4 n)$-competitive for all $\\ell_p$-norms with high probability, $O(\\log n)$-competitive for the $\\ell_\\infty$-norm with high probability, and $O(1)$-competitive for the $\\ell_1$-norm in expectation. This work successfully translates the offline \"all-norms\" guarantee to the online world.\n  Our setting is motivated by a new hardness result that demonstrates a fundamental separation between these objectives in the standard random-order (RO) online model. Namely, while the $\\ell_1$-norm is trivially $O(1)$-approximable in the RO model, we prove that any algorithm in the RO model for the fairness-promoting $\\ell_\\infty$-norm must have a competitive ratio of at least $\\Omega(n^{1/3})$. This highlights the necessity of a different beyond-worst-case model. We complement our algorithm with lower bounds, showing our competitive ratios for the $\\ell_1$- and $\\ell_\\infty$- norms are nearly tight in the AOS model.", "date": "2025-10-16", "categories": []}
{"id": "2407.01247", "title": "Multi-level Reliable Guidance for Unpaired Multi-view Clustering", "abstract": "In this thesis, we address the challenging problem of unpaired multi-view clustering (UMC), which aims to achieve effective joint clustering using unpaired samples observed across multiple views. Traditional incomplete multi-view clustering (IMC) methods typically rely on paired samples to capture complementary information between views. However, such strategies become impractical in the UMC due to the absence of paired samples. Although some researchers have attempted to address this issue by preserving consistent cluster structures across views, effectively mining such consistency remains challenging when the cluster structures {with low confidence}. Therefore, we propose a novel method, Multi-level Reliable Guidance for UMC (MRG-UMC), which integrates multi-level clustering and reliable view guidance to learn consistent and confident cluster structures from three perspectives. Specifically, inner-view multi-level clustering exploits high-confidence sample pairs across different levels to reduce the impact of boundary samples, resulting in more confident cluster structures. Synthesized-view alignment leverages a synthesized-view to mitigate cross-view discrepancies and promote consistency. Cross-view guidance employs a reliable view guidance strategy to enhance the clustering confidence of poorly clustered views. These three modules are jointly optimized across multiple levels to achieve consistent and confident cluster structures. Furthermore, theoretical analyses verify the effectiveness of MRG-UMC in enhancing clustering confidence. Extensive experimental results show that MRG-UMC outperforms state-of-the-art UMC methods, achieving an average NMI improvement of 12.95\\% on multi-view datasets. {The source code is available at: https://anonymous.4open.science/r/MRG-UMC-5E20.", "date": "2024-07-01", "categories": []}
{"id": "2510.14145", "title": "High-Dimensional BWDM: A Robust Nonparametric Clustering Validation Index for Large-Scale Data", "abstract": "Determining the appropriate number of clusters in unsupervised learning is a central problem in statistics and data science. Traditional validity indices such as Calinski-Harabasz, Silhouette, and Davies-Bouldin-depend on centroid-based distances and therefore degrade in high-dimensional or contaminated data. This paper proposes a new robust, nonparametric clustering validation framework, the High-Dimensional Between-Within Distance Median (HD-BWDM), which extends the recently introduced BWDM criterion to high-dimensional spaces. HD-BWDM integrates random projection and principal component analysis to mitigate the curse of dimensionality and applies trimmed clustering and medoid-based distances to ensure robustness against outliers. We derive theoretical results showing consistency and convergence under Johnson-Lindenstrauss embeddings. Extensive simulations demonstrate that HD-BWDM remains stable and interpretable under high-dimensional projections and contamination, providing a robust alternative to traditional centroid-based validation criteria. The proposed method provides a theoretically grounded, computationally efficient stopping rule for nonparametric clustering in modern high-dimensional applications.", "date": "2025-10-15", "categories": []}
{"id": "2209.02935", "title": "Normalised clustering accuracy: An asymmetric external cluster validity measure", "abstract": "There is no, nor will there ever be, single best clustering algorithm. Nevertheless, we would still like to be able to distinguish between methods that work well on certain task types and those that systematically underperform. Clustering algorithms are traditionally evaluated using either internal or external validity measures. Internal measures quantify different aspects of the obtained partitions, e.g., the average degree of cluster compactness or point separability. However, their validity is questionable because the clusterings they endorse can sometimes be meaningless. External measures, on the other hand, compare the algorithms' outputs to fixed ground truth groupings provided by experts. In this paper, we argue that the commonly used classical partition similarity scores, such as the normalised mutual information, Fowlkes-Mallows, or adjusted Rand index, miss some desirable properties. In particular, they do not identify worst-case scenarios correctly, nor are they easily interpretable. As a consequence, the evaluation of clustering algorithms on diverse benchmark datasets can be difficult. To remedy these issues, we propose and analyse a new measure: a version of the optimal set-matching accuracy, which is normalised, monotonic with respect to some similarity relation, scale-invariant, and corrected for the imbalancedness of cluster sizes (but neither symmetric nor adjusted for chance).", "date": "2022-09-07", "categories": []}
{"id": "2303.05679", "title": "Clustering with minimum spanning trees: How good can it be?", "abstract": "Minimum spanning trees (MSTs) provide a convenient representation of datasets in numerous pattern recognition activities. Moreover, they are relatively fast to compute. In this paper, we quantify the extent to which they are meaningful in low-dimensional partitional data clustering tasks. By identifying the upper bounds for the agreement between the best (oracle) algorithm and the expert labels from a large battery of benchmark data, we discover that MST methods can be very competitive. Next, we review, study, extend, and generalise a few existing, state-of-the-art MST-based partitioning schemes. This leads to some new noteworthy approaches. Overall, the Genie and the information-theoretic methods often outperform the non-MST algorithms such as K-means, Gaussian mixtures, spectral clustering, Birch, density-based, and classical hierarchical agglomerative procedures. Nevertheless, we identify that there is still some room for improvement, and thus the development of novel algorithms is encouraged.", "date": "2023-03-10", "categories": []}
{"id": "2302.10359", "title": "Replicable Clustering", "abstract": "We design replicable algorithms in the context of statistical clustering under the recently introduced notion of replicability from Impagliazzo et al. [2022]. According to this definition, a clustering algorithm is replicable if, with high probability, its output induces the exact same partition of the sample space after two executions on different inputs drawn from the same distribution, when its internal randomness is shared across the executions. We propose such algorithms for the statistical $k$-medians, statistical $k$-means, and statistical $k$-centers problems by utilizing approximation routines for their combinatorial counterparts in a black-box manner. In particular, we demonstrate a replicable $O(1)$-approximation algorithm for statistical Euclidean $k$-medians ($k$-means) with $\\operatorname{poly}(d)$ sample complexity. We also describe an $O(1)$-approximation algorithm with an additional $O(1)$-additive error for statistical Euclidean $k$-centers, albeit with $\\exp(d)$ sample complexity. In addition, we provide experiments on synthetic distributions in 2D using the $k$-means++ implementation from sklearn as a black-box that validate our theoretical results.", "date": "2023-02-20", "categories": []}
{"id": "2410.16910", "title": "TreeDiffusion: Hierarchical Generative Clustering for Conditional Diffusion", "abstract": "Generative modeling and clustering are conventionally distinct tasks in machine learning. Variational Autoencoders (VAEs) have been widely explored for their ability to integrate both, providing a framework for generative clustering. However, while VAEs can learn meaningful cluster representations in latent space, they often struggle to generate high-quality samples. This paper addresses this problem by introducing TreeDiffusion, a deep generative model that conditions diffusion models on learned latent hierarchical cluster representations from a VAE to obtain high-quality, cluster-specific generations. Our approach consists of two steps: first, a VAE-based clustering model learns a hierarchical latent representation of the data. Second, a cluster-aware diffusion model generates realistic images conditioned on the learned hierarchical structure. We systematically compare the generative capabilities of our approach with those of alternative conditioning strategies. Empirically, we demonstrate that conditioning diffusion models on hierarchical cluster representations improves the generative performance on real-world datasets compared to other approaches. Moreover, a key strength of our method lies in its ability to generate images that are both representative and specific to each cluster, enabling more detailed visualization of the learned latent structure. Our approach addresses the generative limitations of VAE-based clustering approaches by leveraging their learned structure, thereby advancing the field of generative clustering.", "date": "2024-10-22", "categories": []}
{"id": "2503.14357", "title": "Wasserstein-based Kernel Principal Component Analysis for Clustering Applications", "abstract": "Many data clustering applications must handle objects that cannot be represented as vectors. In this context, the bag-of-vectors representation describes complex objects through discrete distributions, for which the Wasserstein distance provides a well-conditioned dissimilarity measure. Kernel methods extend this by embedding distance information into feature spaces that facilitate analysis. However, an unsupervised framework that combines kernels with Wasserstein distances for clustering distributional data is still lacking. We address this gap by introducing a computationally tractable framework that integrates Wasserstein metrics with kernel methods for clustering. The framework can accommodate both vectorial and distributional data, enabling applications in various domains. It comprises three components: (i) an efficient approximation of pairwise Wasserstein distances using multiple reference distributions; (ii) shifted positive definite kernel functions based on Wasserstein distances, combined with kernel principal component analysis for feature mapping; and (iii) scalable, distance-agnostic validity indices for clustering evaluation and kernel parameter optimization. Experiments on power distribution graphs and real-world time series demonstrate the effectiveness and efficiency of the proposed framework.", "date": "2025-03-18", "categories": []}
{"id": "2510.12669", "title": "Structure-Aware Spectral Sparsification via Uniform Edge Sampling", "abstract": "Spectral clustering is a fundamental method for graph partitioning, but its reliance on eigenvector computation limits scalability to massive graphs. Classical sparsification methods preserve spectral properties by sampling edges proportionally to their effective resistances, but require expensive preprocessing to estimate these resistances. We study whether uniform edge sampling-a simple, structure-agnostic strategy-can suffice for spectral clustering. Our main result shows that for graphs admitting a well-separated $k$-clustering, characterized by a large structure ratio $\\Upsilon(k) = \\lambda_{k+1} / \\rho_G(k)$, uniform sampling preserves the spectral subspace used for clustering. Specifically, we prove that uniformly sampling $O(\\gamma^2 n \\log n / \\epsilon^2)$ edges, where $\\gamma$ is the Laplacian condition number, yields a sparsifier whose top $(n-k)$-dimensional eigenspace is approximately orthogonal to the cluster indicators. This ensures that the spectral embedding remains faithful, and clustering quality is preserved. Our analysis introduces new resistance bounds for intra-cluster edges, a rank-$(n-k)$ effective resistance formulation, and a matrix Chernoff bound adapted to the dominant eigenspace. These tools allow us to bypass importance sampling entirely. Conceptually, our result connects recent coreset-based clustering theory to spectral sparsification, showing that under strong clusterability, even uniform sampling is structure-aware. This provides the first provable guarantee that uniform edge sampling suffices for structure-preserving spectral clustering.", "date": "2025-10-14", "categories": []}
{"id": "2503.09134", "title": "Clustering by Nonparametric Smoothing", "abstract": "A novel formulation of the clustering problem is introduced in which the task is expressed as an estimation problem, where the object to be estimated is a function which maps a point to its distribution of cluster membership. Unlike existing approaches which implicitly estimate such a function, like Gaussian Mixture Models (GMMs), the proposed approach bypasses any explicit modelling assumptions and exploits the flexible estimation potential of nonparametric smoothing. An intuitive approach for selecting the tuning parameters governing estimation is provided, which allows the proposed method to automatically determine both an appropriate level of flexibility and also the number of clusters to extract from a given data set. Experiments on a large collection of publicly available data sets are used to document the strong performance of the proposed approach, in comparison with relevant benchmarks from the literature. R code to implement the proposed approach is available from https://github.com/DavidHofmeyr/CNS", "date": "2025-03-12", "categories": []}
{"id": "2504.18181", "title": "Unveiling 3D Ocean Biogeochemical Provinces in the North Atlantic: A Systematic Comparison and Validation of Clustering Methods", "abstract": "Defining ocean regions and water masses helps to understand marine processes and can serve downstream tasks such as defining marine protected areas. However, such definitions often result from subjective decisions potentially producing misleading, unreproducible outcomes. Here, the aim was to objectively define regions of the North Atlantic through systematic comparison of clustering methods within the Native Emergent Manifold Interrogation (NEMI) framework (Sonnewald, 2023). About 300 million measured salinity, temperature, and oxygen, nitrate, phosphate and silicate concentration values served as input for various clustering methods (k-Means, agglomerative Ward, and Density-Based Spatial Clustering of Applications with Noise (DBSCAN)). Uniform Manifold Approximation and Projection (UMAP) emphasised (dis-)similarities in the data while reducing dimensionality. Based on systematic validation of clustering methods and their hyperparameters using internal, external and relative validation techniques, results showed that UMAP-DBSCAN best represented the data. Strikingly, internal validation metrics proved systematically unreliable for comparing clustering methods. To address stochastic variability, 100 UMAP-DBSCAN clustering runs were conducted and aggregated following NEMI, yielding a final set of 321 clusters. Reproducibility was evaluated via ensemble overlap ($88.81\\pm1.8\\%$) and mean grid cell-wise uncertainty ($15.49\\pm20\\%$). Case studies of the Mediterranean Sea, deep Atlantic waters and Labrador Sea showed strong agreement with common water mass definitions. This study revealed a more detailed regionalisation compared to previous concepts such as the Longhurst provinces through systematic clustering method comparison. The applied method is objective, efficient and reproducible and will support future research on biogeochemical differences and changes in oceanic regions.", "date": "2025-04-25", "categories": []}
{"id": "2504.20982", "title": "Provably faster randomized and quantum algorithms for $k$-means clustering via uniform sampling", "abstract": "The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive in big data applications. This was improved in recent works proposing quantum and quantum-inspired classical algorithms to approximate the $k$-means algorithm locally, in time depending only logarithmically on the number of data points (along with data dependent parameters) [q-means: A quantum algorithm for unsupervised machine learning, Kerenidis, Landman, Luongo, and Prakash, NeurIPS 2019; Do you know what $q$-means?, Cornelissen, Doriguello, Luongo, Tang, QTML 2025]. In this work, we describe a simple randomized mini-batch $k$-means algorithm and a quantum algorithm inspired by the classical algorithm. We demonstrate that the worst case guarantees of these algorithms can significantly improve upon the bounds for algorithms in prior work. Our improvements are due to a careful use of uniform sampling, which preserves certain symmetries of the $k$-means problem that are not preserved in previous algorithms that use data norm-based sampling.", "date": "2025-04-29", "categories": []}
{"id": "2510.09799", "title": "Distributed clustering in partially overlapping feature spaces", "abstract": "We introduce and address a novel distributed clustering problem where each participant has a private dataset containing only a subset of all available features, and some features are included in multiple datasets. This scenario occurs in many real-world applications, such as in healthcare, where different institutions have complementary data on similar patients. We propose two different algorithms suitable for solving distributed clustering problems that exhibit this type of feature space heterogeneity. The first is a federated algorithm in which participants collaboratively update a set of global centroids. The second is a one-shot algorithm in which participants share a statistical parametrization of their local clusters with the central server, who generates and merges synthetic proxy datasets. In both cases, participants perform local clustering using algorithms of their choice, which provides flexibility and personalized computational costs. Pretending that local datasets result from splitting and masking an initial centralized dataset, we identify some conditions under which the proposed algorithms are expected to converge to the optimal centralized solution. Finally, we test the practical performance of the algorithms on three public datasets.", "date": "2025-10-10", "categories": []}
{"id": "2510.09959", "title": "Clustering Result Re-guided Incomplete Multi-view Spectral Clustering", "abstract": "Incomplete multi-view spectral clustering generalizes spectral clustering to multi-view data and simultaneously realizes the partition of multi-view data with missing views. For this category of method, K-means algorithm needs to be performed to generate the clustering result after the procedure of feature extraction. More importantly, the connectivity of samples reflected by the clustering result is not utilized effectively. To overcome these defects, we propose Clustering Result re-Guided Incomplete Multi-view Spectral Clustering (CRG_IMSC). CRG_IMSC obtains the clustering result directly by imposing nonnegative constraint to the extracted feature. Furthermore, it constructs the connectivity matrix according to the result of spectral clustering, and minimizes the residual of self-representation based on the connectivity matrix. A novel iterative algorithm using multiplicative update is developed to solve the optimization problem of CRG_IMSC, and its convergence is proved rigorously. On benchmark datasets, for multi-view data, CRG_IMSC performs better than state-of-the-art clustering methods, and the experimental results also demonstrate the convergence of CRG_IMSC algorithm.", "date": "2025-10-11", "categories": []}
{"id": "2510.10263", "title": "Unveiling Gamer Archetypes through Multi modal feature Correlations and Unsupervised Learning", "abstract": "Profiling gamers provides critical insights for adaptive game design, behavioral understanding, and digital well-being. This study proposes an integrated, data-driven framework that combines psychological measures, behavioral analytics, and machine learning to reveal underlying gamer personas. A structured survey of 250 participants, including 113 active gamers, captured multidimensional behavioral, motivational, and social data. The analysis pipeline integrated feature engineering, association-network, knowledge-graph analysis, and unsupervised clustering to extract meaningful patterns. Correlation statistics uses Cramers V, Tschuprows T, Theils U, and Spearmans quantified feature associations, and network centrality guided feature selection. Dimensionality-reduction techniques such as PCA, SVD, t-SNE are coupled with clustering algorithms like K-Means, Agglomerative, Spectral, DBSCAN, evaluated using Silhouette, Calinski Harabasz, and Davies Bouldin indices. The PCA with K-Means with k = 4 model achieved optimal cluster quality with Silhouette = 0.4, identifying four archetypes as Immersive Social Story-Seekers, Disciplined Optimizers, Strategic Systems Navigators, and Competitive Team-Builders. This research contributes a reproducible pipeline that links correlation-driven network insights with unsupervised learning. The integration of behavioral correlation networks with clustering not only enhances classification accuracy but also offers a holistic lens to connect gameplay motivations with psychological and wellness outcomes.", "date": "2025-10-11", "categories": []}
{"id": "2510.07503", "title": "Time-Frequency Filtering Meets Graph Clustering", "abstract": "We show that the problem of identifying different signal components from a time-frequency representation can be equivalently phrased as a graph clustering problem: given a graph $G=(V,E)$ one aims to identify `clusters', subgraphs that are strongly connected and have relatively few connections between them. The graph clustering problem is well studied, we show how these ideas can suggest (many) new ways to identify signal components. Numerical experiments illustrate the ideas.", "date": "2025-10-08", "categories": []}
{"id": "2510.07639", "title": "Property Classification of Vacation Rental Properties during Covid-19", "abstract": "This study advocates for employing clustering techniques to classify vacation rental properties active during the Covid pandemic to identify inherent patterns and behaviours. The dataset, a collaboration between the ESRC funded Consumer Data Research Centre (CDRC) and AirDNA, encompasses data for over a million properties and hosts. Utilising K-means and K-medoids clustering techniques, we identify homogenous groups and their common characteristics. Our findings enhance comprehension of the intricacies of vacation rental evaluations and could potentially be utilised in the creation of targeted, cluster-specific policies.", "date": "2025-10-09", "categories": []}
{"id": "2509.25775", "title": "Autonomy-Aware Clustering: When Local Decisions Supersede Global Prescriptions", "abstract": "Clustering arises in a wide range of problem formulations, yet most existing approaches assume that the entities under clustering are passive and strictly conform to their assigned groups. In reality, entities often exhibit local autonomy, overriding prescribed associations in ways not fully captured by feature representations. Such autonomy can substantially reshape clustering outcomes -- altering cluster compositions, geometry, and cardinality -- with significant downstream effects on inference and decision-making. We introduce autonomy-aware clustering, a reinforcement learning (RL) framework that learns and accounts for the influence of local autonomy without requiring prior knowledge of its form. Our approach integrates RL with a Deterministic Annealing (DA) procedure, where, to determine underlying clusters, DA naturally promotes exploration in early stages of annealing and transitions to exploitation later. We also show that the annealing procedure exhibits phase transitions that enable design of efficient annealing schedules. To further enhance adaptability, we propose the Adaptive Distance Estimation Network (ADEN), a transformer-based attention model that learns dependencies between entities and cluster representatives within the RL loop, accommodates variable-sized inputs and outputs, and enables knowledge transfer across diverse problem instances. Empirical results show that our framework closely aligns with underlying data dynamics: even without explicit autonomy models, it achieves solutions close to the ground truth (gap ~3-4%), whereas ignoring autonomy leads to substantially larger gaps (~35-40%). The code and data are publicly available at https://github.com/salar96/AutonomyAwareClustering.", "date": "2025-09-30", "categories": []}
{"id": "2510.06907", "title": "Angular Constraint Embedding via SpherePair Loss for Constrained Clustering", "abstract": "Constrained clustering integrates domain knowledge through pairwise constraints. However, existing deep constrained clustering (DCC) methods are either limited by anchors inherent in end-to-end modeling or struggle with learning discriminative Euclidean embedding, restricting their scalability and real-world applicability. To avoid their respective pitfalls, we propose a novel angular constraint embedding approach for DCC, termed SpherePair. Using the SpherePair loss with a geometric formulation, our method faithfully encodes pairwise constraints and leads to embeddings that are clustering-friendly in angular space, effectively separating representation learning from clustering. SpherePair preserves pairwise relations without conflict, removes the need to specify the exact number of clusters, generalizes to unseen data, enables rapid inference of the number of clusters, and is supported by rigorous theoretical guarantees. Comparative evaluations with state-of-the-art DCC methods on diverse benchmarks, along with empirical validation of theoretical insights, confirm its superior performance, scalability, and overall real-world effectiveness. Code is available at \\href{https://github.com/spherepaircc/SpherePairCC/tree/main}{our repository}.", "date": "2025-10-08", "categories": []}
{"id": "2510.06919", "title": "Bayesian Nonparametric Dynamical Clustering of Time Series", "abstract": "We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet process as a prior on the parameters of a Switching Linear Dynamical System and a Gaussian process prior to model the statistical variations in amplitude and temporal alignment within each cluster. By modeling the evolution of time series patterns, the method avoids unnecessary proliferation of clusters in a principled manner. We perform inference by formulating a variational lower bound for off-line and on-line scenarios, enabling efficient learning through optimization. We illustrate the versatility and effectiveness of the approach through several case studies of electrocardiogram analysis using publicly available databases.", "date": "2025-10-08", "categories": []}
{"id": "2410.00927", "title": "Text Clustering as Classification with LLMs", "abstract": "Text clustering serves as a fundamental technique for organizing and interpreting unstructured textual data, particularly in contexts where manual annotation is prohibitively costly. With the rapid advancement of Large Language Models (LLMs) and their demonstrated effectiveness across a broad spectrum of NLP tasks, an emerging body of research has begun to explore their potential in the domain of text clustering. However, existing LLM-based approaches still rely on fine-tuned embedding models and sophisticated similarity metrics, rendering them computationally intensive and necessitating domain-specific adaptation. To address these limitations, we propose a novel framework that reframes text clustering as a classification task by harnessing the in-context learning capabilities of LLMs. Our framework eliminates the need for fine-tuning embedding models or intricate clustering algorithms. It comprises two key steps: first, the LLM is prompted to generate a set of candidate labels based on the dataset and then merges semantically similar labels; second, it assigns the most appropriate label to each text sample. By leveraging the advanced natural language understanding and generalization capabilities of LLMs, the proposed approach enables effective clustering with minimal human intervention. Experimental results on diverse datasets demonstrate that our framework achieves comparable or superior performance to state-of-the-art embedding-based clustering techniques, while significantly reducing computational complexity and resource requirements. These findings underscore the transformative potential of LLMs in simplifying and enhancing text clustering tasks. We make our code available to the public for utilization at https://github.com/ECNU-Text-Computing/Text-Clustering-via-LLM. We also provide the supplementary Appendix within the repository.", "date": "2024-09-30", "categories": []}
{"id": "2501.16894", "title": "DBSCAN in domains with periodic boundary conditions", "abstract": "Many scientific problems involve data that is embedded in a space with periodic boundary conditions. This can for instance be related to an inherent cyclic or rotational symmetry in the data or a spatially extended periodicity. When analyzing such data, well-tailored methods are needed to obtain efficient approaches that obey the periodic boundary conditions of the problem. In this work, we present a method for applying a clustering algorithm to data embedded in a periodic domain based on the DBSCAN algorithm, a widely used unsupervised machine learning method that identifies clusters in data. The proposed method internally leverages the conventional DBSCAN algorithm for domains with open boundaries, such that it remains compatible with all optimized implementations for neighborhood searches in open domains. In this way, it retains the same optimized runtime complexity of $O(N\\log N)$. We demonstrate the workings of the proposed method using synthetic data in one, two and three dimensions and also apply it to a real-world example involving the clustering of bubbles in a turbulent flow. The proposed approach is implemented in a ready-to-use Python package that we make publicly available.", "date": "2025-01-28", "categories": []}
{"id": "2502.08397", "title": "Strong bounds for large-scale Minimum Sum-of-Squares Clustering", "abstract": "Clustering is a fundamental technique in data analysis and machine learning, used to group similar data points together. Among various clustering methods, the Minimum Sum-of-Squares Clustering (MSSC) is one of the most widely used. MSSC aims to minimize the total squared Euclidean distance between data points and their corresponding cluster centroids. Due to the unsupervised nature of clustering, achieving global optimality is crucial, yet computationally challenging. The complexity of finding the global solution increases exponentially with the number of data points, making exact methods impractical for large-scale datasets. Even obtaining strong lower bounds on the optimal MSSC objective value is computationally prohibitive, making it difficult to assess the quality of heuristic solutions. We address this challenge by introducing a novel method to validate heuristic MSSC solutions through optimality gaps. Our approach employs a divide-and-conquer strategy, decomposing the problem into smaller instances that can be handled by an exact solver. The decomposition is guided by an auxiliary optimization problem, the \"anticlustering problem\", for which we design an efficient heuristic. Computational experiments demonstrate the effectiveness of the method for large-scale instances, achieving optimality gaps below 3% in most cases while maintaining reasonable computational times. These results highlight the practicality of our approach in assessing feasible clustering solutions for large datasets, bridging a critical gap in MSSC evaluation.", "date": "2025-02-12", "categories": []}
{"id": "2412.18760", "title": "Data clustering: a fundamental method in data science and management", "abstract": "This paper explores the critical role of data clustering in data science, emphasizing its methodologies, tools, and diverse applications. Traditional techniques, such as partitional and hierarchical clustering, are analyzed alongside advanced approaches such as data stream, density-based, graph-based, and model-based clustering for handling complex structured datasets. The paper highlights key principles underpinning clustering, outlines widely used tools and frameworks, introduces the workflow of clustering in data science, discusses challenges in practical implementation, and examines various applications of clustering. By focusing on these foundations and applications, the discussion underscores clustering's transformative potential. The paper concludes with insights into future research directions, emphasizing clustering's role in driving innovation and enabling data-driven decision-making.", "date": "2024-12-25", "categories": []}
{"id": "2501.02612", "title": "Chameleon2++: An Efficient and Scalable Variant Of Chameleon Clustering", "abstract": "Hierarchical clustering remains a fundamental challenge in data mining, particularly when dealing with large-scale datasets where traditional approaches fail to scale effectively. Recent Chameleon-based algorithms - Chameleon2, M-Chameleon, and INNGS-Chameleon have proposed advanced strategies but they still suffer from $O(n^2)$ computational complexity, especially for large datasets. With Chameleon2 as the base algorithm, we introduce Chameleon2++ that addresses this challenge.\n  Our algorithm has three parts. First, Graph Generation - we propose an approximate $k$-NN search instead of an exact one, specifically we integrate with the Annoy algorithm. This results in fast approximate nearest neighbor computation, significantly reducing the graph generation time. Second, Graph Partitioning - we propose use of a multi-level partitioning algorithm instead of a recursive bisection one. Specifically we adapt the hMETIS algorithm instead of the FM. This is because multi-level algorithms are robust to approximation introduced in the graph generation phase yielding higher-quality partitions, and that too with minimum configuration requirements. Third, Merging - we retain the flood fill heuristic that ensures connected balanced components in the partitions as well as efficient partition merging criteria leading to the final clusters.\n  These enhancements reduce the overall time complexity to $O(n\\log n)$, achieving scalability. On real-world benchmark datasets used in prior Chameleon works, Chameleon2++ delivers an average of 4% improvement in clustering quality. This demonstrates that algorithmic efficiency and clustering quality can co-exist in large-scale hierarchical clustering.", "date": "2025-01-05", "categories": []}
{"id": "2510.02731", "title": "Hybrid-Collaborative Augmentation and Contrastive Sample Adaptive-Differential Awareness for Robust Attributed Graph Clustering", "abstract": "Due to its powerful capability of self-supervised representation learning and clustering, contrastive attributed graph clustering (CAGC) has achieved great success, which mainly depends on effective data augmentation and contrastive objective setting. However, most CAGC methods utilize edges as auxiliary information to obtain node-level embedding representation and only focus on node-level embedding augmentation. This approach overlooks edge-level embedding augmentation and the interactions between node-level and edge-level embedding augmentations across various granularity. Moreover, they often treat all contrastive sample pairs equally, neglecting the significant differences between hard and easy positive-negative sample pairs, which ultimately limits their discriminative capability. To tackle these issues, a novel robust attributed graph clustering (RAGC), incorporating hybrid-collaborative augmentation (HCA) and contrastive sample adaptive-differential awareness (CSADA), is proposed. First, node-level and edge-level embedding representations and augmentations are simultaneously executed to establish a more comprehensive similarity measurement criterion for subsequent contrastive learning. In turn, the discriminative similarity further consciously guides edge augmentation. Second, by leveraging pseudo-label information with high confidence, a CSADA strategy is elaborately designed, which adaptively identifies all contrastive sample pairs and differentially treats them by an innovative weight modulation function. The HCA and CSADA modules mutually reinforce each other in a beneficent cycle, thereby enhancing discriminability in representation learning. Comprehensive graph clustering evaluations over six benchmark datasets demonstrate the effectiveness of the proposed RAGC against several state-of-the-art CAGC methods.", "date": "2025-10-03", "categories": []}
{"id": "2510.03143", "title": "The Computational Complexity of Almost Stable Clustering with Penalties", "abstract": "We investigate the complexity of stable (or perturbation-resilient) instances of $\\mathrm{k-M\\small{EANS}}$ and $\\mathrm{k-M\\small{EDIAN}}$ clustering problems in metrics with small doubling dimension. While these problems have been extensively studied under multiplicative perturbation resilience in low-dimensional Euclidean spaces (e.g., (Friggstad et al., 2019; Cohen-Addad and Schwiegelshohn, 2017)), we adopt a more general notion of stability, termed ``almost stable'', which is closer to the notion of $(\\alpha, \\varepsilon)$-perturbation resilience introduced by Balcan and Liang (2016). Additionally, we extend our results to $\\mathrm{k-M\\small{EANS}}$/$\\mathrm{k-M\\small{EDIAN}}$ with penalties, where each data point is either assigned to a cluster centre or incurs a penalty.\n  We show that certain special cases of almost stable $\\mathrm{k-M\\small{EANS}}$/$\\mathrm{k-M\\small{EDIAN}}$ (with penalties) are solvable in polynomial time. To complement this, we also examine the hardness of almost stable instances and $(1 + \\frac{1}{poly(n)})$-stable instances of $\\mathrm{k-M\\small{EANS}}$/$\\mathrm{k-M\\small{EDIAN}}$ (with penalties), proving super-polynomial lower bounds on the runtime of any exact algorithm under the widely believed Exponential Time Hypothesis (ETH).", "date": "2025-10-03", "categories": []}
{"id": "2307.07449", "title": "Differentially Private Clustering in Data Streams", "abstract": "Clustering problems (such as $k$-means and $k$-median) are fundamental unsupervised machine learning primitives, and streaming clustering algorithms have been extensively studied in the past. However, since data privacy becomes a central concern in many real-world applications, non-private clustering algorithms may not be as applicable in many scenarios.\n  In this work, we provide the first differentially private algorithms for $k$-means and $k$-median clustering of $d$-dimensional Euclidean data points over a stream with length at most $T$ using space that is sublinear (in $T$) in the continual release setting where the algorithm is required to output a clustering at every timestep.\n  We achieve (1) an $O(1)$-multiplicative approximation with $\\tilde{O}(k^{1.5} \\cdot poly(d,\\log(T)))$ space and $poly(k,d,\\log(T))$ additive error, or (2) a $(1+\\gamma)$-multiplicative approximation with $\\tilde{O}_\\gamma(poly(k,2^{O_\\gamma(d)},\\log(T)))$ space for any $\\gamma>0$, and the additive error is $poly(k,2^{O_\\gamma(d)},\\log(T))$. Our main technical contribution is a differentially private clustering framework for data streams which only requires an offline DP coreset or clustering algorithm as a blackbox.", "date": "2023-07-14", "categories": []}
{"id": "2505.12626", "title": "scSiameseClu: A Siamese Clustering Framework for Interpreting single-cell RNA Sequencing Data", "abstract": "Single-cell RNA sequencing (scRNA-seq) reveals cell heterogeneity, with cell clustering playing a key role in identifying cell types and marker genes. Recent advances, especially graph neural networks (GNNs)-based methods, have significantly improved clustering performance. However, the analysis of scRNA-seq data remains challenging due to noise, sparsity, and high dimensionality. Compounding these challenges, GNNs often suffer from over-smoothing, limiting their ability to capture complex biological information. In response, we propose scSiameseClu, a novel Siamese Clustering framework for interpreting single-cell RNA-seq data, comprising of 3 key steps: (1) Dual Augmentation Module, which applies biologically informed perturbations to the gene expression matrix and cell graph relationships to enhance representation robustness; (2) Siamese Fusion Module, which combines cross-correlation refinement and adaptive information fusion to capture complex cellular relationships while mitigating over-smoothing; and (3) Optimal Transport Clustering, which utilizes Sinkhorn distance to efficiently align cluster assignments with predefined proportions while maintaining balance. Comprehensive evaluations on seven real-world datasets demonstrate that scSiameseClu outperforms state-of-the-art methods in single-cell clustering, cell type annotation, and cell type classification, providing a powerful tool for scRNA-seq data interpretation.", "date": "2025-05-19", "categories": []}
{"id": "2404.10351", "title": "On the Use of Relative Validity Indices for Comparing Clustering Approaches", "abstract": "Relative Validity Indices (RVIs) such as the Silhouette Width Criterion and Davies Bouldin indices are the most widely used tools for evaluating and optimising clustering outcomes. Traditionally, their ability to rank collections of candidate dataset partitions has been used to guide the selection of the number of clusters, and to compare partitions from different clustering algorithms. However, there is a growing trend in the literature to use RVIs when selecting a Similarity Paradigm (SP) for clustering - the combination of normalisation procedure, representation method, and distance measure which affects the computation of object dissimilarities used in clustering. Despite the growing prevalence of this practice, there has been no empirical or theoretical investigation into the suitability of RVIs for this purpose. Moreover, since RVIs are computed using object dissimilarities, it remains unclear how they would need to be implemented for fair comparisons of different SPs. This study presents the first comprehensive investigation into the reliability of RVIs for SP selection. We conducted extensive experiments with seven popular RVIs on over 2.7 million clustering partitions of synthetic and real-world datasets, encompassing feature-vector and time-series data. We identified fundamental conceptual limitations undermining the use of RVIs for SP selection, and our empirical findings confirmed this predicted unsuitability. Among our recommendations, we suggest instead that practitioners select SPs by using external validation on high quality labelled datasets or carefully designed outcome-oriented objective criteria, both of which should be informed by careful consideration of dataset characteristics, and domain requirements. Our findings have important implications for clustering methodology and evaluation, suggesting the need for more rigorous approaches to SP selection.", "date": "2024-04-16", "categories": []}
{"id": "2404.06167", "title": "scCDCG: Efficient Deep Structural Clustering for single-cell RNA-seq via Deep Cut-informed Graph Embedding", "abstract": "Single-cell RNA sequencing (scRNA-seq) is essential for unraveling cellular heterogeneity and diversity, offering invaluable insights for bioinformatics advancements. Despite its potential, traditional clustering methods in scRNA-seq data analysis often neglect the structural information embedded in gene expression profiles, crucial for understanding cellular correlations and dependencies. Existing strategies, including graph neural networks, face challenges in handling the inefficiency due to scRNA-seq data's intrinsic high-dimension and high-sparsity. Addressing these limitations, we introduce scCDCG (single-cell RNA-seq Clustering via Deep Cut-informed Graph), a novel framework designed for efficient and accurate clustering of scRNA-seq data that simultaneously utilizes intercellular high-order structural information. scCDCG comprises three main components: (i) A graph embedding module utilizing deep cut-informed techniques, which effectively captures intercellular high-order structural information, overcoming the over-smoothing and inefficiency issues prevalent in prior graph neural network methods. (ii) A self-supervised learning module guided by optimal transport, tailored to accommodate the unique complexities of scRNA-seq data, specifically its high-dimension and high-sparsity. (iii) An autoencoder-based feature learning module that simplifies model complexity through effective dimension reduction and feature extraction. Our extensive experiments on 6 datasets demonstrate scCDCG's superior performance and efficiency compared to 7 established models, underscoring scCDCG's potential as a transformative tool in scRNA-seq data analysis. Our code is available at: https://github.com/XPgogogo/scCDCG.", "date": "2024-04-09", "categories": []}
{"id": "2509.23602", "title": "Deep Taxonomic Networks for Unsupervised Hierarchical Prototype Discovery", "abstract": "Inspired by the human ability to learn and organize knowledge into hierarchical taxonomies with prototypes, this paper addresses key limitations in current deep hierarchical clustering methods. Existing methods often tie the structure to the number of classes and underutilize the rich prototype information available at intermediate hierarchical levels. We introduce deep taxonomic networks, a novel deep latent variable approach designed to bridge these gaps. Our method optimizes a large latent taxonomic hierarchy, specifically a complete binary tree structured mixture-of-Gaussian prior within a variational inference framework, to automatically discover taxonomic structures and associated prototype clusters directly from unlabeled data without assuming true label sizes. We analytically show that optimizing the ELBO of our method encourages the discovery of hierarchical relationships among prototypes. Empirically, our learned models demonstrate strong hierarchical clustering performance, outperforming baselines across diverse image classification datasets using our novel evaluation mechanism that leverages prototype clusters discovered at all hierarchical levels. Qualitative results further reveal that deep taxonomic networks discover rich and interpretable hierarchical taxonomies, capturing both coarse-grained semantic categories and fine-grained visual distinctions.", "date": "2025-09-28", "categories": []}
{"id": "2509.18653", "title": "Subspace Clustering of Subspaces: Unifying Canonical Correlation Analysis and Subspace Clustering", "abstract": "We introduce a novel framework for clustering a collection of tall matrices based on their column spaces, a problem we term Subspace Clustering of Subspaces (SCoS). Unlike traditional subspace clustering methods that assume vectorized data, our formulation directly models each data sample as a matrix and clusters them according to their underlying subspaces. We establish conceptual links to Subspace Clustering and Generalized Canonical Correlation Analysis (GCCA), and clarify key differences that arise in this more general setting. Our approach is based on a Block Term Decomposition (BTD) of a third-order tensor constructed from the input matrices, enabling joint estimation of cluster memberships and partially shared subspaces. We provide the first identifiability results for this formulation and propose scalable optimization algorithms tailored to large datasets. Experiments on real-world hyperspectral imaging datasets demonstrate that our method achieves superior clustering accuracy and robustness, especially under high noise and interference, compared to existing subspace clustering techniques. These results highlight the potential of the proposed framework in challenging high-dimensional applications where structure exists beyond individual data vectors.", "date": "2025-09-23", "categories": []}
{"id": "2509.23742", "title": "GBSK: Skeleton Clustering via Granular-ball Computing and Multi-Sampling for Large-Scale Data", "abstract": "To effectively handle clustering task for large-scale datasets, we propose a novel scalable skeleton clustering algorithm, namely GBSK, which leverages the granular-ball technique to capture the underlying structure of data. By multi-sampling the dataset and constructing multi-grained granular-balls, GBSK progressively uncovers a statistical \"skeleton\" -- a spatial abstraction that approximates the essential structure and distribution of the original data. This strategy enables GBSK to dramatically reduce computational overhead while maintaining high clustering accuracy. In addition, we introduce an adaptive version, AGBSK, with simplified parameter settings to enhance usability and facilitate deployment in real-world scenarios. Extensive experiments conducted on standard computing hardware demonstrate that GBSK achieves high efficiency and strong clustering performance on large-scale datasets, including one with up to 100 million instances across 256 dimensions. Our implementation and experimental results are available at: https://github.com/XFastDataLab/GBSK/.", "date": "2025-09-28", "categories": []}
{"id": "2509.23942", "title": "Efficient Identification of High Similarity Clusters in Polygon Datasets", "abstract": "Advancements in tools like Shapely 2.0 and Triton can significantly improve the efficiency of spatial similarity computations by enabling faster and more scalable geometric operations. However, for extremely large datasets, these optimizations may face challenges due to the sheer volume of computations required. To address this, we propose a framework that reduces the number of clusters requiring verification, thereby decreasing the computational load on these systems. The framework integrates dynamic similarity index thresholding, supervised scheduling, and recall-constrained optimization to efficiently identify clusters with the highest spatial similarity while meeting user-defined precision and recall requirements. By leveraging Kernel Density Estimation (KDE) to dynamically determine similarity thresholds and machine learning models to prioritize clusters, our approach achieves substantial reductions in computational cost without sacrificing accuracy. Experimental results demonstrate the scalability and effectiveness of the method, offering a practical solution for large-scale geospatial analysis.", "date": "2025-09-28", "categories": []}
{"id": "2509.24027", "title": "Joint Superpixel and Self-Representation Learning for Scalable Hyperspectral Image Clustering", "abstract": "Subspace clustering is a powerful unsupervised approach for hyperspectral image (HSI) analysis, but its high computational and memory costs limit scalability. Superpixel segmentation can improve efficiency by reducing the number of data points to process. However, existing superpixel-based methods usually perform segmentation independently of the clustering task, often producing partitions that do not align with the subsequent clustering objective. To address this, we propose a unified end-to-end framework that jointly optimizes superpixel segmentation and subspace clustering. Its core is a feedback mechanism: a self-representation network based on unfolded Alternating Direction Method of Multipliers (ADMM) provides a model-driven signal to guide a differentiable superpixel module. This joint optimization yields clustering-aware partitions that preserve both spectral and spatial structure. Furthermore, our superpixel network learns a unique compactness parameter for each superpixel, enabling more flexible and adaptive segmentation. Extensive experiments on benchmark HSI datasets demonstrate that our method consistently achieves superior accuracy compared with state-of-the-art clustering approaches.", "date": "2025-09-28", "categories": []}
{"id": "2509.20501", "title": "Beyond Visual Similarity: Rule-Guided Multimodal Clustering with explicit domain rules", "abstract": "Traditional clustering techniques often rely solely on similarity in the input data, limiting their ability to capture structural or semantic constraints that are critical in many domains. We introduce the Domain Aware Rule Triggered Variational Autoencoder (DARTVAE), a rule guided multimodal clustering framework that incorporates domain specific constraints directly into the representation learning process. DARTVAE extends the VAE architecture by embedding explicit rules, semantic representations, and data driven features into a unified latent space, while enforcing constraint compliance through rule consistency and violation penalties in the loss function. Unlike conventional clustering methods that rely only on visual similarity or apply rules as post hoc filters, DARTVAE treats rules as first class learning signals. The rules are generated by LLMs, structured into knowledge graphs, and enforced through a loss function combining reconstruction, KL divergence, consistency, and violation penalties. Experiments on aircraft and automotive datasets demonstrate that rule guided clustering produces more operationally meaningful and interpretable clusters for example, isolating UAVs, unifying stealth aircraft, or separating SUVs from sedans while improving traditional clustering metrics. However, the framework faces challenges: LLM generated rules may hallucinate or conflict, excessive rules risk overfitting, and scaling to complex domains increases computational and consistency difficulties. By combining rule encodings with learned representations, DARTVAE achieves more meaningful and consistent clustering outcomes than purely data driven models, highlighting the utility of constraint guided multimodal clustering for complex, knowledge intensive settings.", "date": "2025-09-24", "categories": []}
{"id": "2509.20976", "title": "An Adaptor for Triggering Semi-Supervised Learning to Out-of-Box Serve Deep Image Clustering", "abstract": "Recently, some works integrate SSL techniques into deep clustering frameworks to enhance image clustering performance. However, they all need pretraining, clustering learning, or a trained clustering model as prerequisites, limiting the flexible and out-of-box application of SSL learners in the image clustering task. This work introduces ASD, an adaptor that enables the cold-start of SSL learners for deep image clustering without any prerequisites. Specifically, we first randomly sample pseudo-labeled data from all unlabeled data, and set an instance-level classifier to learn them with semantically aligned instance-level labels. With the ability of instance-level classification, we track the class transitions of predictions on unlabeled data to extract high-level similarities of instance-level classes, which can be utilized to assign cluster-level labels to pseudo-labeled data. Finally, we use the pseudo-labeled data with assigned cluster-level labels to trigger a general SSL learner trained on the unlabeled data for image clustering. We show the superior performance of ASD across various benchmarks against the latest deep image clustering approaches and very slight accuracy gaps compared to SSL methods using ground-truth, e.g., only 1.33% on CIFAR-10. Moreover, ASD can also further boost the performance of existing SSL-embedded deep image clustering methods.", "date": "2025-09-25", "categories": []}
{"id": "2409.02963", "title": "Fair Clustering with Minimum Representation Constraints", "abstract": "Clustering is a well-studied unsupervised learning task that aims to partition data points into a number of clusters. In many applications, these clusters correspond to real-world constructs (e.g., electoral districts, playlists, TV channels), where a group (e.g., social or demographic) benefits only if it reaches a minimum level of representation in the cluster (e.g., 50% to elect their preferred candidate). In this paper, we study the k-means and k-medians clustering problems under the additional fairness constraint that each group must attain a minimum level of representation in at least a specified number of clusters. We formulate this problem as a mixed-integer (nonlinear) optimization problem and propose an alternating minimization algorithm, called MiniReL, to solve it. Although incorporating fairness constraints results in an NP-hard assignment problem within the MiniReL algorithm, we present several heuristic strategies that make the approach practical even for large datasets. Numerical results demonstrate that our method yields fair clusters without increasing clustering cost across standard benchmark datasets.", "date": "2024-09-04", "categories": []}
{"id": "2509.18826", "title": "Graph-based Clustering Revisited: A Relaxation of Kernel $k$-Means Perspective", "abstract": "The well-known graph-based clustering methods, including spectral clustering, symmetric non-negative matrix factorization, and doubly stochastic normalization, can be viewed as relaxations of the kernel $k$-means approach. However, we posit that these methods excessively relax their inherent low-rank, nonnegative, doubly stochastic, and orthonormal constraints to ensure numerical feasibility, potentially limiting their clustering efficacy. In this paper, guided by our theoretical analyses, we propose \\textbf{Lo}w-\\textbf{R}ank \\textbf{D}oubly stochastic clustering (\\textbf{LoRD}), a model that only relaxes the orthonormal constraint to derive a probabilistic clustering results. Furthermore, we theoretically establish the equivalence between orthogonality and block diagonality under the doubly stochastic constraint. By integrating \\textbf{B}lock diagonal regularization into LoRD, expressed as the maximization of the Frobenius norm, we propose \\textbf{B-LoRD}, which further enhances the clustering performance. To ensure numerical solvability, we transform the non-convex doubly stochastic constraint into a linear convex constraint through the introduction of a class probability parameter. We further theoretically demonstrate the gradient Lipschitz continuity of our LoRD and B-LoRD enables the proposal of a globally convergent projected gradient descent algorithm for their optimization. Extensive experiments validate the effectiveness of our approaches. The code is publicly available at https://github.com/lwl-learning/LoRD.", "date": "2025-09-23", "categories": []}
{"id": "2403.01799", "title": "Superpixel Graph Contrastive Clustering with Semantic-Invariant Augmentations for Hyperspectral Images", "abstract": "Hyperspectral images (HSI) clustering is an important but challenging task. The state-of-the-art (SOTA) methods usually rely on superpixels, however, they do not fully utilize the spatial and spectral information in HSI 3-D structure, and their optimization targets are not clustering-oriented. In this work, we first use 3-D and 2-D hybrid convolutional neural networks to extract the high-order spatial and spectral features of HSI through pre-training, and then design a superpixel graph contrastive clustering (SPGCC) model to learn discriminative superpixel representations. Reasonable augmented views are crucial for contrastive clustering, and conventional contrastive learning may hurt the cluster structure since different samples are pushed away in the embedding space even if they belong to the same class. In SPGCC, we design two semantic-invariant data augmentations for HSI superpixels: pixel sampling augmentation and model weight augmentation. Then sample-level alignment and clustering-center-level contrast are performed for better intra-class similarity and inter-class dissimilarity of superpixel embeddings. We perform clustering and network optimization alternatively. Experimental results on several HSI datasets verify the advantages of the proposed SPGCC compared to SOTA methods. Our code is available at https://github.com/jhqi/spgcc.", "date": "2024-03-04", "categories": []}
{"id": "2509.18037", "title": "Kernel K-means clustering of distributional data", "abstract": "We consider the problem of clustering a sample of probability distributions from a random distribution on $\\mathbb R^p$. Our proposed partitioning method makes use of a symmetric, positive-definite kernel $k$ and its associated reproducing kernel Hilbert space (RKHS) $\\mathcal H$. By mapping each distribution to its corresponding kernel mean embedding in $\\mathcal H$, we obtain a sample in this RKHS where we carry out the $K$-means clustering procedure, which provides an unsupervised classification of the original sample. The procedure is simple and computationally feasible even for dimension $p>1$. The simulation studies provide insight into the choice of the kernel and its tuning parameter. The performance of the proposed clustering procedure is illustrated on a collection of Synthetic Aperture Radar (SAR) images.", "date": "2025-09-22", "categories": []}
{"id": "2509.15989", "title": "Model-free algorithms for fast node clustering in SBM type graphs and application to social role inference in animals", "abstract": "We propose a novel family of model-free algorithms for node clustering and parameter inference in graphs generated from the Stochastic Block Model (SBM), a fundamental framework in community detection. Drawing inspiration from the Lloyd algorithm for the $k$-means problem, our approach extends to SBMs with general edge weight distributions. We establish the consistency of our estimator under a natural identifiability condition. Through extensive numerical experiments, we benchmark our methods against state-of-the-art techniques, demonstrating significantly faster computation times with the lower order of estimation error. Finally, we validate the practical relevance of our algorithms by applying them to empirical network data from behavioral ecology.", "date": "2025-09-19", "categories": []}
{"id": "2509.16022", "title": "Generalized Deep Multi-view Clustering via Causal Learning with Partially Aligned Cross-view Correspondence", "abstract": "Multi-view clustering (MVC) aims to explore the common clustering structure across multiple views. Many existing MVC methods heavily rely on the assumption of view consistency, where alignments for corresponding samples across different views are ordered in advance. However, real-world scenarios often present a challenge as only partial data is consistently aligned across different views, restricting the overall clustering performance. In this work, we consider the model performance decreasing phenomenon caused by data order shift (i.e., from fully to partially aligned) as a generalized multi-view clustering problem. To tackle this problem, we design a causal multi-view clustering network, termed CauMVC. We adopt a causal modeling approach to understand multi-view clustering procedure. To be specific, we formulate the partially aligned data as an intervention and multi-view clustering with partially aligned data as an post-intervention inference. However, obtaining invariant features directly can be challenging. Thus, we design a Variational Auto-Encoder for causal learning by incorporating an encoder from existing information to estimate the invariant features. Moreover, a decoder is designed to perform the post-intervention inference. Lastly, we design a contrastive regularizer to capture sample correlations. To the best of our knowledge, this paper is the first work to deal generalized multi-view clustering via causal learning. Empirical experiments on both fully and partially aligned data illustrate the strong generalization and effectiveness of CauMVC.", "date": "2025-09-19", "categories": []}
{"id": "2509.14724", "title": "One-step Multi-view Clustering With Adaptive Low-rank Anchor-graph Learning", "abstract": "In light of their capability to capture structural information while reducing computing complexity, anchor graph-based multi-view clustering (AGMC) methods have attracted considerable attention in large-scale clustering problems. Nevertheless, existing AGMC methods still face the following two issues: 1) They directly embedded diverse anchor graphs into a consensus anchor graph (CAG), and hence ignore redundant information and numerous noises contained in these anchor graphs, leading to a decrease in clustering effectiveness; 2) They drop effectiveness and efficiency due to independent post-processing to acquire clustering indicators. To overcome the aforementioned issues, we deliver a novel one-step multi-view clustering method with adaptive low-rank anchor-graph learning (OMCAL). To construct a high-quality CAG, OMCAL provides a nuclear norm-based adaptive CAG learning model against information redundancy and noise interference. Then, to boost clustering effectiveness and efficiency substantially, we incorporate category indicator acquisition and CAG learning into a unified framework. Numerous studies conducted on ordinary and large-scale datasets indicate that OMCAL outperforms existing state-of-the-art methods in terms of clustering effectiveness and efficiency.", "date": "2025-09-18", "categories": []}
{"id": "2509.13202", "title": "B-TGAT: A Bi-directional Temporal Graph Attention Transformer for Clustering Multivariate Spatiotemporal Data", "abstract": "Clustering high-dimensional multivariate spatiotemporal climate data is challenging due to complex temporal dependencies, evolving spatial interactions, and non-stationary dynamics. Conventional clustering methods, including recurrent and convolutional models, often struggle to capture both local and global temporal relationships while preserving spatial context. We present a time-distributed hybrid U-Net autoencoder that integrates a Bi-directional Temporal Graph Attention Transformer (B-TGAT) to guide efficient temporal clustering of multidimensional spatiotemporal climate datasets. The encoder and decoder are equipped with ConvLSTM2D modules that extract joint spatial--temporal features by modeling localized dynamics and spatial correlations over time, and skip connections that preserve multiscale spatial details during feature compression and reconstruction. At the bottleneck, B-TGAT integrates graph-based spatial modeling with attention-driven temporal encoding, enabling adaptive weighting of temporal neighbors and capturing both short and long-range dependencies across regions. This architecture produces discriminative latent embeddings optimized for clustering. Experiments on three distinct spatiotemporal climate datasets demonstrate superior cluster separability, temporal stability, and alignment with known climate transitions compared to state-of-the-art baselines. The integration of ConvLSTM2D, U-Net skip connections, and B-TGAT enhances temporal clustering performance while providing interpretable insights into complex spatiotemporal variability, advancing both methodological development and climate science applications.", "date": "2025-09-16", "categories": []}
{"id": "2509.12166", "title": "MMM: Clustering Multivariate Longitudinal Mixed-type Data", "abstract": "Multivariate longitudinal data of mixed-type are increasingly collected in many science domains. However, algorithms to cluster this kind of data remain scarce, due to the challenge to simultaneously model the within- and between-time dependence structures for multivariate data of mixed kind. We introduce the Mixture of Mixed-Matrices (MMM) model: reorganizing the data in a three-way structure and assuming that the non-continuous variables are observations of underlying latent continuous variables, the model relies on a mixture of matrix-variate normal distributions to perform clustering in the latent dimension. The MMM model is thus able to handle continuous, ordinal, binary, nominal and count data and to concurrently model the heterogeneity, the association among the responses and the temporal dependence structure in a parsimonious way and without assuming conditional independence. The inference is carried out through an MCMC-EM algorithm, which is detailed. An evaluation of the model through synthetic data shows its inference abilities. A real-world application on financial data is presented.", "date": "2025-09-15", "categories": []}
{"id": "2509.08530", "title": "Data Skeleton Learning: Scalable Active Clustering with Sparse Graph Structures", "abstract": "In this work, we focus on the efficiency and scalability of pairwise constraint-based active clustering, crucial for processing large-scale data in applications such as data mining, knowledge annotation, and AI model pre-training. Our goals are threefold: (1) to reduce computational costs for iterative clustering updates; (2) to enhance the impact of user-provided constraints to minimize annotation requirements for precise clustering; and (3) to cut down memory usage in practical deployments. To achieve these aims, we propose a graph-based active clustering algorithm that utilizes two sparse graphs: one for representing relationships between data (our proposed data skeleton) and another for updating this data skeleton. These two graphs work in concert, enabling the refinement of connected subgraphs within the data skeleton to create nested clusters. Our empirical analysis confirms that the proposed algorithm consistently facilitates more accurate clustering with dramatically less input of user-provided constraints, and outperforms its counterparts in terms of computational performance and scalability, while maintaining robustness across various distance metrics.", "date": "2025-09-10", "categories": []}
{"id": "2506.12514", "title": "Interpretable Text-Guided Image Clustering via Iterative Search", "abstract": "Traditional clustering methods aim to group unlabeled data points based on their similarity to each other. However, clustering, in the absence of additional information, is an ill-posed problem as there may be many different, yet equally valid, ways to partition a dataset. Distinct users may want to use different criteria to form clusters in the same data, e.g. shape v.s. color. Recently introduced text-guided image clustering methods aim to address this ambiguity by allowing users to specify the criteria of interest using natural language instructions. This instruction provides the necessary context and control needed to obtain clusters that are more aligned with the users' intent. We propose a new text-guided clustering approach named ITGC that uses an iterative discovery process, guided by an unsupervised clustering objective, to generate interpretable visual concepts that better capture the criteria expressed in a user's instructions. We report superior performance compared to existing methods across a wide variety of image clustering and fine-grained classification benchmarks.", "date": "2025-06-14", "categories": []}
{"id": "2509.07184", "title": "Dimensionally Reduced Open-World Clustering: DROWCULA", "abstract": "Working with annotated data is the cornerstone of supervised learning. Nevertheless, providing labels to instances is a task that requires significant human effort. Several critical real-world applications make things more complicated because no matter how many labels may have been identified in a task of interest, it could be the case that examples corresponding to novel classes may appear in the future. Not unsurprisingly, prior work in this, so-called, `open-world' context has focused a lot on semi-supervised approaches.\n  Focusing on image classification, somehow paradoxically, we propose a fully unsupervised approach to the problem of determining the novel categories in a particular dataset. Our approach relies on estimating the number of clusters using Vision Transformers, which utilize attention mechanisms to generate vector embeddings. Furthermore, we incorporate manifold learning techniques to refine these embeddings by exploiting the intrinsic geometry of the data, thereby enhancing the overall image clustering performance. Overall, we establish new State-of-the-Art results on single-modal clustering and Novel Class Discovery on CIFAR-10, CIFAR-100, ImageNet-100, and Tiny ImageNet. We do so, both when the number of clusters is known or unknown ahead of time. The code is available at: https://github.com/DROWCULA/DROWCULA.", "date": "2025-09-08", "categories": []}
{"id": "2509.06214", "title": "Metric Embedding Initialization-Based Differentially Private and Explainable Graph Clustering", "abstract": "Graph clustering under the framework of differential privacy, which aims to process graph-structured data while protecting individual privacy, has been receiving increasing attention. Despite significant achievements in current research, challenges such as high noise, low efficiency and poor interpretability continue to severely constrain the development of this field. In this paper, we construct a differentially private and interpretable graph clustering approach based on metric embedding initialization. Specifically, we construct an SDP optimization, extract the key set and provide a well-initialized clustering configuration using an HST-based initialization method. Subsequently, we apply an established k-median clustering strategy to derive the cluster results and offer comparative explanations for the query set through differences from the cluster centers. Extensive experiments on public datasets demonstrate that our proposed framework outperforms existing methods in various clustering metrics while strictly ensuring privacy.", "date": "2025-09-07", "categories": []}
{"id": "2509.06678", "title": "Online Clustering of Seafloor Imagery for Interpretation during Long-Term AUV Operations", "abstract": "As long-endurance and seafloor-resident AUVs become more capable, there is an increasing need for extended, real-time interpretation of seafloor imagery to enable adaptive missions and optimise communication efficiency. Although offline image analysis methods are well established, they rely on access to complete datasets and human-labelled examples to manage the strong influence of environmental and operational conditions on seafloor image appearance-requirements that cannot be met in real-time settings. To address this, we introduce an online clustering framework (OCF) capable of interpreting seafloor imagery without supervision, which is designed to operate in real-time on continuous data streams in a scalable, adaptive, and self-consistent manner. The method enables the efficient review and consolidation of common patterns across the entire data history in constant time by identifying and maintaining a set of representative samples that capture the evolving feature distribution, supporting dynamic cluster merging and splitting without reprocessing the full image history. We evaluate the framework on three diverse seafloor image datasets, analysing the impact of different representative sampling strategies on both clustering accuracy and computational cost. The OCF achieves the highest average F1 score of 0.68 across the three datasets among all comparative online clustering approaches, with a standard deviation of 3% across three distinct survey trajectories, demonstrating its superior clustering capability and robustness to trajectory variation. In addition, it maintains consistently lower and bounded computational time as the data volume increases. These properties are beneficial for generating survey data summaries and supporting informative path planning in long-term, persistent autonomous marine exploration.", "date": "2025-09-08", "categories": []}
{"id": "2504.16943", "title": "Revealing the empirical flexibility of gas units through deep clustering", "abstract": "The flexibility of a power generation unit determines how quickly and often it can ramp up or down. In energy models, it depends on assumptions on the technical characteristics of the unit, such as its installed capacity or turbine technology. In this paper, we learn the empirical flexibility of gas units from their electricity generation, revealing how real-world limitations can lead to substantial differences between units with similar technical characteristics. Using a novel deep clustering approach, we transform 5 years (2019-2023) of unit-level hourly generation data for 49 German units from 100 MWp of installed capacity into low-dimensional embeddings. Our unsupervised approach identifies two clusters of peaker units (high flexibility) and two clusters of non-peaker units (low flexibility). The estimated ramp rates of non-peakers, which constitute half of the sample, display a low empirical flexibility, comparable to coal units. Non-peakers, predominantly owned by industry and municipal utilities, show limited response to low residual load and negative prices, generating on average 1.3 GWh during those hours. As the transition to renewables increases market variability, regulatory changes will be needed to unlock this flexibility potential.", "date": "2025-04-14", "categories": []}
{"id": "2506.19992", "title": "HERCULES: Hierarchical Embedding-based Recursive Clustering Using LLMs for Efficient Summarization", "abstract": "The explosive growth of complex datasets across various modalities necessitates advanced analytical tools that not only group data effectively but also provide human-understandable insights into the discovered structures. We introduce HERCULES (Hierarchical Embedding-based Recursive Clustering Using LLMs for Efficient Summarization), a novel algorithm and Python package designed for hierarchical k-means clustering of diverse data types, including text, images, and numeric data (processed one modality per run). HERCULES constructs a cluster hierarchy by recursively applying k-means clustering, starting from individual data points at level 0. A key innovation is its deep integration of Large Language Models (LLMs) to generate semantically rich titles and descriptions for clusters at each level of the hierarchy, significantly enhancing interpretability. The algorithm supports two main representation modes: `direct' mode, which clusters based on original data embeddings or scaled numeric features, and `description' mode, which clusters based on embeddings derived from LLM-generated summaries. Users can provide a `topic\\_seed' to guide LLM-generated summaries towards specific themes. An interactive visualization tool facilitates thorough analysis and understanding of the clustering results. We demonstrate HERCULES's capabilities and discuss its potential for extracting meaningful, hierarchical knowledge from complex datasets.", "date": "2025-06-24", "categories": []}
{"id": "2306.06534", "title": "K-Tensors: Clustering Positive Semi-Definite Matrices", "abstract": "This paper presents a new clustering algorithm for symmetric positive semi-definite (SPSD) matrices, called K-Tensors. The method identifies structured subsets of the SPSD cone characterized by common principal component (CPC) representations, where each subset corresponds to matrices sharing a common eigenstructure. Unlike conventional clustering approaches that rely on vectorization or transformations of SPSD matrices, thereby losing critical geometric and spectral information, K-Tensors introduces a divergence that respects the intrinsic geometry of SPSD matrices. This divergence preserves the shape and eigenstructure information and yields principal SPSD tensors, defined as a set of representative matrices that summarize the distribution of SPSD matrices. By exploring its theoretical properties, we show that the proposed clustering algorithm is self-consistent under mild distribution assumptions and converges to a local optimum. We demonstrate the use of the algorithm through an application to resting-state functional magnetic resonance imaging (rs-fMRI) data from the Human Connectome Project, where we cluster brain connectivity matrices to discover groups of subjects with shared connectivity structures.", "date": "2023-06-10", "categories": []}
{"id": "2509.00546", "title": "Advanced spectral clustering for heterogeneous data in credit risk monitoring systems", "abstract": "Heterogeneous data, which encompass both numerical financial variables and textual records, present substantial challenges for credit monitoring. To address this issue, we propose Advanced Spectral Clustering (ASC), a method that integrates financial and textual similarities through an optimized weight parameter and selects eigenvectors using a novel eigenvalue-silhouette optimization approach. Evaluated on a dataset comprising 1,428 small and medium-sized enterprises (SMEs), ASC achieves a Silhouette score that is 18% higher than that of a single-type data baseline method. Furthermore, the resulting clusters offer actionable insights; for instance, 51% of low-risk firms are found to include the term 'social recruitment' in their textual records. The robustness of ASC is confirmed across multiple clustering algorithms, including k-means, k-medians, and k-medoids, with {\\Delta}Intra/Inter < 0.13 and {\\Delta}Silhouette Coefficient < 0.02. By bridging spectral clustering theory with heterogeneous data applications, ASC enables the identification of meaningful clusters, such as recruitment-focused SMEs exhibiting a 30% lower default risk, thereby supporting more targeted and effective credit interventions.", "date": "2025-08-30", "categories": []}
{"id": "2509.00943", "title": "Protocol for Clustering 4DSTEM Data for Phase Differentiation in Glasses", "abstract": "Phase-change materials (PCMs) such as Ge-Sb-Te alloys are widely used in non-volatile memory applications due to their rapid and reversible switching between amorphous and crystalline states. However, their functional properties are strongly governed by nanoscale variations in composition and structure, which are challenging to resolve using conventional techniques. Here, we apply unsupervised machine learning to 4-dimensional scanning transmission electron microscopy (4D-STEM) data to identify compositional and structural heterogeneity in Ge-Sb-Te. After preprocessing and dimensionality reduction with principal component analysis (PCA), cluster validation was performed with t-SNE and UMAP, followed by k-means clustering optimized through silhouette scoring. Four distinct clusters were identified which were mapped back to the diffraction data. Elemental intensity histograms revealed chemical signatures change across clusters, oxygen and germanium enrichment in Cluster 1, tellurium in Cluster 2, antimony in Cluster 3, and germanium again in Cluster 4. Furthermore, averaged diffraction patterns from these clusters confirmed structural variations. Together, these findings demonstrate that clustering analysis can provide a powerful framework for correlating local chemical and structural features in PCMs, offering deeper insights into their intrinsic heterogeneity.", "date": "2025-08-31", "categories": []}
{"id": "2509.00990", "title": "Hybrid Topic-Semantic Labeling and Graph Embeddings for Unsupervised Legal Document Clustering", "abstract": "Legal documents pose unique challenges for text classification due to their domain-specific language and often limited labeled data. This paper proposes a hybrid approach for classifying legal texts by combining unsupervised topic and graph embeddings with a supervised model. We employ Top2Vec to learn semantic document embeddings and automatically discover latent topics, and Node2Vec to capture structural relationships via a bipartite graph of legal documents. The embeddings are combined and clustered using KMeans, yielding coherent groupings of documents. Our computations on a legal document dataset demonstrate that the combined Top2Vec+Node2Vec approach improves clustering quality over text-only or graph-only embeddings. We conduct a sensitivity analysis of hyperparameters, such as the number of clusters and the dimensionality of the embeddings, and demonstrate that our method achieves competitive performance against baseline Latent Dirichlet Allocation (LDA) and Non-Negative Matrix Factorization (NMF) models. Key findings indicate that while the pipeline presents an innovative approach to unsupervised legal document analysis by combining semantic topic modeling with graph embedding techniques, its efficacy is contingent upon the quality of initial topic generation and the representational power of the chosen embedding models for specialized legal language. Strategic recommendations include the exploration of domain-specific embeddings, more comprehensive hyperparameter tuning for Node2Vec, dynamic determination of cluster numbers, and robust human-in-the-loop validation processes to enhance legal relevance and trustworthiness. The pipeline demonstrates potential for exploratory legal data analysis and as a precursor to supervised learning tasks but requires further refinement and domain-specific adaptation for practical legal applications.", "date": "2025-08-31", "categories": []}
{"id": "2411.15189", "title": "Categorical Data Clustering via Value Order Estimated Distance Metric Learning", "abstract": "Clustering is a popular machine learning technique for data mining that can process and analyze datasets to automatically reveal sample distribution patterns. Since the ubiquitous categorical data naturally lack a well-defined metric space such as the Euclidean distance space of numerical data, the distribution of categorical data is usually under-represented, and thus valuable information can be easily twisted in clustering. This paper, therefore, introduces a novel order distance metric learning approach to intuitively represent categorical attribute values by learning their optimal order relationship and quantifying their distance in a line similar to that of the numerical attributes. Since subjectively created qualitative categorical values involve ambiguity and fuzziness, the order distance metric is learned in the context of clustering. Accordingly, a new joint learning paradigm is developed to alternatively perform clustering and order distance metric learning with low time complexity and a guarantee of convergence. Due to the clustering-friendly order learning mechanism and the homogeneous ordinal nature of the order distance and Euclidean distance, the proposed method achieves superior clustering accuracy on categorical and mixed datasets. More importantly, the learned order distance metric greatly reduces the difficulty of understanding and managing the non-intuitive categorical data. Experiments with ablation studies, significance tests, case studies, etc., have validated the efficacy of the proposed method. The source code is available at https://github.com/DAJ0612/OCL_Source_Code.", "date": "2024-11-19", "categories": []}
{"id": "2508.21081", "title": "Normalisation of SWIFT Message Counterparties with Feature Extraction and Clustering", "abstract": "Short text clustering is a known use case in the text analytics community. When the structure and content falls in the natural language domain e.g. Twitter posts or instant messages, then natural language techniques can be used, provided texts are of sufficient length to allow for use of (pre)trained models to extract meaningful information, such as part-of-speech or topic annotations. However, natural language models are not suitable for clustering transaction counterparties, as they are found in bank payment messaging systems, such as SWIFT. The manually typed tags are typically physical or legal entity details, which lack sentence structure, while containing all the variations and noise that manual entry introduces. This leaves a gap in an investigator or counter-fraud professional's toolset when looking to augment their knowledge of payment flow originator and beneficiary entities and trace funds and assets. A gap that vendors traditionally try to close with fuzzy matching tools. With these considerations in mind, we are proposing a hybrid string similarity, topic modelling, hierarchical clustering and rule-based pipeline to facilitate clustering of transaction counterparties, also catering for unknown number of expected clusters. We are also devising metrics to supplement the evaluation of the approach, based on the well-known measures of precision and recall. Testing on a real-life labelled dataset demonstrates significantly improved performance over a baseline rule-based ('keyword') approach. The approach retains most of the interpretability found in rule-based systems, as the former adds an additional level of cluster refinement to the latter. The resulting workflow reduces the need for manual review. When only a subset of the population needs to be investigated, such as in sanctions investigations, the approach allows for better control of the risks of missing entity variations.", "date": "2025-08-24", "categories": []}
{"id": "2508.20231", "title": "Bounds on Perfect Node Classification: A Convex Graph Clustering Perspective", "abstract": "We present an analysis of the transductive node classification problem, where the underlying graph consists of communities that agree with the node labels and node features. For node classification, we propose a novel optimization problem that incorporates the node-specific information (labels and features) in a spectral graph clustering framework. Studying this problem, we demonstrate a synergy between the graph structure and node-specific information. In particular, we show that suitable node-specific information guarantees the solution of our optimization problem perfectly recovering the communities, under milder conditions than the bounds on graph clustering alone. We present algorithmic solutions to our optimization problem and numerical experiments that confirm such a synergy.", "date": "2025-08-27", "categories": []}
{"id": "2412.08289", "title": "k-HyperEdge Medoids for Clustering Ensemble", "abstract": "Clustering ensemble has been a popular research topic in data science due to its ability to improve the robustness of the single clustering method. Many clustering ensemble methods have been proposed, most of which can be categorized into clustering-view and sample-view methods. The clustering-view method is generally efficient, but it could be affected by the unreliability that existed in base clustering results. The sample-view method shows good performance, while the construction of the pairwise sample relation is time-consuming. In this paper, the clustering ensemble is formulated as a k-HyperEdge Medoids discovery problem and a clustering ensemble method based on k-HyperEdge Medoids that considers the characteristics of the above two types of clustering ensemble methods is proposed. In the method, a set of hyperedges is selected from the clustering view efficiently, then the hyperedges are diffused and adjusted from the sample view guided by a hyperedge loss function to construct an effective k-HyperEdge Medoid set. The loss function is mainly reduced by assigning samples to the hyperedge with the highest degree of belonging. Theoretical analyses show that the solution can approximate the optimal, the assignment method can gradually reduce the loss function, and the estimation of the belonging degree is statistically reasonable. Experiments on artificial data show the working mechanism of the proposed method. The convergence of the method is verified by experimental analysis of twenty data sets. The effectiveness and efficiency of the proposed method are also verified on these data, with nine representative clustering ensemble algorithms as reference.", "date": "2024-12-11", "categories": []}
{"id": "2501.18028", "title": "KNN and K-means in Gini Prametric Spaces", "abstract": "This paper introduces enhancements to the K-means and K-nearest neighbors (KNN) algorithms based on the concept of Gini prametric spaces, instead of traditional metric spaces. Unlike standard distance metrics, Gini prametrics incorporate both value-based and rank-based measures, offering robustness to noise and outliers. The main contributions include: (1) a Gini prametric that captures rank information alongside value distances; (2) a Gini K-means algorithm that is provably convergent and resilient to noisy data; and (3) a Gini KNN method that performs competitively with state-of-the-art approaches like Hassanat's distance in noisy environments. Experimental evaluations on 16 UCI datasets demonstrate the superior performance and efficiency of the Gini-based algorithms in clustering and classification tasks. This work opens new directions for rank-based prametrics in machine learning and statistical analysis.", "date": "2025-01-29", "categories": []}
{"id": "2508.13814", "title": "Unsupervised Urban Tree Biodiversity Mapping from Street-Level Imagery Using Spatially-Aware Visual Clustering", "abstract": "Urban tree biodiversity is critical for climate resilience, ecological stability, and livability in cities, yet most municipalities lack detailed knowledge of their canopies. Field-based inventories provide reliable estimates of Shannon and Simpson diversity but are costly and time-consuming, while supervised AI methods require labeled data that often fail to generalize across regions. We introduce an unsupervised clustering framework that integrates visual embeddings from street-level imagery with spatial planting patterns to estimate biodiversity without labels. Applied to eight North American cities, the method recovers genus-level diversity patterns with high fidelity, achieving low Wasserstein distances to ground truth for Shannon and Simpson indices and preserving spatial autocorrelation. This scalable, fine-grained approach enables biodiversity mapping in cities lacking detailed inventories and offers a pathway for continuous, low-cost monitoring to support equitable access to greenery and adaptive management of urban ecosystems.", "date": "2025-08-19", "categories": []}
{"id": "2508.17388", "title": "Effective Clustering for Large Multi-Relational Graphs", "abstract": "Multi-relational graphs (MRGs) are an expressive data structure for modeling diverse interactions/relations among real objects (i.e., nodes), which pervade extensive applications and scenarios. Given an MRG G with N nodes, partitioning the node set therein into K disjoint clusters (MRGC) is a fundamental task in analyzing MRGs, which has garnered considerable attention. However, the majority of existing solutions towards MRGC either yield severely compromised result quality by ineffective fusion of heterogeneous graph structures and attributes, or struggle to cope with sizable MRGs with millions of nodes and billions of edges due to the adoption of sophisticated and costly deep learning models.\n  In this paper, we present DEMM and DEMM+, two effective MRGC approaches to address the limitations above. Specifically, our algorithms are built on novel two-stage optimization objectives, where the former seeks to derive high-caliber node feature vectors by optimizing the multi-relational Dirichlet energy specialized for MRGs, while the latter minimizes the Dirichlet energy of clustering results over the node affinity graph. In particular, DEMM+ achieves significantly higher scalability and efficiency over our based method DEMM through a suite of well-thought-out optimizations. Key technical contributions include (i) a highly efficient approximation solver for constructing node feature vectors, and (ii) a theoretically-grounded problem transformation with carefully-crafted techniques that enable linear-time clustering without explicitly materializing the NxN dense affinity matrix. Further, we extend DEMM+ to handle attribute-less MRGs through non-trivial adaptations. Extensive experiments, comparing DEMM+ against 20 baselines over 11 real MRGs, exhibit that DEMM+ is consistently superior in terms of clustering quality measured against ground-truth labels, while often being remarkably faster.", "date": "2025-08-24", "categories": []}
{"id": "2508.15823", "title": "SDEC: Semantic Deep Embedded Clustering", "abstract": "The high dimensional and semantically complex nature of textual Big data presents significant challenges for text clustering, which frequently lead to suboptimal groupings when using conventional techniques like k-means or hierarchical clustering. This work presents Semantic Deep Embedded Clustering (SDEC), an unsupervised text clustering framework that combines an improved autoencoder with transformer-based embeddings to overcome these challenges. This novel method preserves semantic relationships during data reconstruction by combining Mean Squared Error (MSE) and Cosine Similarity Loss (CSL) within an autoencoder. Furthermore, a semantic refinement stage that takes advantage of the contextual richness of transformer embeddings is used by SDEC to further improve a clustering layer with soft cluster assignments and distributional loss. The capabilities of SDEC are demonstrated by extensive testing on five benchmark datasets: AG News, Yahoo! Answers, DBPedia, Reuters 2, and Reuters 5. The framework not only outperformed existing methods with a clustering accuracy of 85.7% on AG News and set a new benchmark of 53.63% on Yahoo! Answers, but also showed robust performance across other diverse text corpora. These findings highlight the significant improvements in accuracy and semantic comprehension of text data provided by SDEC's advances in unsupervised text clustering.", "date": "2025-08-18", "categories": []}
{"id": "2311.02181", "title": "Joint Problems in Learning Multiple Dynamical Systems", "abstract": "Clustering of time series is a well-studied problem, with applications ranging from quantitative, personalized models of metabolism obtained from metabolite concentrations to state discrimination in quantum information theory. We consider a variant, where given a set of trajectories and a number of parts, we jointly partition the set of trajectories and learn linear dynamical system (LDS) models for each part, so as to minimize the maximum error across all the models. We present globally convergent methods and EM heuristics, accompanied by promising computational results. The key highlight of this method is that it does not require a predefined hidden state dimension but instead provides an upper bound. Additionally, it offers guidance for determining regularization in the system identification.", "date": "2023-11-03", "categories": []}
{"id": "2504.15640", "title": "Cequel: Cost-Effective Querying of Large Language Models for Text Clustering", "abstract": "Text clustering aims to automatically partition a collection of documents into coherent groups based on their linguistic features. In the literature, this task is formulated either as metric clustering over pre-trained text embeddings or as graph clustering based on pairwise similarities derived from an oracle, e.g., a large machine learning model. Recent advances in large language models (LLMs) have significantly improved this field by providing high-quality contextualized embeddings and accurate semantic similarity estimates. However, leveraging LLMs at scale introduces substantial computational and financial costs due to the large number of required API queries or inference calls. To address this issue, we propose Cequel, a cost-effective framework that achieves accurate text clustering under a limited budget of LLM queries. At its core, Cequel constructs must-link and cannot-link constraints by selectively querying LLMs on informative text pairs or triplets, identified via our proposed algorithms, EdgeLLM and TriangleLLM. These constraints are then utilized in a weighted constrained clustering algorithm to form high-quality clusters. Specifically, EdgeLLM and TriangleLLM employ carefully designed greedy selection strategies and prompting techniques to identify and extract informative constraints efficiently. Experiments on multiple benchmark datasets demonstrate that Cequel consistently outperforms existing methods in unsupervised text clustering under the same query budget.", "date": "2025-04-22", "categories": []}
{"id": "2508.15231", "title": "Center-Oriented Prototype Contrastive Clustering", "abstract": "Contrastive learning is widely used in clustering tasks due to its discriminative representation. However, the conflict problem between classes is difficult to solve effectively. Existing methods try to solve this problem through prototype contrast, but there is a deviation between the calculation of hard prototypes and the true cluster center. To address this problem, we propose a center-oriented prototype contrastive clustering framework, which consists of a soft prototype contrastive module and a dual consistency learning module. In short, the soft prototype contrastive module uses the probability that the sample belongs to the cluster center as a weight to calculate the prototype of each category, while avoiding inter-class conflicts and reducing prototype drift. The dual consistency learning module aligns different transformations of the same sample and the neighborhoods of different samples respectively, ensuring that the features have transformation-invariant semantic information and compact intra-cluster distribution, while providing reliable guarantees for the calculation of prototypes. Extensive experiments on five datasets show that the proposed method is effective compared to the SOTA. Our code is published on https://github.com/LouisDong95/CPCC.", "date": "2025-08-21", "categories": []}
{"id": "2508.15393", "title": "Federated Learning based on Self-Evolving Gaussian Clustering", "abstract": "In this study, we present an Evolving Fuzzy System within the context of Federated Learning, which adapts dynamically with the addition of new clusters and therefore does not require the number of clusters to be selected apriori. Unlike traditional methods, Federated Learning allows models to be trained locally on clients' devices, sharing only the model parameters with a central server instead of the data. Our method, implemented using PyTorch, was tested on clustering and classification tasks. The results show that our approach outperforms established classification methods on several well-known UCI datasets. While computationally intensive due to overlap condition calculations, the proposed method demonstrates significant advantages in decentralized data processing.", "date": "2025-08-21", "categories": []}
{"id": "2508.15444", "title": "Measures of Overlapping Multivariate Gaussian Clusters in Unsupervised Online Learning", "abstract": "In this paper, we propose a new measure for detecting overlap in multivariate Gaussian clusters. The aim of online learning from data streams is to create clustering, classification, or regression models that can adapt over time based on the conceptual drift of streaming data. In the case of clustering, this can result in a large number of clusters that may overlap and should be merged. Commonly used distribution dissimilarity measures are not adequate for determining overlapping clusters in the context of online learning from streaming data due to their inability to account for all shapes of clusters and their high computational demands. Our proposed dissimilarity measure is specifically designed to detect overlap rather than dissimilarity and can be computed faster compared to existing measures. Our method is several times faster than compared methods and is capable of detecting overlapping clusters while avoiding the merging of orthogonal clusters.", "date": "2025-08-21", "categories": []}
{"id": "2508.13224", "title": "A Recurrent Neural Network based Clustering Method for Binary Data Sets in Education", "abstract": "This paper studies an application of a recurrent neural network to clustering method for the S-P chart: a binary data set used widely in education. As the number of students increases, the S-P chart becomes hard to handle. In order to classify the large chart into smaller charts, we present a simple clustering method based on the network dynamics. In the method, the network has multiple fixed points and basins of attraction give clusters corresponding to small S-P charts. In order to evaluate the clustering performance, we present an important feature quantity: average caution index that characterizes singularity of students answer oatterns. Performing fundamental experiments, effectiveness of the method is confirmed.", "date": "2025-08-17", "categories": []}
{"id": "2508.13499", "title": "Multi-view Clustering via Bi-level Decoupling and Consistency Learning", "abstract": "Multi-view clustering has shown to be an effective method for analyzing underlying patterns in multi-view data. The performance of clustering can be improved by learning the consistency and complementarity between multi-view features, however, cluster-oriented representation learning is often overlooked. In this paper, we propose a novel Bi-level Decoupling and Consistency Learning framework (BDCL) to further explore the effective representation for multi-view data to enhance inter-cluster discriminability and intra-cluster compactness of features in multi-view clustering. Our framework comprises three modules: 1) The multi-view instance learning module aligns the consistent information while preserving the private features between views through reconstruction autoencoder and contrastive learning. 2) The bi-level decoupling of features and clusters enhances the discriminability of feature space and cluster space. 3) The consistency learning module treats the different views of the sample and their neighbors as positive pairs, learns the consistency of their clustering assignments, and further compresses the intra-cluster space. Experimental results on five benchmark datasets demonstrate the superiority of the proposed method compared with the SOTA methods. Our code is published on https://github.com/LouisDong95/BDCL.", "date": "2025-08-19", "categories": []}
{"id": "2508.12450", "title": "Local Cluster Cardinality Estimation for Adaptive Mean Shift", "abstract": "This article presents an adaptive mean shift algorithm designed for datasets with varying local scale and cluster cardinality. Local distance distributions, from a point to all others, are used to estimate the cardinality of the local cluster by identifying a local minimum in the density of the distance distribution. Based on these cardinality estimates, local cluster parameters are then computed for the entire cluster in contrast to KDE-based methods, which provide insight only into localized regions of the cluster. During the mean shift execution, the cluster cardinality estimate is used to adaptively adjust the bandwidth and the mean shift kernel radius threshold. Our algorithm outperformed a recently proposed adaptive mean shift method on its original dataset and demonstrated competitive performance on a broader clustering benchmark.", "date": "2025-08-17", "categories": []}
{"id": "2508.12758", "title": "Constrained Centroid Clustering: A Novel Approach for Compact and Structured Partitioning", "abstract": "This paper presents Constrained Centroid Clustering (CCC), a method that extends classical centroid-based clustering by enforcing a constraint on the maximum distance between the cluster center and the farthest point in the cluster. Using a Lagrangian formulation, we derive a closed-form solution that maintains interpretability while controlling cluster spread. To evaluate CCC, we conduct experiments on synthetic circular data with radial symmetry and uniform angular distribution. Using ring-wise, sector-wise, and joint entropy as evaluation metrics, we show that CCC achieves more compact clusters by reducing radial spread while preserving angular structure, outperforming standard methods such as K-means and GMM. The proposed approach is suitable for applications requiring structured clustering with spread control, including sensor networks, collaborative robotics, and interpretable pattern analysis.", "date": "2025-08-18", "categories": []}
{"id": "2508.10345", "title": "Welfare-Centric Clustering", "abstract": "Fair clustering has traditionally focused on ensuring equitable group representation or equalizing group-specific clustering costs. However, Dickerson et al. (2025) recently showed that these fairness notions may yield undesirable or unintuitive clustering outcomes and advocated for a welfare-centric clustering approach that models the utilities of the groups. In this work, we model group utilities based on both distances and proportional representation and formalize two optimization objectives based on welfare-centric clustering: the Rawlsian (Egalitarian) objective and the Utilitarian objective. We introduce novel algorithms for both objectives and prove theoretical guarantees for them. Empirical evaluations on multiple real-world datasets demonstrate that our methods significantly outperform existing fair clustering baselines.", "date": "2025-08-14", "categories": []}
{"id": "2508.09180", "title": "scAGC: Learning Adaptive Cell Graphs with Contrastive Guidance for Single-Cell Clustering", "abstract": "Accurate cell type annotation is a crucial step in analyzing single-cell RNA sequencing (scRNA-seq) data, which provides valuable insights into cellular heterogeneity. However, due to the high dimensionality and prevalence of zero elements in scRNA-seq data, traditional clustering methods face significant statistical and computational challenges. While some advanced methods use graph neural networks to model cell-cell relationships, they often depend on static graph structures that are sensitive to noise and fail to capture the long-tailed distribution inherent in single-cell populations.To address these limitations, we propose scAGC, a single-cell clustering method that learns adaptive cell graphs with contrastive guidance. Our approach optimizes feature representations and cell graphs simultaneously in an end-to-end manner. Specifically, we introduce a topology-adaptive graph autoencoder that leverages a differentiable Gumbel-Softmax sampling strategy to dynamically refine the graph structure during training. This adaptive mechanism mitigates the problem of a long-tailed degree distribution by promoting a more balanced neighborhood structure. To model the discrete, over-dispersed, and zero-inflated nature of scRNA-seq data, we integrate a Zero-Inflated Negative Binomial (ZINB) loss for robust feature reconstruction. Furthermore, a contrastive learning objective is incorporated to regularize the graph learning process and prevent abrupt changes in the graph topology, ensuring stability and enhancing convergence. Comprehensive experiments on 9 real scRNA-seq datasets demonstrate that scAGC consistently outperforms other state-of-the-art methods, yielding the best NMI and ARI scores on 9 and 7 datasets, respectively.Our code is available at Anonymous Github.", "date": "2025-08-07", "categories": []}
{"id": "2505.04335", "title": "Hyperbolic Fuzzy C-Means with Adaptive Weight-based Filtering for Efficient Clustering", "abstract": "Clustering algorithms play a pivotal role in unsupervised learning by identifying and grouping similar objects based on shared characteristics. Although traditional clustering techniques, such as hard and fuzzy center-based clustering, have been widely used, they struggle with complex, high-dimensional, and non-Euclidean datasets. In particular, the fuzzy $C$-Means (FCM) algorithm, despite its efficiency and popularity, exhibits notable limitations in non-Euclidean spaces. Euclidean spaces assume linear separability and uniform distance scaling, limiting their effectiveness in capturing complex, hierarchical, or non-Euclidean structures in fuzzy clustering. To overcome these challenges, we introduce Filtration-based Hyperbolic Fuzzy C-Means (HypeFCM), a novel clustering algorithm tailored for better representation of data relationships in non-Euclidean spaces. HypeFCM integrates the principles of fuzzy clustering with hyperbolic geometry and employs a weight-based filtering mechanism to improve performance. The algorithm initializes weights using a Dirichlet distribution and iteratively refines cluster centroids and membership assignments based on a hyperbolic metric in the Poincar\\'e Disc model. Extensive experimental evaluations on $6$ synthetic and $12$ real-world datasets demonstrate that HypeFCM significantly outperforms conventional fuzzy clustering methods in non-Euclidean settings, underscoring its robustness and effectiveness.", "date": "2025-05-07", "categories": []}
{"id": "2506.18637", "title": "Granular-Ball-Induced Multiple Kernel K-Means", "abstract": "Most existing multi-kernel clustering algorithms, such as multi-kernel K-means, often struggle with computational efficiency and robustness when faced with complex data distributions. These challenges stem from their dependence on point-to-point relationships for optimization, which can lead to difficulty in accurately capturing data sets' inherent structure and diversity. Additionally, the intricate interplay between multiple kernels in such algorithms can further exacerbate these issues, effectively impacting their ability to cluster data points in high-dimensional spaces. In this paper, we leverage granular-ball computing to improve the multi-kernel clustering framework. The core of granular-ball computing is to adaptively fit data distribution by balls from coarse to acceptable levels. Each ball can enclose data points based on a density consistency measurement. Such ball-based data description thus improves the computational efficiency and the robustness to unknown noises. Specifically, based on granular-ball representations, we introduce the granular-ball kernel (GBK) and its corresponding granular-ball multi-kernel K-means framework (GB-MKKM) for efficient clustering. Using granular-ball relationships in multiple kernel spaces, the proposed GB-MKKM framework shows its superiority in efficiency and clustering performance in the empirical evaluation of various clustering tasks.", "date": "2025-06-23", "categories": []}
{"id": "2508.06857", "title": "A Joint Sparse Self-Representation Learning Method for Multiview Clustering", "abstract": "Multiview clustering (MC) aims to group samples using consistent and complementary information across various views. The subspace clustering, as a fundamental technique of MC, has attracted significant attention. In this paper, we propose a novel joint sparse self-representation learning model for MC, where a featured difference is the extraction of view-specific local information by introducing cardinality (i.e., $\\ell_0$-norm) constraints instead of Graph-Laplacian regularization. Specifically, under each view, cardinality constraints directly restrict the samples used in the self-representation stage to extract reliable local and global structure information, while the low-rank constraint aids in revealing a global coherent structure in the consensus affinity matrix during merging. The attendant challenge is that Augmented Lagrange Method (ALM)-based alternating minimization algorithms cannot guarantee convergence when applied directly to our nonconvex, nonsmooth model, thus resulting in poor generalization ability. To address it, we develop an alternating quadratic penalty (AQP) method with global convergence, where two subproblems are iteratively solved by closed-form solutions. Empirical results on six standard datasets demonstrate the superiority of our model and AQP method, compared to eight state-of-the-art algorithms.", "date": "2025-08-09", "categories": []}
{"id": "2508.07486", "title": "Extracting Overlapping Microservices from Monolithic Code via Deep Semantic Embeddings and Graph Neural Network-Based Soft Clustering", "abstract": "Modern software systems are increasingly shifting from monolithic architectures to microservices to enhance scalability, maintainability, and deployment flexibility. Existing microservice extraction methods typically rely on hard clustering, assigning each software component to a single microservice. This approach often increases inter-service coupling and reduces intra-service cohesion. We propose Mo2oM (Monolithic to Overlapping Microservices), a framework that formulates microservice extraction as a soft clustering problem, allowing components to belong probabilistically to multiple microservices. This approach is inspired by expert-driven decompositions, where practitioners intentionally replicate certain software components across services to reduce communication overhead. Mo2oM combines deep semantic embeddings with structural dependencies extracted from methodcall graphs to capture both functional and architectural relationships. A graph neural network-based soft clustering algorithm then generates the final set of microservices. We evaluate Mo2oM on four open-source monolithic benchmarks and compare it against eight state-of-the-art baselines. Our results demonstrate that Mo2oM achieves improvements of up to 40.97% in structural modularity (balancing cohesion and coupling), 58% in inter-service call percentage (communication overhead), 26.16% in interface number (modularity and decoupling), and 38.96% in non-extreme distribution (service size balance) across all benchmarks.", "date": "2025-08-10", "categories": []}
{"id": "2508.07952", "title": "Shapley-Inspired Feature Weighting in $k$-means with No Additional Hyperparameters", "abstract": "Clustering algorithms often assume all features contribute equally to the data structure, an assumption that usually fails in high-dimensional or noisy settings. Feature weighting methods can address this, but most require additional parameter tuning. We propose SHARK (Shapley Reweighted $k$-means), a feature-weighted clustering algorithm motivated by the use of Shapley values from cooperative game theory to quantify feature relevance, which requires no additional parameters beyond those in $k$-means. We prove that the $k$-means objective can be decomposed into a sum of per-feature Shapley values, providing an axiomatic foundation for unsupervised feature relevance and reducing Shapley computation from exponential to polynomial time. SHARK iteratively re-weights features by the inverse of their Shapley contribution, emphasising informative dimensions and down-weighting irrelevant ones. Experiments on synthetic and real-world data sets show that SHARK consistently matches or outperforms existing methods, achieving superior robustness and accuracy, particularly in scenarios where noise may be present. Software: https://github.com/rickfawley/shark.", "date": "2025-08-11", "categories": []}
{"id": "2508.06353", "title": "Geometric-k-means: A Bound Free Approach to Fast and Eco-Friendly k-means", "abstract": "This paper introduces Geometric-k-means (or Gk-means for short), a novel approach that significantly enhances the efficiency and energy economy of the widely utilized k-means algorithm, which, despite its inception over five decades ago, remains a cornerstone in machine learning applications. The essence of Gk-means lies in its active utilization of geometric principles, specifically scalar projection, to significantly accelerate the algorithm without sacrificing solution quality. This geometric strategy enables a more discerning focus on data points that are most likely to influence cluster updates, which we call as high expressive data (HE). In contrast, low expressive data (LE), does not impact clustering outcome, is effectively bypassed, leading to considerable reductions in computational overhead. Experiments spanning synthetic, real-world and high-dimensional datasets, demonstrate Gk-means is significantly better than traditional and state of the art (SOTA) k-means variants in runtime and distance computations (DC). Moreover, Gk-means exhibits better resource efficiency, as evidenced by its reduced energy footprint, placing it as more sustainable alternative.", "date": "2025-08-08", "categories": []}
{"id": "2411.01576", "title": "Explainable Clustering Beyond Worst-Case Guarantees", "abstract": "We study the explainable clustering problem first posed by Moshkovitz, Dasgupta, Rashtchian, and Frost (ICML 2020). The goal of explainable clustering is to fit an axis-aligned decision tree with $K$ leaves and minimal clustering cost (where every leaf is a cluster). The fundamental theoretical question in this line of work is the \\textit{price of explainability}, defined as the ratio between the clustering cost of the tree and the optimal cost. Numerous papers have provided worst-case guarantees on this quantity. For $K$-medians, it has recently been shown that the worst-case price of explainability is $\\Theta(\\log K)$. While this settles the matter from a data-agnostic point of view, two important questions remain unanswered: Are tighter guarantees possible for well-clustered data? And can we trust decision trees to recover underlying cluster structures? In this paper, we place ourselves in a statistical setting of mixture models to answer both questions. We prove that better guarantees are indeed feasible for well-clustered data. Our algorithm takes as input a mixture model and constructs a tree in data-independent time. We then extend our analysis to kernel clustering, deriving new guarantees that significantly improve over existing worst-case bounds.", "date": "2024-11-03", "categories": []}
{"id": "2508.05437", "title": "Online Sparsification of Bipartite-Like Clusters in Graphs", "abstract": "Graph clustering is an important algorithmic technique for analysing massive graphs, and has been widely applied in many research fields of data science. While the objective of most graph clustering algorithms is to find a vertex set of low conductance, a sequence of recent studies highlights the importance of the inter-connection between vertex sets when analysing real-world datasets. Following this line of research, in this work we study bipartite-like clusters and present efficient and online sparsification algorithms that find such clusters in both undirected graphs and directed ones. We conduct experimental studies on both synthetic and real-world datasets, and show that our algorithms significantly speedup the running time of existing clustering algorithms while preserving their effectiveness.", "date": "2025-08-07", "categories": []}
{"id": "2508.05504", "title": "Parameter-free entropy-regularized multi-view clustering with hierarchical feature selection", "abstract": "Multi-view clustering faces critical challenges in automatically discovering patterns across heterogeneous data while managing high-dimensional features and eliminating irrelevant information. Traditional approaches suffer from manual parameter tuning and lack principled cross-view integration mechanisms. This work introduces two complementary algorithms: AMVFCM-U and AAMVFCM-U, providing a unified parameter-free framework. Our approach replaces fuzzification parameters with entropy regularization terms that enforce adaptive cross-view consensus. The core innovation employs signal-to-noise ratio based regularization ($\\delta_j^h = \\frac{\\bar{x}_j^h}{(\\sigma_j^h)^2}$) for principled feature weighting with convergence guarantees, coupled with dual-level entropy terms that automatically balance view and feature contributions. AAMVFCM-U extends this with hierarchical dimensionality reduction operating at feature and view levels through adaptive thresholding ($\\theta^{h^{(t)}} = \\frac{d_h^{(t)}}{n}$). Evaluation across five diverse benchmarks demonstrates superiority over 15 state-of-the-art methods. AAMVFCM-U achieves up to 97% computational efficiency gains, reduces dimensionality to 0.45% of original size, and automatically identifies critical view combinations for optimal pattern discovery.", "date": "2025-08-07", "categories": []}
{"id": "2411.13922", "title": "Exponentially Consistent Nonparametric Linkage-Based Clustering of Data Sequences", "abstract": "In this paper, we consider nonparametric clustering of $M$ independent and identically distributed (i.i.d.) data sequences generated from {\\em unknown} distributions. The distributions of the $M$ data sequences belong to $K$ underlying distribution clusters. Existing results on exponentially consistent nonparametric clustering algorithms, like single linkage-based (SLINK) clustering and $k$-medoids distribution clustering, assume that the maximum intra-cluster distance ($d_L$) is smaller than the minimum inter-cluster distance ($d_H$). First, in the fixed sample size (FSS) setting, we show that exponential consistency can be achieved for SLINK clustering under a less strict assumption, $d_I < d_H$, where $d_I$ is the maximum distance between any two sub-clusters of a cluster that partition the cluster. Note that $d_I < d_L$ in general. Thus, our results show that SLINK is exponentially consistent for a larger class of problems than previously known. In our simulations, we also identify examples where $k$-medoids clustering is unable to find the true clusters, but SLINK is exponentially consistent. Then, we propose a sequential clustering algorithm, named SLINK-SEQ, based on SLINK and prove that it is also exponentially consistent. Simulation results show that the SLINK-SEQ algorithm requires fewer expected number of samples than the FSS SLINK algorithm for the same probability of error.", "date": "2024-11-21", "categories": []}
{"id": "2508.04071", "title": "Adversarial Fair Multi-View Clustering", "abstract": "Cluster analysis is a fundamental problem in data mining and machine learning. In recent years, multi-view clustering has attracted increasing attention due to its ability to integrate complementary information from multiple views. However, existing methods primarily focus on clustering performance, while fairness-a critical concern in human-centered applications-has been largely overlooked. Although recent studies have explored group fairness in multi-view clustering, most methods impose explicit regularization on cluster assignments, relying on the alignment between sensitive attributes and the underlying cluster structure. However, this assumption often fails in practice and can degrade clustering performance. In this paper, we propose an adversarial fair multi-view clustering (AFMVC) framework that integrates fairness learning into the representation learning process. Specifically, our method employs adversarial training to fundamentally remove sensitive attribute information from learned features, ensuring that the resulting cluster assignments are unaffected by it. Furthermore, we theoretically prove that aligning view-specific clustering assignments with a fairness-invariant consensus distribution via KL divergence preserves clustering consistency without significantly compromising fairness, thereby providing additional theoretical guarantees for our framework. Extensive experiments on data sets with fairness constraints demonstrate that AFMVC achieves superior fairness and competitive clustering performance compared to existing multi-view clustering and fairness-aware clustering methods.", "date": "2025-08-06", "categories": []}
{"id": "2508.04200", "title": "Bootstrap Deep Spectral Clustering with Optimal Transport", "abstract": "Spectral clustering is a leading clustering method. Two of its major shortcomings are the disjoint optimization process and the limited representation capacity. To address these issues, we propose a deep spectral clustering model (named BootSC), which jointly learns all stages of spectral clustering -- affinity matrix construction, spectral embedding, and $k$-means clustering -- using a single network in an end-to-end manner. BootSC leverages effective and efficient optimal-transport-derived supervision to bootstrap the affinity matrix and the cluster assignment matrix. Moreover, a semantically-consistent orthogonal re-parameterization technique is introduced to orthogonalize spectral embeddings, significantly enhancing the discrimination capability. Experimental results indicate that BootSC achieves state-of-the-art clustering performance. For example, it accomplishes a notable 16\\% NMI improvement over the runner-up method on the challenging ImageNet-Dogs dataset. Our code is available at https://github.com/spdj2271/BootSC.", "date": "2025-08-06", "categories": []}
{"id": "2507.10595", "title": "Divide-Then-Rule: A Cluster-Driven Hierarchical Interpolator for Attribute-Missing Graphs", "abstract": "Deep graph clustering (DGC) for attribute-missing graphs is an unsupervised task aimed at partitioning nodes with incomplete attributes into distinct clusters. Addressing this challenging issue is vital for practical applications. However, research in this area remains underexplored. Existing imputation methods for attribute-missing graphs often fail to account for the varying amounts of information available across node neighborhoods, leading to unreliable results, especially for nodes with insufficient known neighborhood. To address this issue, we propose a novel method named Divide-Then-Rule Graph Completion (DTRGC). This method first addresses nodes with sufficient known neighborhood information and treats the imputed results as new knowledge to iteratively impute more challenging nodes, while leveraging clustering information to correct imputation errors. Specifically, Dynamic Cluster-Aware Feature Propagation (DCFP) initializes missing node attributes by adjusting propagation weights based on the clustering structure. Subsequently, Hierarchical Neighborhood-aware Imputation (HNAI) categorizes attribute-missing nodes into three groups based on the completeness of their neighborhood attributes. The imputation is performed hierarchically, prioritizing the groups with nodes that have the most available neighborhood information. The cluster structure is then used to refine the imputation and correct potential errors. Finally, Hop-wise Representation Enhancement (HRE) integrates information across multiple hops, thereby enriching the expressiveness of node representations. Experimental results on six widely used graph datasets show that DTRGC significantly improves the clustering performance of various DGC methods under attribute-missing graphs.", "date": "2025-07-12", "categories": []}
{"id": "2507.13368", "title": "Scalable Attribute-Missing Graph Clustering via Neighborhood Differentiation", "abstract": "Deep graph clustering (DGC), which aims to unsupervisedly separate the nodes in an attribute graph into different clusters, has seen substantial potential in various industrial scenarios like community detection and recommendation. However, the real-world attribute graphs, e.g., social networks interactions, are usually large-scale and attribute-missing. To solve these two problems, we propose a novel DGC method termed \\underline{\\textbf{C}}omplementary \\underline{\\textbf{M}}ulti-\\underline{\\textbf{V}}iew \\underline{\\textbf{N}}eighborhood \\underline{\\textbf{D}}ifferentiation (\\textit{CMV-ND}), which preprocesses graph structural information into multiple views in a complete but non-redundant manner. First, to ensure completeness of the structural information, we propose a recursive neighborhood search that recursively explores the local structure of the graph by completely expanding node neighborhoods across different hop distances. Second, to eliminate the redundancy between neighborhoods at different hops, we introduce a neighborhood differential strategy that ensures no overlapping nodes between the differential hop representations. Then, we construct $K+1$ complementary views from the $K$ differential hop representations and the features of the target node. Last, we apply existing multi-view clustering or DGC methods to the views. Experimental results on six widely used graph datasets demonstrate that CMV-ND significantly improves the performance of various methods.", "date": "2025-07-09", "categories": []}
{"id": "2508.00110", "title": "funOCLUST: Clustering Functional Data with Outliers", "abstract": "Functional data present unique challenges for clustering due to their infinite-dimensional nature and potential sensitivity to outliers. An extension of the OCLUST algorithm to the functional setting is proposed to address these issues. The approach leverages the OCLUST framework, creating a robust method to cluster curves and trim outliers. The methodology is evaluated on both simulated and real-world functional datasets, demonstrating strong performance in clustering and outlier identification.", "date": "2025-07-31", "categories": []}
{"id": "2508.02989", "title": "Scalable Varied-Density Clustering via Graph Propagation", "abstract": "We propose a novel perspective on varied-density clustering for high-dimensional data by framing it as a label propagation process in neighborhood graphs that adapt to local density variations. Our method formally connects density-based clustering with graph connectivity, enabling the use of efficient graph propagation techniques developed in network science. To ensure scalability, we introduce a density-aware neighborhood propagation algorithm and leverage advanced random projection methods to construct approximate neighborhood graphs. Our approach significantly reduces computational cost while preserving clustering quality. Empirically, it scales to datasets with millions of points in minutes and achieves competitive accuracy compared to existing baselines.", "date": "2025-08-05", "categories": []}
{"id": "2505.09805", "title": "Contextual Phenotyping of Pediatric Sepsis Cohort Using Large Language Models", "abstract": "Clustering patient subgroups is essential for personalized care and efficient resource use. Traditional clustering methods struggle with high-dimensional, heterogeneous healthcare data and lack contextual understanding. This study evaluates Large Language Model (LLM) based clustering against classical methods using a pediatric sepsis dataset from a low-income country (LIC), containing 2,686 records with 28 numerical and 119 categorical variables. Patient records were serialized into text with and without a clustering objective. Embeddings were generated using quantized LLAMA 3.1 8B, DeepSeek-R1-Distill-Llama-8B with low-rank adaptation(LoRA), and Stella-En-400M-V5 models. K-means clustering was applied to these embeddings. Classical comparisons included K-Medoids clustering on UMAP and FAMD-reduced mixed data. Silhouette scores and statistical tests evaluated cluster quality and distinctiveness. Stella-En-400M-V5 achieved the highest Silhouette Score (0.86). LLAMA 3.1 8B with the clustering objective performed better with higher number of clusters, identifying subgroups with distinct nutritional, clinical, and socioeconomic profiles. LLM-based methods outperformed classical techniques by capturing richer context and prioritizing key features. These results highlight potential of LLMs for contextual phenotyping and informed decision-making in resource-limited settings.", "date": "2025-05-14", "categories": []}
{"id": "2508.00893", "title": "Multi-Community Spectral Clustering for Geometric Graphs", "abstract": "In this paper, we consider the soft geometric block model (SGBM) with a fixed number $k \\geq 2$ of homogeneous communities in the dense regime, and we introduce a spectral clustering algorithm for community recovery on graphs generated by this model. Given such a graph, the algorithm produces an embedding into $\\mathbb{R}^{k-1}$ using the eigenvectors associated with the $k-1$ eigenvalues of the adjacency matrix of the graph that are closest to a value determined by the parameters of the model. It then applies $k$-means clustering to the embedding. We prove weak consistency and show that a simple local refinement step ensures strong consistency. A key ingredient is an application of a non-standard version of Davis-Kahan theorem to control eigenspace perturbations when eigenvalues are not simple. We also analyze the limiting spectrum of the adjacency matrix, using a combination of combinatorial and matrix techniques.", "date": "2025-07-27", "categories": []}
{"id": "2508.01254", "title": "Self-Enhanced Image Clustering with Cross-Modal Semantic Consistency", "abstract": "While large language-image pre-trained models like CLIP offer powerful generic features for image clustering, existing methods typically freeze the encoder. This creates a fundamental mismatch between the model's task-agnostic representations and the demands of a specific clustering task, imposing a ceiling on performance. To break this ceiling, we propose a self-enhanced framework based on cross-modal semantic consistency for efficient image clustering. Our framework first builds a strong foundation via Cross-Modal Semantic Consistency and then specializes the encoder through Self-Enhancement. In the first stage, we focus on Cross-Modal Semantic Consistency. By mining consistency between generated image-text pairs at the instance, cluster assignment, and cluster center levels, we train lightweight clustering heads to align with the rich semantics of the pre-trained model. This alignment process is bolstered by a novel method for generating higher-quality cluster centers and a dynamic balancing regularizer to ensure well-distributed assignments. In the second stage, we introduce a Self-Enhanced fine-tuning strategy. The well-aligned model from the first stage acts as a reliable pseudo-label generator. These self-generated supervisory signals are then used to feed back the efficient, joint optimization of the vision encoder and clustering heads, unlocking their full potential. Extensive experiments on six mainstream datasets show that our method outperforms existing deep clustering methods by significant margins. Notably, our ViT-B/32 model already matches or even surpasses the accuracy of state-of-the-art methods built upon the far larger ViT-L/14.", "date": "2025-08-02", "categories": []}
{"id": "2310.05288", "title": "Clustering Three-Way Data with Outliers", "abstract": "Matrix-variate distributions are a recent addition to the model-based clustering field, thereby making it possible to analyze data in matrix form with complex structure such as images and time series. Due to its recent appearance, there is limited literature on matrix-variate data, with even less on dealing with outliers in these models. An approach for clustering matrix-variate normal data with outliers is discussed. The approach, which uses the distribution of subset log-likelihoods, extends the OCLUST algorithm to matrix-variate normal data and uses an iterative approach to detect and trim outliers.", "date": "2023-10-08", "categories": []}
{"id": "2507.20980", "title": "LargeMvC-Net: Anchor-based Deep Unfolding Network for Large-scale Multi-view Clustering", "abstract": "Deep anchor-based multi-view clustering methods enhance the scalability of neural networks by utilizing representative anchors to reduce the computational complexity of large-scale clustering. Despite their scalability advantages, existing approaches often incorporate anchor structures in a heuristic or task-agnostic manner, either through post-hoc graph construction or as auxiliary components for message passing. Such designs overlook the core structural demands of anchor-based clustering, neglecting key optimization principles. To bridge this gap, we revisit the underlying optimization problem of large-scale anchor-based multi-view clustering and unfold its iterative solution into a novel deep network architecture, termed LargeMvC-Net. The proposed model decomposes the anchor-based clustering process into three modules: RepresentModule, NoiseModule, and AnchorModule, corresponding to representation learning, noise suppression, and anchor indicator estimation. Each module is derived by unfolding a step of the original optimization procedure into a dedicated network component, providing structural clarity and optimization traceability. In addition, an unsupervised reconstruction loss aligns each view with the anchor-induced latent space, encouraging consistent clustering structures across views. Extensive experiments on several large-scale multi-view benchmarks show that LargeMvC-Net consistently outperforms state-of-the-art methods in terms of both effectiveness and scalability.", "date": "2025-07-28", "categories": []}
{"id": "2507.19095", "title": "GCL-GCN: Graphormer and Contrastive Learning Enhanced Attributed Graph Clustering Network", "abstract": "Attributed graph clustering holds significant importance in modern data analysis. However, due to the complexity of graph data and the heterogeneity of node attributes, leveraging graph information for clustering remains challenging. To address this, we propose a novel deep graph clustering model, GCL-GCN, specifically designed to address the limitations of existing models in capturing local dependencies and complex structures when dealing with sparse and heterogeneous graph data. GCL-GCN introduces an innovative Graphormer module that combines centrality encoding and spatial relationships, effectively capturing both global and local information between nodes, thereby enhancing the quality of node representations. Additionally, we propose a novel contrastive learning module that significantly enhances the discriminative power of feature representations. In the pre-training phase, this module increases feature distinction through contrastive learning on the original feature matrix, ensuring more identifiable initial representations for subsequent graph convolution and clustering tasks. Extensive experimental results on six datasets demonstrate that GCL-GCN outperforms 14 advanced methods in terms of clustering quality and robustness. Specifically, on the Cora dataset, it improves ACC, NMI, and ARI by 4.94%, 13.01%, and 10.97%, respectively, compared to the primary comparison method MBN.", "date": "2025-07-25", "categories": []}
{"id": "2503.23215", "title": "Unsupervised Learning: Comparative Analysis of Clustering Techniques on High-Dimensional Data", "abstract": "This paper presents a comprehensive comparative analysis of prominent clustering algorithms K-means, DBSCAN, and Spectral Clustering on high-dimensional datasets. We introduce a novel evaluation framework that assesses clustering performance across multiple dimensionality reduction techniques (PCA, t-SNE, and UMAP) using diverse quantitative metrics. Experiments conducted on MNIST, Fashion-MNIST, and UCI HAR datasets reveal that preprocessing with UMAP consistently improves clustering quality across all algorithms, with Spectral Clustering demonstrating superior performance on complex manifold structures. Our findings show that algorithm selection should be guided by data characteristics, with Kmeans excelling in computational efficiency, DBSCAN in handling irregular clusters, and Spectral Clustering in capturing complex relationships. This research contributes a systematic approach for evaluating and selecting clustering techniques for high dimensional data applications.", "date": "2025-03-29", "categories": []}
{"id": "2507.04283", "title": "Clustering via Self-Supervised Diffusion", "abstract": "Diffusion models, widely recognized for their success in generative tasks, have not yet been applied to clustering. We introduce Clustering via Diffusion (CLUDI), a self-supervised framework that combines the generative power of diffusion models with pre-trained Vision Transformer features to achieve robust and accurate clustering. CLUDI is trained via a teacher-student paradigm: the teacher uses stochastic diffusion-based sampling to produce diverse cluster assignments, which the student refines into stable predictions. This stochasticity acts as a novel data augmentation strategy, enabling CLUDI to uncover intricate structures in high-dimensional data. Extensive evaluations on challenging datasets demonstrate that CLUDI achieves state-of-the-art performance in unsupervised classification, setting new benchmarks in clustering robustness and adaptability to complex data distributions. Our code is available at https://github.com/BGU-CS-VIL/CLUDI.", "date": "2025-07-06", "categories": []}
{"id": "2206.04841", "title": "Hierarchical mixtures of Gaussians for combined dimensionality reduction and clustering", "abstract": "We introduce hierarchical mixtures of Gaussians (HMoGs), which unify dimensionality reduction and clustering into a single probabilistic model. HMoGs provide closed-form expressions for the model likelihood, exact inference over latent states and cluster membership, and exact algorithms for maximum-likelihood optimization. The novel exponential family parameterization of HMoGs greatly reduces their computational complexity relative to similar model-based methods, allowing them to efficiently model hundreds of latent dimensions, and thereby capture additional structure in high-dimensional data. We demonstrate HMoGs on synthetic experiments and MNIST, and show how joint optimization of dimensionality reduction and clustering facilitates increased model performance. We also explore how sparsity-constrained dimensionality reduction can further improve clustering performance while encouraging interpretability. By bridging classical statistical modelling with the scale of modern data and compute, HMoGs offer a practical approach to high-dimensional clustering that preserves statistical rigour, interpretability, and uncertainty quantification that is often missing from embedding-based, variational, and self-supervised methods.", "date": "2022-06-10", "categories": []}
{"id": "2507.19917", "title": "A mini-batch training strategy for deep subspace clustering networks", "abstract": "Mini-batch training is a cornerstone of modern deep learning, offering computational efficiency and scalability for training complex architectures. However, existing deep subspace clustering (DSC) methods, which typically combine an autoencoder with a self-expressive layer, rely on full-batch processing. The bottleneck arises from the self-expressive module, which requires representations of the entire dataset to construct a self-representation coefficient matrix. In this work, we introduce a mini-batch training strategy for DSC by integrating a memory bank that preserves global feature representations. Our approach enables scalable training of deep architectures for subspace clustering with high-resolution images, overcoming previous limitations. Additionally, to efficiently fine-tune large-scale pre-trained encoders for subspace clustering, we propose a decoder-free framework that leverages contrastive learning instead of autoencoding for representation learning. This design not only eliminates the computational overhead of decoder training but also provides competitive performance. Extensive experiments demonstrate that our approach not only achieves performance comparable to full-batch methods, but outperforms other state-of-the-art subspace clustering methods on the COIL100 and ORL datasets by fine-tuning deep networks.", "date": "2025-07-26", "categories": []}
{"id": "2507.20369", "title": "Clustering by Attention: Leveraging Prior Fitted Transformers for Data Partitioning", "abstract": "Clustering is a core task in machine learning with wide-ranging applications in data mining and pattern recognition. However, its unsupervised nature makes it inherently challenging. Many existing clustering algorithms suffer from critical limitations: they often require careful parameter tuning, exhibit high computational complexity, lack interpretability, or yield suboptimal accuracy, especially when applied to large-scale datasets. In this paper, we introduce a novel clustering approach based on meta-learning. Our approach eliminates the need for parameter optimization while achieving accuracy that outperforms state-of-the-art clustering techniques. The proposed technique leverages a few pre-clustered samples to guide the clustering process for the entire dataset in a single forward pass. Specifically, we employ a pre-trained Prior-Data Fitted Transformer Network (PFN) to perform clustering. The algorithm computes attention between the pre-clustered samples and the unclustered samples, allowing it to infer cluster assignments for the entire dataset based on the learned relation. We theoretically and empirically demonstrate that, given just a few pre-clustered examples, the model can generalize to accurately cluster the rest of the dataset. Experiments on challenging benchmark datasets show that our approach can successfully cluster well-separated data without any pre-clustered samples, and significantly improves performance when a few clustered samples are provided. We show that our approach is superior to the state-of-the-art techniques. These results highlight the effectiveness and scalability of our approach, positioning it as a promising alternative to existing clustering techniques.", "date": "2025-07-27", "categories": []}
{"id": "2507.20505", "title": "Attributed Graph Clustering with Multi-Scale Weight-Based Pairwise Coarsening and Contrastive Learning", "abstract": "This study introduces the Multi-Scale Weight-Based Pairwise Coarsening and Contrastive Learning (MPCCL) model, a novel approach for attributed graph clustering that effectively bridges critical gaps in existing methods, including long-range dependency, feature collapse, and information loss. Traditional methods often struggle to capture high-order graph features due to their reliance on low-order attribute information, while contrastive learning techniques face limitations in feature diversity by overemphasizing local neighborhood structures. Similarly, conventional graph coarsening methods, though reducing graph scale, frequently lose fine-grained structural details. MPCCL addresses these challenges through an innovative multi-scale coarsening strategy, which progressively condenses the graph while prioritizing the merging of key edges based on global node similarity to preserve essential structural information. It further introduces a one-to-many contrastive learning paradigm, integrating node embeddings with augmented graph views and cluster centroids to enhance feature diversity, while mitigating feature masking issues caused by the accumulation of high-frequency node weights during multi-scale coarsening. By incorporating a graph reconstruction loss and KL divergence into its self-supervised learning framework, MPCCL ensures cross-scale consistency of node representations. Experimental evaluations reveal that MPCCL achieves a significant improvement in clustering performance, including a remarkable 15.24% increase in NMI on the ACM dataset and notable robust gains on smaller-scale datasets such as Citeseer, Cora and DBLP.", "date": "2025-07-28", "categories": []}
{"id": "2507.19423", "title": "Perfect Clustering in Very Sparse Diverse Multiplex Networks", "abstract": "The paper studies the DIverse MultiPLEx Signed Generalized Random Dot Product Graph (DIMPLE-SGRDPG) network model (Pensky (2024)), where all layers of the network have the same collection of nodes. In addition, all layers can be partitioned into groups such that the layers in the same group are embedded in the same ambient subspace but otherwise matrices of connection probabilities can be all different. This setting includes majority of multilayer network models as its particular cases. The key task in this model is to recover the groups of layers with unique subspace structures, since the case where all layers of the network are embedded in the same subspace has been fairly well studied. Until now, clustering of layers in such networks was based on the layer-per-layer analysis, which required the multilayer network to be sufficiently dense. Nevertheless, in this paper we succeeded in pooling information in all layers together and providing a tensor-based methodology that ensures perfect clustering for a much sparser network. Our theoretical results, established under intuitive non-restrictive assumptions, assert that the new technique achieves perfect clustering under sparsity conditions that, up to logarithmic factors, coincide with the computational lower bound derived for a much simpler model.", "date": "2025-07-25", "categories": []}
{"id": "2507.13620", "title": "Tri-Learn Graph Fusion Network for Attributed Graph Clustering", "abstract": "In recent years, models based on Graph Convolutional Networks (GCN) have made significant strides in the field of graph data analysis. However, challenges such as over-smoothing and over-compression remain when handling large-scale and complex graph datasets, leading to a decline in clustering quality. Although the Graph Transformer architecture has mitigated some of these issues, its performance is still limited when processing heterogeneous graph data. To address these challenges, this study proposes a novel deep clustering framework that comprising GCN, Autoencoder (AE), and Graph Transformer, termed the Tri-Learn Graph Fusion Network (Tri-GFN). This framework enhances the differentiation and consistency of global and local information through a unique tri-learning mechanism and feature fusion enhancement strategy. The framework integrates GCN, AE, and Graph Transformer modules. These components are meticulously fused by a triple-channel enhancement module, which maximizes the use of both node attributes and topological structures, ensuring robust clustering representation. The tri-learning mechanism allows mutual learning among these modules, while the feature fusion strategy enables the model to capture complex relationships, yielding highly discriminative representations for graph clustering. It surpasses many state-of-the-art methods, achieving an accuracy improvement of approximately 0.87% on the ACM dataset, 14.14 % on the Reuters dataset, and 7.58 % on the USPS dataset. Due to its outstanding performance on the Reuters dataset, Tri-GFN can be applied to automatic news classification, topic retrieval, and related fields.", "date": "2025-07-18", "categories": []}
{"id": "2507.15904", "title": "Fast-VAT: Accelerating Cluster Tendency Visualization using Cython and Numba", "abstract": "Visual Assessment of Cluster Tendency (VAT) is a widely used unsupervised technique to assess the presence of cluster structure in unlabeled datasets. However, its standard implementation suffers from significant performance limitations due to its O(n^2) time complexity and inefficient memory usage. In this work, we present Fast-VAT, a high-performance reimplementation of the VAT algorithm in Python, augmented with Numba's Just-In-Time (JIT) compilation and Cython's static typing and low-level memory optimizations. Our approach achieves up to 50x speedup over the baseline implementation, while preserving the output fidelity of the original method. We validate Fast-VAT on a suite of real and synthetic datasets -- including Iris, Mall Customers, and Spotify subsets -- and verify cluster tendency using Hopkins statistics, PCA, and t-SNE. Additionally, we compare VAT's structural insights with clustering results from DBSCAN and K-Means to confirm its reliability.", "date": "2025-07-21", "categories": []}
{"id": "2502.01250", "title": "Beyond Win Rates: A Clustering-Based Approach to Character Balance Analysis in Team-Based Games", "abstract": "Character diversity in competitive games, while enriching gameplay, often introduces balance challenges that can negatively impact player experience and strategic depth. Traditional balance assessments rely on aggregate metrics like win rates and pick rates, which offer limited insight into the intricate dynamics of team-based games and nuanced character roles. This paper proposes a novel clustering-based methodology to analyze character balance, leveraging in-game data from Valorant to account for team composition influences and reveal latent character roles. By applying hierarchical agglomerative clustering with Jensen-Shannon Divergence to professional match data from the Valorant Champions Tour 2022, our approach identifies distinct clusters of agents exhibiting similar co-occurrence patterns within team compositions. This method not only complements existing quantitative metrics but also provides a more holistic and interpretable perspective on character synergies and potential imbalances, offering game developers a valuable tool for informed and context-aware balance adjustments.", "date": "2025-02-03", "categories": []}
{"id": "2507.15253", "title": "Disentangling Homophily and Heterophily in Multimodal Graph Clustering", "abstract": "Multimodal graphs, which integrate unstructured heterogeneous data with structured interconnections, offer substantial real-world utility but remain insufficiently explored in unsupervised learning. In this work, we initiate the study of multimodal graph clustering, aiming to bridge this critical gap. Through empirical analysis, we observe that real-world multimodal graphs often exhibit hybrid neighborhood patterns, combining both homophilic and heterophilic relationships. To address this challenge, we propose a novel framework -- \\textsc{Disentangled Multimodal Graph Clustering (DMGC)} -- which decomposes the original hybrid graph into two complementary views: (1) a homophily-enhanced graph that captures cross-modal class consistency, and (2) heterophily-aware graphs that preserve modality-specific inter-class distinctions. We introduce a \\emph{Multimodal Dual-frequency Fusion} mechanism that jointly filters these disentangled graphs through a dual-pass strategy, enabling effective multimodal integration while mitigating category confusion. Our self-supervised alignment objectives further guide the learning process without requiring labels. Extensive experiments on both multimodal and multi-relational graph datasets demonstrate that DMGC achieves state-of-the-art performance, highlighting its effectiveness and generalizability across diverse settings. Our code is available at https://github.com/Uncnbb/DMGC.", "date": "2025-07-21", "categories": []}
{"id": "2507.13417", "title": "Soft-ECM: An extension of Evidential C-Means for complex data", "abstract": "Clustering based on belief functions has been gaining increasing attention in the machine learning community due to its ability to effectively represent uncertainty and/or imprecision. However, none of the existing algorithms can be applied to complex data, such as mixed data (numerical and categorical) or non-tabular data like time series. Indeed, these types of data are, in general, not represented in a Euclidean space and the aforementioned algorithms make use of the properties of such spaces, in particular for the construction of barycenters. In this paper, we reformulate the Evidential C-Means (ECM) problem for clustering complex data. We propose a new algorithm, Soft-ECM, which consistently positions the centroids of imprecise clusters requiring only a semi-metric. Our experiments show that Soft-ECM present results comparable to conventional fuzzy clustering approaches on numerical data, and we demonstrate its ability to handle mixed data and its benefits when combining fuzzy clustering with semi-metrics such as DTW for time series data.", "date": "2025-07-17", "categories": []}
{"id": "2507.13765", "title": "Dual-Center Graph Clustering with Neighbor Distribution", "abstract": "Graph clustering is crucial for unraveling intricate data structures, yet it presents significant challenges due to its unsupervised nature. Recently, goal-directed clustering techniques have yielded impressive results, with contrastive learning methods leveraging pseudo-label garnering considerable attention. Nonetheless, pseudo-label as a supervision signal is unreliable and existing goal-directed approaches utilize only features to construct a single-target distribution for single-center optimization, which lead to incomplete and less dependable guidance. In our work, we propose a novel Dual-Center Graph Clustering (DCGC) approach based on neighbor distribution properties, which includes representation learning with neighbor distribution and dual-center optimization. Specifically, we utilize neighbor distribution as a supervision signal to mine hard negative samples in contrastive learning, which is reliable and enhances the effectiveness of representation learning. Furthermore, neighbor distribution center is introduced alongside feature center to jointly construct a dual-target distribution for dual-center optimization. Extensive experiments and analysis demonstrate superior performance and effectiveness of our proposed method.", "date": "2025-07-18", "categories": []}
{"id": "2507.13793", "title": "An Enhanced Model-based Approach for Short Text Clustering", "abstract": "Short text clustering has become increasingly important with the popularity of social media like Twitter, Google+, and Facebook. Existing methods can be broadly categorized into two paradigms: topic model-based approaches and deep representation learning-based approaches. This task is inherently challenging due to the sparse, large-scale, and high-dimensional characteristics of the short text data. Furthermore, the computational intensity required by representation learning significantly increases the running time. To address these issues, we propose a collapsed Gibbs Sampling algorithm for the Dirichlet Multinomial Mixture model (GSDMM), which effectively handles the sparsity and high dimensionality of short texts while identifying representative words for each cluster. Based on several aspects of GSDMM that warrant further refinement, we propose an improved approach, GSDMM+, designed to further optimize its performance. GSDMM+ reduces initialization noise and adaptively adjusts word weights based on entropy, achieving fine-grained clustering that reveals more topic-related information. Additionally, strategic cluster merging is employed to refine clustering granularity, better aligning the predicted distribution with the true category distribution. We conduct extensive experiments, comparing our methods with both classical and state-of-the-art approaches. The experimental results demonstrate the efficiency and effectiveness of our methods. The source code for our model is publicly available at https://github.com/chehaoa/VEMC.", "date": "2025-07-18", "categories": []}
{"id": "2507.12583", "title": "Ranking Vectors Clustering: Theory and Applications", "abstract": "We study the problem of clustering ranking vectors, where each vector represents preferences as an ordered list of distinct integers. Specifically, we focus on the k-centroids ranking vectors clustering problem (KRC), which aims to partition a set of ranking vectors into k clusters and identify the centroid of each cluster. Unlike classical k-means clustering (KMC), KRC constrains both the observations and centroids to be ranking vectors. We establish the NP-hardness of KRC and characterize its feasible set. For the single-cluster case, we derive a closed-form analytical solution for the optimal centroid, which can be computed in linear time. To address the computational challenges of KRC, we develop an efficient approximation algorithm, KRCA, which iteratively refines initial solutions from KMC, referred to as the baseline solution. Additionally, we introduce a branch-and-bound (BnB) algorithm for efficient cluster reconstruction within KRCA, leveraging a decision tree framework to reduce computational time while incorporating a controlling parameter to balance solution quality and efficiency. We establish theoretical error bounds for KRCA and BnB. Through extensive numerical experiments on synthetic and real-world datasets, we demonstrate that KRCA consistently outperforms baseline solutions, delivering significant improvements in solution quality with fast computational times. This work highlights the practical significance of KRC for personalization and large-scale decision making, offering methodological advancements and insights that can be built upon in future studies.", "date": "2025-07-16", "categories": []}
{"id": "2306.06974", "title": "A Computational Theory and Semi-Supervised Algorithm for Clustering", "abstract": "A computational theory for clustering and a semi-supervised clustering algorithm is presented. Clustering is defined to be the obtainment of groupings of data such that each group contains no anomalies with respect to a chosen grouping principle and measure; all other examples are considered to be fringe points, isolated anomalies, anomalous clusters or unknown clusters. More precisely, after appropriate modelling under the assumption of uniform random distribution, any example whose expectation of occurrence is <1 with respect to a group is considered an anomaly; otherwise it is assigned a membership of that group. Thus, clustering is conceived as the dual of anomaly detection. The representation of data is taken to be the Euclidean distance of a point to a cluster median. This is due to the robustness properties of the median to outliers, its approximate location of centrality and so that decision boundaries are general purpose. The kernel of the clustering method is the perception anomaly detection algorithm, resulting in a parameter-free, fast, and efficient clustering algorithm. Acknowledging that clustering is an interactive and iterative process, the algorithm relies on a small fraction of known relationships between examples. These relationships serve as seeds to define the user's objectives and guide the clustering process. The method then expands the clusters accordingly, leaving the remaining examples for exploration and subsequent iterations. Results are presented on synthetic and realworld data sets, demonstrating the advantages over the most popular unsupervised and semi-supervised clustering methods.", "date": "2023-06-12", "categories": []}
{"id": "2405.02700", "title": "Unveiling Differences in Generative Models: A Scalable Differential Clustering Approach", "abstract": "A fine-grained comparison of generative models requires the identification of sample types generated differently by each of the involved models. While quantitative scores have been proposed in the literature to rank different generative models, score-based evaluation and ranking do not reveal the nuanced differences between the generative models in producing different sample types. In this work, we propose solving a differential clustering problem to detect sample types generated differently by two generative models. To solve the differential clustering problem, we develop a spectral method called Fourier-based Identification of Novel Clusters (FINC) to identify modes produced by a generative model with a higher frequency in comparison to a reference distribution. FINC provides a scalable algorithm based on random Fourier features to estimate the eigenspace of kernel covariance matrices of two generative models and utilize the principal eigendirections to detect the sample types present more dominantly in each model. We demonstrate the application of the FINC method to large-scale computer vision datasets and generative modeling frameworks. Our numerical results suggest the scalability of the developed Fourier-based method in highlighting the sample types produced with different frequencies by generative models. The project code is available at https://github.com/buyeah1109/FINC.", "date": "2024-05-04", "categories": []}
{"id": "2507.10710", "title": "Robust Multi-Manifold Clustering via Simplex Paths", "abstract": "This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a locality graph on d-simplices, using the dihedral angle in between adjacent simplices as the graph weights, and then compute infinity path distances in this simplex graph. This procedure gives a metric on simplices which we refer to as the largest angle path distance (LAPD). We analyze the properties of LAPD under random sampling, and prove that with an appropriate denoising procedure, this metric separates the manifold components with high probability. We validate the proposed methodology with extensive numerical experiments on both synthetic and real-world data sets. These experiments demonstrate that the method is robust to noise, curvature, and small intersection angle, and generally out-performs other MMC algorithms. In addition, we provide a highly scalable implementation of the proposed algorithm, which leverages approximation schemes for infinity path distance to achieve quasi-linear computational complexity.", "date": "2025-07-14", "categories": []}
{"id": "2507.09762", "title": "EventHunter: Dynamic Clustering and Ranking of Security Events from Hacker Forum Discussions", "abstract": "Hacker forums provide critical early warning signals for emerging cybersecurity threats, but extracting actionable intelligence from their unstructured and noisy content remains a significant challenge. This paper presents an unsupervised framework that automatically detects, clusters, and prioritizes security events discussed across hacker forum posts. Our approach leverages Transformer-based embeddings fine-tuned with contrastive learning to group related discussions into distinct security event clusters, identifying incidents like zero-day disclosures or malware releases without relying on predefined keywords. The framework incorporates a daily ranking mechanism that prioritizes identified events using quantifiable metrics reflecting timeliness, source credibility, information completeness, and relevance. Experimental evaluation on real-world hacker forum data demonstrates that our method effectively reduces noise and surfaces high-priority threats, enabling security analysts to mount proactive responses. By transforming disparate hacker forum discussions into structured, actionable intelligence, our work addresses fundamental challenges in automated threat detection and analysis.", "date": "2025-07-13", "categories": []}
{"id": "2507.09890", "title": "Soft Graph Clustering for single-cell RNA Sequencing Data", "abstract": "Clustering analysis is fundamental in single-cell RNA sequencing (scRNA-seq) data analysis for elucidating cellular heterogeneity and diversity. Recent graph-based scRNA-seq clustering methods, particularly graph neural networks (GNNs), have significantly improved in tackling the challenges of high-dimension, high-sparsity, and frequent dropout events that lead to ambiguous cell population boundaries. However, their reliance on hard graph constructions derived from thresholded similarity matrices presents challenges:(i) The simplification of intercellular relationships into binary edges (0 or 1) by applying thresholds, which restricts the capture of continuous similarity features among cells and leads to significant information loss.(ii) The presence of significant inter-cluster connections within hard graphs, which can confuse GNN methods that rely heavily on graph structures, potentially causing erroneous message propagation and biased clustering outcomes. To tackle these challenges, we introduce scSGC, a Soft Graph Clustering for single-cell RNA sequencing data, which aims to more accurately characterize continuous similarities among cells through non-binary edge weights, thereby mitigating the limitations of rigid data structures. The scSGC framework comprises three core components: (i) a zero-inflated negative binomial (ZINB)-based feature autoencoder; (ii) a dual-channel cut-informed soft graph embedding module; and (iii) an optimal transport-based clustering optimization module. Extensive experiments across ten datasets demonstrate that scSGC outperforms 13 state-of-the-art clustering models in clustering accuracy, cell type annotation, and computational efficiency. These results highlight its substantial potential to advance scRNA-seq data analysis and deepen our understanding of cellular heterogeneity.", "date": "2025-07-14", "categories": []}
{"id": "2507.10296", "title": "Average Sensitivity of Hierarchical $k$-Median Clustering", "abstract": "Hierarchical clustering is a widely used method for unsupervised learning with numerous applications. However, in the application of modern algorithms, the datasets studied are usually large and dynamic. If the hierarchical clustering is sensitive to small perturbations of the dataset, the usability of the algorithm will be greatly reduced. In this paper, we focus on the hierarchical $k$ -median clustering problem, which bridges hierarchical and centroid-based clustering while offering theoretical appeal, practical utility, and improved interpretability. We analyze the average sensitivity of algorithms for this problem by measuring the expected change in the output when a random data point is deleted. We propose an efficient algorithm for hierarchical $k$-median clustering and theoretically prove its low average sensitivity and high clustering quality. Additionally, we show that single linkage clustering and a deterministic variant of the CLNSS algorithm exhibit high average sensitivity, making them less stable. Finally, we validate the robustness and effectiveness of our algorithm through experiments.", "date": "2025-07-14", "categories": []}
{"id": "2402.10242", "title": "Signed Diverse Multiplex Networks: Clustering and Inference", "abstract": "The paper introduces a Signed Generalized Random Dot Product Graph (SGRDPG) model, which is a variant of the Generalized Random Dot Product Graph (GRDPG), where, in addition, edges can be positive or negative. The setting is extended to a multiplex version, where all layers have the same collection of nodes and follow the SGRDPG. The only common feature of the layers of the network is that they can be partitioned into groups with common subspace structures, while otherwise matrices of connection probabilities can be all different. The setting above is extremely flexible and includes a variety of existing multiplex network models, including GRDPG, as its particular cases.\n  By employing novel methodologies, our paper ensures strongly consistent clustering of layers and highly accurate subspace estimation, which are significant improvements over the results of Pensky and Wang (2024). All algorithms and theoretical results in the paper remain true for both signed and binary networks. In addition, the paper shows that keeping signs of the edges in the process of network construction leads to a better precision of estimation and clustering and, hence, is beneficial for tackling real world problems such as, for example, analysis of brain networks.", "date": "2024-02-14", "categories": []}
{"id": "2507.08311", "title": "CAS Condensed and Accelerated Silhouette: An Efficient Method for Determining the Optimal K in K-Means Clustering", "abstract": "Clustering is a critical component of decision-making in todays data-driven environments. It has been widely used in a variety of fields such as bioinformatics, social network analysis, and image processing. However, clustering accuracy remains a major challenge in large datasets. This paper presents a comprehensive overview of strategies for selecting the optimal value of k in clustering, with a focus on achieving a balance between clustering precision and computational efficiency in complex data environments. In addition, this paper introduces improvements to clustering techniques for text and image data to provide insights into better computational performance and cluster validity. The proposed approach is based on the Condensed Silhouette method, along with statistical methods such as Local Structures, Gap Statistics, Class Consistency Ratio, and a Cluster Overlap Index CCR and COIbased algorithm to calculate the best value of k for K-Means clustering. The results of comparative experiments show that the proposed approach achieves up to 99 percent faster execution times on high-dimensional datasets while retaining both precision and scalability, making it highly suitable for real time clustering needs or scenarios demanding efficient clustering with minimal resource utilization.", "date": "2025-07-11", "categories": []}
{"id": "2507.07582", "title": "Improving Clustering on Occupational Text Data through Dimensionality Reduction", "abstract": "In this study, we focused on proposing an optimal clustering mechanism for the occupations defined in the well-known US-based occupational database, O*NET. Even though all occupations are defined according to well-conducted surveys in the US, their definitions can vary for different firms and countries. Hence, if one wants to expand the data that is already collected in O*NET for the occupations defined with different tasks, a map between the definitions will be a vital requirement. We proposed a pipeline using several BERT-based techniques with various clustering approaches to obtain such a map. We also examined the effect of dimensionality reduction approaches on several metrics used in measuring performance of clustering algorithms. Finally, we improved our results by using a specialized silhouette approach. This new clustering-based mapping approach with dimensionality reduction may help distinguish the occupations automatically, creating new paths for people wanting to change their careers.", "date": "2025-07-10", "categories": []}
{"id": "2305.03565", "title": "The geometry of financial institutions -- Wasserstein clustering of financial data", "abstract": "The increasing availability of granular and big data on various objects of interest has made it necessary to develop methods for condensing this information into a representative and intelligible map. Financial regulation is a field that exemplifies this need, as regulators require diverse and often highly granular data from financial institutions to monitor and assess their activities. However, processing and analyzing such data can be a daunting task, especially given the challenges of dealing with missing values and identifying clusters based on specific features.\n  To address these challenges, we propose a variant of Lloyd's algorithm that applies to probability distributions and uses generalized Wasserstein barycenters to construct a metric space which represents given data on various objects in condensed form. By applying our method to the financial regulation context, we demonstrate its usefulness in dealing with the specific challenges faced by regulators in this domain. We believe that our approach can also be applied more generally to other fields where large and complex data sets need to be represented in concise form.", "date": "2023-05-05", "categories": []}
{"id": "2403.18393", "title": "Tensor-based Graph Learning with Consistency and Specificity for Multi-view Clustering", "abstract": "In the context of multi-view clustering, graph learning is recognized as a crucial technique, which generally involves constructing an adaptive neighbor graph based on probabilistic neighbors, and then learning a consensus graph for clustering. However, it is worth noting that these graph learning methods encounter two significant limitations. Firstly, they often rely on Euclidean distance to measure similarity when constructing the adaptive neighbor graph, which proves inadequate in capturing the intrinsic structure among data points in practice, particularly for high-dimensional data. Secondly, most of these methods focus solely on consensus graph, ignoring unique information from each view. Although a few graph-based studies have considered using specific information as well, the modelling approach employed does not exclude the noise impact from the common or specific components. To this end, we propose a novel tensor-based multi-view graph learning framework that simultaneously considers consistency and specificity, while effectively eliminating the influence of noise. Specifically, we calculate similarity using pseudo-Stiefel manifold distance to preserve the intrinsic properties of data. By making an assumption that the learned neighbor graph of each view comprises a consistent part, a specific part, and a noise part, we formulate a new tensor-based target graph learning paradigm for noise-free graph fusion. Owing to the benefits of tensor singular value decomposition (t-SVD) in uncovering high-order correlations, this model is capable of achieving a comprehensive understanding of the target graph. Furthermore, we derive an algorithm to address the optimization problem. Experiments on six datasets have demonstrated the superiority of our method. We have released the source code on https://github.com/lshi91/CSTGL-Code.", "date": "2024-03-27", "categories": []}
{"id": "2507.03917", "title": "Consistency-Aware Padding for Incomplete Multi-Modal Alignment Clustering Based on Self-Repellent Greedy Anchor Search", "abstract": "Multimodal representation is faithful and highly effective in describing real-world data samples' characteristics by describing their complementary information. However, the collected data often exhibits incomplete and misaligned characteristics due to factors such as inconsistent sensor frequencies and device malfunctions. Existing research has not effectively addressed the issue of filling missing data in scenarios where multiview data are both imbalanced and misaligned. Instead, it relies on class-level alignment of the available data. Thus, it results in some data samples not being well-matched, thereby affecting the quality of data fusion. In this paper, we propose the Consistency-Aware Padding for Incomplete Multimodal Alignment Clustering Based on Self-Repellent Greedy Anchor Search(CAPIMAC) to tackle the problem of filling imbalanced and misaligned data in multimodal datasets. Specifically, we propose a self-repellent greedy anchor search module(SRGASM), which employs a self-repellent random walk combined with a greedy algorithm to identify anchor points for re-representing incomplete and misaligned multimodal data. Subsequently, based on noise-contrastive learning, we design a consistency-aware padding module (CAPM) to effectively interpolate and align imbalanced and misaligned data, thereby improving the quality of multimodal data fusion. Experimental results demonstrate the superiority of our method over benchmark datasets. The code will be publicly released at https://github.com/Autism-mm/CAPIMAC.git.", "date": "2025-07-05", "categories": []}
{"id": "2405.13337", "title": "Semantic Equitable Clustering: A Simple and Effective Strategy for Clustering Vision Tokens", "abstract": "The Vision Transformer (ViT) has gained prominence for its superior relational modeling prowess. However, its global attention mechanism's quadratic complexity poses substantial computational burdens. A common remedy spatially groups tokens for self-attention, reducing computational requirements. Nonetheless, this strategy neglects semantic information in tokens, possibly scattering semantically-linked tokens across distinct groups, thus compromising the efficacy of self-attention intended for modeling inter-token dependencies. Motivated by these insights, we introduce a fast and balanced clustering method, named Semantic Equitable Clustering (SEC). SEC clusters tokens based on their global semantic relevance in an efficient, straightforward manner. In contrast to traditional clustering methods requiring multiple iterations, our method achieves token clustering in a single pass. Additionally, SEC regulates the number of tokens per cluster, ensuring a balanced distribution for effective parallel processing on current computational platforms without necessitating further optimization. Capitalizing on SEC, we propose a versatile vision backbone, SECViT. Comprehensive experiments in image classification, object detection, instance segmentation, and semantic segmentation validate the effectiveness of SECViT. Moreover, SEC can be conveniently and swiftly applied to multimodal large language models (MLLM), such as LLaVA, to serve as a vision language connector, effectively accelerating the model's efficiency while maintaining unchanged or better performance.", "date": "2024-05-22", "categories": []}
{"id": "2507.01501", "title": "Meteoroid stream identification with HDBSCAN unsupervised clustering algorithm", "abstract": "Accurate identification of meteoroid streams is central to understanding their origins and evolution. However, overlapping clusters and background noise hinder classification, an issue amplified for missions such as ESA's LUMIO that rely on meteor shower observations to infer lunar meteoroid impact parameters. This study evaluates the performance of the Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm for unsupervised meteoroid stream identification, comparing its outcomes with the established Cameras for All-Sky Meteor Surveillance (CAMS) look-up table method. We analyze the CAMS Meteoroid Orbit Database v3.0 using three feature vectors: LUTAB (CAMS geocentric parameters), ORBIT (heliocentric orbital elements), and GEO (adapted geocentric parameters). HDBSCAN is applied with varying minimum cluster sizes and two cluster selection methods (eom and leaf). To align HDBSCAN clusters with CAMS classifications, the Hungarian algorithm determines the optimal mapping. Clustering performance is assessed via the Silhouette score, Normalized Mutual Information, and F1 score, with Principal Component Analysis further supporting the analysis. With the GEO vector, HDBSCAN confirms 39 meteoroid streams, 21 strongly aligning with CAMS. The ORBIT vector identifies 30 streams, 13 with high matching scores. Less active showers pose identification challenges. The eom method consistently yields superior performance and agreement with CAMS. Although HDBSCAN requires careful selection of the minimum cluster size, it delivers robust, internally consistent clusters and outperforms the look-up table method in statistical coherence. These results underscore HDBSCAN's potential as a mathematically consistent alternative for meteoroid stream identification, although further validation is needed to assess physical validity.", "date": "2025-07-02", "categories": []}
{"id": "2507.01696", "title": "Dynamic Similarity Graph Construction with Kernel Density Estimation", "abstract": "In the kernel density estimation (KDE) problem, we are given a set $X$ of data points in $\\mathbb{R}^d$, a kernel function $k: \\mathbb{R}^d \\times \\mathbb{R}^d \\rightarrow \\mathbb{R}$, and a query point $\\mathbf{q} \\in \\mathbb{R}^d$, and the objective is to quickly output an estimate of $\\sum_{\\mathbf{x} \\in X} k(\\mathbf{q}, \\mathbf{x})$. In this paper, we consider $\\textsf{KDE}$ in the dynamic setting, and introduce a data structure that efficiently maintains the estimates for a set of query points as data points are added to $X$ over time. Based on this, we design a dynamic data structure that maintains a sparse approximation of the fully connected similarity graph on $X$, and develop a fast dynamic spectral clustering algorithm. We further evaluate the effectiveness of our algorithms on both synthetic and real-world datasets.", "date": "2025-07-02", "categories": []}
{"id": "2409.04698", "title": "Hierarchical Sparse Representation Clustering for High-Dimensional Data Streams", "abstract": "Data stream clustering reveals patterns within continuously arriving, potentially unbounded data sequences. Numerous data stream algorithms have been proposed to cluster data streams. The existing data stream clustering algorithms still face significant challenges when addressing high-dimensional data streams. First, it is intractable to measure the similarities among high-dimensional data objects via Euclidean distances when constructing and merging microclusters. Second, these algorithms are highly sensitive to the noise contained in high-dimensional data streams. In this paper, we propose a hierarchical sparse representation clustering (HSRC) method for clustering high-dimensional data streams. HSRC first employs an $l_1$-minimization technique to learn an affinity matrix for data objects in individual landmark windows with fixed sizes, where the number of neighboring data objects is automatically selected. This approach ensures that highly correlated data samples within clusters are grouped together. Then, HSRC applies a spectral clustering technique to the affinity matrix to generate microclusters. These microclusters are subsequently merged into macroclusters based on their sparse similarity degrees (SSDs). Additionally, HSRC introduces sparsity residual values (SRVs) to adaptively select representative data objects from the current landmark window. These representatives serve as dictionary samples for the next landmark window. Finally, HSRC refines each macrocluster through fine-tuning. In particular, HSRC enables the detection of outliers in high-dimensional data streams via the associated SRVs. The experimental results obtained on several benchmark datasets demonstrate the effectiveness and robustness of HSRC.", "date": "2024-09-07", "categories": []}
{"id": "2503.00854", "title": "FACROC: a fairness measure for FAir Clustering through ROC curves", "abstract": "Fair clustering has attracted remarkable attention from the research community. Many fairness measures for clustering have been proposed; however, they do not take into account the clustering quality w.r.t. the values of the protected attribute. In this paper, we introduce a new visual-based fairness measure for fair clustering through ROC curves, namely FACROC. This fairness measure employs AUCC as a measure of clustering quality and then computes the difference in the corresponding ROC curves for each value of the protected attribute. Experimental results on several popular datasets for fairness-aware machine learning and well-known (fair) clustering models show that FACROC is a beneficial method for visually evaluating the fairness of clustering models.", "date": "2025-03-02", "categories": []}
{"id": "2507.00600", "title": "A Practical Guide to Interpretable Role-Based Clustering in Multi-Layer Financial Networks", "abstract": "Understanding the functional roles of financial institutions within interconnected markets is critical for effective supervision, systemic risk assessment, and resolution planning. We propose an interpretable role-based clustering approach for multi-layer financial networks, designed to identify the functional positions of institutions across different market segments. Our method follows a general clustering framework defined by proximity measures, cluster evaluation criteria, and algorithm selection. We construct explainable node embeddings based on egonet features that capture both direct and indirect trading relationships within and across market layers. Using transaction-level data from the ECB's Money Market Statistical Reporting (MMSR), we demonstrate how the approach uncovers heterogeneous institutional roles such as market intermediaries, cross-segment connectors, and peripheral lenders or borrowers. The results highlight the flexibility and practical value of role-based clustering in analyzing financial networks and understanding institutional behavior in complex market structures.", "date": "2025-07-01", "categories": []}
{"id": "2404.03446", "title": "SP$^2$OT: Semantic-Regularized Progressive Partial Optimal Transport for Imbalanced Clustering", "abstract": "Deep clustering, which learns representation and semantic clustering without labels information, poses a great challenge for deep learning-based approaches. Despite significant progress in recent years, most existing methods focus on uniformly distributed datasets, significantly limiting the practical applicability of their methods. In this paper, we propose a more practical problem setting named deep imbalanced clustering, where the underlying classes exhibit an imbalance distribution. To address this challenge, we introduce a novel optimal transport-based pseudo-label learning framework. Our framework formulates pseudo-label generation as a Semantic-regularized Progressive Partial Optimal Transport (SP$^2$OT) problem, which progressively transports each sample to imbalanced clusters under prior and semantic relation constraints, thus generating high-quality and imbalance-aware pseudo-labels. To solve the SP$^2$OT problem, we propose a projected mirror descent algorithm, which alternates between: (1) computing the gradient of the SP$^2$OT objective, and (2) performing gradient descent with projection via an entropy-regularized progressive partial optimal transport formulation. Furthermore, we formulate the second step as an unbalanced optimal transport problem with augmented constraints and develop an efficient solution based on fast matrix scaling algorithms. Experiments on various datasets, including a human-curated long-tailed CIFAR100, challenging ImageNet-R, and large-scale subsets of fine-grained iNaturalist2018 datasets, demonstrate the superiority of our method. Code is available: https://github.com/rhfeiyang/SPPOT", "date": "2024-04-04", "categories": []}
{"id": "2503.09185", "title": "Incomplete Multi-view Clustering via Diffusion Contrastive Generation", "abstract": "Incomplete multi-view clustering (IMVC) has garnered increasing attention in recent years due to the common issue of missing data in multi-view datasets. The primary approach to address this challenge involves recovering the missing views before applying conventional multi-view clustering methods. Although imputation-based IMVC methods have achieved significant improvements, they still encounter notable limitations: 1) heavy reliance on paired data for training the data recovery module, which is impractical in real scenarios with high missing data rates; 2) the generated data often lacks diversity and discriminability, resulting in suboptimal clustering results. To address these shortcomings, we propose a novel IMVC method called Diffusion Contrastive Generation (DCG). Motivated by the consistency between the diffusion and clustering processes, DCG learns the distribution characteristics to enhance clustering by applying forward diffusion and reverse denoising processes to intra-view data. By performing contrastive learning on a limited set of paired multi-view samples, DCG can align the generated views with the real views, facilitating accurate recovery of views across arbitrary missing view scenarios. Additionally, DCG integrates instance-level and category-level interactive learning to exploit the consistent and complementary information available in multi-view data, achieving robust and end-to-end clustering. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches. The code is available at https://github.com/zhangyuanyang21/2025-AAAI-DCG.", "date": "2025-03-12", "categories": []}
{"id": "2503.22448", "title": "Comparison between neural network clustering, hierarchical clustering and k-means clustering: Applications using fluidic lenses", "abstract": "A comparison between neural network clustering (NNC), hierarchical clustering (HC) and K-means clustering (KMC) is performed to evaluate the computational superiority of these three machine learning (ML) techniques for organizing large datasets into clusters. For NNC, a self-organizing map (SOM) training was applied to a collection of wavefront sensor reconstructions, decomposed in terms of 15 Zernike coefficients, characterizing the optical aberrations of the phase front transmitted by fluidic lenses. In order to understand the distribution and structure of the 15 Zernike variables within an input space, SOM-neighboring weight distances, SOM-sample hits, SOM-weight positions and SOM-weight planes were analyzed to form a visual interpretation of the system's structural properties. In the case of HC, the data was partitioned using a combined dissimilarity-linkage matrix computation. The effectiveness of this method was confirmed by a high cophenetic correlation coefficient value (c=0.9651). Additionally, a maximum number of clusters was established by setting an inconsistency cutoff of 0.8, yielding a total of 7 clusters for system segmentation. In addition, a KMC approach was employed to establish a quantitative measure of clustering segmentation efficiency, obtaining a sillhoute average value of 0.905 for data segmentation into K=5 non-overlapping clusters. On the other hand, the NNC analysis revealed that the 15 variables could be characterized through the collective influence of 8 clusters. It was established that the formation of clusters through the combined linkage and dissimilarity algorithms of HC alongside KMC is a more dependable clustering solution than separate assessment via NNC or HC, where altering the SOM size or inconsistency cutoff can lead to completely new clustering configurations.", "date": "2025-03-28", "categories": []}
{"id": "2506.21695", "title": "Unimodal Strategies in Density-Based Clustering", "abstract": "Density-based clustering methods often surpass centroid-based counterparts, when addressing data with noise or arbitrary data distributions common in real-world problems. In this study, we reveal a key property intrinsic to density-based clustering methods regarding the relation between the number of clusters and the neighborhood radius of core points - we empirically show that it is nearly unimodal, and support this claim theoretically in a specific setting. We leverage this property to devise new strategies for finding appropriate values for the radius more efficiently based on the Ternary Search algorithm. This is especially important for large scale data that is high-dimensional, where parameter tuning is computationally intensive. We validate our methodology through extensive applications across a range of high-dimensional, large-scale NLP, Audio, and Computer Vision tasks, demonstrating its practical effectiveness and robustness. This work not only offers a significant advancement in parameter control for density-based clustering but also broadens the understanding regarding the relations between their guiding parameters. Our code is available at https://github.com/oronnir/UnimodalStrategies.", "date": "2025-06-26", "categories": []}
{"id": "2405.17050", "title": "HeNCler: Node Clustering in Heterophilous Graphs via Learned Asymmetric Similarity", "abstract": "Clustering nodes in heterophilous graphs is challenging as traditional methods assume that effective clustering is characterized by high intra-cluster and low inter-cluster connectivity. To address this, we introduce HeNCler-a novel approach for Heterophilous Node Clustering. HeNCler learns a similarity graph by optimizing a clustering-specific objective based on weighted kernel singular value decomposition. Our approach enables spectral clustering on an asymmetric similarity graph, providing flexibility for both directed and undirected graphs. By solving the primal problem directly, our method overcomes the computational difficulties of traditional adjacency partitioning-based approaches. Experimental results show that HeNCler significantly improves node clustering performance in heterophilous graph settings, highlighting the advantage of its asymmetric graph-learning framework.", "date": "2024-05-27", "categories": []}
{"id": "2506.19410", "title": "Unsupervised Dataset Dictionary Learning for domain shift robust clustering: application to sitting posture identification", "abstract": "This paper introduces a novel approach, Unsupervised Dataset Dictionary Learning (U-DaDiL), for totally unsupervised robust clustering applied to sitting posture identification. Traditional methods often lack adaptability to diverse datasets and suffer from domain shift issues. U-DaDiL addresses these challenges by aligning distributions from different datasets using Wasserstein barycenter based representation. Experimental evaluations on the Office31 dataset demonstrate significant improvements in cluster alignment accuracy. This work also presents a promising step for addressing domain shift and robust clustering for unsupervised sitting posture identification", "date": "2025-06-24", "categories": []}
{"id": "2506.19759", "title": "The Shape of Consumer Behavior: A Symbolic and Topological Analysis of Time Series", "abstract": "Understanding temporal patterns in online search behavior is crucial for real-time marketing and trend forecasting. Google Trends offers a rich proxy for public interest, yet the high dimensionality and noise of its time-series data present challenges for effective clustering. This study evaluates three unsupervised clustering approaches, Symbolic Aggregate approXimation (SAX), enhanced SAX (eSAX), and Topological Data Analysis (TDA), applied to 20 Google Trends keywords representing major consumer categories. Our results show that while SAX and eSAX offer fast and interpretable clustering for stable time series, they struggle with volatility and complexity, often producing ambiguous ``catch-all'' clusters. TDA, by contrast, captures global structural features through persistent homology and achieves more balanced and meaningful groupings.\n  We conclude with practical guidance for using symbolic and topological methods in consumer analytics and suggest that hybrid approaches combining both perspectives hold strong potential for future applications.", "date": "2025-06-24", "categories": []}
{"id": "2506.15703", "title": "Federated Incomplete Multi-view Clustering with Globally Fused Graph Guidance", "abstract": "Federated multi-view clustering has been proposed to mine the valuable information within multi-view data distributed across different devices and has achieved impressive results while preserving the privacy. Despite great progress, most federated multi-view clustering methods only used global pseudo-labels to guide the downstream clustering process and failed to exploit the global information when extracting features. In addition, missing data problem in federated multi-view clustering task is less explored. To address these problems, we propose a novel Federated Incomplete Multi-view Clustering method with globally Fused Graph guidance (FIMCFG). Specifically, we designed a dual-head graph convolutional encoder at each client to extract two kinds of underlying features containing global and view-specific information. Subsequently, under the guidance of the fused graph, the two underlying features are fused into high-level features, based on which clustering is conducted under the supervision of pseudo-labeling. Finally, the high-level features are uploaded to the server to refine the graph fusion and pseudo-labeling computation. Extensive experimental results demonstrate the effectiveness and superiority of FIMCFG. Our code is publicly available at https://github.com/PaddiHunter/FIMCFG.", "date": "2025-05-30", "categories": []}
{"id": "2506.14952", "title": "An Observation on Lloyd's k-Means Algorithm in High Dimensions", "abstract": "Clustering and estimating cluster means are core problems in statistics and machine learning, with k-means and Expectation Maximization (EM) being two widely used algorithms. In this work, we provide a theoretical explanation for the failure of k-means in high-dimensional settings with high noise and limited sample sizes, using a simple Gaussian Mixture Model (GMM). We identify regimes where, with high probability, almost every partition of the data becomes a fixed point of the k-means algorithm. This study is motivated by challenges in the analysis of more complex cases, such as masked GMMs, and those arising from applications in Cryo-Electron Microscopy.", "date": "2025-06-17", "categories": []}
{"id": "2506.08673", "title": "Towards Fair Representation: Clustering and Consensus", "abstract": "Consensus clustering, a fundamental task in machine learning and data analysis, aims to aggregate multiple input clusterings of a dataset, potentially based on different non-sensitive attributes, into a single clustering that best represents the collective structure of the data. In this work, we study this fundamental problem through the lens of fair clustering, as introduced by Chierichetti et al. [NeurIPS'17], which incorporates the disparate impact doctrine to ensure proportional representation of each protected group in the dataset within every cluster. Our objective is to find a consensus clustering that is not only representative but also fair with respect to specific protected attributes. To the best of our knowledge, we are the first to address this problem and provide a constant-factor approximation.\n  As part of our investigation, we examine how to minimally modify an existing clustering to enforce fairness -- an essential postprocessing step in many clustering applications that require fair representation. We develop an optimal algorithm for datasets with equal group representation and near-linear time constant factor approximation algorithms for more general scenarios with different proportions of two group sizes. We complement our approximation result by showing that the problem is NP-hard for two unequal-sized groups. Given the fundamental nature of this problem, we believe our results on Closest Fair Clustering could have broader implications for other clustering problems, particularly those for which no prior approximation guarantees exist for their fair variants.", "date": "2025-06-10", "categories": []}
{"id": "2506.12408", "title": "PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering", "abstract": "While contrastive multi-view clustering has achieved remarkable success, it implicitly assumes balanced class distribution. However, real-world multi-view data primarily exhibits class imbalance distribution. Consequently, existing methods suffer performance degradation due to their inability to perceive and model such imbalance. To address this challenge, we present the first systematic study of imbalanced multi-view clustering, focusing on two fundamental problems: i. perceiving class imbalance distribution, and ii. mitigating representation degradation of minority samples. We propose PROTOCOL, a novel PaRtial Optimal TranspOrt-enhanced COntrastive Learning framework for imbalanced multi-view clustering. First, for class imbalance perception, we map multi-view features into a consensus space and reformulate the imbalanced clustering as a partial optimal transport (POT) problem, augmented with progressive mass constraints and weighted KL divergence for class distributions. Second, we develop a POT-enhanced class-rebalanced contrastive learning at both feature and class levels, incorporating logit adjustment and class-sensitive learning to enhance minority sample representations. Extensive experiments demonstrate that PROTOCOL significantly improves clustering performance on imbalanced multi-view data, filling a critical research gap in this field.", "date": "2025-06-14", "categories": []}
{"id": "2506.12555", "title": "Neuromorphic Online Clustering and Its Application to Spike Sorting", "abstract": "Active dendrites are the basis for biologically plausible neural networks possessing many desirable features of the biological brain including flexibility, dynamic adaptability, and energy efficiency. A formulation for active dendrites using the notational language of conventional machine learning is put forward as an alternative to a spiking neuron formulation. Based on this formulation, neuromorphic dendrites are developed as basic neural building blocks capable of dynamic online clustering. Features and capabilities of neuromorphic dendrites are demonstrated via a benchmark drawn from experimental neuroscience: spike sorting. Spike sorting takes inputs from electrical probes implanted in neural tissue, detects voltage spikes (action potentials) emitted by neurons, and attempts to sort the spikes according to the neuron that emitted them. Many spike sorting methods form clusters based on the shapes of action potential waveforms, under the assumption that spikes emitted by a given neuron have similar shapes and will therefore map to the same cluster. Using a stream of synthetic spike shapes, the accuracy of the proposed dendrite is compared with the more compute-intensive, offline k-means clustering approach. Overall, the dendrite outperforms k-means and has the advantage of requiring only a single pass through the input stream, learning as it goes. The capabilities of the neuromorphic dendrite are demonstrated for a number of scenarios including dynamic changes in the input stream, differing neuron spike rates, and varying neuron counts.", "date": "2025-06-14", "categories": []}
{"id": "2506.12839", "title": "Fair Bayesian Model-Based Clustering", "abstract": "Fair clustering has become a socially significant task with the advancement of machine learning technologies and the growing demand for trustworthy AI. Group fairness ensures that the proportions of each sensitive group are similar in all clusters. Most existing group-fair clustering methods are based on the $K$-means clustering and thus require the distance between instances and the number of clusters to be given in advance. To resolve this limitation, we propose a fair Bayesian model-based clustering called Fair Bayesian Clustering (FBC). We develop a specially designed prior which puts its mass only on fair clusters, and implement an efficient MCMC algorithm. Advantages of FBC are that it can infer the number of clusters and can be applied to any data type as long as the likelihood is defined (e.g., categorical data). Experiments on real-world datasets show that FBC (i) reasonably infers the number of clusters, (ii) achieves a competitive utility-fairness trade-off compared to existing fair clustering methods, and (iii) performs well on categorical data.", "date": "2025-06-15", "categories": []}
{"id": "2506.13533", "title": "Learning Augmented Graph $k$-Clustering", "abstract": "Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize learning-augmented $k$-clustering to operate on general metrics, enabling its application to graph-structured and non-Euclidean domains. Our framework also relaxes restrictive cluster size constraints, providing greater flexibility for datasets with imbalanced or unknown cluster distributions. Furthermore, we extend the hardness of query complexity to general metrics: under the Exponential Time Hypothesis (ETH), we show that any polynomial-time algorithm must perform approximately $\\Omega(k / \\alpha)$ queries to achieve a $(1 + \\alpha)$-approximation. These contributions strengthen both the theoretical foundations and practical applicability of learning-augmented clustering, bridging gaps between traditional methods and real-world challenges.", "date": "2025-06-16", "categories": []}
{"id": "2506.11377", "title": "Scalable Context-Preserving Model-Aware Deep Clustering for Hyperspectral Images", "abstract": "Subspace clustering has become widely adopted for the unsupervised analysis of hyperspectral images (HSIs). Recent model-aware deep subspace clustering methods often use a two-stage framework, involving the calculation of a self-representation matrix with complexity of O(n^2), followed by spectral clustering. However, these methods are computationally intensive, generally incorporating solely either local or non-local spatial structure constraints, and their structural constraints fall short of effectively supervising the entire clustering process.\n  We propose a scalable, context-preserving deep clustering method based on basis representation, which jointly captures local and non-local structures for efficient HSI clustering. To preserve local structure (i.e., spatial continuity within subspaces), we introduce a spatial smoothness constraint that aligns clustering predictions with their spatially filtered versions. For non-local structure (i.e., spectral continuity), we employ a mini-cluster-based scheme that refines predictions at the group level, encouraging spectrally similar pixels to belong to the same subspace. Notably, these two constraints are jointly optimized to reinforce each other.\n  Specifically, our model is designed as an one-stage approach in which the structural constraints are applied to the entire clustering process. The time and space complexity of our method is O(n), making it applicable to large-scale HSI data. Experiments on real-world datasets show that our method outperforms state-of-the-art techniques. Our code is available at: https://github.com/lxlscut/SCDSC", "date": "2025-06-12", "categories": []}
{"id": "2401.12533", "title": "Near-Optimal Algorithms for Constrained k-Center Clustering with Instance-level Background Knowledge", "abstract": "Center-based clustering has attracted significant research interest from both theory and practice. In many practical applications, input data often contain background knowledge that can be used to improve clustering results. In this work, we build on widely adopted $k$-center clustering and model its input background knowledge as must-link (ML) and cannot-link (CL) constraint sets. However, most clustering problems including $k$-center are inherently $\\mathcal{NP}$-hard, while the more complex constrained variants are known to suffer severer approximation and computation barriers that significantly limit their applicability. By employing a suite of techniques including reverse dominating sets, linear programming (LP) integral polyhedron, and LP duality, we arrive at the first efficient approximation algorithm for constrained $k$-center with the best possible ratio of 2. We also construct competitive baseline algorithms and empirically evaluate our approximation algorithm against them on a variety of real datasets. The results validate our theoretical findings and demonstrate the great advantages of our algorithm in terms of clustering cost, clustering quality, and running time.", "date": "2024-01-23", "categories": []}
{"id": "2412.13592", "title": "PASCO (PArallel Structured COarsening): an overlay to speed up graph clustering algorithms", "abstract": "Clustering the nodes of a graph is a cornerstone of graph analysis and has been extensively studied. However, some popular methods are not suitable for very large graphs: e.g., spectral clustering requires the computation of the spectral decomposition of the Laplacian matrix, which is not applicable for large graphs with a large number of communities. This work introduces PASCO, an overlay that accelerates clustering algorithms. Our method consists of three steps: 1-We compute several independent small graphs representing the input graph by applying an efficient and structure-preserving coarsening algorithm. 2-A clustering algorithm is run in parallel onto each small graph and provides several partitions of the initial graph. 3-These partitions are aligned and combined with an optimal transport method to output the final partition. The PASCO framework is based on two key contributions: a novel global algorithm structure designed to enable parallelization and a fast, empirically validated graph coarsening algorithm that preserves structural properties. We demonstrate the strong performance of 1 PASCO in terms of computational efficiency, structural preservation, and output partition quality, evaluated on both synthetic and real-world graph datasets.", "date": "2024-12-18", "categories": []}
{"id": "2506.09202", "title": "Policy-Based Trajectory Clustering in Offline Reinforcement Learning", "abstract": "We introduce a novel task of clustering trajectories from offline reinforcement learning (RL) datasets, where each cluster center represents the policy that generated its trajectories. By leveraging the connection between the KL-divergence of offline trajectory distributions and a mixture of policy-induced distributions, we formulate a natural clustering objective. To solve this, we propose Policy-Guided K-means (PG-Kmeans) and Centroid-Attracted Autoencoder (CAAE). PG-Kmeans iteratively trains behavior cloning (BC) policies and assigns trajectories based on policy generation probabilities, while CAAE resembles the VQ-VAE framework by guiding the latent representations of trajectories toward the vicinity of specific codebook entries to achieve clustering. Theoretically, we prove the finite-step convergence of PG-Kmeans and identify a key challenge in offline trajectory clustering: the inherent ambiguity of optimal solutions due to policy-induced conflicts, which can result in multiple equally valid but structurally distinct clusterings. Experimentally, we validate our methods on the widely used D4RL dataset and custom GridWorld environments. Our results show that both PG-Kmeans and CAAE effectively partition trajectories into meaningful clusters. They offer a promising framework for policy-based trajectory clustering, with broad applications in offline RL and beyond.", "date": "2025-06-10", "categories": []}
{"id": "2506.10094", "title": "Unsupervised Deep Clustering of MNIST with Triplet-Enhanced Convolutional Autoencoders", "abstract": "This research implements an advanced unsupervised clustering system for MNIST handwritten digits through two-phase deep autoencoder architecture. A deep neural autoencoder requires a training process during phase one to develop minimal yet interpretive representations of images by minimizing reconstruction errors. During the second phase we unify the reconstruction error with a KMeans clustering loss for learned latent embeddings through a joint distance-based objective. Our model contains three elements which include batch normalization combined with dropout and weight decay for achieving generalized and stable results. The framework achieves superior clustering performance during extensive tests which used intrinsic measurements including Silhouette Score and Davies-Bouldin Index coupled with extrinsic metrics NMI and ARI when processing image features. The research uses t-SNE visualization to present learned embeddings that show distinct clusters for digits. Our approach reaches an optimal combination between data reconstruction accuracy and cluster separation purity when adding the benefit of understandable results and scalable implementations. The approach creates a dependable base that helps deploy unsupervised representation learning in different large-scale image clustering applications.", "date": "2025-06-11", "categories": []}
{"id": "2506.06990", "title": "Modified K-means Algorithm with Local Optimality Guarantees", "abstract": "The K-means algorithm is one of the most widely studied clustering algorithms in machine learning. While extensive research has focused on its ability to achieve a globally optimal solution, there still lacks a rigorous analysis of its local optimality guarantees. In this paper, we first present conditions under which the K-means algorithm converges to a locally optimal solution. Based on this, we propose simple modifications to the K-means algorithm which ensure local optimality in both the continuous and discrete sense, with the same computational complexity as the original K-means algorithm. As the dissimilarity measure, we consider a general Bregman divergence, which is an extension of the squared Euclidean distance often used in the K-means algorithm. Numerical experiments confirm that the K-means algorithm does not always find a locally optimal solution in practice, while our proposed methods provide improved locally optimal solutions with reduced clustering loss. Our code is available at https://github.com/lmingyi/LO-K-means.", "date": "2025-06-08", "categories": []}
{"id": "2506.08143", "title": "Accelerating Spectral Clustering under Fairness Constraints", "abstract": "Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the general population. We present a new efficient method for fair spectral clustering (Fair SC) by casting the Fair SC problem within the difference of convex functions (DC) framework. To this end, we introduce a novel variable augmentation strategy and employ an alternating direction method of multipliers type of algorithm adapted to DC problems. We show that each associated subproblem can be solved efficiently, resulting in higher computational efficiency compared to prior work, which required a computationally expensive eigendecomposition. Numerical experiments demonstrate the effectiveness of our approach on both synthetic and real-world benchmarks, showing significant speedups in computation time over prior art, especially as the problem size grows. This work thus represents a considerable step forward towards the adoption of fair clustering in real-world applications.", "date": "2025-06-09", "categories": []}
{"id": "2406.13342", "title": "ZeroDL: Zero-shot Distribution Learning for Text Clustering via Large Language Models", "abstract": "The advancements in large language models (LLMs) have brought significant progress in NLP tasks. However, if a task cannot be fully described in prompts, the models could fail to carry out the task. In this paper, we propose a simple yet effective method to contextualize a task toward a LLM. The method utilizes (1) open-ended zero-shot inference from the entire dataset, (2) aggregate the inference results, and (3) finally incorporate the aggregated meta-information for the actual task. We show the effectiveness in text clustering tasks, empowering LLMs to perform text-to-text-based clustering and leading to improvements on several datasets. Furthermore, we explore the generated class labels for clustering, showing how the LLM understands the task through data.", "date": "2024-06-19", "categories": []}
{"id": "2506.05877", "title": "Interpretable Clustering Ensemble", "abstract": "Clustering ensemble has emerged as an important research topic in the field of machine learning. Although numerous methods have been proposed to improve clustering quality, most existing approaches overlook the need for interpretability in high-stakes applications. In domains such as medical diagnosis and financial risk assessment, algorithms must not only be accurate but also interpretable to ensure transparent and trustworthy decision-making. Therefore, to fill the gap of lack of interpretable algorithms in the field of clustering ensemble, we propose the first interpretable clustering ensemble algorithm in the literature. By treating base partitions as categorical variables, our method constructs a decision tree in the original feature space and use the statistical association test to guide the tree building process. Experimental results demonstrate that our algorithm achieves comparable performance to state-of-the-art (SOTA) clustering ensemble methods while maintaining an additional feature of interpretability. To the best of our knowledge, this is the first interpretable algorithm specifically designed for clustering ensemble, offering a new perspective for future research in interpretable clustering.", "date": "2025-06-06", "categories": []}
{"id": "2410.00023", "title": "Self-Tuning Spectral Clustering for Speaker Diarization", "abstract": "Spectral clustering has proven effective in grouping speech representations for speaker diarization tasks, although post-processing the affinity matrix remains difficult due to the need for careful tuning before constructing the Laplacian. In this study, we present a novel pruning algorithm to create a sparse affinity matrix called spectral clustering on p-neighborhood retained affinity matrix (SC-pNA). Our method improves on node-specific fixed neighbor selection by allowing a variable number of neighbors, eliminating the need for external tuning data as the pruning parameters are derived directly from the affinity matrix. SC-pNA does so by identifying two clusters in every row of the initial affinity matrix, and retains only the top p % similarity scores from the cluster containing larger similarities. Spectral clustering is performed subsequently, with the number of clusters determined as the maximum eigengap. Experimental results on the challenging DIHARD-III dataset highlight the superiority of SC-pNA, which is also computationally more efficient than existing auto-tuning approaches. Our implementations are available at https://github.com/nikhilraghav29/SC-pNA.", "date": "2024-09-16", "categories": []}
{"id": "2506.04045", "title": "Similarity-based fuzzy clustering scientific articles: potentials and challenges from mathematical and computational perspectives", "abstract": "Fuzzy clustering, which allows an article to belong to multiple clusters with soft membership degrees, plays a vital role in analyzing publication data. This problem can be formulated as a constrained optimization model, where the goal is to minimize the discrepancy between the similarity observed from data and the similarity derived from a predicted distribution. While this approach benefits from leveraging state-of-the-art optimization algorithms, tailoring them to work with real, massive databases like OpenAlex or Web of Science - containing about 70 million articles and a billion citations - poses significant challenges. We analyze potentials and challenges of the approach from both mathematical and computational perspectives. Among other things, second-order optimality conditions are established, providing new theoretical insights, and practical solution methods are proposed by exploiting the structure of the problem. Specifically, we accelerate the gradient projection method using GPU-based parallel computing to efficiently handle large-scale data.", "date": "2025-06-04", "categories": []}
{"id": "2211.04634", "title": "Learning Optimal Graph Filters for Clustering of Attributed Graphs", "abstract": "Many real-world systems can be represented as graphs where the different entities in the system are presented by nodes and their interactions by edges. An important task in studying large datasets with graphical structure is graph clustering. While there has been a lot of work on graph clustering using the connectivity between the nodes, many real-world networks also have node attributes. Clustering attributed graphs requires joint modeling of graph structure and node attributes. Recent work has focused on combining these two complementary sources of information through graph convolutional networks and graph filtering. However, these methods are mostly limited to lowpass filtering and do not explicitly learn the filter parameters for the clustering task. In this paper, we introduce a graph signal processing based approach, where we learn the parameters of Finite Impulse Response (FIR) and Autoregressive Moving Average (ARMA) graph filters optimized for clustering. The proposed approach is formulated as a two-step iterative optimization problem, focusing on learning interpretable graph filters that are optimal for the given data and that maximize the separation between different clusters. The proposed approach is evaluated on attributed networks and compared to the state-of-the-art methods.", "date": "2022-11-09", "categories": []}
{"id": "2312.03940", "title": "PECANN: Parallel Efficient Clustering with Graph-Based Approximate Nearest Neighbor Search", "abstract": "This paper studies density-based clustering of point sets. These methods use dense regions of points to detect clusters of arbitrary shapes. In particular, we study variants of density peaks clustering, a popular type of algorithm that has been shown to work well in practice. Our goal is to cluster large high-dimensional datasets, which are prevalent in practice. Prior solutions are either sequential, and cannot scale to large data, or are specialized for low-dimensional data.\n  This paper unifies the different variants of density peaks clustering into a single framework, PECANN, by abstracting out several key steps common to this class of algorithms. One such key step is to find nearest neighbors that satisfy a predicate function, and one of the main contributions of this paper is an efficient way to do this predicate search using graph-based approximate nearest neighbor search (ANNS). To provide ample parallelism, we propose a doubling search technique that enables points to find an approximate nearest neighbor satisfying the predicate in a small number of rounds. Our technique can be applied to many existing graph-based ANNS algorithms, which can all be plugged into PECANN.\n  We implement five clustering algorithms with PECANN and evaluate them on synthetic and real-world datasets with up to 1.28 million points and up to 1024 dimensions on a 30-core machine with two-way hyper-threading. Compared to the state-of-the-art FASTDP algorithm for high-dimensional density peaks clustering, which is sequential, our best algorithm is 45x-734x faster while achieving competitive ARI scores. Compared to the state-of-the-art parallel DPC-based algorithm, which is optimized for low dimensions, we show that PECANN is two orders of magnitude faster. As far as we know, our work is the first to evaluate DPC variants on large high-dimensional real-world image and text embedding datasets.", "date": "2023-12-06", "categories": []}
{"id": "2403.19516", "title": "Spectral Clustering for Directed Graphs via Likelihood Estimation on Stochastic Block Models", "abstract": "Graph clustering is a fundamental task in unsupervised learning with broad real-world applications. While spectral clustering methods for undirected graphs are well-established and guided by a minimum cut optimization consensus, their extension to directed graphs remains relatively underexplored due to the additional complexity introduced by edge directions. In this paper, we leverage statistical inference on stochastic block models to guide the development of a spectral clustering algorithm for directed graphs. Specifically, we study the maximum likelihood estimation under a widely used directed stochastic block model, and derive a global objective function that aligns with the underlying community structure. We further establish a theoretical upper bound on the misclustering error of its spectral relaxation, and based on this relaxation, introduce a novel, self-adaptive spectral clustering method for directed graphs. Extensive experiments on synthetic and real-world datasets demonstrate significant performance gains over existing baselines.", "date": "2024-03-28", "categories": []}
{"id": "2412.03238", "title": "Dynamic Consistent $k$-Center Clustering with Optimal Recourse", "abstract": "Given points from an arbitrary metric space and a sequence of point updates sent by an adversary, what is the minimum recourse per update (i.e., the minimum number of changes needed to the set of centers after an update), in order to maintain a constant-factor approximation to a $k$-clustering problem? This question has received attention in recent years under the name consistent clustering.\n  Previous works by Lattanzi and Vassilvitskii [ICLM '17] and Fichtenberger, Lattanzi, Norouzi-Fard, and Svensson [SODA '21] studied $k$-clustering objectives, including the $k$-center and the $k$-median objectives, under only point insertions. In this paper we study the $k$-center objective in the fully dynamic setting, where the update is either a point insertion or a point deletion. Before our work, {\\L}\\k{a}cki, Haeupler, Grunau, Rozho\\v{n}, and Jayaram [SODA '24] gave a deterministic fully dynamic constant-factor approximation algorithm for the $k$-center objective with worst-case recourse of $2$ per update.\n  In this work, we prove that the $k$-center clustering problem admits optimal recourse bounds by developing a deterministic fully dynamic constant-factor approximation algorithm with worst-case recourse of $1$ per update. Moreover our algorithm performs simple choices based on light data structures, and thus is arguably more direct and faster than the previous one which uses a sophisticated combinatorial structure. Additionally, we develop a new deterministic decremental algorithm and a new deterministic incremental algorithm, both of which maintain a $6$-approximate $k$-center solution with worst-case recourse of $1$ per update. Our incremental algorithm improves over the $8$-approximation algorithm by Charikar, Chekuri, Feder, and Motwani [STOC '97]. Finally, we remark that since all three of our algorithms are deterministic, they work against an adaptive adversary.", "date": "2024-12-04", "categories": []}
{"id": "2506.02053", "title": "Generalization Performance of Ensemble Clustering: From Theory to Algorithm", "abstract": "Ensemble clustering has demonstrated great success in practice; however, its theoretical foundations remain underexplored. This paper examines the generalization performance of ensemble clustering, focusing on generalization error, excess risk and consistency. We derive a convergence rate of generalization error bound and excess risk bound both of $\\mathcal{O}(\\sqrt{\\frac{\\log n}{m}}+\\frac{1}{\\sqrt{n}})$, with $n$ and $m$ being the numbers of samples and base clusterings. Based on this, we prove that when $m$ and $n$ approach infinity and $m$ is significantly larger than log $n$, i.e., $m,n\\to \\infty, m\\gg \\log n$, ensemble clustering is consistent. Furthermore, recognizing that $n$ and $m$ are finite in practice, the generalization error cannot be reduced to zero. Thus, by assigning varying weights to finite clusterings, we minimize the error between the empirical average clusterings and their expectation. From this, we theoretically demonstrate that to achieve better clustering performance, we should minimize the deviation (bias) of base clustering from its expectation and maximize the differences (diversity) among various base clusterings. Additionally, we derive that maximizing diversity is nearly equivalent to a robust (min-max) optimization model. Finally, we instantiate our theory to develop a new ensemble clustering algorithm. Compared with SOTA methods, our approach achieves average improvements of 6.1%, 7.3%, and 6.0% on 10 datasets w.r.t. NMI, ARI, and Purity. The code is available at https://github.com/xuz2019/GPEC.", "date": "2025-06-01", "categories": []}
{"id": "2506.02068", "title": "Enhancing Interpretability of Quantum-Assisted Blockchain Clustering via AI Agent-Based Qualitative Analysis", "abstract": "Blockchain transaction data is inherently high dimensional, noisy, and entangled, posing substantial challenges for traditional clustering algorithms. While quantum enhanced clustering models have demonstrated promising performance gains, their interpretability remains limited, restricting their application in sensitive domains such as financial fraud detection and blockchain governance. To address this gap, we propose a two stage analysis framework that synergistically combines quantitative clustering evaluation with AI Agent assisted qualitative interpretation. In the first stage, we employ classical clustering methods and evaluation metrics including the Silhouette Score, Davies Bouldin Index, and Calinski Harabasz Index to determine the optimal cluster count and baseline partition quality. In the second stage, we integrate an AI Agent to generate human readable, semantic explanations of clustering results, identifying intra cluster characteristics and inter cluster relationships. Our experiments reveal that while fully trained Quantum Neural Networks (QNN) outperform random Quantum Features (QF) in quantitative metrics, the AI Agent further uncovers nuanced differences between these methods, notably exposing the singleton cluster phenomenon in QNN driven models. The consolidated insights from both stages consistently endorse the three cluster configuration, demonstrating the practical value of our hybrid approach. This work advances the interpretability frontier in quantum assisted blockchain analytics and lays the groundwork for future autonomous AI orchestrated clustering frameworks.", "date": "2025-06-02", "categories": []}
{"id": "2301.00384", "title": "Correlation Clustering Algorithm for Dynamic Complete Signed Graphs: An Index-based Approach", "abstract": "In this paper, we reduce the complexity of approximating the correlation clustering problem from $O(m\\times\\left( 2+ \\alpha (G) \\right)+n)$ to $O(m+n)$ for any given value of $\\varepsilon$ for a complete signed graph with $n$ vertices and $m$ positive edges where $\\alpha(G)$ is the arboricity of the graph. Our approach gives the same output as the original algorithm and makes it possible to implement the algorithm in a full dynamic setting where edge sign flipping and vertex addition/removal are allowed. Constructing this index costs $O(m)$ memory and $O(m\\times\\alpha(G))$ time. We also studied the structural properties of the non-agreement measure used in the approximation algorithm. The theoretical results are accompanied by a full set of experiments concerning seven real-world graphs. These results shows superiority of our index-based algorithm to the non-index one by a decrease of %34 in time on average.", "date": "2023-01-01", "categories": []}
{"id": "2401.06634", "title": "CCFC: Bridging Federated Clustering and Contrastive Learning", "abstract": "Federated clustering, an essential extension of centralized clustering for federated scenarios, enables multiple data-holding clients to collaboratively group data while keeping their data locally. In centralized scenarios, clustering driven by representation learning has made significant advancements in handling high-dimensional complex data. However, the combination of federated clustering and representation learning remains underexplored. To bridge this, we first tailor a cluster-contrastive model for learning clustering-friendly representations. Then, we harness this model as the foundation for proposing a new federated clustering method, named cluster-contrastive federated clustering (CCFC). Benefiting from representation learning, the clustering performance of CCFC even double those of the best baseline methods in some cases. Compared to the most related baseline, the benefit results in substantial NMI score improvements of up to 0.4155 on the most conspicuous case. Moreover, CCFC also shows superior performance in handling device failures from a practical viewpoint.", "date": "2024-01-12", "categories": []}
{"id": "2406.04610", "title": "Contrastive Explainable Clustering with Differential Privacy", "abstract": "This paper presents a novel approach to Explainable AI (XAI) that combines contrastive explanations with differential privacy for clustering algorithms. Focusing on k-median and k-means problems, we calculate contrastive explanations as the utility difference between original clustering and clustering with a centroid fixed to a specific data point. This method provides personalized insights into centroid placement. Our key contribution is demonstrating that these differentially private explanations achieve essentially the same utility bounds as non-private explanations. Experiments across various datasets show that our approach offers meaningful, privacy-preserving, and individually relevant explanations without significantly compromising clustering utility. This work advances privacy-aware machine learning by balancing data protection, explanation quality, and personalization in clustering tasks.", "date": "2024-06-07", "categories": []}
{"id": "2408.16993", "title": "A Scalable k-Medoids Clustering via Whale Optimization Algorithm", "abstract": "Unsupervised clustering has emerged as a critical tool for uncovering hidden patterns in vast, unlabeled datasets. However, traditional methods, such as Partitioning Around Medoids (PAM), struggle with scalability owing to their quadratic computational complexity. To address this limitation, we introduce WOA-kMedoids, a novel unsupervised clustering method that incorporates the Whale Optimization Algorithm (WOA), a nature-inspired metaheuristic inspired by the hunting strategies of humpback whales. By optimizing the centroid selection, WOA-kMedoids reduces the computational complexity from quadratic to near-linear with respect to the number of observations, enabling scalability to large datasets while maintaining high clustering accuracy. We evaluated WOA-kMedoids using 25 diverse time-series datasets from the UCR archive. Our empirical results show that WOA-kMedoids achieved a clustering performance comparable to PAM, with an average Rand Index (RI) of 0.731 compared to PAM's 0.739, outperforming PAM on 12 out of 25 datasets. While exhibiting a slightly higher runtime than PAM on small datasets (<300 observations), WOA-kMedoids outperformed PAM on larger datasets, with an average speedup of 1.7x and a maximum of 2.3x. The scalability of WOA-kMedoids, combined with its high accuracy, makes them a promising choice for unsupervised clustering in big data applications. This method has implications for efficient knowledge discovery in massive unlabeled datasets, particularly where traditional k-medoids methods are computationally infeasible, including IoT anomaly detection, biomedical signal analysis, and customer behavior clustering.", "date": "2024-08-30", "categories": []}
{"id": "2506.00277", "title": "Hierarchical Level-Wise News Article Clustering via Multilingual Matryoshka Embeddings", "abstract": "Contextual large language model embeddings are increasingly utilized for topic modeling and clustering. However, current methods often scale poorly, rely on opaque similarity metrics, and struggle in multilingual settings. In this work, we present a novel, scalable, interpretable, hierarchical, and multilingual approach to clustering news articles and social media data. To do this, we first train multilingual Matryoshka embeddings that can determine story similarity at varying levels of granularity based on which subset of the dimensions of the embeddings is examined. This embedding model achieves state-of-the-art performance on the SemEval 2022 Task 8 test dataset (Pearson $\\rho$ = 0.816). Once trained, we develop an efficient hierarchical clustering algorithm that leverages the hierarchical nature of Matryoshka embeddings to identify unique news stories, narratives, and themes. We conclude by illustrating how our approach can identify and cluster stories, narratives, and overarching themes within real-world news datasets.", "date": "2025-05-30", "categories": []}
{"id": "2506.00410", "title": "JojoSCL: Shrinkage Contrastive Learning for single-cell RNA sequence Clustering", "abstract": "Single-cell RNA sequencing (scRNA-seq) has revolutionized our understanding of cellular processes by enabling gene expression analysis at the individual cell level. Clustering allows for the identification of cell types and the further discovery of intrinsic patterns in single-cell data. However, the high dimensionality and sparsity of scRNA-seq data continue to challenge existing clustering models. In this paper, we introduce JojoSCL, a novel self-supervised contrastive learning framework for scRNA-seq clustering. By incorporating a shrinkage estimator based on hierarchical Bayesian estimation, which adjusts gene expression estimates towards more reliable cluster centroids to reduce intra-cluster dispersion, and optimized using Stein's Unbiased Risk Estimate (SURE), JojoSCL refines both instance-level and cluster-level contrastive learning. Experiments on ten scRNA-seq datasets substantiate that JojoSCL consistently outperforms prevalent clustering methods, with further validation of its practicality through robustness analysis and ablation studies. JojoSCL's code is available at: https://github.com/ziwenwang28/JojoSCL.", "date": "2025-05-31", "categories": []}
{"id": "2505.24365", "title": "Anomaly Detection and Improvement of Clusters using Enhanced K-Means Algorithm", "abstract": "This paper introduces a unified approach to cluster refinement and anomaly detection in datasets. We propose a novel algorithm that iteratively reduces the intra-cluster variance of N clusters until a global minimum is reached, yielding tighter clusters than the standard k-means algorithm. We evaluate the method using intrinsic measures for unsupervised learning, including the silhouette coefficient, Calinski-Harabasz index, and Davies-Bouldin index, and extend it to anomaly detection by identifying points whose assignment causes a significant variance increase. External validation on synthetic data and the UCI Breast Cancer and UCI Wine Quality datasets employs the Jaccard similarity score, V-measure, and F1 score. Results show variance reductions of 18.7% and 88.1% on the synthetic and Wine Quality datasets, respectively, along with accuracy and F1 score improvements of 22.5% and 20.8% on the Wine Quality dataset.", "date": "2025-05-30", "categories": []}
{"id": "2505.22991", "title": "Number of Clusters in a Dataset: A Regularized K-means Approach", "abstract": "Finding the number of meaningful clusters in an unlabeled dataset is important in many applications. Regularized k-means algorithm is a possible approach frequently used to find the correct number of distinct clusters in datasets. The most common formulation of the regularization function is the additive linear term $\\lambda k$, where $k$ is the number of clusters and $\\lambda$ a positive coefficient. Currently, there are no principled guidelines for setting a value for the critical hyperparameter $\\lambda$. In this paper, we derive rigorous bounds for $\\lambda$ assuming clusters are {\\em ideal}. Ideal clusters (defined as $d$-dimensional spheres with identical radii) are close proxies for k-means clusters ($d$-dimensional spherically symmetric distributions with identical standard deviations). Experiments show that the k-means algorithm with additive regularizer often yields multiple solutions. Thus, we also analyze k-means algorithm with multiplicative regularizer. The consensus among k-means solutions with additive and multiplicative regularizations reduces the ambiguity of multiple solutions in certain cases. We also present selected experiments that demonstrate performance of the regularized k-means algorithms as clusters deviate from the ideal assumption.", "date": "2025-05-29", "categories": []}
{"id": "2503.22241", "title": "Agent-Centric Personalized Multiple Clustering with Multi-Modal LLMs", "abstract": "Personalized multiple clustering aims to generate diverse partitions of a dataset based on different user-specific aspects, rather than a single clustering. It has recently drawn research interest for accommodating varying user preferences. Recent approaches primarily use CLIP embeddings with proxy learning to extract representations biased toward user clustering preferences. However, CLIP primarily focuses on coarse image-text alignment, lacking a deep contextual understanding of user interests. To overcome these limitations, we propose an agent-centric personalized clustering framework that leverages multi-modal large language models (MLLMs) as agents to comprehensively traverse a relational graph to search for clusters based on user interests. Due to the advanced reasoning mechanism of MLLMs, the obtained clusters align more closely with user-defined criteria than those obtained from CLIP-based representations. To reduce computational overhead, we shorten the agents' traversal path by constructing a relational graph using user-interest-biased embeddings extracted by MLLMs. A large number of weakly connected edges can be filtered out based on embedding similarity, facilitating an efficient traversal search for agents. Experimental results show that the proposed method achieves NMI scores of 0.9667 and 0.9481 on the Card Order and Card Suits benchmarks, respectively, largely improving the SOTA model by over 140%.", "date": "2025-03-28", "categories": []}
{"id": "2412.13690", "title": "Personalized Clustering via Targeted Representation Learning", "abstract": "Clustering traditionally aims to reveal a natural grouping structure within unlabeled data. However, this structure may not always align with users' preferences. In this paper, we propose a personalized clustering method that explicitly performs targeted representation learning by interacting with users via modicum task information (e.g., $\\textit{must-link}$ or $\\textit{cannot-link}$ pairs) to guide the clustering direction. We query users with the most informative pairs, i.e., those pairs most hard to cluster and those most easy to miscluster, to facilitate the representation learning in terms of the clustering preference. Moreover, by exploiting attention mechanism, the targeted representation is learned and augmented. By leveraging the targeted representation and constrained contrastive loss as well, personalized clustering is obtained. Theoretically, we verify that the risk of personalized clustering is tightly bounded, guaranteeing that active queries to users do mitigate the clustering risk. Experimentally, extensive results show that our method performs well across different clustering tasks and datasets, even when only a limited number of queries are available.", "date": "2024-12-18", "categories": []}
{"id": "2505.21387", "title": "Automatically Identify and Rectify: Robust Deep Contrastive Multi-view Clustering in Noisy Scenarios", "abstract": "Leveraging the powerful representation learning capabilities, deep multi-view clustering methods have demonstrated reliable performance by effectively integrating multi-source information from diverse views in recent years. Most existing methods rely on the assumption of clean views. However, noise is pervasive in real-world scenarios, leading to a significant degradation in performance. To tackle this problem, we propose a novel multi-view clustering framework for the automatic identification and rectification of noisy data, termed AIRMVC. Specifically, we reformulate noisy identification as an anomaly identification problem using GMM. We then design a hybrid rectification strategy to mitigate the adverse effects of noisy data based on the identification results. Furthermore, we introduce a noise-robust contrastive mechanism to generate reliable representations. Additionally, we provide a theoretical proof demonstrating that these representations can discard noisy information, thereby improving the performance of downstream tasks. Extensive experiments on six benchmark datasets demonstrate that AIRMVC outperforms state-of-the-art algorithms in terms of robustness in noisy scenarios. The code of AIRMVC are available at https://github.com/xihongyang1999/AIRMVC on Github.", "date": "2025-05-27", "categories": []}
{"id": "2308.08167", "title": "A Quantum Approximation Scheme for k-Means", "abstract": "We give a quantum approximation scheme (i.e., $(1 + \\varepsilon)$-approximation for every $\\varepsilon > 0$) for the classical $k$-means clustering problem in the QRAM model with a running time that has only polylogarithmic dependence on the number of data points. More specifically, given a dataset $V$ with $N$ points in $\\mathbb{R}^d$ stored in QRAM data structure, our quantum algorithm runs in time $\\tilde{O} \\left( 2^{\\tilde{O}(\\frac{k}{\\varepsilon})} \\eta^2 d\\right)$ and with high probability outputs a set $C$ of $k$ centers such that $cost(V, C) \\leq (1+\\varepsilon) \\cdot cost(V, C_{OPT})$. Here $C_{OPT}$ denotes the optimal $k$-centers, $cost(.)$ denotes the standard $k$-means cost function (i.e., the sum of the squared distance of points to the closest center), and $\\eta$ is the aspect ratio (i.e., the ratio of maximum distance to minimum distance). This is the first quantum algorithm with a polylogarithmic running time that gives a provable approximation guarantee of $(1+\\varepsilon)$ for the $k$-means problem. Also, unlike previous works on unsupervised learning, our quantum algorithm does not require quantum linear algebra subroutines and has a running time independent of parameters (e.g., condition number) that appear in such procedures.", "date": "2023-08-16", "categories": []}
{"id": "2504.02087", "title": "An Introductory Survey to Autoencoder-based Deep Clustering -- Sandboxes for Combining Clustering with Deep Learning", "abstract": "Autoencoders offer a general way of learning low-dimensional, non-linear representations from data without labels. This is achieved without making any particular assumptions about the data type or other domain knowledge. The generality and domain agnosticism in combination with their simplicity make autoencoders a perfect sandbox for researching and developing novel (deep) clustering algorithms. Clustering methods group data based on similarity, a task that benefits from the lower-dimensional representation learned by an autoencoder, mitigating the curse of dimensionality. Specifically, the combination of deep learning with clustering, called Deep Clustering, enables to learn a representation tailored to specific clustering tasks, leading to high-quality results. This survey provides an introduction to fundamental autoencoder-based deep clustering algorithms that serve as building blocks for many modern approaches.", "date": "2025-04-02", "categories": []}
{"id": "2505.18180", "title": "Clustering scientific publications: lessons learned through experiments with a real citation network", "abstract": "Clustering scientific publications can reveal underlying research structures within bibliographic databases. Graph-based clustering methods, such as spectral, Louvain, and Leiden algorithms, are frequently utilized due to their capacity to effectively model citation networks. However, their performance may degrade when applied to real-world data. This study evaluates the performance of these clustering algorithms on a citation graph comprising approx. 700,000 papers and 4.6 million citations extracted from Web of Science. The results show that while scalable methods like Louvain and Leiden perform efficiently, their default settings often yield poor partitioning. Meaningful outcomes require careful parameter tuning, especially for large networks with uneven structures, including a dense core and loosely connected papers. These findings highlight practical lessons about the challenges of large-scale data, method selection and tuning based on specific structures of bibliometric clustering tasks.", "date": "2025-05-15", "categories": []}
{"id": "2505.18420", "title": "LocalKMeans: Convergence of Lloyd's Algorithm with Distributed Local Iterations", "abstract": "In this paper, we analyze the classical $K$-means alternating-minimization algorithm, also known as Lloyd's algorithm (Lloyd, 1956), for a mixture of Gaussians in a data-distributed setting that incorporates local iteration steps. Assuming unlabeled data distributed across multiple machines, we propose an algorithm, LocalKMeans, that performs Lloyd's algorithm in parallel in the machines by running its iterations on local data, synchronizing only every $L$ of such local steps. We characterize the cost of these local iterations against the non-distributed setting, and show that the price paid for the local steps is a higher required signal-to-noise ratio. While local iterations were theoretically studied in the past for gradient-based learning methods, the analysis of unsupervised learning methods is more involved owing to the presence of latent variables, e.g. cluster identities, than that of an iterative gradient-based algorithm. To obtain our results, we adapt a virtual iterate method to work with a non-convex, non-smooth objective function, in conjunction with a tight statistical analysis of Lloyd steps.", "date": "2025-05-23", "categories": []}
{"id": "2312.14920", "title": "A New Similarity Function for Spectral Clustering with Application to Plant Phenotypic Data", "abstract": "Clustering species of the same plant into different groups is an important step in developing new species of the concerned plant. Phenotypic (or physical) characteristics of plant species are commonly used to perform clustering. Hierarchical Clustering (HC) is popularly used for this task, and this algorithm suffers from low accuracy. In one of the recent works (Shastri et al., 2021), the authors have used the standard Spectral Clustering (SC) algorithm to improve the clustering accuracy. They have demonstrated the efficacy of their algorithm on soybean species.\n  In the SC algorithm, one of the crucial steps is building the similarity matrix. A Gaussian similarity function is the standard choice to build this matrix. In the past, many works have proposed variants of the Gaussian similarity function to improve the performance of the SC algorithm, however, all have focused on the variance or scaling of the Gaussian. None of the past works have investigated upon the choice of base \"e\" (Euler's number) of the Gaussian similarity function (natural exponential function).\n  Based upon spectral graph theory, specifically the Cheeger's inequality, in this work we propose use of a base \"a\" exponential function as the similarity function. We also integrate this new approach with the notion of \"local scaling\" from one of the first works that experimented with the scaling of the Gaussian similarity function (Zelnik-Manor et al., 2004).\n  Using an eigenvalue analysis, we theoretically justify that our proposed algorithm should work better than the existing one. With evaluation on 2376 soybean species and 1865 rice species, we experimentally demonstrate that our new SC is 35% and 11% better than the standard SC, respectively.", "date": "2023-12-22", "categories": []}
{"id": "2505.17039", "title": "A new classification system of beer categories and styles based on large-scale data mining and self-organizing maps of beer recipes", "abstract": "A data-driven quantitative approach was used to develop a novel classification system for beer categories and styles. Sixty-two thousand one hundred twenty-one beer recipes were mined and analyzed, considering ingredient profiles, fermentation parameters, and recipe vital statistics. Statistical analyses combined with self-organizing maps (SOMs) identified four major superclusters that showed distinctive malt and hop usage patterns, style characteristics, and historical brewing traditions. Cold fermented styles showed a conservative grain and hop composition, whereas hot fermented beers exhibited high heterogeneity, reflecting regional preferences and innovation. This new taxonomy offers a reproducible and objective framework beyond traditional sensory-based classifications, providing brewers, researchers, and educators with a scalable tool for recipe analysis and beer development. The findings in this work provide an understanding of beer diversity and open avenues for linking ingredient usage with fermentation profiles and flavor outcomes.", "date": "2025-05-13", "categories": []}
{"id": "2505.17819", "title": "Quantifying uncertainty in spectral clusterings: expectations for perturbed and incomplete data", "abstract": "Spectral clustering is a popular unsupervised learning technique which is able to partition unlabelled data into disjoint clusters of distinct shapes. However, the data under consideration are often experimental data, implying that the data is subject to measurement errors and measurements may even be lost or invalid. These uncertainties in the corrupted input data induce corresponding uncertainties in the resulting clusters, and the clusterings thus become unreliable.\n  Modelling the uncertainties as random processes, we discuss a mathematical framework based on random set theory for the computational Monte Carlo approximation of statistically expected clusterings in case of corrupted, i.e., perturbed, incomplete, and possibly even additional, data. We propose several computationally accessible quantities of interest and analyze their consistency in the infinite data point and infinite Monte Carlo sample limit. Numerical experiments are provided to illustrate and compare the proposed quantities.", "date": "2025-05-23", "categories": []}
{"id": "2502.16139", "title": "An Improved Deep Learning Model for Word Embeddings Based Clustering for Large Text Datasets", "abstract": "In this paper, an improved clustering technique for large textual datasets by leveraging fine-tuned word embeddings is presented. WEClustering technique is used as the base model. WEClustering model is fur-ther improvements incorporating fine-tuning contextual embeddings, advanced dimensionality reduction methods, and optimization of clustering algorithms. Experimental results on benchmark datasets demon-strate significant improvements in clustering metrics such as silhouette score, purity, and adjusted rand index (ARI). An increase of 45% and 67% of median silhouette score is reported for the proposed WE-Clustering_K++ (based on K-means) and WEClustering_A++ (based on Agglomerative models), respec-tively. The proposed technique will help to bridge the gap between semantic understanding and statistical robustness for large-scale text-mining tasks.", "date": "2025-02-22", "categories": []}
{"id": "2503.15582", "title": "Hierarchical clustering with maximum density paths and mixture models", "abstract": "Hierarchical clustering is an effective, interpretable method for analyzing structure in data. It reveals insights at multiple scales without requiring a predefined number of clusters and captures nested patterns and subtle relationships, which are often missed by flat clustering approaches. However, existing hierarchical clustering methods struggle with high-dimensional data, especially when there are no clear density gaps between modes. In this work, we introduce t-NEB, a probabilistically grounded hierarchical clustering method, which yields state-of-the-art clustering performance on naturalistic high-dimensional data. t-NEB consists of three steps: (1) density estimation via overclustering; (2) finding maximum density paths between clusters; (3) creating a hierarchical structure via bottom-up cluster merging. t-NEB uses a probabilistic parametric density model for both overclustering and cluster merging, which yields both high clustering performance and a meaningful hierarchy, making it a valuable tool for exploratory data analysis. Code is available at https://github.com/ecker-lab/tneb clustering.", "date": "2025-03-19", "categories": []}
{"id": "2505.15022", "title": "Infinite hierarchical contrastive clustering for personal digital envirotyping", "abstract": "Daily environments have profound influence on our health and behavior. Recent work has shown that digital envirotyping, where computer vision is applied to images of daily environments taken during ecological momentary assessment (EMA), can be used to identify meaningful relationships between environmental features and health outcomes of interest. To systematically study such effects on an individual level, it is helpful to group images into distinct environments encountered in an individual's daily life; these may then be analyzed, further grouped into related environments with similar features, and linked to health outcomes. Here we introduce infinite hierarchical contrastive clustering to address this challenge. Building on the established contrastive clustering framework, our method a) allows an arbitrary number of clusters without requiring the full Dirichlet Process machinery by placing a stick-breaking prior on predicted cluster probabilities; and b) encourages distinct environments to form well-defined sub-clusters within each cluster of related environments by incorporating a participant-specific prediction loss. Our experiments show that our model effectively identifies distinct personal environments and groups these environments into meaningful environment types. We then illustrate how the resulting clusters can be linked to various health outcomes, highlighting the potential of our approach to advance the envirotyping paradigm.", "date": "2025-05-21", "categories": []}
{"id": "2401.05502", "title": "Diversity-aware clustering: Computational Complexity and Approximation Algorithms", "abstract": "In this work, we study diversity-aware clustering problems where the data points are associated with multiple attributes resulting in intersecting groups. A clustering solution needs to ensure that the number of chosen cluster centers from each group should be within the range defined by a lower and upper bound threshold for each group, while simultaneously minimizing the clustering objective, which can be either $k$-median, $k$-means or $k$-supplier. We study the computational complexity of the proposed problems, offering insights into their NP-hardness, polynomial-time inapproximability, and fixed-parameter intractability. We present parameterized approximation algorithms with approximation ratios $1+ \\frac{2}{e} + \\epsilon \\approx 1.736$, $1+\\frac{8}{e} + \\epsilon \\approx 3.943$, and $5$ for diversity-aware $k$-median, diversity-aware $k$-means and diversity-aware $k$-supplier, respectively. Assuming Gap-ETH, the approximation ratios are tight for the diversity-aware $k$-median and diversity-aware $k$-means problems. Our results imply the same approximation factors for their respective fair variants with disjoint groups -- fair $k$-median, fair $k$-means, and fair $k$-supplier -- with lower bound requirements.", "date": "2024-01-10", "categories": []}
{"id": "2402.16383", "title": "Self Supervised Correlation-based Permutations for Multi-View Clustering", "abstract": "Combining data from different sources can improve data analysis tasks such as clustering. However, most of the current multi-view clustering methods are limited to specific domains or rely on a suboptimal and computationally intensive two-stage process of representation learning and clustering. We propose an end-to-end deep learning-based multi-view clustering framework for general data types (such as images and tables). Our approach involves generating meaningful fused representations using a novel permutation-based canonical correlation objective. We provide a theoretical analysis showing how the learned embeddings approximate those obtained by supervised linear discriminant analysis (LDA). Cluster assignments are learned by identifying consistent pseudo-labels across multiple views. Additionally, we establish a theoretical bound on the error caused by incorrect pseudo-labels in the unsupervised representations compared to LDA. Extensive experiments on ten multi-view clustering benchmark datasets provide empirical evidence for the effectiveness of the proposed model.", "date": "2024-02-26", "categories": []}
{"id": "2505.14040", "title": "Unsupervised Graph Clustering with Deep Structural Entropy", "abstract": "Research on Graph Structure Learning (GSL) provides key insights for graph-based clustering, yet current methods like Graph Neural Networks (GNNs), Graph Attention Networks (GATs), and contrastive learning often rely heavily on the original graph structure. Their performance deteriorates when the original graph's adjacency matrix is too sparse or contains noisy edges unrelated to clustering. Moreover, these methods depend on learning node embeddings and using traditional techniques like k-means to form clusters, which may not fully capture the underlying graph structure between nodes. To address these limitations, this paper introduces DeSE, a novel unsupervised graph clustering framework incorporating Deep Structural Entropy. It enhances the original graph with quantified structural information and deep neural networks to form clusters. Specifically, we first propose a method for calculating structural entropy with soft assignment, which quantifies structure in a differentiable form. Next, we design a Structural Learning layer (SLL) to generate an attributed graph from the original feature data, serving as a target to enhance and optimize the original structural graph, thereby mitigating the issue of sparse connections between graph nodes. Finally, our clustering assignment method (ASS), based on GNNs, learns node embeddings and a soft assignment matrix to cluster on the enhanced graph. The ASS layer can be stacked to meet downstream task requirements, minimizing structural entropy for stable clustering and maximizing node consistency with edge-based cross-entropy loss. Extensive comparative experiments are conducted on four benchmark datasets against eight representative unsupervised graph clustering baselines, demonstrating the superiority of the DeSE in both effectiveness and interpretability.", "date": "2025-05-20", "categories": []}
{"id": "2505.14044", "title": "Generalized Category Discovery via Token Manifold Capacity Learning", "abstract": "Generalized category discovery (GCD) is essential for improving deep learning models' robustness in open-world scenarios by clustering unlabeled data containing both known and novel categories. Traditional GCD methods focus on minimizing intra-cluster variations, often sacrificing manifold capacity, which limits the richness of intra-class representations. In this paper, we propose a novel approach, Maximum Token Manifold Capacity (MTMC), that prioritizes maximizing the manifold capacity of class tokens to preserve the diversity and complexity of data. MTMC leverages the nuclear norm of singular values as a measure of manifold capacity, ensuring that the representation of samples remains informative and well-structured. This method enhances the discriminability of clusters, allowing the model to capture detailed semantic features and avoid the loss of critical information during clustering. Through theoretical analysis and extensive experiments on coarse- and fine-grained datasets, we demonstrate that MTMC outperforms existing GCD methods, improving both clustering accuracy and the estimation of category numbers. The integration of MTMC leads to more complete representations, better inter-class separability, and a reduction in dimensional collapse, establishing MTMC as a vital component for robust open-world learning. Code is in github.com/lytang63/MTMC.", "date": "2025-05-20", "categories": []}
{"id": "2505.14421", "title": "A system identification approach to clustering vector autoregressive time series", "abstract": "Clustering of time series based on their underlying dynamics is keeping attracting researchers due to its impacts on assisting complex system modelling. Most current time series clustering methods handle only scalar time series, treat them as white noise, or rely on domain knowledge for high-quality feature construction, where the autocorrelation pattern/feature is mostly ignored. Instead of relying on heuristic feature/metric construction, the system identification approach allows treating vector time series clustering by explicitly considering their underlying autoregressive dynamics. We first derive a clustering algorithm based on a mixture autoregressive model. Unfortunately it turns out to have significant computational problems. We then derive a `small-noise' limiting version of the algorithm, which we call k-LMVAR (Limiting Mixture Vector AutoRegression), that is computationally manageable. We develop an associated BIC criterion for choosing the number of clusters and model order. The algorithm performs very well in comparative simulations and also scales well computationally.", "date": "2025-05-20", "categories": []}
{"id": "2505.14596", "title": "CSTS: A Benchmark for the Discovery of Correlation Structures in Time Series Clustering", "abstract": "Time series clustering promises to uncover hidden structural patterns in data with applications across healthcare, finance, industrial systems, and other critical domains. However, without validated ground truth information, researchers cannot objectively assess clustering quality or determine whether poor results stem from absent structures in the data, algorithmic limitations, or inappropriate validation methods, raising the question whether clustering is \"more art than science\" (Guyon et al., 2009). To address these challenges, we introduce CSTS (Correlation Structures in Time Series), a synthetic benchmark for evaluating the discovery of correlation structures in multivariate time series data. CSTS provides a clean benchmark that enables researchers to isolate and identify specific causes of clustering failures by differentiating between correlation structure deterioration and limitations of clustering algorithms and validation methods. Our contributions are: (1) a comprehensive benchmark for correlation structure discovery with distinct correlation structures, systematically varied data conditions, established performance thresholds, and recommended evaluation protocols; (2) empirical validation of correlation structure preservation showing moderate distortion from downsampling and minimal effects from distribution shifts and sparsification; and (3) an extensible data generation framework enabling structure-first clustering evaluation. A case study demonstrates CSTS's practical utility by identifying an algorithm's previously undocumented sensitivity to non-normal distributions, illustrating how the benchmark enables precise diagnosis of methodological limitations. CSTS advances rigorous evaluation standards for correlation-based time series clustering.", "date": "2025-05-20", "categories": []}
{"id": "2402.15679", "title": "Scalable Density-based Clustering with Random Projections", "abstract": "We present sDBSCAN, a scalable density-based clustering algorithm in high dimensions with cosine distance. Utilizing the neighborhood-preserving property of random projections, sDBSCAN can quickly identify core points and their neighborhoods, the primary hurdle of density-based clustering. Theoretically, sDBSCAN outputs a clustering structure similar to DBSCAN under mild conditions with high probability. To further facilitate sDBSCAN, we present sOPTICS, a scalable OPTICS for interactive exploration of the intrinsic clustering structure. We also extend sDBSCAN and sOPTICS to L2, L1, $\\chi^2$, and Jensen-Shannon distances via random kernel features. Empirically, sDBSCAN is significantly faster and provides higher accuracy than many other clustering algorithms on real-world million-point data sets. On these data sets, sDBSCAN and sOPTICS run in a few minutes, while the scikit-learn's counterparts demand several hours or cannot run due to memory constraints.", "date": "2024-02-24", "categories": []}
{"id": "2504.07285", "title": "A Scalable Approach to Clustering Embedding Projections", "abstract": "Interactive visualization of embedding projections is a useful technique for understanding data and evaluating machine learning models. Labeling data within these visualizations is critical for interpretation, as labels provide an overview of the projection and guide user navigation. However, most methods for producing labels require clustering the points, which can be computationally expensive as the number of points grows. In this paper, we describe an efficient clustering approach using kernel density estimation in the projected 2D space instead of points. This algorithm can produce high-quality cluster regions from a 2D density map in a few hundred milliseconds, orders of magnitude faster than current approaches. We contribute the design of the algorithm, benchmarks, and applications that demonstrate the utility of the algorithm, including labeling and summarization.", "date": "2025-04-09", "categories": []}
{"id": "2505.11904", "title": "K*-Means: A Parameter-free Clustering Algorithm", "abstract": "Clustering is a widely used and powerful machine learning technique, but its effectiveness is often limited by the need to specify the number of clusters, k, or by relying on thresholds that implicitly determine k. We introduce k*-means, a novel clustering algorithm that eliminates the need to set k or any other parameters. Instead, it uses the minimum description length principle to automatically determine the optimal number of clusters, k*, by splitting and merging clusters while also optimising the standard k-means objective. We prove that k*-means is guaranteed to converge and demonstrate experimentally that it significantly outperforms existing methods in scenarios where k is unknown. We also show that it is accurate in estimating k, and that empirically its runtime is competitive with existing methods, and scales well with dataset size.", "date": "2025-05-17", "categories": []}
{"id": "2504.12270", "title": "Comparative analysis of unsupervised clustering techniques using validation metrics: Study on cognitive features from the Canadian Longitudinal Study on Aging (CLSA)", "abstract": "Purpose: The primary goal of this study is to explore the application of evaluation metrics to different clustering algorithms using the data provided from the Canadian Longitudinal Study (CLSA), focusing on cognitive features. The objective of our work is to discover potential clinically relevant clusters that contribute to the development of dementia over time-based on cognitive changes. Method: The CLSA dataset includes 18,891 participants with data available at both baseline and follow-up assessments, to which clustering algorithms were applied. The clustering methodologies employed in this analysis are K-means (KM) clustering, Hierarchical Clustering (HC) and Partitioning Around Medoids (PAM). We use multiple evaluation metrics to assess our analysis. For internal evaluation metrics, we use: Average silhouette Width, Within and Between the sum of square Ratio (WB.Ratio), Entropy, Calinski-Harabasz Index (CH Index), and Separation Index. For clustering comparison metrics, we used: Homogeneity, Completeness, Adjusted Rand Index (ARI), Rand Index (RI), and Variation Information. Results: Using evaluation metrics to compare the results of the three clustering techniques, K-means and Partitioning Around Medoids (PAM) produced similar results. In contrast, there are significant differences between K-means clustering and Hierarchical Clustering. Our study highlights the importance of the two internal evaluation metrics: entropy and separation index. In between clustering comparison metrics, the Adjusted Rand Index is a key tool. Conclusion: The study results have the potential to contribute to understanding dementia. Researchers can also benefit by applying the suggested evaluation metrics to other areas of healthcare research. Overall, our study improves the understanding of using clustering techniques and evaluation metrics to reveal complex patterns in medical data.", "date": "2025-04-07", "categories": []}
{"id": "2505.10699", "title": "Clustering Rooftop PV Systems via Probabilistic Embeddings", "abstract": "As the number of rooftop photovoltaic (PV) installations increases, aggregators and system operators are required to monitor and analyze these systems, raising the challenge of integration and management of large, spatially distributed time-series data that are both high-dimensional and affected by missing values. In this work, a probabilistic entity embedding-based clustering framework is proposed to address these problems. This method encodes each PV system's characteristic power generation patterns and uncertainty as a probability distribution, then groups systems by their statistical distances and agglomerative clustering. Applied to a multi-year residential PV dataset, it produces concise, uncertainty-aware cluster profiles that outperform a physics-based baseline in representativeness and robustness, and support reliable missing-value imputation. A systematic hyperparameter study further offers practical guidance for balancing model performance and robustness.", "date": "2025-05-15", "categories": []}
{"id": "2505.11182", "title": "Imputation-free and Alignment-free: Incomplete Multi-view Clustering Driven by Consensus Semantic Learning", "abstract": "In incomplete multi-view clustering (IMVC), missing data induce prototype shifts within views and semantic inconsistencies across views. A feasible solution is to explore cross-view consistency in paired complete observations, further imputing and aligning the similarity relationships inherently shared across views. Nevertheless, existing methods are constrained by two-tiered limitations: (1) Neither instance- nor cluster-level consistency learning construct a semantic space shared across views to learn consensus semantics. The former enforces cross-view instances alignment, and wrongly regards unpaired observations with semantic consistency as negative pairs; the latter focuses on cross-view cluster counterparts while coarsely handling fine-grained intra-cluster relationships within views. (2) Excessive reliance on consistency results in unreliable imputation and alignment without incorporating view-specific cluster information. Thus, we propose an IMVC framework, imputation- and alignment-free for consensus semantics learning (FreeCSL). To bridge semantic gaps across all observations, we learn consensus prototypes from available data to discover a shared space, where semantically similar observations are pulled closer for consensus semantics learning. To capture semantic relationships within specific views, we design a heuristic graph clustering based on modularity to recover cluster structure with intra-cluster compactness and inter-cluster separation for cluster semantics enhancement. Extensive experiments demonstrate, compared to state-of-the-art competitors, FreeCSL achieves more confident and robust assignments on IMVC task.", "date": "2025-05-16", "categories": []}
{"id": "2505.11359", "title": "LGBQPC: Local Granular-Ball Quality Peaks Clustering", "abstract": "The density peaks clustering (DPC) algorithm has attracted considerable attention for its ability to detect arbitrarily shaped clusters based on a simple yet effective assumption. Recent advancements integrating granular-ball (GB) computing with DPC have led to the GB-based DPC (GBDPC) algorithm, which improves computational efficiency. However, GBDPC demonstrates limitations when handling complex clustering tasks, particularly those involving data with complex manifold structures or non-uniform density distributions. To overcome these challenges, this paper proposes the local GB quality peaks clustering (LGBQPC) algorithm, which offers comprehensive improvements to GBDPC in both GB generation and clustering processes based on the principle of justifiable granularity (POJG). Firstly, an improved GB generation method, termed GB-POJG+, is developed, which systematically refines the original GB-POJG in four key aspects: the objective function, termination criterion for GB division, definition of abnormal GB, and granularity level adaptation strategy. GB-POJG+ simplifies parameter configuration by requiring only a single penalty coefficient and ensures high-quality GB generation while maintaining the number of generated GBs within an acceptable range. In the clustering phase, two key innovations are introduced based on the GB k-nearest neighbor graph: relative GB quality for density estimation and geodesic distance for GB distance metric. These modifications substantially improve the performance of GBDPC on datasets with complex manifold structures or non-uniform density distributions. Extensive numerical experiments on 40 benchmark datasets, including both synthetic and publicly available datasets, validate the superior performance of the proposed LGBQPC algorithm.", "date": "2025-05-16", "categories": []}
{"id": "2504.01953", "title": "Deep Representation Learning for Unsupervised Clustering of Myocardial Fiber Trajectories in Cardiac Diffusion Tensor Imaging", "abstract": "Understanding the complex myocardial architecture is critical for diagnosing and treating heart disease. However, existing methods often struggle to accurately capture this intricate structure from Diffusion Tensor Imaging (DTI) data, particularly due to the lack of ground truth labels and the ambiguous, intertwined nature of fiber trajectories. We present a novel deep learning framework for unsupervised clustering of myocardial fibers, providing a data-driven approach to identifying distinct fiber bundles. We uniquely combine a Bidirectional Long Short-Term Memory network to capture local sequential information along fibers, with a Transformer autoencoder to learn global shape features, with pointwise incorporation of essential anatomical context. Clustering these representations using a density-based algorithm identifies 33 to 62 robust clusters, successfully capturing the subtle distinctions in fiber trajectories with varying levels of granularity. Our framework offers a new, flexible, and quantitative way to analyze myocardial structure, achieving a level of delineation that, to our knowledge, has not been previously achieved, with potential applications in improving surgical planning, characterizing disease-related remodeling, and ultimately, advancing personalized cardiac care.", "date": "2025-04-02", "categories": []}
{"id": "2504.17551", "title": "Unsupervised Urban Land Use Mapping with Street View Contrastive Clustering and a Geographical Prior", "abstract": "Urban land use classification and mapping are critical for urban planning, resource management, and environmental monitoring. Existing remote sensing techniques often lack precision in complex urban environments due to the absence of ground-level details. Unlike aerial perspectives, street view images provide a ground-level view that captures more human and social activities relevant to land use in complex urban scenes. Existing street view-based methods primarily rely on supervised classification, which is challenged by the scarcity of high-quality labeled data and the difficulty of generalizing across diverse urban landscapes. This study introduces an unsupervised contrastive clustering model for street view images with a built-in geographical prior, to enhance clustering performance. When combined with a simple visual assignment of the clusters, our approach offers a flexible and customizable solution to land use mapping, tailored to the specific needs of urban planners. We experimentally show that our method can generate land use maps from geotagged street view image datasets of two cities. As our methodology relies on the universal spatial coherence of geospatial data (\"Tobler's law\"), it can be adapted to various settings where street view images are available, to enable scalable, unsupervised land use mapping and updating. The code will be available at https://github.com/lin102/CCGP.", "date": "2025-04-24", "categories": []}
{"id": "2505.08594", "title": "Clustering of Incomplete Data via a Bipartite Graph Structure", "abstract": "There are various approaches to graph learning for data clustering, incorporating different spectral and structural constraints through diverse graph structures. Some methods rely on bipartite graph models, where nodes are divided into two classes: centers and members. These models typically require access to data for the center nodes in addition to observations from the member nodes. However, such additional data may not always be available in many practical scenarios. Moreover, popular Gaussian models for graph learning have demonstrated limited effectiveness in modeling data with heavy-tailed distributions, which are common in financial markets. In this paper, we propose a clustering method based on a bipartite graph model that addresses these challenges. First, it can infer clusters from incomplete data without requiring information about the center nodes. Second, it is designed to effectively handle heavy-tailed data. Numerical experiments using real financial data validate the efficiency of the proposed method for data clustering.", "date": "2025-05-13", "categories": []}
{"id": "2505.06259", "title": "Fair Clustering with Clusterlets", "abstract": "Given their widespread usage in the real world, the fairness of clustering methods has become of major interest. Theoretical results on fair clustering show that fairness enjoys transitivity: given a set of small and fair clusters, a trivial centroid-based clustering algorithm yields a fair clustering. Unfortunately, discovering a suitable starting clustering can be computationally expensive, rather complex or arbitrary.\n  In this paper, we propose a set of simple \\emph{clusterlet}-based fuzzy clustering algorithms that match single-class clusters, optimizing fair clustering. Matching leverages clusterlet distance, optimizing for classic clustering objectives, while also regularizing for fairness. Empirical results show that simple matching strategies are able to achieve high fairness, and that appropriate parameter tuning allows to achieve high cohesion and low overlap.", "date": "2025-05-03", "categories": []}
{"id": "2505.06863", "title": "Masked Subspace Clustering Methods", "abstract": "To further utilize the unsupervised features and pairwise information, we propose a general Bilevel Clustering Optimization (BCO) framework to improve the performance of clustering. And then we introduce three special cases on subspace clustering with two different types of masks. At first, we reformulate the original subspace clustering as a Basic Masked Subspace Clustering (BMSC), which reformulate the diagonal constraints to a hard mask. Then, we provide a General Masked Subspace Clustering (GMSC) method to integrate different clustering via a soft mask. Furthermore, based on BCO and GMSC, we induce a learnable soft mask and design a Recursive Masked Subspace Clustering (RMSC) method that can alternately update the affinity matrix and the soft mask. Numerical experiments show that our models obtain significant improvement compared with the baselines on several commonly used datasets, such as MNIST, USPS, ORL, COIL20 and COIL100.", "date": "2025-05-11", "categories": []}
{"id": "2505.07702", "title": "4TaStiC: Time and trend traveling time series clustering for classifying long-term type 2 diabetes patients", "abstract": "Diabetes is one of the most prevalent diseases worldwide, characterized by persistently high blood sugar levels, capable of damaging various internal organs and systems. Diabetes patients require routine check-ups, resulting in a time series of laboratory records, such as hemoglobin A1c, which reflects each patient's health behavior over time and informs their doctor's recommendations. Clustering patients into groups based on their entire time series data assists doctors in making recommendations and choosing treatments without the need to review all records. However, time series clustering of this type of dataset introduces some challenges; patients visit their doctors at different time points, making it difficult to capture and match trends, peaks, and patterns. Additionally, two aspects must be considered: differences in the levels of laboratory results and differences in trends and patterns. To address these challenges, we introduce a new clustering algorithm called Time and Trend Traveling Time Series Clustering (4TaStiC), using a base dissimilarity measure combined with Euclidean and Pearson correlation metrics. We evaluated this algorithm on artificial datasets, comparing its performance with that of seven existing methods. The results show that 4TaStiC outperformed the other methods on the targeted datasets. Finally, we applied 4TaStiC to cluster a cohort of 1,989 type 2 diabetes patients at Siriraj Hospital. Each group of patients exhibits clear characteristics that will benefit doctors in making efficient clinical decisions. Furthermore, the proposed algorithm can be applied to contexts outside the medical field.", "date": "2025-05-12", "categories": []}
{"id": "2505.05748", "title": "kFuse: A novel density based agglomerative clustering", "abstract": "Agglomerative clustering has emerged as a vital tool in data analysis due to its intuitive and flexible characteristics. However, existing agglomerative clustering methods often involve additional parameters for sub-cluster partitioning and inter-cluster similarity assessment. This necessitates different parameter settings across various datasets, which is undoubtedly challenging in the absence of prior knowledge. Moreover, existing agglomerative clustering techniques are constrained by the calculation method of connection distance, leading to unstable clustering results. To address these issues, this paper introduces a novel density-based agglomerative clustering method, termed kFuse. kFuse comprises four key components: (1) sub-cluster partitioning based on natural neighbors; (2) determination of boundary connectivity between sub-clusters through the computation of adjacent samples and shortest distances; (3) assessment of density similarity between sub-clusters via the calculation of mean density and variance; and (4) establishment of merging rules between sub-clusters based on boundary connectivity and density similarity. kFuse requires the specification of the number of clusters only at the final merging stage. Additionally, by comprehensively considering adjacent samples, distances, and densities among different sub-clusters, kFuse significantly enhances accuracy during the merging phase, thereby greatly improving its identification capability. Experimental results on both synthetic and real-world datasets validate the effectiveness of kFuse.", "date": "2025-05-09", "categories": []}
{"id": "2501.13093", "title": "Guaranteed Recovery of Unambiguous Clusters", "abstract": "  Clustering is often a challenging problem because of the inherent ambiguity\nin what the \"correct\" clustering should be. Even when the number of clusters\n$K$ is known, this ambiguity often still exists, particularly when there is\nvariation in density among different clusters, and clusters have multiple\nrelatively separated regions of high density. In this paper we propose an\ninformation-theoretic characterization of when a $K$-clustering is ambiguous,\nand design an algorithm that recovers the clustering whenever it is\nunambiguous. This characterization formalizes the situation when two high\ndensity regions within a cluster are separable enough that they look more like\ntwo distinct clusters than two truly distinct clusters in the $K$-clustering.\nThe algorithm first identifies $K$ partial clusters (or \"seeds\") using a\ndensity-based approach, and then adds unclustered points to the initial $K$\npartial clusters in a greedy manner to form a complete clustering. We implement\nand test a version of the algorithm that is modified to effectively handle\noverlapping clusters, and observe that it requires little parameter selection\nand displays improved performance on many datasets compared to widely used\nalgorithms for non-convex cluster recovery.\n", "date": "2025-01-22", "categories": []}
{"id": "2505.04339", "title": "Adaptive and Robust DBSCAN with Multi-agent Reinforcement Learning", "abstract": "  DBSCAN, a well-known density-based clustering algorithm, has gained\nwidespread popularity and usage due to its effectiveness in identifying\nclusters of arbitrary shapes and handling noisy data. However, it encounters\nchallenges in producing satisfactory cluster results when confronted with\ndatasets of varying density scales, a common scenario in real-world\napplications. In this paper, we propose a novel Adaptive and Robust DBSCAN with\nMulti-agent Reinforcement Learning cluster framework, namely AR-DBSCAN. First,\nwe model the initial dataset as a two-level encoding tree and categorize the\ndata vertices into distinct density partitions according to the information\nuncertainty determined in the encoding tree. Each partition is then assigned to\nan agent to find the best clustering parameters without manual assistance. The\nallocation is density-adaptive, enabling AR-DBSCAN to effectively handle\ndiverse density distributions within the dataset by utilizing distinct agents\nfor different partitions. Second, a multi-agent deep reinforcement learning\nguided automatic parameter searching process is designed. The process of\nadjusting the parameter search direction by perceiving the clustering\nenvironment is modeled as a Markov decision process. Using a weakly-supervised\nreward training policy network, each agent adaptively learns the optimal\nclustering parameters by interacting with the clusters. Third, a recursive\nsearch mechanism adaptable to the data's scale is presented, enabling efficient\nand controlled exploration of large parameter spaces. Extensive experiments are\nconducted on nine artificial datasets and a real-world dataset. The results of\noffline and online tasks show that AR-DBSCAN not only improves clustering\naccuracy by up to 144.1% and 175.3% in the NMI and ARI metrics, respectively,\nbut also is capable of robustly finding dominant parameters.\n", "date": "2025-05-07", "categories": []}
{"id": "2505.04440", "title": "Towards Initialization-Agnostic Clustering with Iterative Adaptive\n  Resonance Theory", "abstract": "  The clustering performance of Fuzzy Adaptive Resonance Theory (Fuzzy ART) is\nhighly dependent on the preset vigilance parameter, where deviations in its\nvalue can lead to significant fluctuations in clustering results, severely\nlimiting its practicality for non-expert users. Existing approaches generally\nenhance vigilance parameter robustness through adaptive mechanisms such as\nparticle swarm optimization and fuzzy logic rules. However, they often\nintroduce additional hyperparameters or complex frameworks that contradict the\noriginal simplicity of the algorithm. To address this, we propose Iterative\nRefinement Adaptive Resonance Theory (IR-ART), which integrates three key\nphases into a unified iterative framework: (1) Cluster Stability Detection: A\ndynamic stability detection module that identifies unstable clusters by\nanalyzing the change of sample size (number of samples in the cluster) in\niteration. (2) Unstable Cluster Deletion: An evolutionary pruning module that\neliminates low-quality clusters. (3) Vigilance Region Expansion: A vigilance\nregion expansion mechanism that adaptively adjusts similarity thresholds.\nIndependent of the specific execution of clustering, these three phases\nsequentially focus on analyzing the implicit knowledge within the iterative\nprocess, adjusting weights and vigilance parameters, thereby laying a\nfoundation for the next iteration. Experimental evaluation on 15 datasets\ndemonstrates that IR-ART improves tolerance to suboptimal vigilance parameter\nvalues while preserving the parameter simplicity of Fuzzy ART. Case studies\nvisually confirm the algorithm's self-optimization capability through iterative\nrefinement, making it particularly suitable for non-expert users in\nresource-constrained scenarios.\n", "date": "2025-05-07", "categories": []}
{"id": "2505.02173", "title": "Ranked differences Pearson correlation dissimilarity with an application\n  to electricity users time series clustering", "abstract": "  Time series clustering is an unsupervised learning method for classifying\ntime series data into groups with similar behavior. It is used in applications\nsuch as healthcare, finance, economics, energy, and climate science. Several\ntime series clustering methods have been introduced and used for over four\ndecades. Most of them focus on measuring either Euclidean distances or\nassociation dissimilarities between time series. In this work, we propose a new\ndissimilarity measure called ranked Pearson correlation dissimilarity (RDPC),\nwhich combines a weighted average of a specified fraction of the largest\nelement-wise differences with the well-known Pearson correlation dissimilarity.\nIt is incorporated into hierarchical clustering. The performance is evaluated\nand compared with existing clustering algorithms. The results show that the\nRDPC algorithm outperforms others in complicated cases involving different\nseasonal patterns, trends, and peaks. Finally, we demonstrate our method by\nclustering a random sample of customers from a Thai electricity consumption\ntime series dataset into seven groups with unique characteristics.\n", "date": "2025-05-04", "categories": []}
{"id": "2505.03848", "title": "Advanced Clustering Framework for Semiconductor Image Analytics\n  Integrating Deep TDA with Self-Supervised and Transfer Learning Techniques", "abstract": "  Semiconductor manufacturing generates vast amounts of image data, crucial for\ndefect identification and yield optimization, yet often exceeds manual\ninspection capabilities. Traditional clustering techniques struggle with\nhigh-dimensional, unlabeled data, limiting their effectiveness in capturing\nnuanced patterns. This paper introduces an advanced clustering framework that\nintegrates deep Topological Data Analysis (TDA) with self-supervised and\ntransfer learning techniques, offering a novel approach to unsupervised image\nclustering. TDA captures intrinsic topological features, while self-supervised\nlearning extracts meaningful representations from unlabeled data, reducing\nreliance on labeled datasets. Transfer learning enhances the framework's\nadaptability and scalability, allowing fine-tuning to new datasets without\nretraining from scratch. Validated on synthetic and open-source semiconductor\nimage datasets, the framework successfully identifies clusters aligned with\ndefect patterns and process variations. This study highlights the\ntransformative potential of combining TDA, self-supervised learning, and\ntransfer learning, providing a scalable solution for proactive process\nmonitoring and quality control in semiconductor manufacturing and other domains\nwith large-scale image datasets.\n", "date": "2025-05-05", "categories": []}
{"id": "2505.04464", "title": "Discriminative Ordering Through Ensemble Consensus", "abstract": "  Evaluating the performance of clustering models is a challenging task where\nthe outcome depends on the definition of what constitutes a cluster. Due to\nthis design, current existing metrics rarely handle multiple clustering models\nwith diverse cluster definitions, nor do they comply with the integration of\nconstraints when available. In this work, we take inspiration from consensus\nclustering and assume that a set of clustering models is able to uncover hidden\nstructures in the data. We propose to construct a discriminative ordering\nthrough ensemble clustering based on the distance between the connectivity of a\nclustering model and the consensus matrix. We first validate the proposed\nmethod with synthetic scenarios, highlighting that the proposed score ranks the\nmodels that best match the consensus first. We then show that this simple\nranking score significantly outperforms other scoring methods when comparing\nsets of different clustering algorithms that are not restricted to a fixed\nnumber of clusters and is compatible with clustering constraints.\n", "date": "2025-05-07", "categories": []}
{"id": "2505.04484", "title": "A Tutorial on Discriminative Clustering and Mutual Information", "abstract": "  To cluster data is to separate samples into distinctive groups that should\nideally have some cohesive properties. Today, numerous clustering algorithms\nexist, and their differences lie essentially in what can be perceived as\n``cohesive properties''. Therefore, hypotheses on the nature of clusters must\nbe set: they can be either generative or discriminative. As the last decade\nwitnessed the impressive growth of deep clustering methods that involve neural\nnetworks to handle high-dimensional data often in a discriminative manner; we\nconcentrate mainly on the discriminative hypotheses. In this paper, our aim is\nto provide an accessible historical perspective on the evolution of\ndiscriminative clustering methods and notably how the nature of assumptions of\nthe discriminative models changed over time: from decision boundaries to\ninvariance critics. We notably highlight how mutual information has been a\nhistorical cornerstone of the progress of (deep) discriminative clustering\nmethods. We also show some known limitations of mutual information and how\ndiscriminative clustering methods tried to circumvent those. We then discuss\nthe challenges that discriminative clustering faces with respect to the\nselection of the number of clusters. Finally, we showcase these techniques\nusing the dedicated Python package, GemClus, that we have developed for\ndiscriminative clustering.\n", "date": "2025-05-07", "categories": []}
{"id": "2505.03207", "title": "Partial Label Clustering", "abstract": "  Partial label learning (PLL) is a significant weakly supervised learning\nframework, where each training example corresponds to a set of candidate labels\nand only one label is the ground-truth label. For the first time, this paper\ninvestigates the partial label clustering problem, which takes advantage of the\nlimited available partial labels to improve the clustering performance.\nSpecifically, we first construct a weight matrix of examples based on their\nrelationships in the feature space and disambiguate the candidate labels to\nestimate the ground-truth label based on the weight matrix. Then, we construct\na set of must-link and cannot-link constraints based on the disambiguation\nresults. Moreover, we propagate the initial must-link and cannot-link\nconstraints based on an adversarial prior promoted dual-graph learning\napproach. Finally, we integrate weight matrix construction, label\ndisambiguation, and pairwise constraints propagation into a joint model to\nachieve mutual enhancement. We also theoretically prove that a better\ndisambiguated label matrix can help improve clustering performance.\nComprehensive experiments demonstrate our method realizes superior performance\nwhen comparing with state-of-the-art constrained clustering methods, and\noutperforms PLL and semi-supervised PLL methods when only limited samples are\nannotated. The code is publicly available at https://github.com/xyt-ml/PLC.\n", "date": "2025-05-06", "categories": []}
{"id": "2505.03390", "title": "Concept Factorization via Self-Representation and Adaptive Graph\n  Structure Learning", "abstract": "  Concept Factorization (CF) models have attracted widespread attention due to\ntheir excellent performance in data clustering. In recent years, many variant\nmodels based on CF have achieved great success in clustering by taking into\naccount the internal geometric manifold structure of the dataset and using\ngraph regularization techniques. However, their clustering performance depends\ngreatly on the construction of the initial graph structure. In order to enable\nadaptive learning of the graph structure of the data, we propose a Concept\nFactorization Based on Self-Representation and Adaptive Graph Structure\nLearning (CFSRAG) Model. CFSRAG learns the affinity relationship between data\nthrough a self-representation method, and uses the learned affinity matrix to\nimplement dynamic graph regularization constraints, thereby ensuring dynamic\nlearning of the internal geometric structure of the data. Finally, we give the\nCFSRAG update rule and convergence analysis, and conduct comparative\nexperiments on four real datasets. The results show that our model outperforms\nother state-of-the-art models.\n", "date": "2025-05-06", "categories": []}
{"id": "2408.13431", "title": "Face Clustering via Early Stopping and Edge Recall", "abstract": "  Large-scale face clustering has achieved significant progress, with many\nefforts dedicated to learning to cluster large-scale faces with\nsupervised-learning. However, complex model design and tedious clustering\nprocesses are typical in existing methods. Such limitations result in\ninfeasible clustering in real-world applications. Reasonable and efficient\nmodel design and training need to be taken into account. Besides, developing\nunsupervised face clustering algorithms is crucial, which are more realistic in\nreal-world applications. In this paper, we propose a novel unsupervised face\nclustering algorithm FC-ES and a novel supervised face clustering algorithm\nFC-ESER to address these issues. An efficient and effective neighbor-based edge\nprobability and a novel early stopping strategy are proposed in FC-ES,\nguaranteeing the accuracy and recall of large-scale face clustering\nsimultaneously. Furthermore, to take advantage of supervised learning, a novel\nedge recall strategy is proposed in FC-ESER to further recall the edge\nconnections that are not connected in FC-ES. Extensive experiments on multiple\nbenchmarks for face, person, and vehicle clustering show that our proposed\nFC-ES and FC-ESER significantly outperform previous state-of-the-art methods.\nOur code will be available at https://github.com/jumptoliujj/FC-ESER.\n", "date": "2024-08-24", "categories": []}
{"id": "2402.08978", "title": "Prismatic: Interactive Multi-View Cluster Analysis of Concept Stocks", "abstract": "  Financial cluster analysis allows investors to discover investment\nalternatives and avoid undertaking excessive risks. However, this analytical\ntask faces substantial challenges arising from many pairwise comparisons, the\ndynamic correlations across time spans, and the ambiguity in deriving\nimplications from business relational knowledge. We propose Prismatic, a visual\nanalytics system that integrates quantitative analysis of historical\nperformance and qualitative analysis of business relational knowledge to\ncluster correlated businesses interactively. Prismatic features three\nclustering processes: dynamic cluster generation, knowledge-based cluster\nexploration, and correlation-based cluster validation. Utilizing a multi-view\nclustering approach, it enriches data-driven clusters with knowledge-driven\nsimilarity, providing a nuanced understanding of business correlations. Through\nwell-coordinated visual views, Prismatic facilitates a comprehensive\ninterpretation of intertwined quantitative and qualitative features,\ndemonstrating its usefulness and effectiveness via case studies on formulating\nconcept stocks and extensive interviews with domain experts.\n", "date": "2024-02-14", "categories": []}
{"id": "2505.00056", "title": "Clustering Internet Memes Through Template Matching and\n  Multi-Dimensional Similarity", "abstract": "  Meme clustering is critical for toxicity detection, virality modeling, and\ntyping, but it has received little attention in previous research. Clustering\nsimilar Internet memes is challenging due to their multimodality, cultural\ncontext, and adaptability. Existing approaches rely on databases, overlook\nsemantics, and struggle to handle diverse dimensions of similarity. This paper\nintroduces a novel method that uses template-based matching with\nmulti-dimensional similarity features, thus eliminating the need for predefined\ndatabases and supporting adaptive matching. Memes are clustered using local and\nglobal features across similarity categories such as form, visual content,\ntext, and identity. Our combined approach outperforms existing clustering\nmethods, producing more consistent and coherent clusters, while\nsimilarity-based feature sets enable adaptability and align with human\nintuition. We make all supporting code publicly available to support subsequent\nresearch.\n", "date": "2025-04-30", "categories": []}
{"id": "2504.21472", "title": "Robust Orthogonal NMF with Label Propagation for Image Clustering", "abstract": "  Non-negative matrix factorization (NMF) is a popular unsupervised learning\napproach widely used in image clustering. However, in real-world clustering\nscenarios, most existing NMF methods are highly sensitive to noise corruption\nand are unable to effectively leverage limited supervised information. To\novercome these drawbacks, we propose a unified non-convex framework with label\npropagation called robust orthogonal nonnegative matrix factorization (RONMF).\nThis method not only considers the graph Laplacian and label propagation as\nregularization terms but also introduces a more effective non-convex structure\nto measure the reconstruction error and imposes orthogonal constraints on the\nbasis matrix to reduce the noise corruption, thereby achieving higher\nrobustness. To solve RONMF, we develop an alternating direction method of\nmultipliers (ADMM)-based optimization algorithm. In particular, all subproblems\nhave closed-form solutions, which ensures its efficiency. Experimental\nevaluations on eight public image datasets demonstrate that the proposed RONMF\noutperforms state-of-the-art NMF methods across various standard metrics and\nshows excellent robustness. The code will be available at\nhttps://github.com/slinda-liu.\n", "date": "2025-04-30", "categories": []}
{"id": "2504.20293", "title": "Radius-Guided Post-Clustering for Shape-Aware, Scalable Refinement of\n  k-Means Results", "abstract": "  Traditional k-means clustering underperforms on non-convex shapes and\nrequires the number of clusters k to be specified in advance. We propose a\nsimple geometric enhancement: after standard k-means, each cluster center is\nassigned a radius (the distance to its farthest assigned point), and clusters\nwhose radii overlap are merged. This post-processing step loosens the\nrequirement for exact k: as long as k is overestimated (but not excessively),\nthe method can often reconstruct non-convex shapes through meaningful merges.\nWe also show that this approach supports recursive partitioning: clustering can\nbe performed independently on tiled regions of the feature space, then globally\nmerged, making the method scalable and suitable for distributed systems.\nImplemented as a lightweight post-processing step atop scikit-learn's k-means,\nthe algorithm performs well on benchmark datasets, achieving high accuracy with\nminimal additional computation.\n", "date": "2025-04-28", "categories": []}
{"id": "2504.20390", "title": "Manifold Clustering with Schatten p-norm Maximization", "abstract": "  Manifold clustering, with its exceptional ability to capture complex data\nstructures, holds a pivotal position in cluster analysis. However, existing\nmethods often focus only on finding the optimal combination between K-means and\nmanifold learning, and overlooking the consistency between the data structure\nand labels. To address this issue, we deeply explore the relationship between\nK-means and manifold learning, and on this basis, fuse them to develop a new\nclustering framework. Specifically, the algorithm uses labels to guide the\nmanifold structure and perform clustering on it, which ensures the consistency\nbetween the data structure and labels. Furthermore, in order to naturally\nmaintain the class balance in the clustering process, we maximize the Schatten\np-norm of labels, and provide a theoretical proof to support this.\nAdditionally, our clustering framework is designed to be flexible and\ncompatible with many types of distance functions, which facilitates efficient\nprocessing of nonlinear separable data. The experimental results of several\ndatabases confirm the superiority of our proposed model.\n", "date": "2025-04-29", "categories": []}
{"id": "2401.06089", "title": "PANDORA: A Parallel Dendrogram Construction Algorithm for Single Linkage\n  Clustering on GPU", "abstract": "  This paper presents \\pandora, a novel parallel algorithm for efficiently\nconstructing dendrograms for single-linkage hierarchical clustering, including\n\\hdbscan. Traditional dendrogram construction methods from a minimum spanning\ntree (MST), such as agglomerative or divisive techniques, often fail to\nefficiently parallelize, especially with skewed dendrograms common in\nreal-world data.\n  \\pandora addresses these challenges through a unique recursive tree\ncontraction method, which simplifies the tree for initial dendrogram\nconstruction and then progressively reconstructs the complete dendrogram. This\nprocess makes \\pandora asymptotically work-optimal, independent of dendrogram\nskewness. All steps in \\pandora are fully parallel and suitable for massively\nthreaded accelerators such as GPUs.\n  Our implementation is written in Kokkos, providing support for both CPUs and\nmulti-vendor GPUs (e.g., Nvidia, AMD). The multithreaded version of \\pandora is\n2.2$\\times$ faster than the current best-multithreaded implementation, while\nthe GPU \\pandora implementation achieved 6-20$\\times$ on \\amdgpu and\n10-37$\\times$ on \\nvidiagpu speed-up over multithreaded \\pandora. These\nadvancements lead to up to a 6-fold speedup for \\hdbscan on GPUs over the\ncurrent best, which only offload MST construction to GPUs and perform\nmultithreaded dendrogram construction.\n", "date": "2024-01-11", "categories": []}
{"id": "2503.06635", "title": "Deep Cut-informed Graph Embedding and Clustering", "abstract": "  Graph clustering aims to divide the graph into different clusters. The\nrecently emerging deep graph clustering approaches are largely built on graph\nneural networks (GNN). However, GNN is designed for general graph encoding and\nthere is a common issue of representation collapse in existing GNN-based deep\ngraph clustering algorithms. We attribute two main reasons for such issues: (i)\nthe inductive bias of GNN models: GNNs tend to generate similar representations\nfor proximal nodes. Since graphs often contain a non-negligible amount of\ninter-cluster links, the bias results in error message passing and leads to\nbiased clustering; (ii) the clustering guided loss function: most traditional\napproaches strive to make all samples closer to pre-learned cluster centers,\nwhich causes a degenerate solution assigning all data points to a single label\nthus making all samples similar and less discriminative. To address these\nchallenges, we investigate graph clustering from a graph cut perspective and\npropose an innovative and non-GNN-based Deep Cut-informed Graph embedding and\nClustering framework, namely DCGC. This framework includes two modules: (i)\ncut-informed graph encoding; (ii) self-supervised graph clustering via optimal\ntransport. For the encoding module, we derive a cut-informed graph embedding\nobjective to fuse graph structure and attributes by minimizing their joint\nnormalized cut. For the clustering module, we utilize the optimal transport\ntheory to obtain the clustering assignments, which can balance the guidance of\n\"proximity to the pre-learned cluster center\". With the above two tailored\ndesigns, DCGC is more suitable for the graph clustering task, which can\neffectively alleviate the problem of representation collapse and achieve better\nperformance. We conduct extensive experiments to demonstrate that our method is\nsimple but effective compared with benchmarks.\n", "date": "2025-03-09", "categories": []}
{"id": "2502.02185", "title": "Generative Kernel Spectral Clustering", "abstract": "  Modern clustering approaches often trade interpretability for performance,\nparticularly in deep learning-based methods. We present Generative Kernel\nSpectral Clustering (GenKSC), a novel model combining kernel spectral\nclustering with generative modeling to produce both well-defined clusters and\ninterpretable representations. By augmenting weighted variance maximization\nwith reconstruction and clustering losses, our model creates an explorable\nlatent space where cluster characteristics can be visualized through traversals\nalong cluster directions. Results on MNIST and FashionMNIST datasets\ndemonstrate the model's ability to learn meaningful cluster representations.\n", "date": "2025-02-04", "categories": []}
{"id": "2311.15887", "title": "FLASC: A Flare-Sensitive Clustering Algorithm", "abstract": "  Clustering algorithms are often used to find subpopulations in exploratory\ndata analysis workflows. Not only the clusters themselves, but also their shape\ncan represent meaningful subpopulations. In this paper, we present FLASC, an\nalgorithm that detects branches within clusters to identify such\nsubpopulations. FLASC builds upon HDBSCAN*, a state-of-the-art density-based\nclustering algorithm, and detects branches in a post-processing step that\ndescribes within-cluster connectivity. Two variants of the algorithm are\npresented, which trade computational cost for noise robustness. We show that\nboth variants scale similarly to HDBSCAN* in terms of computational cost and\nprovide stable outputs using synthetic data sets, resulting in an efficient\nflare-sensitive clustering algorithm. In addition, we demonstrate the benefit\nof branch-detection on two real-world data sets.\n", "date": "2023-11-27", "categories": []}
{"id": "2504.15580", "title": "On the Price of Differential Privacy for Hierarchical Clustering", "abstract": "  Hierarchical clustering is a fundamental unsupervised machine learning task\nwith the aim of organizing data into a hierarchy of clusters. Many applications\nof hierarchical clustering involve sensitive user information, therefore\nmotivating recent studies on differentially private hierarchical clustering\nunder the rigorous framework of Dasgupta's objective. However, it has been\nshown that any privacy-preserving algorithm under edge-level differential\nprivacy necessarily suffers a large error. To capture practical applications of\nthis problem, we focus on the weight privacy model, where each edge of the\ninput graph is at least unit weight. We present a novel algorithm in the weight\nprivacy model that shows significantly better approximation than known\nimpossibility results in the edge-level DP setting. In particular, our\nalgorithm achieves $O(\\log^{1.5}n/\\varepsilon)$ multiplicative error for\n$\\varepsilon$-DP and runs in polynomial time, where $n$ is the size of the\ninput graph, and the cost is never worse than the optimal additive error in\nexisting work. We complement our algorithm by showing if the unit-weight\nconstraint does not apply, the lower bound for weight-level DP hierarchical\nclustering is essentially the same as the edge-level DP, i.e.\n$\\Omega(n^2/\\varepsilon)$ additive error. As a result, we also obtain a new\nlower bound of $\\tilde{\\Omega}(1/\\varepsilon)$ additive error for balanced\nsparsest cuts in the weight-level DP model, which may be of independent\ninterest. Finally, we evaluate our algorithm on synthetic and real-world\ndatasets. Our experimental results show that our algorithm performs well in\nterms of extra cost and has good scalability to large graphs.\n", "date": "2025-04-22", "categories": []}
{"id": "2404.09243", "title": "Learning Self-Growth Maps for Fast and Accurate Imbalanced Streaming\n  Data Clustering", "abstract": "  Streaming data clustering is a popular research topic in data mining and\nmachine learning. Since streaming data is usually analyzed in data chunks, it\nis more susceptible to encounter the dynamic cluster imbalance issue. That is,\nthe imbalance ratio of clusters changes over time, which can easily lead to\nfluctuations in either the accuracy or the efficiency of streaming data\nclustering. Therefore, we propose an accurate and efficient streaming data\nclustering approach to adapt the drifting and imbalanced cluster distributions.\nWe first design a Self-Growth Map (SGM) that can automatically arrange neurons\non demand according to local distribution, and thus achieve fast and\nincremental adaptation to the streaming distributions. Since SGM allocates an\nexcess number of density-sensitive neurons to describe the global distribution,\nit can avoid missing small clusters among imbalanced distributions. We also\npropose a fast hierarchical merging strategy to combine the neurons that break\nup the relatively large clusters. It exploits the maintained SGM to quickly\nretrieve the intra-cluster distribution pairs for merging, which circumvents\nthe most laborious global searching. It turns out that the proposed SGM can\nincrementally adapt to the distributions of new chunks, and the Self-grOwth\nmap-guided Hierarchical merging for Imbalanced data clustering (SOHI) approach\ncan quickly explore a true number of imbalanced clusters. Extensive experiments\ndemonstrate that SOHI can efficiently and accurately explore cluster\ndistributions for streaming data.\n", "date": "2024-04-14", "categories": []}
{"id": "2504.12683", "title": "Cluster weighted models with multivariate skewed distributions for\n  functional data", "abstract": "  We propose a clustering method, funWeightClustSkew, based on mixtures of\nfunctional linear regression models and three skewed multivariate\ndistributions: the variance-gamma distribution, the skew-t distribution, and\nthe normal-inverse Gaussian distribution. Our approach follows the framework of\nthe functional high dimensional data clustering (funHDDC) method, and we extend\nto functional data the cluster weighted models based on skewed distributions\nused for finite dimensional multivariate data. We consider several parsimonious\nmodels, and to estimate the parameters we construct an expectation maximization\n(EM) algorithm. We illustrate the performance of funWeightClustSkew for\nsimulated data and for the Air Quality dataset.\n", "date": "2025-04-17", "categories": []}
{"id": "2504.11621", "title": "Robust Markov stability for community detection at a scale learned based\n  on the structure", "abstract": "  Community detection, the unsupervised task of clustering nodes of a graph,\nfinds applications across various fields. The common approaches for community\ndetection involve optimizing an objective function to partition the nodes into\ncommunities at a single scale of granularity. However, the single-scale\napproaches often fall short of producing partitions that are robust and at a\nsuitable scale. The existing algorithm, PyGenStability, returns multiple robust\npartitions for a network by optimizing the multi-scale Markov stability\nfunction. However, in cases where the suitable scale is not known or assumed by\nthe user, there is no principled method to select a single robust partition at\na suitable scale from the multiple partitions that PyGenStability produces. Our\nproposed method combines the Markov stability framework with a pre-trained\nmachine learning model for scale selection to obtain one robust partition at a\nscale that is learned based on the graph structure. This automatic scale\nselection involves using a gradient boosting model pre-trained on hand-crafted\nand embedding-based network features from a labeled dataset of 10k benchmark\nnetworks. This model was trained to predicts the scale value that maximizes the\nsimilarity of the output partition to the planted partition of the benchmark\nnetwork. Combining our scale selection algorithm with the PyGenStability\nalgorithm results in PyGenStabilityOne (PO): a hyperparameter-free multi-scale\ncommunity detection algorithm that returns one robust partition at a suitable\nscale without the need for any assumptions, input, or tweaking from the user.\nWe compare the performance of PO against 29 algorithms and show that it\noutperforms 25 other algorithms by statistically meaningful margins. Our\nresults facilitate choosing between community detection algorithms, among which\nPO stands out as the accurate, robust, and hyperparameter-free method.\n", "date": "2025-04-15", "categories": []}
{"id": "2409.10908", "title": "Clustering with Non-adaptive Subset Queries", "abstract": "  Recovering the underlying clustering of a set $U$ of $n$ points by asking\npair-wise same-cluster queries has garnered significant interest in the last\ndecade. Given a query $S \\subset U$, $|S|=2$, the oracle returns yes if the\npoints are in the same cluster and no otherwise. For adaptive algorithms with\npair-wise queries, the number of required queries is known to be $\\Theta(nk)$,\nwhere $k$ is the number of clusters. However, non-adaptive schemes require\n$\\Omega(n^2)$ queries, which matches the trivial $O(n^2)$ upper bound attained\nby querying every pair of points.\n  To break the quadratic barrier for non-adaptive queries, we study a\ngeneralization of this problem to subset queries for $|S|>2$, where the oracle\nreturns the number of clusters intersecting $S$. Allowing for subset queries of\nunbounded size, $O(n)$ queries is possible with an adaptive scheme\n(Chakrabarty-Liao, 2024). However, the realm of non-adaptive algorithms is\ncompletely unknown.\n  In this paper, we give the first non-adaptive algorithms for clustering with\nsubset queries. Our main result is a non-adaptive algorithm making $O(n \\log k\n\\cdot (\\log k + \\log\\log n)^2)$ queries, which improves to $O(n \\log \\log n)$\nwhen $k$ is a constant. We also consider algorithms with a restricted query\nsize of at most $s$. In this setting we prove that $\\Omega(\\max(n^2/s^2,n))$\nqueries are necessary and obtain algorithms making $\\tilde{O}(n^2k/s^2)$\nqueries for any $s \\leq \\sqrt{n}$ and $\\tilde{O}(n^2/s)$ queries for any $s\n\\leq n$. We also consider the natural special case when the clusters are\nbalanced, obtaining non-adaptive algorithms which make $O(n \\log k) +\n\\tilde{O}(k)$ and $O(n\\log^2 k)$ queries. Finally, allowing two rounds of\nadaptivity, we give an algorithm making $O(n \\log k)$ queries in the general\ncase and $O(n \\log \\log k)$ queries when the clusters are balanced.\n", "date": "2024-09-17", "categories": []}
{"id": "2503.12427", "title": "Towards Learnable Anchor for Deep Multi-View Clustering", "abstract": "  Deep multi-view clustering incorporating graph learning has presented\ntremendous potential. Most methods encounter costly square time consumption\nw.r.t. data size. Theoretically, anchor-based graph learning can alleviate this\nlimitation, but related deep models mainly rely on manual discretization\napproaches to select anchors, which indicates that 1) the anchors are fixed\nduring model training and 2) they may deviate from the true cluster\ndistribution. Consequently, the unreliable anchors may corrupt clustering\nresults. In this paper, we propose the Deep Multi-view Anchor Clustering (DMAC)\nmodel that performs clustering in linear time. Concretely, the initial anchors\nare intervened by the positive-incentive noise sampled from Gaussian\ndistribution, such that they can be optimized with a newly designed anchor\nlearning loss, which promotes a clear relationship between samples and anchors.\nAfterwards, anchor graph convolution is devised to model the cluster structure\nformed by the anchors, and the mutual information maximization loss is built to\nprovide cross-view clustering guidance. In this way, the learned anchors can\nbetter represent clusters. With the optimal anchors, the full sample graph is\ncalculated to derive a discriminative embedding for clustering. Extensive\nexperiments on several datasets demonstrate the superior performance and\nefficiency of DMAC compared to state-of-the-art competitors.\n", "date": "2025-03-16", "categories": []}
{"id": "2503.20737", "title": "Ontology-based Semantic Similarity Measures for Clustering Medical\n  Concepts in Drug Safety", "abstract": "  Semantic similarity measures (SSMs) are widely used in biomedical research\nbut remain underutilized in pharmacovigilance. This study evaluates six\nontology-based SSMs for clustering MedDRA Preferred Terms (PTs) in drug safety\ndata. Using the Unified Medical Language System (UMLS), we assess each method's\nability to group PTs around medically meaningful centroids. A high-throughput\nframework was developed with a Java API and Python and R interfaces support\nlarge-scale similarity computations. Results show that while path-based methods\nperform moderately with F1 scores of 0.36 for WUPALMER and 0.28 for LCH,\nintrinsic information content (IC)-based measures, especially INTRINSIC-LIN and\nSOKAL, consistently yield better clustering accuracy (F1 score of 0.403).\nValidated against expert review and standard MedDRA queries (SMQs), our\nfindings highlight the promise of IC-based SSMs in enhancing pharmacovigilance\nworkflows by improving early signal detection and reducing manual review.\n", "date": "2025-03-26", "categories": []}
{"id": "2504.05670", "title": "Dual Boost-Driven Graph-Level Clustering Network", "abstract": "  Graph-level clustering remains a pivotal yet formidable challenge in graph\nlearning. Recently, the integration of deep learning with representation\nlearning has demonstrated notable advancements, yielding performance\nenhancements to a certain degree. However, existing methods suffer from at\nleast one of the following issues: 1. the original graph structure has noise,\nand 2. during feature propagation and pooling processes, noise is gradually\naggregated into the graph-level embeddings through information propagation.\nConsequently, these two limitations mask clustering-friendly information,\nleading to suboptimal graph-level clustering performance. To this end, we\npropose a novel Dual Boost-Driven Graph-Level Clustering Network (DBGCN) to\nalternately promote graph-level clustering and filtering out interference\ninformation in a unified framework. Specifically, in the pooling step, we\nevaluate the contribution of features at the global and optimize them using a\nlearnable transformation matrix to obtain high-quality graph-level\nrepresentation, such that the model's reasoning capability can be improved.\nMoreover, to enable reliable graph-level clustering, we first identify and\nsuppress information detrimental to clustering by evaluating similarities\nbetween graph-level representations, providing more accurate guidance for\nmulti-view fusion. Extensive experiments demonstrated that DBGCN outperforms\nthe state-of-the-art graph-level clustering methods on six benchmark datasets.\n", "date": "2025-04-08", "categories": []}
{"id": "2504.09449", "title": "aweSOM: a CPU/GPU-accelerated Self-organizing Map and Statistically\n  Combined Ensemble Framework for Machine-learning Clustering Analysis", "abstract": "  We introduce aweSOM, an open-source Python package for machine learning (ML)\nclustering and classification, using a Self-organizing Maps (SOM) algorithm\nthat incorporates CPU/GPU acceleration to accommodate large ($N > 10^6$, where\n$N$ is the number of data points), multidimensional datasets. aweSOM consists\nof two main modules, one that handles the initialization and training of the\nSOM, and another that stacks the results of multiple SOM realizations to obtain\nmore statistically robust clusters. Existing Python-based SOM implementations\n(e.g., POPSOM, Yuan (2018); MiniSom, Vettigli (2018); sklearn-som) primarily\nserve as proof-of-concept demonstrations, optimized for smaller datasets, but\nlacking scalability for large, multidimensional data. aweSOM provides a\nsolution for this gap in capability, with good performance scaling up to $\\sim\n10^8$ individual points, and capable of utilizing multiple features per point.\nWe compare the code performance against the legacy implementations it is based\non, and find a 10-100x speed up, as well as significantly improved memory\nefficiency, due to several built-in optimizations.\n", "date": "2025-04-13", "categories": []}
{"id": "2504.10109", "title": "Lightweight Trustworthy Distributed Clustering", "abstract": "  Ensuring data trustworthiness within individual edge nodes while facilitating\ncollaborative data processing poses a critical challenge in edge computing\nsystems (ECS), particularly in resource-constrained scenarios such as\nautonomous systems sensor networks, industrial IoT, and smart cities. This\npaper presents a lightweight, fully distributed k-means clustering algorithm\nspecifically adapted for edge environments, leveraging a distributed averaging\napproach with additive secret sharing, a secure multiparty computation\ntechnique, during the cluster center update phase to ensure the accuracy and\ntrustworthiness of data across nodes.\n", "date": "2025-04-14", "categories": []}
{"id": "2411.00870", "title": "K-Means Clustering With Incomplete Data with the Use of Mahalanobis\n  Distances", "abstract": "  Effectively applying the K-means algorithm to clustering tasks with\nincomplete features remains an important research area due to its impact on\nreal-world applications. Recent work has shown that unifying K-means clustering\nand imputation into one single objective function and solving the resultant\noptimization yield superior results compared to handling imputation and\nclustering separately.\n  In this work, we extend this approach by developing a unified K-means\nalgorithm that incorporates Mahalanobis distances, instead of the traditional\nEuclidean distances, which previous research has shown to perform better for\nclusters with elliptical shapes.\n  We conducted extensive experiments on synthetic datasets containing up to ten\nelliptical clusters, as well as the IRIS dataset. Using the Adjusted Rand Index\n(ARI) and Normalized Mutual Information (NMI), we demonstrate that our\nalgorithm consistently outperforms both standalone imputation followed by\nK-means (using either Mahalanobis or Euclidean distance) and K-Means with\nIncomplete Data, the recent K-means algorithms that integrate imputation and\nclustering for handling incomplete data. These results hold across both the\nIRIS dataset and randomly generated data with elliptical clusters.\n", "date": "2024-10-31", "categories": []}
{"id": "2412.03332", "title": "On Approximability of $\\ell_2^2$ Min-Sum Clustering", "abstract": "  The $\\ell_2^2$ min-sum $k$-clustering problem is to partition an input set\ninto clusters $C_1,\\ldots,C_k$ to minimize $\\sum_{i=1}^k\\sum_{p,q\\in\nC_i}\\|p-q\\|_2^2$. Although $\\ell_2^2$ min-sum $k$-clustering is NP-hard, it is\nnot known whether it is NP-hard to approximate $\\ell_2^2$ min-sum\n$k$-clustering beyond a certain factor.\n  In this paper, we give the first hardness-of-approximation result for the\n$\\ell_2^2$ min-sum $k$-clustering problem. We show that it is NP-hard to\napproximate the objective to a factor better than $1.056$ and moreover,\nassuming a balanced variant of the Johnson Coverage Hypothesis, it is NP-hard\nto approximate the objective to a factor better than 1.327.\n  We then complement our hardness result by giving a nearly linear time\nparameterized PTAS for $\\ell_2^2$ min-sum $k$-clustering running in time\n$O\\left(n^{1+o(1)}d\\cdot \\exp((k\\cdot\\varepsilon^{-1})^{O(1)})\\right)$, where\n$d$ is the underlying dimension of the input dataset.\n  Finally, we consider a learning-augmented setting, where the algorithm has\naccess to an oracle that outputs a label $i\\in[k]$ for input point, thereby\nimplicitly partitioning the input dataset into $k$ clusters that induce an\napproximately optimal solution, up to some amount of adversarial error\n$\\alpha\\in\\left[0,\\frac{1}{2}\\right)$. We give a polynomial-time algorithm that\noutputs a $\\frac{1+\\gamma\\alpha}{(1-\\alpha)^2}$-approximation to $\\ell_2^2$\nmin-sum $k$-clustering, for a fixed constant $\\gamma>0$.\n", "date": "2024-12-04", "categories": []}
{"id": "2310.12806", "title": "DCSI -- An improved measure of cluster separability based on separation\n  and connectedness", "abstract": "  Whether class labels in a given data set correspond to meaningful clusters is\ncrucial for the evaluation of clustering algorithms using real-world data sets.\nThis property can be quantified by separability measures. The central aspects\nof separability for density-based clustering are between-class separation and\nwithin-class connectedness, and neither classification-based complexity\nmeasures nor cluster validity indices (CVIs) adequately incorporate them. A\nnewly developed measure (density cluster separability index, DCSI) aims to\nquantify these two characteristics and can also be used as a CVI. Extensive\nexperiments on synthetic data indicate that DCSI correlates strongly with the\nperformance of DBSCAN measured via the adjusted Rand index (ARI) but lacks\nrobustness when it comes to multi-class data sets with overlapping classes that\nare ill-suited for density-based hard clustering. Detailed evaluation on\nfrequently used real-world data sets shows that DCSI can correctly identify\ntouching or overlapping classes that do not correspond to meaningful\ndensity-based clusters.\n", "date": "2023-10-19", "categories": []}
{"id": "2504.07578", "title": "Privacy-Preserving Vertical K-Means Clustering", "abstract": "  Clustering is a fundamental data processing task used for grouping records\nbased on one or more features. In the vertically partitioned setting, data is\ndistributed among entities, with each holding only a subset of those features.\nA key challenge in this scenario is that computing distances between records\nrequires access to all distributed features, which may be privacy-sensitive and\ncannot be directly shared with other parties. The goal is to compute the joint\nclusters while preserving the privacy of each entity's dataset. Existing\nsolutions using secret sharing or garbled circuits implement privacy-preserving\nvariants of Lloyd's algorithm but incur high communication costs, scaling as\nO(nkt), where n is the number of data points, k the number of clusters, and t\nthe number of rounds. These methods become impractical for large datasets or\nseveral parties, limiting their use to LAN settings only. On the other hand, a\ndifferent line of solutions rely on differential privacy (DP) to outsource the\nlocal features of the parties to a central server. However, they often\nsignificantly degrade the utility of the clustering outcome due to excessive\nnoise. In this work, we propose a novel solution based on homomorphic\nencryption and DP, reducing communication complexity to O(n+kt). In our method,\nparties securely outsource their features once, allowing a computing party to\nperform clustering operations under encryption. DP is applied only to the\nclusters' centroids, ensuring privacy with minimal impact on utility. Our\nsolution clusters 100,000 two-dimensional points into five clusters using only\n73MB of communication, compared to 101GB for existing works, and completes in\njust under 3 minutes on a 100Mbps network, whereas existing works take over 1\nday. This makes our solution practical even for WAN deployments, all while\nmaintaining accuracy comparable to plaintext k-means algorithms.\n", "date": "2025-04-10", "categories": []}
{"id": "2504.04079", "title": "Scalable Robust Bayesian Co-Clustering with Compositional ELBOs", "abstract": "  Co-clustering exploits the duality of instances and features to\nsimultaneously uncover meaningful groups in both dimensions, often\noutperforming traditional clustering in high-dimensional or sparse data\nsettings. Although recent deep learning approaches successfully integrate\nfeature learning and cluster assignment, they remain susceptible to noise and\ncan suffer from posterior collapse within standard autoencoders. In this paper,\nwe present the first fully variational Co-clustering framework that directly\nlearns row and column clusters in the latent space, leveraging a doubly\nreparameterized ELBO to improve gradient signal-to-noise separation. Our\nunsupervised model integrates a Variational Deep Embedding with a Gaussian\nMixture Model (GMM) prior for both instances and features, providing a built-in\nclustering mechanism that naturally aligns latent modes with row and column\nclusters. Furthermore, our regularized end-to-end noise learning Compositional\nELBO architecture jointly reconstructs the data while regularizing against\nnoise through the KL divergence, thus gracefully handling corrupted or missing\ninputs in a single training pipeline. To counteract posterior collapse, we\nintroduce a scale modification that increases the encoder's latent means only\nin the reconstruction pathway, preserving richer latent representations without\ninflating the KL term. Finally, a mutual information-based cross-loss ensures\ncoherent co-clustering of rows and columns. Empirical results on diverse\nreal-world datasets from multiple modalities, numerical, textual, and\nimage-based, demonstrate that our method not only preserves the advantages of\nprior Co-clustering approaches but also exceeds them in accuracy and\nrobustness, particularly in high-dimensional or noisy settings.\n", "date": "2025-04-05", "categories": []}
{"id": "2504.05320", "title": "Document clustering with evolved multiword search queries", "abstract": "  Text clustering holds significant value across various domains due to its\nability to identify patterns and group related information. Current approaches\nwhich rely heavily on a computed similarity measure between documents are often\nlimited in accuracy and interpretability. We present a novel approach to the\nproblem based on a set of evolved search queries. Clusters are formed as the\nset of documents matched by a single search query in the set of queries. The\nqueries are optimized to maximize the number of documents returned and to\nminimize the overlap between clusters (documents returned by more than one\nquery). Where queries contain more than one word they are interpreted\ndisjunctively. We have found it useful to assign one word to be the root and\nconstrain the query construction such that the set of documents returned by any\nadditional query words intersect with the set returned by the root word. Not\nall documents in a collection are returned by any of the search queries in a\nset, so once the search query evolution is completed a second stage is\nperformed whereby a KNN algorithm is applied to assign all unassigned documents\nto their nearest cluster. We describe the method and present results using 8\ntext datasets comparing effectiveness with well-known existing algorithms. We\nnote that as well as achieving the highest accuracy on these datasets the\nsearch query format provides the qualitative benefits of being interpretable\nand modifiable whilst providing a causal explanation of cluster construction.\n", "date": "2025-02-24", "categories": []}
{"id": "2312.11952", "title": "Automatic Parameter Selection for Non-Redundant Clustering", "abstract": "  High-dimensional datasets often contain multiple meaningful clusterings in\ndifferent subspaces. For example, objects can be clustered either by color,\nweight, or size, revealing different interpretations of the given dataset. A\nvariety of approaches are able to identify such non-redundant clusterings.\nHowever, most of these methods require the user to specify the expected number\nof subspaces and clusters for each subspace. Stating these values is a\nnon-trivial problem and usually requires detailed knowledge of the input\ndataset. In this paper, we propose a framework that utilizes the Minimum\nDescription Length Principle (MDL) to detect the number of subspaces and\nclusters per subspace automatically. We describe an efficient procedure that\ngreedily searches the parameter space by splitting and merging subspaces and\nclusters within subspaces. Additionally, an encoding strategy is introduced\nthat allows us to detect outliers in each subspace. Extensive experiments show\nthat our approach is highly competitive to state-of-the-art methods.\n", "date": "2023-12-19", "categories": []}
{"id": "2504.03928", "title": "Random Normed k-Means: A Paradigm-Shift in Clustering within\n  Probabilistic Metric Spaces", "abstract": "  Existing approaches remain largely constrained by traditional distance\nmetrics, limiting their effectiveness in handling random data. In this work, we\nintroduce the first k-means variant in the literature that operates within a\nprobabilistic metric space, replacing conventional distance measures with a\nwell-defined distance distribution function. This pioneering approach enables\nmore flexible and robust clustering in both deterministic and random datasets,\nestablishing a new foundation for clustering in stochastic environments. By\nadopting a probabilistic perspective, our method not only introduces a fresh\nparadigm but also establishes a rigorous theoretical framework that is expected\nto serve as a key reference for future clustering research involving random\ndata. Extensive experiments on diverse real and synthetic datasets assess our\nmodel's effectiveness using widely recognized evaluation metrics, including\nSilhouette, Davies-Bouldin, Calinski Harabasz, the adjusted Rand index, and\ndistortion. Comparative analyses against established methods such as k-means++,\nfuzzy c-means, and kernel probabilistic k-means demonstrate the superior\nperformance of our proposed random normed k-means (RNKM) algorithm. Notably,\nRNKM exhibits a remarkable ability to identify nonlinearly separable\nstructures, making it highly effective in complex clustering scenarios. These\nfindings position RNKM as a groundbreaking advancement in clustering research,\noffering a powerful alternative to traditional techniques while addressing a\nlong-standing gap in the literature. By bridging probabilistic metrics with\nclustering, this study provides a foundational reference for future\ndevelopments and opens new avenues for advanced data analysis in dynamic,\ndata-driven applications.\n", "date": "2025-04-04", "categories": []}
{"id": "2504.04314", "title": "Balancing Complexity and Informativeness in LLM-Based Clustering:\n  Finding the Goldilocks Zone", "abstract": "  The challenge of clustering short text data lies in balancing informativeness\nwith interpretability. Traditional evaluation metrics often overlook this\ntrade-off. Inspired by linguistic principles of communicative efficiency, this\npaper investigates the optimal number of clusters by quantifying the trade-off\nbetween informativeness and cognitive simplicity. We use large language models\n(LLMs) to generate cluster names and evaluate their effectiveness through\nsemantic density, information theory, and clustering accuracy. Our results show\nthat Gaussian Mixture Model (GMM) clustering on embeddings generated by a LLM,\nincreases semantic density compared to random assignment, effectively grouping\nsimilar bios. However, as clusters increase, interpretability declines, as\nmeasured by a generative LLM's ability to correctly assign bios based on\ncluster names. A logistic regression analysis confirms that classification\naccuracy depends on the semantic similarity between bios and their assigned\ncluster names, as well as their distinction from alternatives.\n  These findings reveal a \"Goldilocks zone\" where clusters remain distinct yet\ninterpretable. We identify an optimal range of 16-22 clusters, paralleling\nlinguistic efficiency in lexical categorization. These insights inform both\ntheoretical models and practical applications, guiding future research toward\noptimising cluster interpretability and usefulness.\n", "date": "2025-04-06", "categories": []}
{"id": "2504.04676", "title": "Dual Consistent Constraint via Disentangled Consistency and\n  Complementarity for Multi-view Clustering", "abstract": "  Multi-view clustering can explore common semantics from multiple views and\nhas received increasing attention in recent years. However, current methods\nfocus on learning consistency in representation, neglecting the contribution of\neach view's complementarity aspect in representation learning. This limit poses\na significant challenge in multi-view representation learning. This paper\nproposes a novel multi-view clustering framework that introduces a disentangled\nvariational autoencoder that separates multi-view into shared and private\ninformation, i.e., consistency and complementarity information. We first learn\ninformative and consistent representations by maximizing mutual information\nacross different views through contrastive learning. This process will ignore\ncomplementary information. Then, we employ consistency inference constraints to\nexplicitly utilize complementary information when attempting to seek the\nconsistency of shared information across all views. Specifically, we perform a\nwithin-reconstruction using the private and shared information of each view and\na cross-reconstruction using the shared information of all views. The dual\nconsistency constraints are not only effective in improving the representation\nquality of data but also easy to extend to other scenarios, especially in\ncomplex multi-view scenes. This could be the first attempt to employ dual\nconsistent constraint in a unified MVC theoretical framework. During the\ntraining procedure, the consistency and complementarity features are jointly\noptimized. Extensive experiments show that our method outperforms baseline\nmethods.\n", "date": "2025-04-07", "categories": []}
{"id": "2504.05125", "title": "Interpretable Style Takagi-Sugeno-Kang Fuzzy Clustering", "abstract": "  Clustering is an efficient and essential technique for exploring latent\nknowledge of data. However, limited attention has been given to the\ninterpretability of the clusters detected by most clustering algorithms. In\naddition, due to the homogeneity of data, different groups of data have their\nown homogeneous styles. In this paper, the above two aspects are considered,\nand an interpretable style Takagi-Sugeno-Kang (TSK) fuzzy clustering\n(IS-TSK-FC) algorithm is proposed. The clustering behavior of IS-TSK-FC is\nfully guided by the TSK fuzzy inference on fuzzy rules. In particular, samples\nare grouped into clusters represented by the corresponding consequent vectors\nof all fuzzy rules learned in an unsupervised manner. This can explain how the\nclusters are generated in detail, thus making the underlying decision-making\nprocess of the IS-TSK-FC interpretable. Moreover, a series of style matrices\nare introduced to facilitate the consequents of fuzzy rules in IS-TSK-FC by\ncapturing the styles of clusters as well as the nuances between different\nstyles. Consequently, all the fuzzy rules in IS-TSK-FC have powerful data\nrepresentation capability. After determining the antecedents of all the fuzzy\nrules, the optimization problem of IS-TSK-FC can be iteratively solved in an\nalternation manner. The effectiveness of IS-TSK-FC as an interpretable\nclustering tool is validated through extensive experiments on benchmark\ndatasets with unknown implicit/explicit styles. Specially, the superior\nclustering performance of IS-TSK-FC is demonstrated on case studies where\ndifferent groups of data present explicit styles. The source code of IS-TSK-FC\ncan be downloaded from https://github.com/gusuhang10/IS-TSK-FC.\n", "date": "2025-04-07", "categories": []}
{"id": "2312.12050", "title": "Extension of the Dip-test Repertoire -- Efficient and Differentiable\n  p-value Calculation for Clustering", "abstract": "  Over the last decade, the Dip-test of unimodality has gained increasing\ninterest in the data mining community as it is a parameter-free statistical\ntest that reliably rates the modality in one-dimensional samples. It returns a\nso called Dip-value and a corresponding probability for the sample's\nunimodality (Dip-p-value). These two values share a sigmoidal relationship.\nHowever, the specific transformation is dependent on the sample size. Many\nDip-based clustering algorithms use bootstrapped look-up tables translating\nDip- to Dip-p-values for a certain limited amount of sample sizes. We propose a\nspecifically designed sigmoid function as a substitute for these\nstate-of-the-art look-up tables. This accelerates computation and provides an\napproximation of the Dip- to Dip-p-value transformation for every single sample\nsize. Further, it is differentiable and can therefore easily be integrated in\nlearning schemes using gradient descent. We showcase this by exploiting our\nfunction in a novel subspace clustering algorithm called Dip'n'Sub. We\nhighlight in extensive experiments the various benefits of our proposal.\n", "date": "2023-12-19", "categories": []}
{"id": "2403.02998", "title": "Towards Calibrated Deep Clustering Network", "abstract": "  Deep clustering has exhibited remarkable performance; however, the over\nconfidence problem, i.e., the estimated confidence for a sample belonging to a\nparticular cluster greatly exceeds its actual prediction accuracy, has been\nover looked in prior research. To tackle this critical issue, we pioneer the\ndevelopment of a calibrated deep clustering framework. Specifically, we propose\na novel dual head (calibration head and clustering head) deep clustering model\nthat can effectively calibrate the estimated confidence and the actual\naccuracy. The calibration head adjusts the overconfident predictions of the\nclustering head, generating prediction confidence that matches the model\nlearning status. Then, the clustering head dynamically selects reliable\nhigh-confidence samples estimated by the calibration head for pseudo-label\nself-training. Additionally, we introduce an effective network initialization\nstrategy that enhances both training speed and network robustness. The\neffectiveness of the proposed calibration approach and initialization strategy\nare both endorsed with solid theoretical guarantees. Extensive experiments\ndemonstrate the proposed calibrated deep clustering model not only surpasses\nthe state-of-the-art deep clustering methods by 5x on average in terms of\nexpected calibration error, but also significantly outperforms them in terms of\nclustering accuracy. The code is available at\nhttps://github.com/ChengJianH/CDC.\n", "date": "2024-03-04", "categories": []}
{"id": "2504.01605", "title": "Multi-Relation Graph-Kernel Strengthen Network for Graph-Level\n  Clustering", "abstract": "  Graph-level clustering is a fundamental task of data mining, aiming at\ndividing unlabeled graphs into distinct groups. However, existing deep methods\nthat are limited by pooling have difficulty extracting diverse and complex\ngraph structure features, while traditional graph kernel methods rely on\nexhaustive substructure search, unable to adaptive handle multi-relational\ndata. This limitation hampers producing robust and representative graph-level\nembeddings. To address this issue, we propose a novel Multi-Relation\nGraph-Kernel Strengthen Network for Graph-Level Clustering (MGSN), which\nintegrates multi-relation modeling with graph kernel techniques to fully\nleverage their respective advantages. Specifically, MGSN constructs\nmulti-relation graphs to capture diverse semantic relationships between nodes\nand graphs, which employ graph kernel methods to extract graph similarity\nfeatures, enriching the representation space. Moreover, a relation-aware\nrepresentation refinement strategy is designed, which adaptively aligns\nmulti-relation information across views while enhancing graph-level features\nthrough a progressive fusion process. Extensive experiments on multiple\nbenchmark datasets demonstrate the superiority of MGSN over state-of-the-art\nmethods. The results highlight its ability to leverage multi-relation\nstructures and graph kernel features, establishing a new paradigm for robust\ngraph-level clustering.\n", "date": "2025-04-02", "categories": []}
{"id": "2403.13846", "title": "A Clustering Method with Graph Maximum Decoding Information", "abstract": "  The clustering method based on graph models has garnered increased attention\nfor its widespread applicability across various knowledge domains. Its\nadaptability to integrate seamlessly with other relevant applications endows\nthe graph model-based clustering analysis with the ability to robustly extract\n\"natural associations\" or \"graph structures\" within datasets, facilitating the\nmodelling of relationships between data points. Despite its efficacy, the\ncurrent clustering method utilizing the graph-based model overlooks the\nuncertainty associated with random walk access between nodes and the embedded\nstructural information in the data. To address this gap, we present a novel\nClustering method for Maximizing Decoding Information within graph-based\nmodels, named CMDI. CMDI innovatively incorporates two-dimensional structural\ninformation theory into the clustering process, consisting of two phases: graph\nstructure extraction and graph vertex partitioning. Within CMDI, graph\npartitioning is reformulated as an abstract clustering problem, leveraging\nmaximum decoding information to minimize uncertainty associated with random\nvisits to vertices. Empirical evaluations on three real-world datasets\ndemonstrate that CMDI outperforms classical baseline methods, exhibiting a\nsuperior decoding information ratio (DI-R). Furthermore, CMDI showcases\nheightened efficiency, particularly when considering prior knowledge (PK).\nThese findings underscore the effectiveness of CMDI in enhancing decoding\ninformation quality and computational efficiency, positioning it as a valuable\ntool in graph-based clustering analyses.\n", "date": "2024-03-18", "categories": []}
{"id": "2502.02234", "title": "Mask-informed Deep Contrastive Incomplete Multi-view Clustering", "abstract": "  Multi-view clustering (MvC) utilizes information from multiple views to\nuncover the underlying structures of data. Despite significant advancements in\nMvC, mitigating the impact of missing samples in specific views on the\nintegration of knowledge from different views remains a critical challenge.\nThis paper proposes a novel Mask-informed Deep Contrastive Incomplete\nMulti-view Clustering (Mask-IMvC) method, which elegantly identifies a\nview-common representation for clustering. Specifically, we introduce a\nmask-informed fusion network that aggregates incomplete multi-view information\nwhile considering the observation status of samples across various views as a\nmask, thereby reducing the adverse effects of missing values. Additionally, we\ndesign a prior knowledge-assisted contrastive learning loss that boosts the\nrepresentation capability of the aggregated view-common representation by\ninjecting neighborhood information of samples from different views. Finally,\nextensive experiments are conducted to demonstrate the superiority of the\nproposed Mask-IMvC method over state-of-the-art approaches across multiple MvC\ndatasets, both in complete and incomplete scenarios.\n", "date": "2025-02-04", "categories": []}
{"id": "2503.22932", "title": "Bi-Level Multi-View fuzzy Clustering with Exponential Distance", "abstract": "  In this study, we propose extension of fuzzy c-means (FCM) clustering in\nmulti-view environments. First, we introduce an exponential multi-view FCM\n(E-MVFCM). E-MVFCM is a centralized MVC with consideration to heat-kernel\ncoefficients (H-KC) and weight factors. Secondly, we propose an exponential\nbi-level multi-view fuzzy c-means clustering (EB-MVFCM). Different to E-MVFCM,\nEB-MVFCM does automatic computation of feature and weight factors\nsimultaneously. Like E-MVFCM, EB-MVFCM present explicit forms of the H-KC to\nsimplify the generation of the heat-kernel $\\mathcal{K}(t)$ in powers of the\nproper time $t$ during the clustering process. All the features used in this\nstudy, including tools and functions of proposed algorithms will be made\navailable at https://www.github.com/KristinaP09/EB-MVFCM.\n", "date": "2025-03-29", "categories": []}
{"id": "2503.24012", "title": "Tree-Guided $L_1$-Convex Clustering", "abstract": "  Convex clustering is a modern clustering framework that guarantees globally\noptimal solutions and performs comparably to other advanced clustering methods.\nHowever, obtaining a complete dendrogram (clusterpath) for large-scale datasets\nremains computationally challenging due to the extensive costs associated with\niterative optimization approaches. To address this limitation, we develop a\nnovel convex clustering algorithm called Tree-Guided $L_1$-Convex Clustering\n(TGCC). We first focus on the fact that the loss function of $L_1$-convex\nclustering with tree-structured weights can be efficiently optimized using a\ndynamic programming approach. We then develop an efficient cluster fusion\nalgorithm that utilizes the tree structure of the weights to accelerate the\noptimization process and eliminate the issue of cluster splits commonly\nobserved in convex clustering. By combining the dynamic programming approach\nwith the cluster fusion algorithm, the TGCC algorithm achieves superior\ncomputational efficiency without sacrificing clustering performance.\nRemarkably, our TGCC algorithm can construct a complete clusterpath for $10^6$\npoints in $\\mathbb{R}^2$ within 15 seconds on a standard laptop without the\nneed for parallel or distributed computing frameworks. Moreover, we extend the\nTGCC algorithm to develop biclustering and sparse convex clustering algorithms.\n", "date": "2025-03-31", "categories": []}
{"id": "2503.21431", "title": "Nearest Neighbour Equilibrium Clustering", "abstract": "  A novel and intuitive nearest neighbours based clustering algorithm is\nintroduced, in which a cluster is defined in terms of an equilibrium condition\nwhich balances its size and cohesiveness. The formulation of the equilibrium\ncondition allows for a quantification of the strength of alignment of each\npoint to a cluster, with these cluster alignment strengths leading naturally to\na model selection criterion which renders the proposed approach fully\nautomatable. The algorithm is simple to implement and computationally\nefficient, and produces clustering solutions of extremely high quality in\ncomparison with relevant benchmarks from the literature. R code to implement\nthe approach is available from https://github.com/DavidHofmeyr/NNEC.\n", "date": "2025-03-27", "categories": []}
{"id": "2503.22211", "title": "Fuzzy Cluster-Aware Contrastive Clustering for Time Series", "abstract": "  The rapid growth of unlabeled time series data, driven by the Internet of\nThings (IoT), poses significant challenges in uncovering underlying patterns.\nTraditional unsupervised clustering methods often fail to capture the complex\nnature of time series data. Recent deep learning-based clustering approaches,\nwhile effective, struggle with insufficient representation learning and the\nintegration of clustering objectives. To address these issues, we propose a\nfuzzy cluster-aware contrastive clustering framework (FCACC) that jointly\noptimizes representation learning and clustering.\n  Our approach introduces a novel three-view data augmentation strategy to\nenhance feature extraction by leveraging various characteristics of time series\ndata. Additionally, we propose a cluster-aware hard negative sample generation\nmechanism that dynamically constructs high-quality negative samples using\nclustering structure information, thereby improving the model's discriminative\nability.\n  By leveraging fuzzy clustering, FCACC dynamically generates cluster\nstructures to guide the contrastive learning process, resulting in more\naccurate clustering. Extensive experiments on 40 benchmark datasets show that\nFCACC outperforms the selected baseline methods (eight in total), providing an\neffective solution for unsupervised time series learning.\n", "date": "2025-03-28", "categories": []}
{"id": "2503.20488", "title": "Adaptive Local Clustering over Attributed Graphs", "abstract": "  Given a graph $G$ and a seed node $v_s$, the objective of local graph\nclustering (LGC) is to identify a subgraph $C_s \\in G$ (a.k.a. local cluster)\nsurrounding $v_s$ in time roughly linear with the size of $C_s$. This approach\nyields personalized clusters without needing to access the entire graph, which\nmakes it highly suitable for numerous applications involving large graphs.\nHowever, most existing solutions merely rely on the topological connectivity\nbetween nodes in $G$, rendering them vulnerable to missing or noisy links that\nare commonly present in real-world graphs.\n  To address this issue, this paper resorts to leveraging the complementary\nnature of graph topology and node attributes to enhance local clustering\nquality. To effectively exploit the attribute information, we first formulate\nthe LGC as an estimation of the bidirectional diffusion distribution (BDD),\nwhich is specialized for capturing the multi-hop affinity between nodes in the\npresence of attributes. Furthermore, we propose LACA, an efficient and\neffective approach for LGC that achieves superb empirical performance on\nmultiple real datasets while maintaining strong locality. The core components\nof LACA include (i) a fast and theoretically-grounded preprocessing technique\nfor node attributes, (ii) an adaptive algorithm for diffusing any vectors over\n$G$ with rigorous theoretical guarantees and expedited convergence, and (iii)\nan effective three-step scheme for BDD approximation. Extensive experiments,\ncomparing 17 competitors on 8 real datasets, show that LACA outperforms all\ncompetitors in terms of result quality measured against ground truth local\nclusters, while also being up to orders of magnitude faster. The code is\navailable at https://github.com/HaoranZ99/alac.\n", "date": "2025-03-26", "categories": []}
{"id": "2503.19067", "title": "Clustering data by reordering them", "abstract": "  Grouping elements into families to analyse them separately is a standard\nanalysis procedure in many areas of sciences. We propose herein a new algorithm\nbased on the simple idea that members from a family look like each other, and\ndon't resemble elements foreign to the family. After reordering the data\naccording to the distance between elements, the analysis is automatically\nperformed with easily-understandable parameters. Noise is explicitly taken into\naccount to deal with the variety of problems of a data-driven world. We applied\nthe algorithm to sort biomolecules conformations, gene sequences, cells,\nimages, and experimental conditions.\n", "date": "2025-03-24", "categories": []}
{"id": "2503.19324", "title": "How to optimize K-means?", "abstract": "  Center-based clustering algorithms (e.g., K-means) are popular for clustering\ntasks, but they usually struggle to achieve high accuracy on complex datasets.\nWe believe the main reason is that traditional center-based clustering\nalgorithms identify only one clustering center in each cluster. Once the\ndistribution of the dataset is complex, a single clustering center cannot\nstrongly represent distant objects within the cluster. How to optimize the\nexisting center-based clustering algorithms will be valuable research. In this\npaper, we propose a general optimization method called ECAC, and it can\noptimize different center-based clustering algorithms. ECAC is independent of\nthe clustering principle and is embedded as a component between the center\nprocess and the category assignment process of center-based clustering\nalgorithms. Specifically, ECAC identifies several extended-centers for each\nclustering center. The extended-centers will act as relays to expand the\nrepresentative capability of the clustering center in the complex cluster, thus\nimproving the accuracy of center-based clustering algorithms. We conducted\nnumerous experiments to verify the robustness and effectiveness of ECAC. ECAC\nis robust to diverse datasets and diverse clustering centers. After ECAC\noptimization, the accuracy (NMI as well as RI) of center-based clustering\nalgorithms improves by an average of 33.4% and 64.1%, respectively, and even\nK-means accurately identifies complex-shaped clusters.\n", "date": "2025-03-25", "categories": []}
{"id": "2412.07217", "title": "Incremental Gaussian Mixture Clustering for Data Streams", "abstract": "  The problem of analyzing data streams of very large volumes is important and\nis very desirable for many application domains. In this paper we present and\ndemonstrate effective working of an algorithm to find clusters and anomalous\ndata points in a streaming datasets. Entropy minimization is used as a\ncriterion for defining and updating clusters formed from a streaming dataset.\nAs the clusters are formed we also identify anomalous datapoints that show up\nfar away from all known clusters. With a number of 2-D datasets we demonstrate\nthe effectiveness of discovering the clusters and also identifying anomalous\ndata points.\n", "date": "2024-12-10", "categories": []}
{"id": "2503.17633", "title": "Enhancing Martian Terrain Recognition with Deep Constrained Clustering", "abstract": "  Martian terrain recognition is pivotal for advancing our understanding of\ntopography, geomorphology, paleoclimate, and habitability. While deep\nclustering methods have shown promise in learning semantically homogeneous\nfeature embeddings from Martian rover imagery, the natural variations in\nintensity, scale, and rotation pose significant challenges for accurate terrain\nclassification. To address these limitations, we propose Deep Constrained\nClustering with Metric Learning (DCCML), a novel algorithm that leverages\nmultiple constraint types to guide the clustering process. DCCML incorporates\nsoft must-link constraints derived from spatial and depth similarities between\nneighboring patches, alongside hard constraints from stereo camera pairs and\ntemporally adjacent images. Experimental evaluation on the Curiosity rover\ndataset (with 150 clusters) demonstrates that DCCML increases homogeneous\nclusters by 16.7 percent while reducing the Davies-Bouldin Index from 3.86 to\n1.82 and boosting retrieval accuracy from 86.71 percent to 89.86 percent. This\nimprovement enables more precise classification of Martian geological features,\nadvancing our capacity to analyze and understand the planet's landscape.\n", "date": "2025-03-22", "categories": []}
{"id": "2501.07729", "title": "Autoencoded UMAP-Enhanced Clustering for Unsupervised Learning", "abstract": "  We propose a novel approach to unsupervised learning by constructing a\nnon-linear embedding of the data into a low-dimensional space followed by any\nconventional clustering algorithm. The embedding promotes clusterability of the\ndata and is comprised of two mappings: the encoder of an autoencoder neural\nnetwork and the output of UMAP algorithm. The autoencoder is trained with a\ncomposite loss function that incorporates both a conventional data\nreconstruction as a regularization component and a clustering-promoting\ncomponent built using the spectral graph theory. The two embeddings and the\nsubsequent clustering are integrated into a three-stage unsupervised learning\nframework, referred to as Autoencoded UMAP-Enhanced Clustering (AUEC). When\napplied to MNIST data, AUEC significantly outperforms the state-of-the-art\ntechniques in terms of clustering accuracy.\n", "date": "2025-01-13", "categories": []}
{"id": "2503.15777", "title": "Line Space Clustering (LSC): Feature-Based Clustering using K-medians\n  and Dynamic Time Warping for Versatility", "abstract": "  Clustering high-dimensional data is a critical challenge in machine learning\ndue to the curse of dimensionality and the presence of noise. Traditional\nclustering algorithms often fail to capture the intrinsic structures in such\ndata. This paper explores a combination of clustering methods, which we called\nLine Space Clustering (LSC), a representation that transforms data points into\nlines in a newly defined feature space, enabling clustering based on the\nsimilarity of feature value patterns, essentially treating features as\nsequences. LSC employs a combined distance metric that uses Euclidean and\nDynamic Time Warping (DTW) distances, weighted by a parameter {\\alpha},\nallowing flexibility in emphasizing shape or magnitude similarities. We delve\ndeeply into the mechanics of DTW and the Savitzky Golay filter, explaining\ntheir roles in the algorithm. Extensive experiments demonstrate the efficacy of\nLSC on synthetic and real-world datasets, showing that randomly experimenting\nwith time-series optimized methods sometimes might surprisingly work on a\ncomplex dataset, particularly in noisy environments.\n  Source code and experiments are available at:\nhttps://github.com/JoanikijChulev/LSC.\n", "date": "2025-03-20", "categories": []}
{"id": "2410.18113", "title": "Scalable Co-Clustering for Large-Scale Data through Dynamic Partitioning\n  and Hierarchical Merging", "abstract": "  Co-clustering simultaneously clusters rows and columns, revealing more\nfine-grained groups. However, existing co-clustering methods suffer from poor\nscalability and cannot handle large-scale data. This paper presents a novel and\nscalable co-clustering method designed to uncover intricate patterns in\nhigh-dimensional, large-scale datasets. Specifically, we first propose a large\nmatrix partitioning algorithm that partitions a large matrix into smaller\nsubmatrices, enabling parallel co-clustering. This method employs a\nprobabilistic model to optimize the configuration of submatrices, balancing the\ncomputational efficiency and depth of analysis. Additionally, we propose a\nhierarchical co-cluster merging algorithm that efficiently identifies and\nmerges co-clusters from these submatrices, enhancing the robustness and\nreliability of the process. Extensive evaluations validate the effectiveness\nand efficiency of our method. Experimental results demonstrate a significant\nreduction in computation time, with an approximate 83% decrease for dense\nmatrices and up to 30% for sparse matrices.\n", "date": "2024-10-09", "categories": []}
{"id": "2401.10927", "title": "Semidefinite programming relaxations and debiasing for MAXCUT-based\n  clustering", "abstract": "  In this paper, we consider the problem of partitioning a small data sample of\nsize $n$ drawn from a mixture of 2 sub-gaussian distributions in $\\R^p$. We\nconsider semidefinite programming relaxations of an integer quadratic program\nthat is formulated as finding the maximum cut on a graph, where edge weights in\nthe cut represent dissimilarity scores between two nodes based on their $p$\nfeatures. We are interested in the case that individual features are of low\naverage quality $\\gamma$, and we want to use as few of them as possible to\ncorrectly partition the sample. Denote by $\\Delta^2:=p \\gamma$ the $\\ell_2^2$\ndistance between two centers (mean vectors) in $\\R^p$. The goal is to allow a\nfull range of tradeoffs between $n, p, \\gamma$ in the sense that partial\nrecovery (success rate $< 100%$) is feasible once the signal to noise ratio\n$s^2 := \\min{np \\gamma^2, \\Delta^2}$ is lower bounded by a constant. For both\nbalanced and unbalanced cases, we allow each population to have distinct\ncovariance structures with diagonal matrices as special cases. In the present\nwork, (a) we provide a unified framework for analyzing three computationally\nefficient algorithms, namely, SDP1, BalancedSDP, and Spectral clustering; and\n(b) we prove that the misclassification error decays exponentially with respect\nto the SNR $s^2$ for SDP1. Moreover, for balanced partitions, we design an\nestimator $\\bf {BalancedSDP}$ with a superb debiasing property. Indeed, with\nthis new estimator, we remove an assumption (A2) on bounding the trace\ndifference between the two population covariance matrices while proving the\nexponential error bound as stated above. These estimators and their statistical\nanalyses are novel to the best of our knowledge. We provide simulation evidence\nilluminating the theoretical predictions.\n", "date": "2024-01-16", "categories": []}
{"id": "2503.11209", "title": "Clustering Items through Bandit Feedback: Finding the Right Feature out\n  of Many", "abstract": "  We study the problem of clustering a set of items based on bandit feedback.\nEach of the $n$ items is characterized by a feature vector, with a possibly\nlarge dimension $d$. The items are partitioned into two unknown groups such\nthat items within the same group share the same feature vector. We consider a\nsequential and adaptive setting in which, at each round, the learner selects\none item and one feature, then observes a noisy evaluation of the item's\nfeature. The learner's objective is to recover the correct partition of the\nitems, while keeping the number of observations as small as possible. We\nprovide an algorithm which relies on finding a relevant feature for the\nclustering task, leveraging the Sequential Halving algorithm. With probability\nat least $1-\\delta$, we obtain an accurate recovery of the partition and derive\nan upper bound on the budget required. Furthermore, we derive an\ninstance-dependent lower bound, which is tight in some relevant cases.\n", "date": "2025-03-14", "categories": []}
{"id": "2503.14393", "title": "On the clustering behavior of sliding windows", "abstract": "  Things can go spectacularly wrong when clustering timeseries data that has\nbeen preprocessed with a sliding window. We highlight three surprising failures\nthat emerge depending on how the window size compares with the timeseries\nlength. In addition to computational examples, we present theoretical\nexplanations for each of these failure modes.\n", "date": "2025-03-18", "categories": []}
{"id": "2503.14500", "title": "Utilization of Neighbor Information for Image Classification with\n  Different Levels of Supervision", "abstract": "  We propose to bridge the gap between semi-supervised and unsupervised image\nrecognition with a flexible method that performs well for both generalized\ncategory discovery (GCD) and image clustering. Despite the overlap in\nmotivation between these tasks, the methods themselves are restricted to a\nsingle task -- GCD methods are reliant on the labeled portion of the data, and\ndeep image clustering methods have no built-in way to leverage the labels\nefficiently. We connect the two regimes with an innovative approach that\nUtilizes Neighbor Information for Classification (UNIC) both in the\nunsupervised (clustering) and semisupervised (GCD) setting. State-of-the-art\nclustering methods already rely heavily on nearest neighbors. We improve on\ntheir results substantially in two parts, first with a sampling and cleaning\nstrategy where we identify accurate positive and negative neighbors, and\nsecondly by finetuning the backbone with clustering losses computed by sampling\nboth types of neighbors. We then adapt this pipeline to GCD by utilizing the\nlabelled images as ground truth neighbors. Our method yields state-of-the-art\nresults for both clustering (+3% ImageNet-100, Imagenet200) and GCD (+0.8%\nImageNet-100, +5% CUB, +2% SCars, +4% Aircraft).\n", "date": "2025-03-18", "categories": []}
{"id": "2407.12864", "title": "Clustering Time-Evolving Networks Using the Spatio-Temporal Graph\n  Laplacian", "abstract": "  Time-evolving graphs arise frequently when modeling complex dynamical systems\nsuch as social networks, traffic flow, and biological processes. Developing\ntechniques to identify and analyze communities in these time-varying graph\nstructures is an important challenge. In this work, we generalize existing\nspectral clustering algorithms from static to dynamic graphs using canonical\ncorrelation analysis (CCA) to capture the temporal evolution of clusters. Based\non this extended canonical correlation framework, we define the spatio-temporal\ngraph Laplacian and investigate its spectral properties. We connect these\nconcepts to dynamical systems theory via transfer operators, and illustrate the\nadvantages of our method on benchmark graphs by comparison with existing\nmethods. We show that the spatio-temporal graph Laplacian allows for a clear\ninterpretation of cluster structure evolution over time for directed and\nundirected graphs.\n", "date": "2024-07-12", "categories": []}
{"id": "2503.11706", "title": "Refining Filter Global Feature Weighting for Fully-Unsupervised\n  Clustering", "abstract": "  In the context of unsupervised learning, effective clustering plays a vital\nrole in revealing patterns and insights from unlabeled data. However, the\nsuccess of clustering algorithms often depends on the relevance and\ncontribution of features, which can differ between various datasets. This paper\nexplores feature weighting for clustering and presents new weighting\nstrategies, including methods based on SHAP (SHapley Additive exPlanations), a\ntechnique commonly used for providing explainability in various supervised\nmachine learning tasks. By taking advantage of SHAP values in a way other than\njust to gain explainability, we use them to weight features and ultimately\nimprove the clustering process itself in unsupervised scenarios.\n  Our empirical evaluations across five benchmark datasets and clustering\nmethods demonstrate that feature weighting based on SHAP can enhance\nunsupervised clustering quality, achieving up to a 22.69\\% improvement over\nother weighting methods (from 0.586 to 0.719 in terms of the Adjusted Rand\nIndex). Additionally, these situations where the weighted data boosts the\nresults are highlighted and thoroughly explored, offering insight for practical\napplications.\n", "date": "2025-03-12", "categories": []}
{"id": "2501.10157", "title": "Structure-guided Deep Multi-View Clustering", "abstract": "  Deep multi-view clustering seeks to utilize the abundant information from\nmultiple views to improve clustering performance. However, most of the existing\nclustering methods often neglect to fully mine multi-view structural\ninformation and fail to explore the distribution of multi-view data, limiting\nclustering performance. To address these limitations, we propose a\nstructure-guided deep multi-view clustering model. Specifically, we introduce a\npositive sample selection strategy based on neighborhood relationships, coupled\nwith a corresponding loss function. This strategy constructs multi-view nearest\nneighbor graphs to dynamically redefine positive sample pairs, enabling the\nmining of local structural information within multi-view data and enhancing the\nreliability of positive sample selection. Additionally, we introduce a Gaussian\ndistribution model to uncover latent structural information and introduce a\nloss function to reduce discrepancies between view embeddings. These two\nstrategies explore multi-view structural information and data distribution from\ndifferent perspectives, enhancing consistency across views and increasing\nintra-cluster compactness. Experimental evaluations demonstrate the efficacy of\nour method, showing significant improvements in clustering performance on\nmultiple benchmark datasets compared to state-of-the-art multi-view clustering\napproaches.\n", "date": "2025-01-17", "categories": []}
{"id": "2503.11017", "title": "Deep Incomplete Multi-view Clustering with Distribution Dual-Consistency\n  Recovery Guidance", "abstract": "  Multi-view clustering leverages complementary representations from diverse\nsources to enhance performance. However, real-world data often suffer\nincomplete cases due to factors like privacy concerns and device malfunctions.\nA key challenge is effectively utilizing available instances to recover missing\nviews. Existing methods frequently overlook the heterogeneity among views\nduring recovery, leading to significant distribution discrepancies between\nrecovered and true data. Additionally, many approaches focus on cross-view\ncorrelations, neglecting insights from intra-view reliable structure and\ncross-view clustering structure. To address these issues, we propose BURG, a\nnovel method for incomplete multi-view clustering with distriBution\ndUal-consistency Recovery Guidance. We treat each sample as a distinct category\nand perform cross-view distribution transfer to predict the distribution space\nof missing views. To compensate for the lack of reliable category information,\nwe design a dual-consistency guided recovery strategy that includes intra-view\nalignment guided by neighbor-aware consistency and cross-view alignment guided\nby prototypical consistency. Extensive experiments on benchmarks demonstrate\nthe superiority of BURG in the incomplete multi-view scenario.\n", "date": "2025-03-14", "categories": []}
{"id": "2503.09260", "title": "Neural Normalized Cut: A Differential and Generalizable Approach for\n  Spectral Clustering", "abstract": "  Spectral clustering, as a popular tool for data clustering, requires an\neigen-decomposition step on a given affinity to obtain the spectral embedding.\nNevertheless, such a step suffers from the lack of generalizability and\nscalability. Moreover, the obtained spectral embeddings can hardly provide a\ngood approximation to the ground-truth partition and thus a k-means step is\nadopted to quantize the embedding. In this paper, we propose a simple yet\neffective scalable and generalizable approach, called Neural Normalized Cut\n(NeuNcut), to learn the clustering membership for spectral clustering directly.\nIn NeuNcut, we properly reparameterize the unknown cluster membership via a\nneural network, and train the neural network via stochastic gradient descent\nwith a properly relaxed normalized cut loss. As a result, our NeuNcut enjoys a\ndesired generalization ability to directly infer clustering membership for\nout-of-sample unseen data and hence brings us an efficient way to handle\nclustering task with ultra large-scale data. We conduct extensive experiments\non both synthetic data and benchmark datasets and experimental results validate\nthe effectiveness and the superiority of our approach. Our code is available\nat: https://github.com/hewei98/NeuNcut.\n", "date": "2025-03-12", "categories": []}
{"id": "2402.04412", "title": "The VampPrior Mixture Model", "abstract": "  Widely used deep latent variable models (DLVMs), in particular Variational\nAutoencoders (VAEs), employ overly simplistic priors on the latent space. To\nachieve strong clustering performance, existing methods that replace the\nstandard normal prior with a Gaussian mixture model (GMM) require defining the\nnumber of clusters to be close to the number of expected ground truth classes\na-priori and are susceptible to poor initializations. We leverage VampPrior\nconcepts (Tomczak and Welling, 2018) to fit a Bayesian GMM prior, resulting in\nthe VampPrior Mixture Model (VMM), a novel prior for DLVMs. In a VAE, the VMM\nattains highly competitive clustering performance on benchmark datasets.\nIntegrating the VMM into scVI (Lopez et al., 2018), a popular scRNA-seq\nintegration method, significantly improves its performance and automatically\narranges cells into clusters with similar biological characteristics.\n", "date": "2024-02-06", "categories": []}
{"id": "2502.03405", "title": "Deep Clustering via Probabilistic Ratio-Cut Optimization", "abstract": "  We propose a novel approach for optimizing the graph ratio-cut by modeling\nthe binary assignments as random variables. We provide an upper bound on the\nexpected ratio-cut, as well as an unbiased estimate of its gradient, to learn\nthe parameters of the assignment variables in an online setting. The clustering\nresulting from our probabilistic approach (PRCut) outperforms the Rayleigh\nquotient relaxation of the combinatorial problem, its online learning\nextensions, and several widely used methods. We demonstrate that the PRCut\nclustering closely aligns with the similarity measure and can perform as well\nas a supervised classifier when label-based similarities are provided. This\nnovel approach can leverage out-of-the-box self-supervised representations to\nachieve competitive performance and serve as an evaluation method for the\nquality of these representations.\n", "date": "2025-02-05", "categories": []}
{"id": "2503.07917", "title": "Hyperoctant Search Clustering: A Method for Clustering Data in\n  High-Dimensional Hyperspheres", "abstract": "  Clustering of high-dimensional data sets is a growing need in artificial\nintelligence, machine learning and pattern recognition. In this paper, we\npropose a new clustering method based on a combinatorial-topological approach\napplied to regions of space defined by signs of coordinates (hyperoctants). In\nhigh-dimensional spaces, this approach often reduces the size of the dataset\nwhile preserving sufficient topological features. According to a density\ncriterion, the method builds clusters of data points based on the partitioning\nof a graph, whose vertices represent hyperoctants, and whose edges connect\nneighboring hyperoctants under the Levenshtein distance. We call this method\nHyperOctant Search Clustering. We prove some mathematical properties of the\nmethod. In order to as assess its performance, we choose the application of\ntopic detection, which is an important task in text mining. Our results suggest\nthat our method is more stable under variations of the main hyperparameter, and\nremarkably, it is not only a clustering method, but also a tool to explore the\ndataset from a topological perspective, as it directly provides information\nabout the number of hyperoctants where there are data points. We also discuss\nthe possible connections between our clustering method and other research\nfields.\n", "date": "2025-03-10", "categories": []}
{"id": "2503.08246", "title": "Dynamic DBSCAN with Euler Tour Sequences", "abstract": "  We propose a fast and dynamic algorithm for Density-Based Spatial Clustering\nof Applications with Noise (DBSCAN) that efficiently supports online updates.\nTraditional DBSCAN algorithms, designed for batch processing, become\ncomputationally expensive when applied to dynamic datasets, particularly in\nlarge-scale applications where data continuously evolves. To address this\nchallenge, our algorithm leverages the Euler Tour Trees data structure,\nenabling dynamic clustering updates without the need to reprocess the entire\ndataset. This approach preserves a near-optimal accuracy in density estimation,\nas achieved by the state-of-the-art static DBSCAN method (Esfandiari et al.,\n2021) Our method achieves an improved time complexity of $O(d \\log^3(n) +\n\\log^4(n))$ for every data point insertion and deletion, where $n$ and $d$\ndenote the total number of updates and the data dimension, respectively.\nEmpirical studies also demonstrate significant speedups over conventional\nDBSCANs in real-time clustering of dynamic datasets, while maintaining\ncomparable or superior clustering quality.\n", "date": "2025-03-11", "categories": []}
{"id": "2409.02066", "title": "Robust Clustering on High-Dimensional Data with Stochastic Quantization", "abstract": "  This paper addresses the limitations of conventional vector quantization\nalgorithms, particularly K-Means and its variant K-Means++, and investigates\nthe Stochastic Quantization (SQ) algorithm as a scalable alternative for\nhigh-dimensional unsupervised and semi-supervised learning tasks. Traditional\nclustering algorithms often suffer from inefficient memory utilization during\ncomputation, necessitating the loading of all data samples into memory, which\nbecomes impractical for large-scale datasets. While variants such as Mini-Batch\nK-Means partially mitigate this issue by reducing memory usage, they lack\nrobust theoretical convergence guarantees due to the non-convex nature of\nclustering problems. In contrast, the Stochastic Quantization algorithm\nprovides strong theoretical convergence guarantees, making it a robust\nalternative for clustering tasks. We demonstrate the computational efficiency\nand rapid convergence of the algorithm on an image classification problem with\npartially labeled data, comparing model accuracy across various ratios of\nlabeled to unlabeled data. To address the challenge of high dimensionality, we\nemploy a Triplet Network to encode images into low-dimensional representations\nin a latent space, which serve as a basis for comparing the efficiency of both\nthe Stochastic Quantization algorithm and traditional quantization algorithms.\nFurthermore, we enhance the algorithm's convergence speed by introducing\nmodifications with an adaptive learning rate.\n", "date": "2024-09-03", "categories": []}
{"id": "2503.05746", "title": "Unsupervised Clustering Approaches for Autism Screening: Achieving\n  95.31% Accuracy with a Gaussian Mixture Model", "abstract": "  Autism spectrum disorder (ASD) remains a challenging condition to diagnose\neffectively and promptly, despite global efforts in public health, clinical\nscreening, and scientific research. Traditional diagnostic methods, primarily\nreliant on supervised learning approaches, presuppose the availability of\nlabeled data, which can be both time-consuming and resource-intensive to\nobtain. Unsupervised learning, in contrast, offers a means of gaining insights\nfrom unlabeled datasets in a manner that can expedite or support the diagnostic\nprocess. This paper explores the use of four distinct unsupervised clustering\nalgorithms K-Means, Gaussian Mixture Model (GMM), Agglomerative Clustering, and\nDBSCAN to analyze a publicly available dataset of 704 adult individuals\nscreened for ASD. After extensive hyperparameter tuning via cross-validation,\nthe study documents how the Gaussian Mixture Model achieved the highest\nclustering-to-label accuracy (95.31%) when mapped to the original ASD/NO\nclassification (4). Other key performance metrics included the Adjusted Rand\nIndex (ARI) and silhouette scores, which further illustrated the internal\ncoherence of each cluster. The dataset underwent preprocessing procedures\nincluding data cleaning, label encoding of categorical features, and standard\nscaling, followed by a thorough cross-validation approach to assess and compare\nthe four clustering methods (5). These results highlight the significant\npotential of unsupervised methods in assisting ASD screening, especially in\ncontexts where labeled data may be sparse, uncertain, or prohibitively\nexpensive to obtain. With continued methodological refinements, unsupervised\napproaches hold promise for augmenting early detection initiatives and guiding\nresource allocation to individuals at high risk.\n", "date": "2025-02-20", "categories": []}
{"id": "2503.07227", "title": "Coreset Spectral Clustering", "abstract": "  Coresets have become an invaluable tool for solving $k$-means and kernel\n$k$-means clustering problems on large datasets with small numbers of clusters.\nOn the other hand, spectral clustering works well on sparse graphs and has\nrecently been extended to scale efficiently to large numbers of clusters. We\nexploit the connection between kernel $k$-means and the normalised cut problem\nto combine the benefits of both. Our main result is a coreset spectral\nclustering algorithm for graphs that clusters a coreset graph to infer a good\nlabelling of the original graph. We prove that an $\\alpha$-approximation for\nthe normalised cut problem on the coreset graph is an $O(\\alpha)$-approximation\non the original. We also improve the running time of the state-of-the-art\ncoreset algorithm for kernel $k$-means on sparse kernels, from $\\tilde{O}(nk)$\nto $\\tilde{O}(n\\cdot \\min \\{k, d_{avg}\\})$, where $d_{avg}$ is the average\nnumber of non-zero entries in each row of the $n\\times n$ kernel matrix. Our\nexperiments confirm our coreset algorithm is asymptotically faster on large\nreal-world graphs with many clusters, and show that our clustering algorithm\novercomes the main challenge faced by coreset kernel $k$-means on sparse\nkernels which is getting stuck in local optima.\n", "date": "2025-03-10", "categories": []}
{"id": "2503.04447", "title": "A Graph-Partitioning Based Continuous Optimization Approach to\n  Semi-supervised Clustering Problems", "abstract": "  Semi-supervised clustering is a basic problem in various applications. Most\nexisting methods require knowledge of the ideal cluster number, which is often\ndifficult to obtain in practice. Besides, satisfying the must-link constraints\nis another major challenge for these methods. In this work, we view the\nsemi-supervised clustering task as a partitioning problem on a graph associated\nwith the given dataset, where the similarity matrix includes a scaling\nparameter to reflect the must-link constraints. Utilizing a relaxation\ntechnique, we formulate the graph partitioning problem into a continuous\noptimization model that does not require the exact cluster number, but only an\noverestimate of it. We then propose a block coordinate descent algorithm to\nefficiently solve this model, and establish its convergence result. Based on\nthe obtained solution, we can construct the clusters that theoretically meet\nthe must-link constraints under mild assumptions. Furthermore, we verify the\neffectiveness and efficiency of our proposed method through comprehensive\nnumerical experiments.\n", "date": "2025-03-06", "categories": []}
{"id": "2503.03733", "title": "Rethinking Deep Clustering Paradigms: Self-Supervision Is All You Need", "abstract": "  The recent advances in deep clustering have been made possible by significant\nprogress in self-supervised and pseudo-supervised learning. However, the\ntrade-off between self-supervision and pseudo-supervision can give rise to\nthree primary issues. The joint training causes Feature Randomness and Feature\nDrift, whereas the independent training causes Feature Randomness and Feature\nTwist. In essence, using pseudo-labels generates random and unreliable\nfeatures. The combination of pseudo-supervision and self-supervision drifts the\nreliable clustering-oriented features. Moreover, moving from self-supervision\nto pseudo-supervision can twist the curved latent manifolds. This paper\naddresses the limitations of existing deep clustering paradigms concerning\nFeature Randomness, Feature Drift, and Feature Twist. We propose a new paradigm\nwith a new strategy that replaces pseudo-supervision with a second round of\nself-supervision training. The new strategy makes the transition between\ninstance-level self-supervision and neighborhood-level self-supervision\nsmoother and less abrupt. Moreover, it prevents the drifting effect that is\ncaused by the strong competition between instance-level self-supervision and\nclustering-level pseudo-supervision. Moreover, the absence of the\npseudo-supervision prevents the risk of generating random features. With this\nnovel approach, our paper introduces a Rethinking of the Deep Clustering\nParadigms, denoted by R-DC. Our model is specifically designed to address three\nprimary challenges encountered in Deep Clustering: Feature Randomness, Feature\nDrift, and Feature Twist. Experimental results conducted on six datasets have\nshown that the two-level self-supervision training yields substantial\nimprovements.\n", "date": "2025-03-05", "categories": []}
{"id": "2503.02449", "title": "Joint Tensor and Inter-View Low-Rank Recovery for Incomplete Multiview\n  Clustering", "abstract": "  Incomplete multiview clustering (IMVC) has gained significant attention for\nits effectiveness in handling missing sample challenges across various views in\nreal-world multiview clustering applications. Most IMVC approaches tackle this\nproblem by either learning consensus representations from available views or\nreconstructing missing samples using the underlying manifold structure.\nHowever, the reconstruction of learned similarity graph tensor in prior studies\nonly exploits the low-tubal-rank information, neglecting the exploration of\ninter-view correlations. This paper propose a novel joint tensor and inter-view\nlow-rank Recovery (JTIV-LRR), framing IMVC as a joint optimization problem that\nintegrates incomplete similarity graph learning and tensor representation\nrecovery. By leveraging both intra-view and inter-view low rank information,\nthe method achieves robust estimation of the complete similarity graph tensor\nthrough sparse noise removal and low-tubal-rank constraints along different\nmodes. Extensive experiments on both synthetic and real-world datasets\ndemonstrate the superiority of the proposed approach, achieving significant\nimprovements in clustering accuracy and robustness compared to state-of-the-art\nmethods.\n", "date": "2025-03-04", "categories": []}
{"id": "2303.16716", "title": "Topological Point Cloud Clustering", "abstract": "  We present Topological Point Cloud Clustering (TPCC), a new method to cluster\npoints in an arbitrary point cloud based on their contribution to global\ntopological features. TPCC synthesizes desirable features from spectral\nclustering and topological data analysis and is based on considering the\nspectral properties of a simplicial complex associated to the considered point\ncloud. As it is based on considering sparse eigenvector computations, TPCC is\nsimilarly easy to interpret and implement as spectral clustering. However, by\nfocusing not just on a single matrix associated to a graph created from the\npoint cloud data, but on a whole set of Hodge-Laplacians associated to an\nappropriately constructed simplicial complex, we can leverage a far richer set\nof topological features to characterize the data points within the point cloud\nand benefit from the relative robustness of topological techniques against\nnoise. We test the performance of TPCC on both synthetic and real-world data\nand compare it with classical spectral clustering.\n", "date": "2023-03-29", "categories": []}
{"id": "2411.02275", "title": "Breaking the Reclustering Barrier in Centroid-based Deep Clustering", "abstract": "  This work investigates an important phenomenon in centroid-based deep\nclustering (DC) algorithms: Performance quickly saturates after a period of\nrapid early gains. Practitioners commonly address early saturation with\nperiodic reclustering, which we demonstrate to be insufficient to address\nperformance plateaus. We call this phenomenon the \"reclustering barrier\" and\nempirically show when the reclustering barrier occurs, what its underlying\nmechanisms are, and how it is possible to Break the Reclustering Barrier with\nour algorithm BRB. BRB avoids early over-commitment to initial clusterings and\nenables continuous adaptation to reinitialized clustering targets while\nremaining conceptually simple. Applying our algorithm to widely-used\ncentroid-based DC algorithms, we show that (1) BRB consistently improves\nperformance across a wide range of clustering benchmarks, (2) BRB enables\ntraining from scratch, and (3) BRB performs competitively against\nstate-of-the-art DC algorithms when combined with a contrastive loss. We\nrelease our code and pre-trained models at\nhttps://github.com/Probabilistic-and-Interactive-ML/breaking-the-reclustering-barrier .\n", "date": "2024-11-04", "categories": []}
{"id": "2503.01097", "title": "Measuring the Validity of Clustering Validation Datasets", "abstract": "  Clustering techniques are often validated using benchmark datasets where\nclass labels are used as ground-truth clusters. However, depending on the\ndatasets, class labels may not align with the actual data clusters, and such\nmisalignment hampers accurate validation. Therefore, it is essential to\nevaluate and compare datasets regarding their cluster-label matching (CLM),\ni.e., how well their class labels match actual clusters. Internal validation\nmeasures (IVMs), like Silhouette, can compare CLM over different labeling of\nthe same dataset, but are not designed to do so across different datasets. We\nthus introduce Adjusted IVMs as fast and reliable methods to evaluate and\ncompare CLM across datasets. We establish four axioms that require validation\nmeasures to be independent of data properties not related to cluster structure\n(e.g., dimensionality, dataset size). Then, we develop standardized protocols\nto convert any IVM to satisfy these axioms, and use these protocols to adjust\nsix widely used IVMs. Quantitative experiments (1) verify the necessity and\neffectiveness of our protocols and (2) show that adjusted IVMs outperform the\ncompetitors, including standard IVMs, in accurately evaluating CLM both within\nand across datasets. We also show that the datasets can be filtered or improved\nusing our method to form more reliable benchmarks for clustering validation.\n", "date": "2025-03-03", "categories": []}
{"id": "2405.10378", "title": "A Polynomial-Time Approximation for Pairwise Fair $k$-Median Clustering", "abstract": "  In this work, we study pairwise fair clustering with $\\ell \\ge 2$ groups,\nwhere for every cluster $C$ and every group $i \\in [\\ell]$, the number of\npoints in $C$ from group $i$ must be at most $t$ times the number of points in\n$C$ from any other group $j \\in [\\ell]$, for a given integer $t$. To the best\nof our knowledge, only bi-criteria approximation and exponential-time\nalgorithms follow for this problem from the prior work on fair clustering\nproblems when $\\ell > 2$. In our work, focusing on the $\\ell > 2$ case, we\ndesign the first polynomial-time $O(k^2\\cdot \\ell \\cdot t)$-approximation for\nthis problem with $k$-median cost that does not violate the fairness\nconstraints. We complement our algorithmic result by providing hardness of\napproximation results, which show that our problem even when $\\ell=2$ is almost\nas hard as the popular uniform capacitated $k$-median, for which no\npolynomial-time algorithm with an approximation factor of $o(\\log k)$ is known.\n", "date": "2024-05-16", "categories": []}
{"id": "2502.19897", "title": "Graph Probability Aggregation Clustering", "abstract": "  Traditional clustering methods typically focus on either cluster-wise global\nclustering or point-wise local clustering to reveal the intrinsic structures in\nunlabeled data. Global clustering optimizes an objective function to explore\nthe relationships between clusters, but this approach may inevitably lead to\ncoarse partition. In contrast, local clustering heuristically groups data based\non detailed point relationships, but it tends to be less coherence and\nefficient. To bridge the gap between these two concepts and utilize the\nstrengths of both, we propose Graph Probability Aggregation Clustering (GPAC),\na graph-based fuzzy clustering algorithm. GPAC unifies the global clustering\nobjective function with a local clustering constraint. The entire GPAC\nframework is formulated as a multi-constrained optimization problem, which can\nbe solved using the Lagrangian method. Through the optimization process, the\nprobability of a sample belonging to a specific cluster is iteratively\ncalculated by aggregating information from neighboring samples within the\ngraph. We incorporate a hard assignment variable into the objective function to\nfurther improve the convergence and stability of optimization. Furthermore, to\nefficiently handle large-scale datasets, we introduce an acceleration program\nthat reduces the computational complexity from quadratic to linear, ensuring\nscalability. Extensive experiments conducted on synthetic, real-world, and deep\nlearning datasets demonstrate that GPAC not only exceeds existing\nstate-of-the-art methods in clustering performance but also excels in\ncomputational efficiency, making it a powerful tool for complex clustering\nchallenges.\n", "date": "2025-02-27", "categories": []}
{"id": "2502.19938", "title": "Flexible Bivariate Beta Mixture Model: A Probabilistic Approach for\n  Clustering Complex Data Structures", "abstract": "  Clustering is essential in data analysis and machine learning, but\ntraditional algorithms like $k$-means and Gaussian Mixture Models (GMM) often\nfail with nonconvex clusters. To address the challenge, we introduce the\nFlexible Bivariate Beta Mixture Model (FBBMM), which utilizes the flexibility\nof the bivariate beta distribution to handle diverse and irregular cluster\nshapes. Using the Expectation Maximization (EM) algorithm and Sequential Least\nSquares Programming (SLSQP) optimizer for parameter estimation, we validate\nFBBMM on synthetic and real-world datasets, demonstrating its superior\nperformance in clustering complex data structures, offering a robust solution\nfor big data analytics across various domains. We release the experimental code\nat https://github.com/yung-peng/MBMM-and-FBBMM.\n", "date": "2025-02-27", "categories": []}
{"id": "2502.19291", "title": "Global Graph Propagation with Hierarchical Information Transfer for\n  Incomplete Contrastive Multi-view Clustering", "abstract": "  Incomplete multi-view clustering has become one of the important research\nproblems due to the extensive missing multi-view data in the real world.\nAlthough the existing methods have made great progress, there are still some\nproblems: 1) most methods cannot effectively mine the information hidden in the\nmissing data; 2) most methods typically divide representation learning and\nclustering into two separate stages, but this may affect the clustering\nperformance as the clustering results directly depend on the learned\nrepresentation. To address these problems, we propose a novel incomplete\nmulti-view clustering method with hierarchical information transfer. Firstly,\nwe design the view-specific Graph Convolutional Networks (GCN) to obtain the\nrepresentation encoding the graph structure, which is then fused into the\nconsensus representation. Secondly, considering that one layer of GCN transfers\none-order neighbor node information, the global graph propagation with the\nconsensus representation is proposed to handle the missing data and learn deep\nrepresentation. Finally, we design a weight-sharing pseudo-classifier with\ncontrastive learning to obtain an end-to-end framework that combines\nview-specific representation learning, global graph propagation with\nhierarchical information transfer, and contrastive clustering for joint\noptimization. Extensive experiments conducted on several commonly-used datasets\ndemonstrate the effectiveness and superiority of our method in comparison with\nother state-of-the-art approaches. The code is available at\nhttps://github.com/KelvinXuu/GHICMC.\n", "date": "2025-02-26", "categories": []}
{"id": "2502.19337", "title": "Consistent Amortized Clustering via Generative Flow Networks", "abstract": "  Neural models for amortized probabilistic clustering yield samples of cluster\nlabels given a set-structured input, while avoiding lengthy Markov chain runs\nand the need for explicit data likelihoods. Existing methods which label each\ndata point sequentially, like the Neural Clustering Process, often lead to\ncluster assignments highly dependent on the data order. Alternatively, methods\nthat sequentially create full clusters, do not provide assignment\nprobabilities. In this paper, we introduce GFNCP, a novel framework for\namortized clustering. GFNCP is formulated as a Generative Flow Network with a\nshared energy-based parametrization of policy and reward. We show that the flow\nmatching conditions are equivalent to consistency of the clustering posterior\nunder marginalization, which in turn implies order invariance. GFNCP also\noutperforms existing methods in clustering performance on both synthetic and\nreal-world data.\n", "date": "2025-02-26", "categories": []}
{"id": "2312.04065", "title": "A Robust and Efficient Boundary Point Detection Method by Measuring\n  Local Direction Dispersion", "abstract": "  Boundary point detection aims to outline the external contour structure of\nclusters and enhance the inter-cluster discrimination, thus bolstering the\nperformance of the downstream classification and clustering tasks. However,\nexisting boundary point detectors are sensitive to density heterogeneity or\ncannot identify boundary points in concave structures and high-dimensional\nmanifolds. In this work, we propose a robust and efficient boundary point\ndetection method based on Local Direction Dispersion (LoDD). The core of\nboundary point detection lies in measuring the difference between boundary\npoints and internal points. It is a common observation that an internal point\nis surrounded by its neighbors in all directions, while the neighbors of a\nboundary point tend to be distributed only in a certain directional range. By\nconsidering this observation, we adopt density-independent K-Nearest Neighbors\n(KNN) method to determine neighboring points and design a centrality metric\nLoDD using the eigenvalues of the covariance matrix to depict the distribution\nuniformity of KNN. We also develop a grid-structure assumption of data\ndistribution to determine the parameters adaptively. The effectiveness of LoDD\nis demonstrated on synthetic datasets, real-world benchmarks, and application\nof training set split for deep learning model and hole detection on point cloud\ndata. The datasets and toolkit are available at:\nhttps://github.com/ZPGuiGroupWhu/lodd.\n", "date": "2023-12-07", "categories": []}
{"id": "2502.17523", "title": "UNCA: A Neutrosophic-Based Framework for Robust Clustering and Enhanced\n  Data Interpretation", "abstract": "  Accurately representing the complex linkages and inherent uncertainties\nincluded in huge datasets is still a major difficulty in the field of data\nclustering. We address these issues with our proposed Unified Neutrosophic\nClustering Algorithm (UNCA), which combines a multifaceted strategy with\nNeutrosophic logic to improve clustering performance. UNCA starts with a\nfull-fledged similarity examination via a {\\lambda}-cutting matrix that filters\nmeaningful relationships between each two points of data. Then, we initialize\ncentroids for Neutrosophic K-Means clustering, where the membership values are\nbased on their degrees of truth, indeterminacy and falsity. The algorithm then\nintegrates with a dynamic network visualization and MST (Minimum Spanning Tree)\nso that a visual interpretation of the relationships between the clusters can\nbe clearly represented. UNCA employs SingleValued Neutrosophic Sets (SVNSs) to\nrefine cluster assignments, and after fuzzifying similarity measures,\nguarantees a precise clustering result. The final step involves solidifying the\nclustering results through defuzzification methods, offering definitive cluster\nassignments. According to the performance evaluation results, UNCA outperforms\nconventional approaches in several metrics: it achieved a Silhouette Score of\n0.89 on the Iris Dataset, a Davies-Bouldin Index of 0.59 on the Wine Dataset,\nan Adjusted Rand Index (ARI) of 0.76 on the Digits Dataset, and a Normalized\nMutual Information (NMI) of 0.80 on the Customer Segmentation Dataset. These\nresults demonstrate how UNCA enhances interpretability and resilience in\naddition to improving clustering accuracy when contrasted with Fuzzy C-Means\n(FCM), Neutrosophic C-Means (NCM), as well as Kernel Neutrosophic C-Means\n(KNCM). This makes UNCA a useful tool for complex data processing tasks\n", "date": "2025-02-23", "categories": []}
{"id": "2308.15642", "title": "Gap-Free Clustering: Sensitivity and Robustness of SDP", "abstract": "  We study graph clustering in the Stochastic Block Model (SBM) in the presence\nof both large clusters and small, unrecoverable clusters. Previous convex\nrelaxation approaches achieving exact recovery do not allow any small clusters\nof size $o(\\sqrt{n})$, or require a size gap between the smallest recovered\ncluster and the largest non-recovered cluster. We provide an algorithm based on\nsemidefinite programming (SDP) which removes these requirements and provably\nrecovers large clusters regardless of the remaining cluster sizes. Mid-sized\nclusters pose unique challenges to the analysis, since their proximity to the\nrecovery threshold makes them highly sensitive to small noise perturbations and\nprecludes a closed-form candidate solution. We develop novel techniques,\nincluding a leave-one-out-style argument which controls the correlation between\nSDP solutions and noise vectors even when the removal of one row of noise can\ndrastically change the SDP solution. We also develop improved eigenvalue\nperturbation bounds of potential independent interest. Our results are robust\nto certain semirandom settings that are challenging for alternative algorithms.\nUsing our gap-free clustering procedure, we obtain efficient algorithms for the\nproblem of clustering with a faulty oracle with superior query complexities,\nnotably achieving $o(n^2)$ sample complexity even in the presence of a large\nnumber of small clusters. Our gap-free clustering procedure also leads to\nimproved algorithms for recursive clustering.\n", "date": "2023-08-29", "categories": []}
{"id": "2502.17020", "title": "Moving Past Single Metrics: Exploring Short-Text Clustering Across\n  Multiple Resolutions", "abstract": "  Cluster number is typically a parameter selected at the outset in clustering\nproblems, and while impactful, the choice can often be difficult to justify.\nInspired by bioinformatics, this study examines how the nature of clusters\nvaries with cluster number, presenting a method for determining cluster\nrobustness, and providing a systematic method for deciding on the cluster\nnumber. The study focuses specifically on short-text clustering, involving\n30,000 political Twitter bios, where the sparse co-occurrence of words between\ntexts makes finding meaningful clusters challenging. A metric of proportional\nstability is introduced to uncover the stability of specific clusters between\ncluster resolutions, and the results are visualised using Sankey diagrams to\nprovide an interrogative tool for understanding the nature of the dataset. The\nvisualisation provides an intuitive way to track cluster subdivision and\nreorganisation as cluster number increases, offering insights that static,\nsingle-resolution metrics cannot capture. The results show that instead of\nseeking a single 'optimal' solution, choosing a cluster number involves\nbalancing informativeness and complexity.\n", "date": "2025-02-24", "categories": []}
{"id": "2303.14301", "title": "Natural Language-Based Synthetic Data Generation for Cluster Analysis", "abstract": "  Cluster analysis relies on effective benchmarks for evaluating and comparing\ndifferent algorithms. Simulation studies on synthetic data are popular because\nimportant features of the data sets, such as the overlap between clusters, or\nthe variation in cluster shapes, can be effectively varied. Unfortunately,\ncreating evaluation scenarios is often laborious, as practitioners must\ntranslate higher-level scenario descriptions like \"clusters with very different\nshapes\" into lower-level geometric parameters such as cluster centers,\ncovariance matrices, etc. To make benchmarks more convenient and informative,\nwe propose synthetic data generation based on direct specification of\nhigh-level scenarios, either through verbal descriptions or high-level\ngeometric parameters. Our open-source Python package repliclust implements this\nworkflow, making it easy to set up interpretable and reproducible benchmarks\nfor cluster analysis. A demo of data generation from verbal inputs is available\nat https://demo.repliclust.org.\n", "date": "2023-03-24", "categories": []}
{"id": "2309.09907", "title": "Quantum Vision Clustering", "abstract": "  Unsupervised visual clustering has garnered significant attention in recent\ntimes, aiming to characterize distributions of unlabeled visual images through\nclustering based on a parameterized appearance approach. Alternatively,\nclustering algorithms can be viewed as assignment problems, often characterized\nas NP-hard, yet precisely solvable for small instances on contemporary\nhardware. Adiabatic quantum computing (AQC) emerges as a promising solution,\npoised to deliver substantial speedups for a range of NP-hard optimization\nproblems. However, existing clustering formulations face challenges in quantum\ncomputing adoption due to scalability issues. In this study, we present the\nfirst clustering formulation tailored for resolution using Adiabatic quantum\ncomputing. An Ising model is introduced to represent the quantum mechanical\nsystem implemented on AQC. The proposed approach demonstrates high\ncompetitiveness compared to state-of-the-art optimization-based methods, even\nwhen utilizing off-the-shelf integer programming solvers. Lastly, this work\nshowcases the solvability of the proposed clustering problem on\ncurrent-generation real quantum computers for small examples and analyzes the\nproperties of the obtained solutions\n", "date": "2023-09-18", "categories": []}
{"id": "2502.13000", "title": "Edge-Colored Clustering in Hypergraphs: Beyond Minimizing Unsatisfied\n  Edges", "abstract": "  We consider a framework for clustering edge-colored hypergraphs, where the\ngoal is to cluster (equivalently, to color) objects based on the primary type\nof multiway interactions they participate in. One well-studied objective is to\ncolor nodes to minimize the number of unsatisfied hyperedges -- those\ncontaining one or more nodes whose color does not match the hyperedge color. We\nmotivate and present advances for several directions that extend beyond this\nminimization problem. We first provide new algorithms for maximizing satisfied\nedges, which is the same at optimality but is much more challenging to\napproximate, with all prior work restricted to graphs. We develop the first\napproximation algorithm for hypergraphs, and then refine it to improve the\nbest-known approximation factor for graphs. We then introduce new objective\nfunctions that incorporate notions of balance and fairness, and provide new\nhardness results, approximations, and fixed-parameter tractability results.\n", "date": "2025-02-18", "categories": []}
{"id": "2502.13049", "title": "$k$-Graph: A Graph Embedding for Interpretable Time Series Clustering", "abstract": "  Time series clustering poses a significant challenge with diverse\napplications across domains. A prominent drawback of existing solutions lies in\ntheir limited interpretability, often confined to presenting users with\ncentroids. In addressing this gap, our work presents $k$-Graph, an unsupervised\nmethod explicitly crafted to augment interpretability in time series\nclustering. Leveraging a graph representation of time series subsequences,\n$k$-Graph constructs multiple graph representations based on different\nsubsequence lengths. This feature accommodates variable-length time series\nwithout requiring users to predetermine subsequence lengths. Our experimental\nresults reveal that $k$-Graph outperforms current state-of-the-art time series\nclustering algorithms in accuracy, while providing users with meaningful\nexplanations and interpretations of the clustering outcomes.\n", "date": "2025-02-18", "categories": []}
{"id": "2502.07081", "title": "Fast Clustering of Categorical Big Data", "abstract": "  The K-Modes algorithm, developed for clustering categorical data, is of high\nalgorithmic simplicity but suffers from unreliable performances in clustering\nquality and clustering efficiency, both heavily influenced by the choice of\ninitial cluster centers. In this paper, we investigate Bisecting K-Modes\n(BK-Modes), a successive bisecting process to find clusters, in examining how\ngood the cluster centers out of the bisecting process will be when used as\ninitial centers for the K-Modes. The BK-Modes works by splitting a dataset into\nmultiple clusters iteratively with one cluster being chosen and bisected into\ntwo clusters in each iteration. We use the sum of distances of data to their\ncluster centers as the selection metric to choose a cluster to be bisected in\neach iteration. This iterative process stops when K clusters are produced. The\ncenters of these K clusters are then used as the initial cluster centers for\nthe K-Modes. Experimental studies of the BK-Modes were carried out and were\ncompared against the K-Modes with multiple sets of initial cluster centers as\nwell as the best of the existing methods we found so far in our survey.\nExperimental results indicated good performances of BK-Modes both in the\nclustering quality and efficiency for large datasets.\n", "date": "2025-02-10", "categories": []}
{"id": "2502.07511", "title": "Quantitative evaluation of unsupervised clustering algorithms for\n  dynamic total-body PET image analysis", "abstract": "  Background. Recently, dynamic total-body positron emission tomography (PET)\nimaging has become possible due to new scanner devices. While clustering\nalgorithms have been proposed for PET analysis already earlier, there is still\nlittle research systematically evaluating these algorithms for processing of\ndynamic total-body PET images. Materials and methods. Here, we compare the\nperformance of 15 unsupervised clustering methods, including K-means either by\nitself or after principal component analysis (PCA) or independent component\nanalysis (ICA), Gaussian mixture model (GMM), fuzzy c-means (FCM),\nagglomerative clustering, spectral clustering, and several newer clustering\nalgorithms, for classifying time activity curves (TACs) in dynamic PET images.\nWe use dynamic total-body $^{15}$O-water PET images collected from 30 patients\nwith suspected or confirmed coronary artery disease. To evaluate the clustering\nalgorithms in a quantitative way, we use them to classify 5000 TACs from each\nimage based on whether the curve is taken from brain, right heart ventricle,\nright kidney, lower right lung lobe, or urinary bladder. Results. According to\nour results, the best methods are GMM, FCM, and ICA combined with mini batch\nK-means, which classified the TACs with a median accuracies of 89\\%, 83\\%, and\n81\\%, respectively, in a processing time of half a second or less on average\nfor each image. Conclusion. GMM, FCM, and ICA with mini batch K-means show\npromise for dynamic total-body PET analysis.\n", "date": "2025-02-11", "categories": []}
{"id": "2307.00677", "title": "SDC-HSDD-NDSA: Structure Detecting Cluster by Hierarchical Secondary\n  Directed Differential with Normalized Density and Self-Adaption", "abstract": "  Density-based clustering is the most popular clustering algorithm since it\ncan identify clusters of arbitrary shape as long as they are separated by\nlow-density regions. However, a high-density region that is not separated by\nlow-density ones might also have different structures belonging to multiple\nclusters. As far as we know, all previous density-based clustering algorithms\nfail to detect such structures. In this paper, we provide a novel density-based\nclustering scheme to address this problem. It is the rst clustering algorithm\nthat can detect meticulous structures in a high-density region that is not\nseparated by low-density ones and thus extends the range of applications of\nclustering. The algorithm employs secondary directed differential, hierarchy,\nnormalized density, as well as the self-adaption coefficient, called Structure\nDetecting Cluster by Hierarchical Secondary Directed Differential with\nNormalized Density and Self-Adaption, dubbed SDC-HSDD-NDSA. Experiments on\nsynthetic and real datasets are implemented to verify the effectiveness,\nrobustness, and granularity independence of the algorithm, and the scheme is\ncompared to unsupervised schemes in the Python package Scikit-learn. Results\ndemonstrate that our algorithm outperforms previous ones in many situations,\nespecially significantly when clusters have regular internal structures. For\nexample, averaging over the eight noiseless synthetic datasets with structures\nemploying ARI and NMI criteria, previous algorithms obtain scores below 0.6 and\n0.7, while the presented algorithm obtains scores higher than 0.9 and 0.95,\nrespectively.\n", "date": "2023-07-02", "categories": []}
{"id": "2312.10270", "title": "Random Models for Fuzzy Clustering Similarity Measures", "abstract": "  The Adjusted Rand Index (ARI) is a widely used method for comparing hard\nclusterings, but requires a choice of random model that is often left implicit.\nSeveral recent works have extended the Rand Index to fuzzy clusterings, but the\nassumptions of the most common random model is difficult to justify in fuzzy\nsettings. We propose a single framework for computing the ARI with three random\nmodels that are intuitive and explainable for both hard and fuzzy clusterings,\nalong with the benefit of lower computational complexity. The theory and\nassumptions of the proposed models are contrasted with the existing permutation\nmodel. Computations on synthetic and benchmark data show that each model has\ndistinct behaviour, meaning that accurate model selection is important for the\nreliability of results.\n", "date": "2023-12-16", "categories": []}
{"id": "2412.11550", "title": "THESAURUS: Contrastive Graph Clustering by Swapping Fused\n  Gromov-Wasserstein Couplings", "abstract": "  Graph node clustering is a fundamental unsupervised task. Existing methods\ntypically train an encoder through selfsupervised learning and then apply\nK-means to the encoder output. Some methods use this clustering result directly\nas the final assignment, while others initialize centroids based on this\ninitial clustering and then finetune both the encoder and these learnable\ncentroids. However, due to their reliance on K-means, these methods inherit its\ndrawbacks when the cluster separability of encoder output is low, facing\nchallenges from the Uniform Effect and Cluster Assimilation. We summarize three\nreasons for the low cluster separability in existing methods: (1) lack of\ncontextual information prevents discrimination between similar nodes from\ndifferent clusters; (2) training tasks are not sufficiently aligned with the\ndownstream clustering task; (3) the cluster information in the graph structure\nis not appropriately exploited. To address these issues, we propose conTrastive\ngrapH clustEring by SwApping fUsed gRomov-wasserstein coUplingS (THESAURUS).\nOur method introduces semantic prototypes to provide contextual information,\nand employs a cross-view assignment prediction pretext task that aligns well\nwith the downstream clustering task. Additionally, it utilizes\nGromov-Wasserstein Optimal Transport (GW-OT) along with the proposed prototype\ngraph to thoroughly exploit cluster information in the graph structure. To\nadapt to diverse real-world data, THESAURUS updates the prototype graph and the\nprototype marginal distribution in OT by using momentum. Extensive experiments\ndemonstrate that THESAURUS achieves higher cluster separability than the prior\nart, effectively mitigating the Uniform Effect and Cluster Assimilation issues\n", "date": "2024-12-16", "categories": []}
{"id": "2502.10106", "title": "Data-Adaptive Low-Rank Sparse Subspace Clustering", "abstract": "  Low-rank sparse subspace clustering (LRSSC) algorithms built on\nself-expressive model effectively capture both the global and local structure\nof the data. However, existing solutions, primarily based on proximal operators\nassociated with Sp/Lp , p e {0, 1/2, 2/3, 1}, norms are not data-adaptive. In\nthis work, we propose an LRSSC algorithm incorporating a data-adaptive\nsurrogate for the S0/L0 quasi-norm. We provide a numerical solution for the\ncorresponding proximal operator in cases where an analytical expression is\nunavailable. The proposed LRSSC algorithm is formulated within the proximal\nmapping framework, and we present theoretical proof of its global convergence\ntoward a stationary point. We evaluate the performance of the proposed method\non three well known datasets, comparing it against LRSSC algorithms constrained\nby Sp/Lp, p e {0, 1/2, 2/3, 1}, norms.\n", "date": "2025-02-14", "categories": []}
{"id": "2310.17869", "title": "Grid Jigsaw Representation with CLIP: A New Perspective on Image\n  Clustering", "abstract": "  Unsupervised representation learning for image clustering is essential in\ncomputer vision. Although the advancement of visual models has improved image\nclustering with efficient visual representations, challenges still remain.\nFirstly, existing features often lack the ability to represent the internal\nstructure of images, hindering the accurate clustering of visually similar\nimages. Secondly, finer-grained semantic labels are often missing, limiting the\nability to capture nuanced differences and similarities between images. In this\npaper, we propose a new perspective on image clustering, the pretrain-based\nGrid Jigsaw Representation (pGJR). Inspired by human jigsaw puzzle processing,\nwe modify the traditional jigsaw learning to gain a more sequential and\nincremental understanding of image structure. We also leverage the pretrained\nCLIP to extract the prior features which can benefit from the enhanced\ncross-modal representation for richer and more nuanced semantic information and\nlabel level differentiation. Our experiments demonstrate that using the\npretrained model as a feature extractor can accelerate the convergence of\nclustering. We append the GJR module to pGJR and observe significant\nimprovements on common-use benchmark datasets. The experimental results\nhighlight the effectiveness of our approach in the clustering task, as\nevidenced by improvements in the ACC, NMI, and ARI metrics, as well as the\nsuper-fast convergence speed.\n", "date": "2023-10-27", "categories": []}
{"id": "2502.08549", "title": "Copula-based mixture model identification for subgroup clustering with\n  imaging applications", "abstract": "  Model-based clustering techniques have been widely applied to various\napplication areas, while most studies focus on canonical mixtures with unique\ncomponent distribution form. However, this strict assumption is often hard to\nsatisfy. In this paper, we consider the more flexible Copula-Based Mixture\nModels (CBMMs) for clustering, which allow heterogeneous component\ndistributions composed by flexible choices of marginal and copula forms. More\nspecifically, we propose an adaptation of the Generalized Iterative Conditional\nEstimation (GICE) algorithm to identify the CBMMs in an unsupervised manner,\nwhere the marginal and copula forms and their parameters are estimated\niteratively. GICE is adapted from its original version developed for switching\nMarkov model identification with the choice of realization time. Our CBMM-GICE\nclustering method is then tested on synthetic two-cluster data (N=2000 samples)\nwith discussion of the factors impacting its convergence. Finally, it is\ncompared to the Expectation Maximization identified mixture models with unique\ncomponent form on the entire MNIST database (N=70000), and on real cardiac\nmagnetic resonance data (N=276) to illustrate its value for imaging\napplications.\n", "date": "2025-02-12", "categories": []}
{"id": "2409.05072", "title": "A General Framework for Clustering and Distribution Matching with Bandit\n  Feedback", "abstract": "  We develop a general framework for clustering and distribution matching\nproblems with bandit feedback. We consider a $K$-armed bandit model where some\nsubset of $K$ arms is partitioned into $M$ groups. Within each group, the\nrandom variable associated to each arm follows the same distribution on a\nfinite alphabet. At each time step, the decision maker pulls an arm and\nobserves its outcome from the random variable associated to that arm.\nSubsequent arm pulls depend on the history of arm pulls and their outcomes. The\ndecision maker has no knowledge of the distributions of the arms or the\nunderlying partitions. The task is to devise an online algorithm to learn the\nunderlying partition of arms with the least number of arm pulls on average and\nwith an error probability not exceeding a pre-determined value~$\\delta$.\nSeveral existing problems fall under our general framework, including finding\n$M$ pairs of arms, odd arm identification, and $N$-ary clustering of $K$ arms\nbelong to our general framework. We derive a non-asymptotic lower bound on the\naverage number of arm pulls for any online algorithm with an error probability\nnot exceeding $\\delta$. Furthermore, we develop a computationally-efficient\nonline algorithm based on the Track-and-Stop method and Frank--Wolfe algorithm,\nand show that the average number of arm pulls of our algorithm asymptotically\nmatches that of the lower bound. Our refined analysis also uncovers a novel\nbound on the speed at which the average number of arm pulls of our algorithm\nconverges to the fundamental limit as $\\delta$ vanishes.\n", "date": "2024-09-08", "categories": []}
{"id": "2502.06879", "title": "CluStRE: Streaming Graph Clustering with Multi-Stage Refinement", "abstract": "  We present CluStRE, a novel streaming graph clustering algorithm that\nbalances computational efficiency with high-quality clustering using\nmulti-stage refinement. Unlike traditional in-memory clustering approaches,\nCluStRE processes graphs in a streaming setting, significantly reducing memory\noverhead while leveraging re-streaming and evolutionary heuristics to improve\nsolution quality. Our method dynamically constructs a quotient graph, enabling\nmodularity-based optimization while efficiently handling large-scale graphs. We\nintroduce multiple configurations of CluStRE to provide trade-offs between\nspeed, memory consumption, and clustering quality. Experimental evaluations\ndemonstrate that CluStRE improves solution quality by 89.8%, operates 2.6 times\nfaster, and uses less than two-thirds of the memory required by the\nstate-of-the-art streaming clustering algorithm on average. Moreover, our\nstrongest mode enhances solution quality by up to 150% on average. With this,\nCluStRE achieves comparable solution quality to in-memory algorithms, i.e. over\n96% of the quality of clustering approaches, including Louvain, effectively\nbridging the gap between streaming and traditional clustering methods.\n", "date": "2025-02-08", "categories": []}
{"id": "2502.06117", "title": "Revisiting Dynamic Graph Clustering via Matrix Factorization", "abstract": "  Dynamic graph clustering aims to detect and track time-varying clusters in\ndynamic graphs, revealing the evolutionary mechanisms of complex real-world\ndynamic systems. Matrix factorization-based methods are promising approaches\nfor this task; however, these methods often struggle with scalability and can\nbe time-consuming when applied to large-scale dynamic graphs. Moreover, they\ntend to lack robustness and are vulnerable to real-world noisy data. To address\nthese issues, we make three key contributions. First, to improve scalability,\nwe propose temporal separated matrix factorization, where a single matrix is\ndivided into multiple smaller matrices for independent factorization, resulting\nin faster computation. Second, to improve robustness, we introduce\nbi-clustering regularization, which jointly optimizes graph embedding and\nclustering, thereby filtering out noisy features from the graph embeddings.\nThird, to further enhance effectiveness and efficiency, we propose selective\nembedding updating, where we update only the embeddings of dynamic nodes while\nthe embeddings of static nodes are fixed among different timestamps.\nExperimental results on six synthetic and five real-world benchmarks\ndemonstrate the scalability, robustness and effectiveness of our proposed\nmethod. Source code is available at https://github.com/Clearloveyuan/DyG-MF.\n", "date": "2025-02-10", "categories": []}
{"id": "2502.06163", "title": "Scalable k-Means Clustering for Large k via Seeded Approximate\n  Nearest-Neighbor Search", "abstract": "  For very large values of $k$, we consider methods for fast $k$-means\nclustering of massive datasets with $10^7\\sim10^9$ points in high-dimensions\n($d\\geq100$). All current practical methods for this problem have runtimes at\nleast $\\Omega(k^2)$. We find that initialization routines are not a bottleneck\nfor this case. Instead, it is critical to improve the speed of Lloyd's\nlocal-search algorithm, particularly the step that reassigns points to their\nclosest center. Attempting to improve this step naturally leads us to leverage\napproximate nearest-neighbor search methods, although this alone is not enough\nto be practical. Instead, we propose a family of problems we call \"Seeded\nApproximate Nearest-Neighbor Search\", for which we propose \"Seeded\nSearch-Graph\" methods as a solution.\n", "date": "2025-02-10", "categories": []}
{"id": "2502.06587", "title": "evclust: Python library for evidential clustering", "abstract": "  A recent developing trend in clustering is the advancement of algorithms that\nnot only identify clusters within data, but also express and capture the\nuncertainty of cluster membership. Evidential clustering addresses this by\nusing the Dempster-Shafer theory of belief functions, a framework designed to\nmanage and represent uncertainty. This approach results in a credal partition,\na structured set of mass functions that quantify the uncertain assignment of\neach object to potential groups. The Python framework evclust, presented in\nthis paper, offers a suite of efficient evidence clustering algorithms as well\nas tools for visualizing, evaluating and analyzing credal partitions.\n", "date": "2025-02-10", "categories": []}
{"id": "2405.02644", "title": "Interpretable Multi-View Clustering", "abstract": "  Multi-view clustering has become a significant area of research, with\nnumerous methods proposed over the past decades to enhance clustering accuracy.\nHowever, in many real-world applications, it is crucial to demonstrate a clear\ndecision-making process-specifically, explaining why samples are assigned to\nparticular clusters. Consequently, there remains a notable gap in developing\ninterpretable methods for clustering multi-view data. To fill this crucial gap,\nwe make the first attempt towards this direction by introducing an\ninterpretable multi-view clustering framework. Our method begins by extracting\nembedded features from each view and generates pseudo-labels to guide the\ninitial construction of the decision tree. Subsequently, it iteratively\noptimizes the feature representation for each view along with refining the\ninterpretable decision tree. Experimental results on real datasets demonstrate\nthat our method not only provides a transparent clustering process for\nmulti-view data but also delivers performance comparable to state-of-the-art\nmulti-view clustering methods. To the best of our knowledge, this is the first\neffort to design an interpretable clustering framework specifically for\nmulti-view data, opening a new avenue in this field.\n", "date": "2024-05-04", "categories": []}
{"id": "2406.13103", "title": "A Generic Method for Fine-grained Category Discovery in Natural Language\n  Texts", "abstract": "  Fine-grained category discovery using only coarse-grained supervision is a\ncost-effective yet challenging task. Previous training methods focus on\naligning query samples with positive samples and distancing them from\nnegatives. They often neglect intra-category and inter-category semantic\nsimilarities of fine-grained categories when navigating sample distributions in\nthe embedding space. Furthermore, some evaluation techniques that rely on\npre-collected test samples are inadequate for real-time applications. To\naddress these shortcomings, we introduce a method that successfully detects\nfine-grained clusters of semantically similar texts guided by a novel objective\nfunction. The method uses semantic similarities in a logarithmic space to guide\nsample distributions in the Euclidean space and to form distinct clusters that\nrepresent fine-grained categories. We also propose a centroid inference\nmechanism to support real-time applications. The efficacy of the method is both\ntheoretically justified and empirically confirmed on three benchmark tasks. The\nproposed objective function is integrated in multiple contrastive learning\nbased neural models. Its results surpass existing state-of-the-art approaches\nin terms of Accuracy, Adjusted Rand Index and Normalized Mutual Information of\nthe detected fine-grained categories. Code and data will be available at Code\nand data are publicly available at\nhttps://github.com/changtianluckyforever/F-grained-STAR.\n", "date": "2024-06-18", "categories": []}
{"id": "2412.08933", "title": "Deep clustering using adversarial net based clustering loss", "abstract": "  Deep clustering is a recent deep learning technique which combines deep\nlearning with traditional unsupervised clustering. At the heart of deep\nclustering is a loss function which penalizes samples for being an outlier from\ntheir ground truth cluster centers in the latent space. The probabilistic\nvariant of deep clustering reformulates the loss using KL divergence. Often,\nthe main constraint of deep clustering is the necessity of a closed form loss\nfunction to make backpropagation tractable. Inspired by deep clustering and\nadversarial net, we reformulate deep clustering as an adversarial net over\ntraditional closed form KL divergence. Training deep clustering becomes a task\nof minimizing the encoder and maximizing the discriminator. At optimality, this\nmethod theoretically approaches the JS divergence between the distribution\nassumption of the encoder and the discriminator. We demonstrated the\nperformance of our proposed method on several well cited datasets such as\nMNIST, REUTERS10K and CIFAR10, achieving on-par or better performance with some\nof the state-of-the-art deep clustering methods.\n", "date": "2024-12-12", "categories": []}
{"id": "2501.02564", "title": "Balanced Multi-view Clustering", "abstract": "  Multi-view clustering (MvC) aims to integrate information from different\nviews to enhance the capability of the model in capturing the underlying data\nstructures. The widely used joint training paradigm in MvC is potentially not\nfully leverage the multi-view information, since the imbalanced and\nunder-optimized view-specific features caused by the uniform learning objective\nfor all views. For instance, particular views with more discriminative\ninformation could dominate the learning process in the joint training paradigm,\nleading to other views being under-optimized. To alleviate this issue, we first\nanalyze the imbalanced phenomenon in the joint-training paradigm of multi-view\nclustering from the perspective of gradient descent for each view-specific\nfeature extractor. Then, we propose a novel balanced multi-view clustering\n(BMvC) method, which introduces a view-specific contrastive regularization\n(VCR) to modulate the optimization of each view. Concretely, VCR preserves the\nsample similarities captured from the joint features and view-specific ones\ninto the clustering distributions corresponding to view-specific features to\nenhance the learning process of view-specific feature extractors. Additionally,\na theoretical analysis is provided to illustrate that VCR adaptively modulates\nthe magnitudes of gradients for updating the parameters of view-specific\nfeature extractors to achieve a balanced multi-view learning procedure. In such\na manner, BMvC achieves a better trade-off between the exploitation of\nview-specific patterns and the exploration of view-invariance patterns to fully\nlearn the multi-view information for the clustering task. Finally, a set of\nexperiments are conducted to verify the superiority of the proposed method\ncompared with state-of-the-art approaches on eight benchmark MvC datasets.\n", "date": "2025-01-05", "categories": []}
{"id": "2502.02079", "title": "Online Clustering of Dueling Bandits", "abstract": "  The contextual multi-armed bandit (MAB) is a widely used framework for\nproblems requiring sequential decision-making under uncertainty, such as\nrecommendation systems. In applications involving a large number of users, the\nperformance of contextual MAB can be significantly improved by facilitating\ncollaboration among multiple users. This has been achieved by the clustering of\nbandits (CB) methods, which adaptively group the users into different clusters\nand achieve collaboration by allowing the users in the same cluster to share\ndata. However, classical CB algorithms typically rely on numerical reward\nfeedback, which may not be practical in certain real-world applications. For\ninstance, in recommendation systems, it is more realistic and reliable to\nsolicit preference feedback between pairs of recommended items rather than\nabsolute rewards. To address this limitation, we introduce the first\n\"clustering of dueling bandit algorithms\" to enable collaborative\ndecision-making based on preference feedback. We propose two novel algorithms:\n(1) Clustering of Linear Dueling Bandits (COLDB) which models the user reward\nfunctions as linear functions of the context vectors, and (2) Clustering of\nNeural Dueling Bandits (CONDB) which uses a neural network to model complex,\nnon-linear user reward functions. Both algorithms are supported by rigorous\ntheoretical analyses, demonstrating that user collaboration leads to improved\nregret bounds. Extensive empirical evaluations on synthetic and real-world\ndatasets further validate the effectiveness of our methods, establishing their\npotential in real-world applications involving multiple users with\npreference-based feedback.\n", "date": "2025-02-04", "categories": []}
{"id": "2502.02085", "title": "A New Rejection Sampling Approach to $k$-$\\mathtt{means}$++ With\n  Improved Trade-Offs", "abstract": "  The $k$-$\\mathtt{means}$++ seeding algorithm (Arthur & Vassilvitskii, 2007)\nis widely used in practice for the $k$-means clustering problem where the goal\nis to cluster a dataset $\\mathcal{X} \\subset \\mathbb{R} ^d$ into $k$ clusters.\n  The popularity of this algorithm is due to its simplicity and provable\nguarantee of being $O(\\log k)$ competitive with the optimal solution in\nexpectation. However, its running time is $O(|\\mathcal{X}|kd)$, making it\nexpensive for large datasets.\n  In this work, we present a simple and effective rejection sampling based\napproach for speeding up $k$-$\\mathtt{means}$++.\n  Our first method runs in time $\\tilde{O}(\\mathtt{nnz} (\\mathcal{X}) + \\beta\nk^2d)$ while still being $O(\\log k )$ competitive in expectation. Here, $\\beta$\nis a parameter which is the ratio of the variance of the dataset to the optimal\n$k$-$\\mathtt{means}$ cost in expectation and $\\tilde{O}$ hides logarithmic\nfactors in $k$ and $|\\mathcal{X}|$.\n  Our second method presents a new trade-off between computational cost and\nsolution quality. It incurs an additional scale-invariant factor of $\nk^{-\\Omega( m/\\beta)} \\operatorname{Var} (\\mathcal{X})$ in addition to the\n$O(\\log k)$ guarantee of $k$-$\\mathtt{means}$++ improving upon a result of\n(Bachem et al, 2016a) who get an additional factor of\n$m^{-1}\\operatorname{Var}(\\mathcal{X})$ while still running in time\n$\\tilde{O}(\\mathtt{nnz}(\\mathcal{X}) + mk^2d)$. We perform extensive empirical\nevaluations to validate our theoretical results and to show the effectiveness\nof our approach on real datasets.\n", "date": "2025-02-04", "categories": []}
{"id": "2303.14581", "title": "Shapley-based Explainable AI for Clustering Applications in Fault\n  Diagnosis and Prognosis", "abstract": "  Data-driven artificial intelligence models require explainability in\nintelligent manufacturing to streamline adoption and trust in modern industry.\nHowever, recently developed explainable artificial intelligence (XAI)\ntechniques that estimate feature contributions on a model-agnostic level such\nas SHapley Additive exPlanations (SHAP) have not yet been evaluated for\nsemi-supervised fault diagnosis and prognosis problems characterized by class\nimbalance and weakly labeled datasets. This paper explores the potential of\nutilizing Shapley values for a new clustering framework compatible with\nsemi-supervised learning problems, loosening the strict supervision requirement\nof current XAI techniques. This broad methodology is validated on two case\nstudies: a heatmap image dataset obtained from a semiconductor manufacturing\nprocess featuring class imbalance, and a benchmark dataset utilized in the 2021\nPrognostics and Health Management (PHM) Data Challenge. Semi-supervised\nclustering based on Shapley values significantly improves upon clustering\nquality compared to the fully unsupervised case, deriving information-dense and\nmeaningful clusters that relate to underlying fault diagnosis model\npredictions. These clusters can also be characterized by high-precision\ndecision rules in terms of original feature values, as demonstrated in the\nsecond case study. The rules, limited to 1-2 terms utilizing original feature\nscales, describe 12 out of the 16 derived equipment failure clusters with\nprecision exceeding 0.85, showcasing the promising utility of the explainable\nclustering framework for intelligent manufacturing applications.\n", "date": "2023-03-25", "categories": []}
{"id": "2409.08245", "title": "Style-based Clustering of Visual Artworks and the Play of Neural\n  Style-Representations", "abstract": "  Clustering artworks based on style can have many potential real-world\napplications like art recommendations, style-based search and retrieval, and\nthe study of artistic style evolution of an artist or in an artwork corpus. We\nintroduce and deliberate over the notion of 'Style-based clustering of visual\nartworks'. We argue that clustering artworks based on style is largely an\nunaddressed problem. We explore and devise different neural feature\nrepresentations - from the style-classification, style-transfer to large\nlanguage vision models - that can be then used for style-based clustering. Our\nobjective is to assess the relative effectiveness of these devised style-based\nclustering approaches through qualitative and quantitative analysis by applying\nthem to multiple artwork corpora and curated synthetically styled datasets.\nBesides providing a broad framework for style-based clustering and evaluation,\nour analysis provides some key novel insights on feature representations,\narchitectures and implications for style-based clustering.\n", "date": "2024-09-12", "categories": []}
{"id": "2501.19285", "title": "OneBatchPAM: A Fast and Frugal K-Medoids Algorithm", "abstract": "  This paper proposes a novel k-medoids approximation algorithm to handle\nlarge-scale datasets with reasonable computational time and memory complexity.\nWe develop a local-search algorithm that iteratively improves the medoid\nselection based on the estimation of the k-medoids objective. A single batch of\nsize m << n provides the estimation, which reduces the required memory size and\nthe number of pairwise dissimilarities computations to O(mn), instead of O(n^2)\ncompared to most k-medoids baselines. We obtain theoretical results\nhighlighting that a batch of size m = O(log(n)) is sufficient to guarantee,\nwith strong probability, the same performance as the original local-search\nalgorithm. Multiple experiments conducted on real datasets of various sizes and\ndimensions show that our algorithm provides similar performances as\nstate-of-the-art methods such as FasterPAM and BanditPAM++ with a drastically\nreduced running time.\n", "date": "2025-01-31", "categories": []}
{"id": "2304.14185", "title": "HPSCAN: Human Perception-Based Scattered Data Clustering", "abstract": "  Cluster separation is a task typically tackled by widely used clustering\ntechniques, such as k-means or DBSCAN. However, these algorithms are based on\nnon-perceptual metrics, and our experiments demonstrate that their output does\nnot reflect human cluster perception. To bridge the gap between human cluster\nperception and machine-computed clusters, we propose HPSCAN, a learning\nstrategy that operates directly on scattered data. To learn perceptual cluster\nseparation on such data, we crowdsourced the labeling of 7,320 bivariate\n(scatterplot) datasets to 384 human participants. We train our HPSCAN model on\nthese human-annotated data. Instead of rendering these data as scatterplot\nimages, we used their x and y point coordinates as input to a modified\nPointNet++ architecture, enabling direct inference on point clouds. In this\nwork, we provide details on how we collected our dataset, report statistics of\nthe resulting annotations, and investigate the perceptual agreement of cluster\nseparation for real-world data. We also report the training and evaluation\nprotocol for HPSCAN and introduce a novel metric, that measures the accuracy\nbetween a clustering technique and a group of human annotators. We explore\npredicting point-wise human agreement to detect ambiguities. Finally, we\ncompare our approach to ten established clustering techniques and demonstrate\nthat HPSCAN is capable of generalizing to unseen and out-of-scope data.\n", "date": "2023-04-27", "categories": []}
{"id": "2411.06572", "title": "Fitting Multiple Machine Learning Models with Performance Based\n  Clustering", "abstract": "  Traditional machine learning approaches assume that data comes from a single\ngenerating mechanism, which may not hold for most real life data. In these\ncases, the single mechanism assumption can result in suboptimal performance. We\nintroduce a clustering framework that eliminates this assumption by grouping\nthe data according to the relations between the features and the target values\nand we obtain multiple separate models to learn different parts of the data. We\nfurther extend our framework to applications having streaming data where we\nproduce outcomes using an ensemble of models. For this, the ensemble weights\nare updated based on the incoming data batches. We demonstrate the performance\nof our approach over the widely-studied real life datasets, showing significant\nimprovements over the traditional single-model approaches.\n", "date": "2024-11-10", "categories": []}
{"id": "2501.18112", "title": "ACTGNN: Assessment of Clustering Tendency with Synthetically-Trained\n  Graph Neural Networks", "abstract": "  Determining clustering tendency in datasets is a fundamental but challenging\ntask, especially in noisy or high-dimensional settings where traditional\nmethods, such as the Hopkins Statistic and Visual Assessment of Tendency (VAT),\noften struggle to produce reliable results. In this paper, we propose ACTGNN, a\ngraph-based framework designed to assess clustering tendency by leveraging\ngraph representations of data. Node features are constructed using\nLocality-Sensitive Hashing (LSH), which captures local neighborhood\ninformation, while edge features incorporate multiple similarity metrics, such\nas the Radial Basis Function (RBF) kernel, to model pairwise relationships. A\nGraph Neural Network (GNN) is trained exclusively on synthetic datasets,\nenabling robust learning of clustering structures under controlled conditions.\nExtensive experiments demonstrate that ACTGNN significantly outperforms\nbaseline methods on both synthetic and real-world datasets, exhibiting superior\nperformance in detecting faint clustering structures, even in high-dimensional\nor noisy data. Our results highlight the generalizability and effectiveness of\nthe proposed approach, making it a promising tool for robust clustering\ntendency assessment.\n", "date": "2025-01-30", "categories": []}
{"id": "2501.18143", "title": "Dual-Bounded Nonlinear Optimal Transport for Size Constrained Min Cut\n  Clustering", "abstract": "  Min cut is an important graph partitioning method. However, current solutions\nto the min cut problem suffer from slow speeds, difficulty in solving, and\noften converge to simple solutions. To address these issues, we relax the min\ncut problem into a dual-bounded constraint and, for the first time, treat the\nmin cut problem as a dual-bounded nonlinear optimal transport problem.\nAdditionally, we develop a method for solving dual-bounded nonlinear optimal\ntransport based on the Frank-Wolfe method (abbreviated as DNF). Notably, DNF\nnot only solves the size constrained min cut problem but is also applicable to\nall dual-bounded nonlinear optimal transport problems. We prove that for convex\nproblems satisfying Lipschitz smoothness, the DNF method can achieve a\nconvergence rate of \\(\\mathcal{O}(\\frac{1}{t})\\). We apply the DNF method to\nthe min cut problem and find that it achieves state-of-the-art performance in\nterms of both the loss function and clustering accuracy at the fastest speed,\nwith a convergence rate of \\(\\mathcal{O}(\\frac{1}{\\sqrt{t}})\\). Moreover, the\nDNF method for the size constrained min cut problem requires no parameters and\nexhibits better stability.\n", "date": "2025-01-30", "categories": []}
{"id": "2311.15384", "title": "Dirichlet Process-based Robust Clustering using the Median-of-Means\n  Estimator", "abstract": "  Clustering stands as one of the most prominent challenges in unsupervised\nmachine learning. Among centroid-based methods, the classic $k$-means\nalgorithm, based on Lloyd's heuristic, is widely used. Nonetheless, it is a\nwell-known fact that $k$-means and its variants face several challenges,\nincluding heavy reliance on initial cluster centroids, susceptibility to\nconverging into local minima of the objective function, and sensitivity to\noutliers and noise in the data. When data contains noise or outliers, the\nMedian-of-Means (MoM) estimator offers a robust alternative for stabilizing\ncentroid-based methods. On a different note, another limitation in many\ncommonly used clustering methods is the need to specify the number of clusters\nbeforehand. Model-based approaches, such as Bayesian nonparametric models,\naddress this issue by incorporating infinite mixture models, which eliminate\nthe requirement for predefined cluster counts. Motivated by these facts, in\nthis article, we propose an efficient and automatic clustering technique by\nintegrating the strengths of model-based and centroid-based methodologies. Our\nmethod mitigates the effect of noise on the quality of clustering; while at the\nsame time, estimates the number of clusters. Statistical guarantees on an upper\nbound of clustering error, and rigorous assessment through simulated and real\ndatasets, suggest the advantages of our proposed method over existing\nstate-of-the-art clustering algorithms.\n", "date": "2023-11-26", "categories": []}
{"id": "2501.11422", "title": "Multi-View Spectral Clustering for Graphs with Multiple View Structures", "abstract": "  Despite the fundamental importance of clustering, to this day, much of the\nrelevant research is still based on ambiguous foundations, leading to an\nunclear understanding of whether or how the various clustering methods are\nconnected with each other. In this work, we provide an additional stepping\nstone towards resolving such ambiguities by presenting a general clustering\nframework that subsumes a series of seemingly disparate clustering methods,\nincluding various methods belonging to the widely popular spectral clustering\nframework. In fact, the generality of the proposed framework is additionally\ncapable of shedding light to the largely unexplored area of multi-view graphs\nwhere each view may have differently clustered nodes. In turn, we propose\nGenClus: a method that is simultaneously an instance of this framework and a\ngeneralization of spectral clustering, while also being closely related to\nk-means as well. This results in a principled alternative to the few existing\nmethods studying this special type of multi-view graphs. Then, we conduct\nin-depth experiments, which demonstrate that GenClus is more computationally\nefficient than existing methods, while also attaining similar or better\nclustering performance. Lastly, a qualitative real-world case-study further\ndemonstrates the ability of GenClus to produce meaningful clusterings.\n", "date": "2025-01-20", "categories": []}
{"id": "2408.17244", "title": "Categorical data clustering: 25 years beyond K-modes", "abstract": "  The clustering of categorical data is a common and important task in computer\nscience, offering profound implications across a spectrum of applications.\nUnlike purely numerical data, categorical data often lack inherent ordering as\nin nominal data, or have varying levels of order as in ordinal data, thus\nrequiring specialized methodologies for efficient organization and analysis.\nThis review provides a comprehensive synthesis of categorical data clustering\nin the past twenty-five years, starting from the introduction of K-modes. It\nelucidates the pivotal role of categorical data clustering in diverse fields\nsuch as health sciences, natural sciences, social sciences, education,\nengineering and economics. Practical comparisons are conducted for algorithms\nhaving public implementations, highlighting distinguishing clustering\nmethodologies and revealing the performance of recent algorithms on several\nbenchmark categorical datasets. Finally, challenges and opportunities in the\nfield are discussed.\n", "date": "2024-08-30", "categories": []}
{"id": "2501.11139", "title": "Community Detection for Contextual-LSBM: Theoretical Limitations of\n  Misclassification Rate and Efficient Algorithms", "abstract": "  The integration of network information and node attribute information has\nrecently gained significant attention in the community detection literature. In\nthis work, we consider community detection in the Contextual Labeled Stochastic\nBlock Model (CLSBM), where the network follows an LSBM and node attributes\nfollow a Gaussian Mixture Model (GMM). Our primary focus is the\nmisclassification rate, which measures the expected number of nodes\nmisclassified by community detection algorithms. We first establish a lower\nbound on the optimal misclassification rate that holds for any algorithm. When\nwe specialize our setting to the LSBM (which preserves only network\ninformation) or the GMM (which preserves only node attribute information), our\nlower bound recovers prior results. Moreover, we present an efficient\nspectral-based algorithm tailored for the CLSBM and derive an upper bound on\nits misclassification rate. Although the algorithm does not attain the lower\nbound, it serves as a reliable starting point for designing more accurate\ncommunity detection algorithms (as many algorithms use spectral method as an\ninitial step, followed by refinement procedures to enhance accuracy).\n", "date": "2025-01-19", "categories": []}
{"id": "2501.15542", "title": "Estimating the Optimal Number of Clusters in Categorical Data Clustering\n  by Silhouette Coefficient", "abstract": "  The problem of estimating the number of clusters (say k) is one of the major\nchallenges for the partitional clustering. This paper proposes an algorithm\nnamed k-SCC to estimate the optimal k in categorical data clustering. For the\nclustering step, the algorithm uses the kernel density estimation approach to\ndefine cluster centers. In addition, it uses an information-theoretic based\ndissimilarity to measure the distance between centers and objects in each\ncluster. The silhouette analysis based approach is then used to evaluate the\nquality of different clustering obtained in the former step to choose the best\nk. Comparative experiments were conducted on both synthetic and real datasets\nto compare the performance of k-SCC with three other algorithms. Experimental\nresults show that k-SCC outperforms the compared algorithms in determining the\nnumber of clusters for each dataset.\n", "date": "2025-01-26", "categories": []}
{"id": "2501.16113", "title": "Fixed-sized clusters $k$-Means", "abstract": "  We present a $k$-means-based clustering algorithm, which optimizes the mean\nsquare error, for given cluster sizes. A straightforward application is\nbalanced clustering, where the sizes of each cluster are equal. In the\n$k$-means assignment phase, the algorithm solves an assignment problem using\nthe Hungarian algorithm. This makes the assignment phase time complexity\n$O(n^3)$. This enables clustering of datasets of size more than 5000 points.\n", "date": "2025-01-27", "categories": []}
{"id": "2501.13597", "title": "A Comprehensive Survey on Spectral Clustering with Graph Structure\n  Learning", "abstract": "  Spectral clustering is a powerful technique for clustering high-dimensional\ndata, utilizing graph-based representations to detect complex, non-linear\nstructures and non-convex clusters. The construction of a similarity graph is\nessential for ensuring accurate and effective clustering, making graph\nstructure learning (GSL) central for enhancing spectral clustering performance\nin response to the growing demand for scalable solutions. Despite advancements\nin GSL, there is a lack of comprehensive surveys specifically addressing its\nrole within spectral clustering. To bridge this gap, this survey presents a\ncomprehensive review of spectral clustering methods, emphasizing on the\ncritical role of GSL. We explore various graph construction techniques,\nincluding pairwise, anchor, and hypergraph-based methods, in both fixed and\nadaptive settings. Additionally, we categorize spectral clustering approaches\ninto single-view and multi-view frameworks, examining their applications within\none-step and two-step clustering processes. We also discuss multi-view\ninformation fusion techniques and their impact on clustering data. By\naddressing current challenges and proposing future research directions, this\nsurvey provides valuable insights for advancing spectral clustering\nmethodologies and highlights the pivotal role of GSL in tackling large-scale\nand high-dimensional data clustering tasks.\n", "date": "2025-01-23", "categories": []}
{"id": "2411.17354", "title": "DWCL: Dual-Weighted Contrastive Learning for Multi-View Clustering", "abstract": "  Multi-view contrastive clustering (MVCC) has gained significant attention for\ngenerating consistent clustering structures from multiple views through\ncontrastive learning. However, most existing MVCC methods create cross-views by\ncombining any two views, leading to a high volume of unreliable pairs.\nFurthermore, these approaches often overlook discrepancies in multi-view\nrepresentations, resulting in representation degeneration. To address these\nchallenges, we introduce a novel model called Dual-Weighted Contrastive\nLearning (DWCL) for Multi-View Clustering. Specifically, to reduce the impact\nof unreliable cross-views, we introduce an innovative Best-Other (B-O)\ncontrastive mechanism that enhances the representation of individual views at a\nlow computational cost. Furthermore, we develop a dual weighting strategy that\ncombines a view quality weight, reflecting the quality of each view, with a\nview discrepancy weight. This approach effectively mitigates representation\ndegeneration by downplaying cross-views that are both low in quality and high\nin discrepancy. We theoretically validate the efficiency of the B-O contrastive\nmechanism and the effectiveness of the dual weighting strategy. Extensive\nexperiments demonstrate that DWCL outperforms previous methods across eight\nmulti-view datasets, showcasing superior performance and robustness in MVCC.\nSpecifically, our method achieves absolute accuracy improvements of 5.4\\% and\n5.6\\% compared to state-of-the-art methods on the Caltech6V7 and MSRCv1\ndatasets, respectively.\n", "date": "2024-11-26", "categories": []}
{"id": "2501.06368", "title": "Towards Robust Nonlinear Subspace Clustering: A Kernel Learning Approach", "abstract": "  Kernel-based subspace clustering, which addresses the nonlinear structures in\ndata, is an evolving area of research. Despite noteworthy progressions,\nprevailing methodologies predominantly grapple with limitations relating to (i)\nthe influence of predefined kernels on model performance; (ii) the difficulty\nof preserving the original manifold structures in the nonlinear space; (iii)\nthe dependency of spectral-type strategies on the ideal block diagonal\nstructure of the affinity matrix. This paper presents DKLM, a novel paradigm\nfor kernel-induced nonlinear subspace clustering. DKLM provides a data-driven\napproach that directly learns the kernel from the data's self-representation,\nensuring adaptive weighting and satisfying the multiplicative triangle\ninequality constraint, which enhances the robustness of the learned kernel. By\nleveraging this learned kernel, DKLM preserves the local manifold structure of\ndata in a nonlinear space while promoting the formation of an optimal\nblock-diagonal affinity matrix. A thorough theoretical examination of DKLM\nreveals its relationship with existing clustering paradigms. Comprehensive\nexperiments on synthetic and real-world datasets demonstrate the effectiveness\nof the proposed method.\n", "date": "2025-01-10", "categories": []}
{"id": "2501.11898", "title": "Highly Efficient Rotation-Invariant Spectral Embedding for Scalable\n  Incomplete Multi-View Clustering", "abstract": "  Incomplete multi-view clustering presents significant challenges due to\nmissing views. Although many existing graph-based methods aim to recover\nmissing instances or complete similarity matrices with promising results, they\nstill face several limitations: (1) Recovered data may be unsuitable for\nspectral clustering, as these methods often ignore guidance from spectral\nanalysis; (2) Complex optimization processes require high computational burden,\nhindering scalability to large-scale problems; (3) Most methods do not address\nthe rotational mismatch problem in spectral embeddings. To address these\nissues, we propose a highly efficient rotation-invariant spectral embedding\n(RISE) method for scalable incomplete multi-view clustering. RISE learns\nview-specific embeddings from incomplete bipartite graphs to capture the\ncomplementary information. Meanwhile, a complete consensus representation with\nsecond-order rotation-invariant property is recovered from these incomplete\nembeddings in a unified model. Moreover, we design a fast alternating\noptimization algorithm with linear complexity and promising convergence to\nsolve the proposed formulation. Extensive experiments on multiple datasets\ndemonstrate the effectiveness, scalability, and efficiency of RISE compared to\nthe state-of-the-art methods.\n", "date": "2025-01-21", "categories": []}
{"id": "2501.10084", "title": "Two-level Solar Irradiance Clustering with Season Identification: A\n  Comparative Analysis", "abstract": "  Solar irradiance clustering can enhance solar power capacity planning and\nhelp improve forecasting models by identifying similar irradiance patterns\ninfluenced by seasonal and weather changes. In this study, we adopt an\nefficient two-level clustering approach to automatically identify seasons using\nthe clear sky irradiance in first level and subsequently to identify daily\ncloud level as clear, cloudy and partly cloudy within each season in second\nlevel. In the second level of clustering, three methods are compared, namely,\nDaily Irradiance Index (DII or $\\beta$), Euclidean Distance (ED), and Dynamic\nTime Warping (DTW) distance. The DII is computed as the ratio of time integral\nof measured irradiance to time integral of the clear sky irradiance. The\nidentified clusters were compared quantitatively using established clustering\nmetrics and qualitatively by comparing the mean irradiance profiles. The\nresults clearly establish the superiority of the $\\beta$-based clustering\napproach as the leader, setting a new benchmark for solar irradiance clustering\nstudies. Moreover, $\\beta$-based clustering remains effective even for annual\ndata unlike the time-series methods which suffer significant performance\ndegradation. Interestingly, contrary to expectations, ED-based clustering\noutperforms the more compute-intensive DTW distance-based clustering. The\nmethod has been rigorously validated using data from two distinct US locations,\ndemonstrating robust scalability for larger datasets and potential\napplicability for other locations.\n", "date": "2025-01-17", "categories": []}
{"id": "2305.14641", "title": "Graph Analysis Using a GPU-based Parallel Algorithm: Quantum Clustering", "abstract": "  The article introduces a new method for applying Quantum Clustering to graph\nstructures. Quantum Clustering (QC) is a novel density-based unsupervised\nlearning method that determines cluster centers by constructing a potential\nfunction. In this method, we use the Graph Gradient Descent algorithm to find\nthe centers of clusters. GPU parallelization is utilized for computing\npotential values. We also conducted experiments on five widely used datasets\nand evaluated using four indicators. The results show superior performance of\nthe method. Finally, we discuss the influence of $\\sigma$ on the experimental\nresults.\n", "date": "2023-05-24", "categories": []}
{"id": "2501.00230", "title": "Federated Deep Subspace Clustering", "abstract": "  This paper introduces FDSC, a private-protected subspace clustering (SC)\napproach with federated learning (FC) schema. In each client, there is a deep\nsubspace clustering network accounting for grouping the isolated data, composed\nof a encode network, a self-expressive layer, and a decode network. FDSC is\nachieved by uploading the encode network to communicate with other clients in\nthe server. Besides, FDSC is also enhanced by preserving the local neighborhood\nrelationship in each client. With the effects of federated learning and\nlocality preservation, the learned data features from the encoder are boosted\nso as to enhance the self-expressiveness learning and result in better\nclustering performance. Experiments test FDSC on public datasets and compare\nwith other clustering methods, demonstrating the effectiveness of FDSC.\n", "date": "2024-12-31", "categories": []}
{"id": "2501.08416", "title": "A Survey on Recent Advances in Self-Organizing Maps", "abstract": "  Self-organising maps are a powerful tool for cluster analysis in a wide range\nof data contexts. From the pioneer work of Kohonen, many variants and\nimprovements have been proposed. This review focuses on the last decade, in\norder to provide an overview of the main evolution of the seminal SOM algorithm\nas well as of the methodological developments that have been achieved in order\nto better fit to various application contexts and users' requirements. We also\nhighlight a specific and important application field that is related to\ncommercial use of SOM, which involves specific data management.\n", "date": "2024-12-10", "categories": []}
{"id": "2501.08717", "title": "$\\texttt{InfoHier}$: Hierarchical Information Extraction via Encoding\n  and Embedding", "abstract": "  Analyzing large-scale datasets, especially involving complex and\nhigh-dimensional data like images, is particularly challenging. While\nself-supervised learning (SSL) has proven effective for learning\nrepresentations from unlabelled data, it typically focuses on flat,\nnon-hierarchical structures, missing the multi-level relationships present in\nmany real-world datasets. Hierarchical clustering (HC) can uncover these\nrelationships by organizing data into a tree-like structure, but it often\nrelies on rigid similarity metrics that struggle to capture the complexity of\ndiverse data types. To address these we envision $\\texttt{InfoHier}$, a\nframework that combines SSL with HC to jointly learn robust latent\nrepresentations and hierarchical structures. This approach leverages SSL to\nprovide adaptive representations, enhancing HC's ability to capture complex\npatterns. Simultaneously, it integrates HC loss to refine SSL training,\nresulting in representations that are more attuned to the underlying\ninformation hierarchy. $\\texttt{InfoHier}$ has the potential to improve the\nexpressiveness and performance of both clustering and representation learning,\noffering significant benefits for data analysis, management, and information\nretrieval.\n", "date": "2025-01-15", "categories": []}
{"id": "2501.06588", "title": "A Tight VC-Dimension Analysis of Clustering Coresets with Applications", "abstract": "  We consider coresets for $k$-clustering problems, where the goal is to assign\npoints to centers minimizing powers of distances. A popular example is the\n$k$-median objective $\\sum_{p}\\min_{c\\in C}dist(p,C)$. Given a point set $P$, a\ncoreset $\\Omega$ is a small weighted subset that approximates the cost of $P$\nfor all candidate solutions $C$ up to a $(1\\pm\\varepsilon )$ multiplicative\nfactor. In this paper, we give a sharp VC-dimension based analysis for coreset\nconstruction. As a consequence, we obtain improved $k$-median coreset bounds\nfor the following metrics:\n  Coresets of size $\\tilde{O}\\left(k\\varepsilon^{-2}\\right)$ for shortest path\nmetrics in planar graphs, improving over the bounds\n$\\tilde{O}\\left(k\\varepsilon^{-6}\\right)$ by [Cohen-Addad, Saulpic,\nSchwiegelshohn, STOC'21] and $\\tilde{O}\\left(k^2\\varepsilon^{-4}\\right)$ by\n[Braverman, Jiang, Krauthgamer, Wu, SODA'21].\n  Coresets of size $\\tilde{O}\\left(kd\\ell\\varepsilon^{-2}\\log m\\right)$ for\nclustering $d$-dimensional polygonal curves of length at most $m$ with curves\nof length at most $\\ell$ with respect to Frechet metrics, improving over the\nbounds $\\tilde{O}\\left(k^3d\\ell\\varepsilon^{-3}\\log m\\right)$ by [Braverman,\nCohen-Addad, Jiang, Krauthgamer, Schwiegelshohn, Toftrup, and Wu, FOCS'22] and\n$\\tilde{O}\\left(k^2d\\ell\\varepsilon^{-2}\\log m \\log |P|\\right)$ by [Conradi,\nKolbe, Psarros, Rohde, SoCG'24].\n", "date": "2025-01-11", "categories": []}
{"id": "2403.03670", "title": "CDC: A Simple Framework for Complex Data Clustering", "abstract": "  In today's data-driven digital era, the amount as well as complexity, such as\nmulti-view, non-Euclidean, and multi-relational, of the collected data are\ngrowing exponentially or even faster. Clustering, which unsupervisely extracts\nvalid knowledge from data, is extremely useful in practice. However, existing\nmethods are independently developed to handle one particular challenge at the\nexpense of the others. In this work, we propose a simple but effective\nframework for complex data clustering (CDC) that can efficiently process\ndifferent types of data with linear complexity. We first utilize graph\nfiltering to fuse geometry structure and attribute information. We then reduce\nthe complexity with high-quality anchors that are adaptively learned via a\nnovel similarity-preserving regularizer. We illustrate the cluster-ability of\nour proposed method theoretically and experimentally. In particular, we deploy\nCDC to graph data of size 111M.\n", "date": "2024-03-06", "categories": []}
{"id": "2412.09902", "title": "One Node One Model: Featuring the Missing-Half for Graph Clustering", "abstract": "  Most existing graph clustering methods primarily focus on exploiting\ntopological structure, often neglecting the ``missing-half\" node feature\ninformation, especially how these features can enhance clustering performance.\nThis issue is further compounded by the challenges associated with\nhigh-dimensional features. Feature selection in graph clustering is\nparticularly difficult because it requires simultaneously discovering clusters\nand identifying the relevant features for these clusters. To address this gap,\nwe introduce a novel paradigm called ``one node one model\", which builds an\nexclusive model for each node and defines the node label as a combination of\npredictions for node groups. Specifically, the proposed ``Feature Personalized\nGraph Clustering (FPGC)\" method identifies cluster-relevant features for each\nnode using a squeeze-and-excitation block, integrating these features into each\nmodel to form the final representations. Additionally, the concept of feature\ncross is developed as a data augmentation technique to learn low-order feature\ninteractions. Extensive experimental results demonstrate that FPGC outperforms\nstate-of-the-art clustering methods. Moreover, the plug-and-play nature of our\nmethod provides a versatile solution to enhance GNN-based models from a feature\nperspective.\n", "date": "2024-12-13", "categories": []}
{"id": "2412.18930", "title": "Graph Cut-guided Maximal Coding Rate Reduction for Learning Image\n  Embedding and Clustering", "abstract": "  In the era of pre-trained models, image clustering task is usually addressed\nby two relevant stages: a) to produce features from pre-trained vision models;\nand b) to find clusters from the pre-trained features. However, these two\nstages are often considered separately or learned by different paradigms,\nleading to suboptimal clustering performance. In this paper, we propose a\nunified framework, termed graph Cut-guided Maximal Coding Rate Reduction\n(CgMCR$^2$), for jointly learning the structured embeddings and the clustering.\nTo be specific, we attempt to integrate an efficient clustering module into the\nprincipled framework for learning structured representation, in which the\nclustering module is used to provide partition information to guide the\ncluster-wise compression and the learned embeddings is aligned to desired\ngeometric structures in turn to help for yielding more accurate partitions. We\nconduct extensive experiments on both standard and out-of-domain image datasets\nand experimental results validate the effectiveness of our approach.\n", "date": "2024-12-25", "categories": []}
{"id": "2412.16487", "title": "Trusted Mamba Contrastive Network for Multi-View Clustering", "abstract": "  Multi-view clustering can partition data samples into their categories by\nlearning a consensus representation in an unsupervised way and has received\nmore and more attention in recent years. However, there is an untrusted fusion\nproblem. The reasons for this problem are as follows: 1) The current methods\nignore the presence of noise or redundant information in the view; 2) The\nsimilarity of contrastive learning comes from the same sample rather than the\nsame cluster in deep multi-view clustering. It causes multi-view fusion in the\nwrong direction. This paper proposes a novel multi-view clustering network to\naddress this problem, termed as Trusted Mamba Contrastive Network (TMCN).\nSpecifically, we present a new Trusted Mamba Fusion Network (TMFN), which\nachieves a trusted fusion of multi-view data through a selective mechanism.\nMoreover, we align the fused representation and the view-specific\nrepresentation using the Average-similarity Contrastive Learning (AsCL) module.\nAsCL increases the similarity of view presentation from the same cluster, not\nmerely from the same sample. Extensive experiments show that the proposed\nmethod achieves state-of-the-art results in deep multi-view clustering tasks.\nThe source code is available at https://github.com/HackerHyper/TMCN.\n", "date": "2024-12-21", "categories": []}
{"id": "2501.01595", "title": "Adaptive Homophily Clustering: Structure Homophily Graph Learning with\n  Adaptive Filter for Hyperspectral Image", "abstract": "  Hyperspectral image (HSI) clustering has been a fundamental but challenging\ntask with zero training labels. Currently, some deep graph clustering methods\nhave been successfully explored for HSI due to their outstanding performance in\neffective spatial structural information encoding. Nevertheless, insufficient\nstructural information utilization, poor feature presentation ability, and weak\ngraph update capability limit their performance. Thus, in this paper, a\nhomophily structure graph learning with an adaptive filter clustering method\n(AHSGC) for HSI is proposed. Specifically, homogeneous region generation is\nfirst developed for HSI processing and constructing the original graph.\nAfterward, an adaptive filter graph encoder is designed to adaptively capture\nthe high and low frequency features on the graph for subsequence processing.\nThen, a graph embedding clustering self-training decoder is developed with KL\nDivergence, with which the pseudo-label is generated for network training.\nMeanwhile, homophily-enhanced structure learning is introduced to update the\ngraph according to the clustering task, in which the orient correlation\nestimation is adopted to estimate the node connection, and graph edge\nsparsification is designed to adjust the edges in the graph dynamically.\nFinally, a joint network optimization is introduced to achieve network\nself-training and update the graph. The K-means is adopted to express the\nlatent features. Extensive experiments and repeated comparative analysis have\nverified that our AHSGC contains high clustering accuracy, low computational\ncomplexity, and strong robustness. The code source will be available at\nhttps://github.com/DY-HYX.\n", "date": "2025-01-03", "categories": []}
{"id": "2307.07346", "title": "Clusterability test for categorical data", "abstract": "  The objective of clusterability evaluation is to check whether a clustering\nstructure exists within the data set. As a crucial yet often-overlooked issue\nin cluster analysis, it is essential to conduct such a test before applying any\nclustering algorithm. If a data set is unclusterable, any subsequent clustering\nanalysis would not yield valid results. Despite its importance, the majority of\nexisting studies focus on numerical data, leaving the clusterability evaluation\nissue for categorical data as an open problem. Here we present TestCat, a\ntesting-based approach to assess the clusterability of categorical data in\nterms of an analytical $p$-value. The key idea underlying TestCat is that\nclusterable categorical data possess many strongly associated attribute pairs\nand hence the sum of chi-squared statistics of all attribute pairs is employed\nas the test statistic for $p$-value calculation. We apply our method to a set\nof benchmark categorical data sets, showing that TestCat outperforms those\nsolutions based on existing clusterability evaluation methods for numeric data.\nTo the best of our knowledge, our work provides the first way to effectively\nrecognize the clusterability of categorical data in a statistically sound\nmanner.\n", "date": "2023-07-14", "categories": []}
{"id": "2501.01484", "title": "Sequencing Silicates in the IRS Debris Disk Catalog I: Methodology for\n  Unsupervised Clustering", "abstract": "  Debris disks, which consist of dust, planetesimals, planets, and gas, offer a\nunique window into the mineralogical composition of their parent bodies,\nespecially during the critical phase of terrestrial planet formation spanning\n10 to a few hundred million years. Observations from the $\\textit{Spitzer}$\nSpace Telescope have unveiled thousands of debris disks, yet systematic studies\nremain scarce, let alone those with unsupervised clustering techniques. This\nstudy introduces $\\texttt{CLUES}$ (CLustering UnsupErvised with Sequencer), a\nnovel, non-parametric, fully-interpretable machine-learning spectral analysis\ntool designed to analyze and classify the spectral data of debris disks.\n$\\texttt{CLUES}$ combines multiple unsupervised clustering methods with\nmulti-scale distance measures to discern new groupings and trends, offering\ninsights into compositional diversity and geophysical processes within these\ndisks. Our analysis allows us to explore a vast parameter space in debris disk\nmineralogy and also offers broader applications in fields such as\nprotoplanetary disks and solar system objects. This paper details the\nmethodology, implementation, and initial results of $\\texttt{CLUES}$, setting\nthe stage for more detailed follow-up studies focusing on debris disk\nmineralogy and demographics.\n", "date": "2025-01-02", "categories": []}
{"id": "2408.00056", "title": "Temporal Subspace Clustering for Molecular Dynamics Data", "abstract": "  We introduce MOSCITO (MOlecular Dynamics Subspace Clustering with Temporal\nObservance), a subspace clustering for molecular dynamics data. MOSCITO groups\nthose timesteps of a molecular dynamics trajectory together into clusters in\nwhich the molecule has similar conformations. In contrast to state-of-the-art\nmethods, MOSCITO takes advantage of sequential relationships found in time\nseries data. Unlike existing work, MOSCITO does not need a two-step procedure\nwith tedious post-processing, but directly models essential properties of the\ndata. Interpreting clusters as Markov states allows us to evaluate the\nclustering performance based on the resulting Markov state models. In\nexperiments on 60 trajectories and 4 different proteins, we show that the\nperformance of MOSCITO achieves state-of-the-art performance in a novel\nsingle-step method. Moreover, by modeling temporal aspects, MOSCITO obtains\nbetter segmentation of trajectories, especially for small numbers of clusters.\n", "date": "2024-07-31", "categories": []}
{"id": "2411.12329", "title": "Attributed Graph Clustering in Collaborative Settings", "abstract": "  Graph clustering is an unsupervised machine learning method that partitions\nthe nodes in a graph into different groups. Despite achieving significant\nprogress in exploiting both attributed and structured data information, graph\nclustering methods often face practical challenges related to data isolation.\nMoreover, the absence of collaborative methods for graph clustering limits\ntheir effectiveness.\n  In this paper, we propose a collaborative graph clustering framework for\nattributed graphs, supporting attributed graph clustering over vertically\npartitioned data with different participants holding distinct features of the\nsame data. Our method leverages a novel technique that reduces the sample\nspace, improving the efficiency of the attributed graph clustering method.\nFurthermore, we compare our method to its centralized counterpart under a\nproximity condition, demonstrating that the successful local results of each\nparticipant contribute to the overall success of the collaboration.\n  We fully implement our approach and evaluate its utility and efficiency by\nconducting experiments on four public datasets. The results demonstrate that\nour method achieves comparable accuracy levels to centralized attributed graph\nclustering methods. Our collaborative graph clustering framework provides an\nefficient and effective solution for graph clustering challenges related to\ndata isolation.\n", "date": "2024-11-19", "categories": []}
{"id": "2412.20035", "title": "A Greedy Strategy for Graph Cut", "abstract": "  We propose a Greedy strategy to solve the problem of Graph Cut, called GGC.\nIt starts from the state where each data sample is regarded as a cluster and\ndynamically merges the two clusters which reduces the value of the global\nobjective function the most until the required number of clusters is obtained,\nand the monotonicity of the sequence of objective function values is proved. To\nreduce the computational complexity of GGC, only mergers between clusters and\ntheir neighbors are considered. Therefore, GGC has a nearly linear\ncomputational complexity with respect to the number of samples. Also, unlike\nother algorithms, due to the greedy strategy, the solution of the proposed\nalgorithm is unique. In other words, its performance is not affected by\nrandomness. We apply the proposed method to solve the problem of normalized cut\nwhich is a widely concerned graph cut problem. Extensive experiments show that\nbetter solutions can often be achieved compared to the traditional two-stage\noptimization algorithm (eigendecomposition + k-means), on the normalized cut\nproblem. In addition, the performance of GGC also has advantages compared to\nseveral state-of-the-art clustering algorithms.\n", "date": "2024-12-28", "categories": []}
{"id": "2412.20341", "title": "Asynchronous Federated Clustering with Unknown Number of Clusters", "abstract": "  Federated Clustering (FC) is crucial to mining knowledge from unlabeled\nnon-Independent Identically Distributed (non-IID) data provided by multiple\nclients while preserving their privacy. Most existing attempts learn cluster\ndistributions at local clients, and then securely pass the desensitized\ninformation to the server for aggregation. However, some tricky but common FC\nproblems are still relatively unexplored, including the heterogeneity in terms\nof clients' communication capacity and the unknown number of proper clusters\n$k^*$. To further bridge the gap between FC and real application scenarios,\nthis paper first shows that the clients' communication asynchrony and unknown\n$k^*$ are complex coupling problems, and then proposes an Asynchronous\nFederated Cluster Learning (AFCL) method accordingly. It spreads the excessive\nnumber of seed points to the clients as a learning medium and coordinates them\nacross the clients to form a consensus. To alleviate the distribution imbalance\ncumulated due to the unforeseen asynchronous uploading from the heterogeneous\nclients, we also design a balancing mechanism for seeds updating. As a result,\nthe seeds gradually adapt to each other to reveal a proper number of clusters.\nExtensive experiments demonstrate the efficacy of AFCL.\n", "date": "2024-12-29", "categories": []}
{"id": "2412.20582", "title": "Bridging the Gap: A Decade Review of Time-Series Clustering Methods", "abstract": "  Time series, as one of the most fundamental representations of sequential\ndata, has been extensively studied across diverse disciplines, including\ncomputer science, biology, geology, astronomy, and environmental sciences. The\nadvent of advanced sensing, storage, and networking technologies has resulted\nin high-dimensional time-series data, however, posing significant challenges\nfor analyzing latent structures over extended temporal scales. Time-series\nclustering, an established unsupervised learning strategy that groups similar\ntime series together, helps unveil hidden patterns in these complex datasets.\nIn this survey, we trace the evolution of time-series clustering methods from\nclassical approaches to recent advances in neural networks. While previous\nsurveys have focused on specific methodological categories, we bridge the gap\nbetween traditional clustering methods and emerging deep learning-based\nalgorithms, presenting a comprehensive, unified taxonomy for this research\narea. This survey highlights key developments and provides insights to guide\nfuture research in time-series clustering.\n", "date": "2024-12-29", "categories": []}
{"id": "2412.18838", "title": "DiFiC: Your Diffusion Model Holds the Secret to Fine-Grained Clustering", "abstract": "  Fine-grained clustering is a practical yet challenging task, whose essence\nlies in capturing the subtle differences between instances of different\nclasses. Such subtle differences can be easily disrupted by data augmentation\nor be overwhelmed by redundant information in data, leading to significant\nperformance degradation for existing clustering methods. In this work, we\nintroduce DiFiC a fine-grained clustering method building upon the conditional\ndiffusion model. Distinct from existing works that focus on extracting\ndiscriminative features from images, DiFiC resorts to deducing the textual\nconditions used for image generation. To distill more precise and\nclustering-favorable object semantics, DiFiC further regularizes the diffusion\ntarget and guides the distillation process utilizing neighborhood similarity.\nExtensive experiments demonstrate that DiFiC outperforms both state-of-the-art\ndiscriminative and generative clustering methods on four fine-grained image\nclustering benchmarks. We hope the success of DiFiC will inspire future\nresearch to unlock the potential of diffusion models in tasks beyond\ngeneration. The code will be released.\n", "date": "2024-12-25", "categories": []}
{"id": "2412.18847", "title": "TPCH: Tensor-interacted Projection and Cooperative Hashing for\n  Multi-view Clustering", "abstract": "  In recent years, anchor and hash-based multi-view clustering methods have\ngained attention for their efficiency and simplicity in handling large-scale\ndata. However, existing methods often overlook the interactions among\nmulti-view data and higher-order cooperative relationships during projection,\nnegatively impacting the quality of hash representation in low-dimensional\nspaces, clustering performance, and sensitivity to noise. To address this\nissue, we propose a novel approach named Tensor-Interacted Projection and\nCooperative Hashing for Multi-View Clustering(TPCH). TPCH stacks multiple\nprojection matrices into a tensor, taking into account the synergies and\ncommunications during the projection process. By capturing higher-order\nmulti-view information through dual projection and Hamming space, TPCH employs\nan enhanced tensor nuclear norm to learn more compact and distinguishable hash\nrepresentations, promoting communication within and between views. Experimental\nresults demonstrate that this refined method significantly outperforms\nstate-of-the-art methods in clustering on five large-scale multi-view datasets.\nMoreover, in terms of CPU time, TPCH achieves substantial acceleration compared\nto the most advanced current methods. The code is available at\n\\textcolor{red}{\\url{https://github.com/jankin-wang/TPCH}}.\n", "date": "2024-12-25", "categories": []}
{"id": "2412.15295", "title": "Log-Time K-Means Clustering for 1D Data: Novel Approaches with Proof and\n  Implementation", "abstract": "  Clustering is a key task in machine learning, with $k$-means being widely\nused for its simplicity and effectiveness. While 1D clustering is common,\nexisting methods often fail to exploit the structure of 1D data, leading to\ninefficiencies. This thesis introduces optimized algorithms for $k$-means++\ninitialization and Lloyd's algorithm, leveraging sorted data, prefix sums, and\nbinary search for improved computational performance. The main contributions\nare: (1) an optimized $k$-cluster algorithm achieving $O(l \\cdot k^2 \\cdot \\log\nn)$ complexity for greedy $k$-means++ initialization and $O(i \\cdot k \\cdot\n\\log n)$ for Lloyd's algorithm, where $l$ is the number of greedy $k$-means++\nlocal trials, and $i$ is the number of Lloyd's algorithm iterations, and (2) a\nbinary search-based two-cluster algorithm, achieving $O(\\log n)$ runtime with\ndeterministic convergence to a Lloyd's algorithm local minimum. Benchmarks\ndemonstrate over a 4500x speedup compared to scikit-learn for large datasets\nwhile maintaining clustering quality measured by within-cluster sum of squares\n(WCSS). Additionally, the algorithms achieve a 300x speedup in an LLM\nquantization task, highlighting their utility in emerging applications. This\nthesis bridges theory and practice for 1D $k$-means clustering, delivering\nefficient and sound algorithms implemented in a JIT-optimized open-source\nPython library.\n", "date": "2024-12-19", "categories": []}
{"id": "2412.18207", "title": "Sharper Error Bounds in Late Fusion Multi-view Clustering Using\n  Eigenvalue Proportion", "abstract": "  Multi-view clustering (MVC) aims to integrate complementary information from\nmultiple views to enhance clustering performance. Late Fusion Multi-View\nClustering (LFMVC) has shown promise by synthesizing diverse clustering results\ninto a unified consensus. However, current LFMVC methods struggle with noisy\nand redundant partitions and often fail to capture high-order correlations\nacross views. To address these limitations, we present a novel theoretical\nframework for analyzing the generalization error bounds of multiple kernel\n$k$-means, leveraging local Rademacher complexity and principal eigenvalue\nproportions. Our analysis establishes a convergence rate of $\\mathcal{O}(1/n)$,\nsignificantly improving upon the existing rate in the order of\n$\\mathcal{O}(\\sqrt{k/n})$. Building on this insight, we propose a low-pass\ngraph filtering strategy within a multiple linear $k$-means framework to\nmitigate noise and redundancy, further refining the principal eigenvalue\nproportion and enhancing clustering accuracy. Experimental results on benchmark\ndatasets confirm that our approach outperforms state-of-the-art methods in\nclustering performance and robustness. The related codes is available at\nhttps://github.com/csliangdu/GMLKM .\n", "date": "2024-12-24", "categories": []}
{"id": "2412.16519", "title": "Anchor Learning with Potential Cluster Constraints for Multi-view\n  Clustering", "abstract": "  Anchor-based multi-view clustering (MVC) has received extensive attention due\nto its efficient performance. Existing methods only focus on how to dynamically\nlearn anchors from the original data and simultaneously construct anchor graphs\ndescribing the relationships between samples and perform clustering, while\nignoring the reality of anchors, i.e., high-quality anchors should be generated\nuniformly from different clusters of data rather than scattered outside the\nclusters. To deal with this problem, we propose a noval method termed Anchor\nLearning with Potential Cluster Constraints for Multi-view Clustering (ALPC)\nmethod. Specifically, ALPC first establishes a shared latent semantic module to\nconstrain anchors to be generated from specific clusters, and subsequently,\nALPC improves the representativeness and discriminability of anchors by\nadapting the anchor graph to capture the common clustering center of mass from\nsamples and anchors, respectively. Finally, ALPC combines anchor learning and\ngraph construction into a unified framework for collaborative learning and\nmutual optimization to improve the clustering performance. Extensive\nexperiments demonstrate the effectiveness of our proposed method compared to\nsome state-of-the-art MVC methods. Our source code is available at\nhttps://github.com/whbdmu/ALPC.\n", "date": "2024-12-21", "categories": []}
{"id": "2412.16713", "title": "A Unifying Family of Data-Adaptive Partitioning Algorithms", "abstract": "  Clustering algorithms remain valuable tools for grouping and summarizing the\nmost important aspects of data. Example areas where this is the case include\nimage segmentation, dimension reduction, signals analysis, model order\nreduction, numerical analysis, and others. As a consequence, many clustering\napproaches have been developed to satisfy the unique needs of each particular\nfield. In this article, we present a family of data-adaptive partitioning\nalgorithms that unifies several well-known methods (e.g., k-means and\nk-subspaces). Indexed by a single parameter and employing a common minimization\nstrategy, the algorithms are easy to use and interpret, and scale well to\nlarge, high-dimensional problems. In addition, we develop an adaptive mechanism\nthat (a) exhibits skill at automatically uncovering data structures and problem\nparameters without any expert knowledge and, (b) can be used to augment other\nexisting methods. By demonstrating the performance of our methods on examples\nfrom disparate fields including subspace clustering, model order reduction, and\nmatrix approximation, we hope to highlight their versatility and potential for\nextending the boundaries of existing scientific domains. We believe our\nfamily's parametrized structure represents a synergism of algorithms that will\nfoster new developments and directions, not least within the data science\ncommunity.\n", "date": "2024-12-21", "categories": []}
{"id": "2412.17647", "title": "An Adaptive Framework for Multi-View Clustering Leveraging Conditional\n  Entropy Optimization", "abstract": "  Multi-view clustering (MVC) has emerged as a powerful technique for\nextracting valuable insights from data characterized by multiple perspectives\nor modalities. Despite significant advancements, existing MVC methods struggle\nwith effectively quantifying the consistency and complementarity among views,\nand are particularly susceptible to the adverse effects of noisy views, known\nas the Noisy-View Drawback (NVD). To address these challenges, we propose\nCE-MVC, a novel framework that integrates an adaptive weighting algorithm with\na parameter-decoupled deep model. Leveraging the concept of conditional entropy\nand normalized mutual information, CE-MVC quantitatively assesses and weights\nthe informative contribution of each view, facilitating the construction of\nrobust unified representations. The parameter-decoupled design enables\nindependent processing of each view, effectively mitigating the influence of\nnoise and enhancing overall clustering performance. Extensive experiments\ndemonstrate that CE-MVC outperforms existing approaches, offering a more\nresilient and accurate solution for multi-view clustering tasks.\n", "date": "2024-12-23", "categories": []}
{"id": "2408.10136", "title": "Robust spectral clustering with rank statistics", "abstract": "  This paper analyzes the statistical performance of a robust spectral\nclustering method for latent structure recovery in noisy data matrices. We\nconsider eigenvector-based clustering applied to a matrix of nonparametric rank\nstatistics that is derived entrywise from the raw, original data matrix. This\napproach is robust in the sense that, unlike traditional spectral clustering\nprocedures, it can provably recover population-level latent block structure\neven when the observed data matrix includes heavy-tailed entries and has a\nheterogeneous variance profile.\n  Our main theoretical contributions are threefold and hold under flexible data\ngenerating conditions. First, we establish that robust spectral clustering with\nrank statistics can consistently recover latent block structure, viewed as\ncommunities of nodes in a graph, in the sense that unobserved community\nmemberships for all but a vanishing fraction of nodes are correctly recovered\nwith high probability when the data matrix is large. Second, we refine the\nformer result and further establish that, under certain conditions, the\ncommunity membership of any individual, specified node of interest can be\nasymptotically exactly recovered with probability tending to one in the\nlarge-data limit. Third, we establish asymptotic normality results associated\nwith the truncated eigenstructure of matrices whose entries are rank\nstatistics, made possible by synthesizing contemporary entrywise matrix\nperturbation analysis with the classical nonparametric theory of so-called\nsimple linear rank statistics. Collectively, these results demonstrate the\nstatistical utility of rank-based data transformations when paired with\nspectral techniques for dimensionality reduction. Additionally, for a dataset\nof human connectomes, our approach yields parsimonious dimensionality reduction\nand improved recovery of ground-truth neuroanatomical cluster structure.\n", "date": "2024-08-19", "categories": []}
{"id": "2412.15257", "title": "An Incremental Clustering Baseline for Event Detection on Twitter", "abstract": "  Event detection in text streams is a crucial task for the analysis of online\nmedia and social networks. One of the current challenges in this field is\nestablishing a performance standard while maintaining an acceptable level of\ncomputational complexity. In our study, we use an incremental clustering\nalgorithm combined with recent advancements in sentence embeddings. Our\nobjective is to compare our findings with previous studies, specifically those\nby Cao et al. (2024) and Mazoyer et al. (2020). Our results demonstrate\nsignificant improvements and could serve as a relevant baseline for future\nresearch in this area.\n", "date": "2024-12-16", "categories": []}
{"id": "2404.15379", "title": "Clustering of timed sequences -- Application to the analysis of care\n  pathways", "abstract": "  Improving the future of healthcare starts by better understanding the current\nactual practices in hospital settings. This motivates the objective of\ndiscovering typical care pathways from patient data. Revealing typical care\npathways can be achieved through clustering. The difficulty in clustering care\npathways, represented by sequences of timestamped events, lies in defining a\nsemantically appropriate metric and clustering algorithms. In this article, we\nadapt two methods developed for time series to the clustering of timed\nsequences: the drop-DTW metric and the DBA approach for the construction of\naveraged time sequences. These methods are then applied in clustering\nalgorithms to propose original and sound clustering algorithms for timed\nsequences. This approach is experimented with and evaluated on synthetic and\nreal-world data.\n", "date": "2024-04-23", "categories": []}
{"id": "2412.13550", "title": "Multi-view Granular-ball Contrastive Clustering", "abstract": "  Previous multi-view contrastive learning methods typically operate at two\nscales: instance-level and cluster-level. Instance-level approaches construct\npositive and negative pairs based on sample correspondences, aiming to bring\npositive pairs closer and push negative pairs further apart in the latent\nspace. Cluster-level methods focus on calculating cluster assignments for\nsamples under each view and maximize view consensus by reducing distribution\ndiscrepancies, e.g., minimizing KL divergence or maximizing mutual information.\nHowever, these two types of methods either introduce false negatives, leading\nto reduced model discriminability, or overlook local structures and cannot\nmeasure relationships between clusters across views explicitly. To this end, we\npropose a method named Multi-view Granular-ball Contrastive Clustering (MGBCC).\nMGBCC segments the sample set into coarse-grained granular balls, and\nestablishes associations between intra-view and cross-view granular balls.\nThese associations are reinforced in a shared latent space, thereby achieving\nmulti-granularity contrastive learning. Granular balls lie between instances\nand clusters, naturally preserving the local topological structure of the\nsample set. We conduct extensive experiments to validate the effectiveness of\nthe proposed method.\n", "date": "2024-12-18", "categories": []}
{"id": "2412.14867", "title": "Graph-Convolutional Networks: Named Entity Recognition and Large\n  Language Model Embedding in Document Clustering", "abstract": "  Recent advances in machine learning, particularly Large Language Models\n(LLMs) such as BERT and GPT, provide rich contextual embeddings that improve\ntext representation. However, current document clustering approaches often\nignore the deeper relationships between named entities (NEs) and the potential\nof LLM embeddings. This paper proposes a novel approach that integrates Named\nEntity Recognition (NER) and LLM embeddings within a graph-based framework for\ndocument clustering. The method builds a graph with nodes representing\ndocuments and edges weighted by named entity similarity, optimized using a\ngraph-convolutional network (GCN). This ensures a more effective grouping of\nsemantically related documents. Experimental results indicate that our approach\noutperforms conventional co-occurrence-based methods in clustering, notably for\ndocuments rich in named entities.\n", "date": "2024-12-19", "categories": []}
{"id": "2207.02404", "title": "Careful Seeding for k-Medois Clustering with Incremental k-Means++\n  Initialization", "abstract": "  K-medoids clustering is a popular variant of k-means clustering and widely\nused in pattern recognition and machine learning. A main drawback of k-medoids\nclustering is that an improper initialization can cause it to get trapped in\nlocal optima. An improved k-medoids clustering algorithm, called INCKM\nalgorithm, which is the first to apply incremental initialization to k-medoids\nclustering, was recently proposed to overcome this drawback. The INCKM\nalgorithm requires the construction of a subset of candidate medoids determined\nby one hyperparameter for initialization, and meanwhile, it always fails when\ndealing with imbalanced datasets with an incorrect hyperparameter selection. In\nthis paper, we propose a novel k-medoids clustering algorithm, called\nincremental k-means++ (INCKPP) algorithm, which initializes with a novel\nincremental manner, attempting to optimally add one new cluster center at each\nstage through a nonparametric and stochastic k-means++ initialization. The\nINCKPP algorithm overcomes the difficulty of hyperparameter selection in the\nINCKM algorithm, improves the clustering performance, and can deal with\nimbalanced datasets well. However, the INCKPP algorithm is not computationally\nefficient enough. To deal with this, we further propose an improved INCKPP\nalgorithm, called INCKPPsample algorithm, which improves the clustering\nefficiency while maintaining the clustering performance of the INCKPP\nalgorithm. Extensive results from experiments on both synthetic and real-world\ndatasets, including imbalanced datasets, illustrate that the proposed\nalgorithms outperforms than the other compared algorithms.\n", "date": "2022-07-06", "categories": []}
{"id": "2408.10493", "title": "Clustering by Mining Density Distributions and Splitting Manifold\n  Structure", "abstract": "  Spectral clustering requires the time-consuming decomposition of the\nLaplacian matrix of the similarity graph, thus limiting its applicability to\nlarge datasets. To improve the efficiency of spectral clustering, a top-down\napproach was recently proposed, which first divides the data into several\nmicro-clusters (granular-balls), then splits these micro-clusters when they are\nnot ``compact'', and finally uses these micro-clusters as nodes to construct a\nsimilarity graph for more efficient spectral clustering. However, this top-down\napproach is challenging to adapt to unevenly distributed or structurally\ncomplex data. This is because constructing micro-clusters as a rough ball\nstruggles to capture the shape and structure of data in a local range, and the\nsimplistic splitting rule that solely targets ``compactness'' is susceptible to\nnoise and variations in data density and leads to micro-clusters with varying\nshapes, making it challenging to accurately measure the similarity between\nthem. To resolve these issues and improve spectral clustering, this paper first\nproposes to start from local structures to obtain micro-clusters, such that the\ncomplex structural information inside local neighborhoods is well captured by\nthem. Moreover, by noting that Euclidean distance is more suitable for convex\nsets, this paper further proposes a data splitting rule that couples local\ndensity and data manifold structures, so that the similarities of the obtained\nmicro-clusters can be easily characterized. A novel similarity measure between\nmicro-clusters is then proposed for the final spectral clustering. A series of\nexperiments based on synthetic and real-world datasets demonstrate that the\nproposed method has better adaptability to structurally complex data than\ngranular-ball based methods.\n", "date": "2024-08-20", "categories": []}
{"id": "2412.13534", "title": "Information-Theoretic Generative Clustering of Documents", "abstract": "  We present {\\em generative clustering} (GC) for clustering a set of\ndocuments, $\\mathrm{X}$, by using texts $\\mathrm{Y}$ generated by large\nlanguage models (LLMs) instead of by clustering the original documents\n$\\mathrm{X}$. Because LLMs provide probability distributions, the similarity\nbetween two documents can be rigorously defined in an information-theoretic\nmanner by the KL divergence. We also propose a natural, novel clustering\nalgorithm by using importance sampling. We show that GC achieves the\nstate-of-the-art performance, outperforming any previous clustering method\noften by a large margin. Furthermore, we show an application to generative\ndocument retrieval in which documents are indexed via hierarchical clustering\nand our method improves the retrieval accuracy.\n", "date": "2024-12-18", "categories": []}
{"id": "2411.01859", "title": "A Novel Deep Learning Tractography Fiber Clustering Framework for\n  Functionally Consistent White Matter Parcellation Using Multimodal Diffusion\n  MRI and Functional MRI", "abstract": "  Tractography fiber clustering using diffusion MRI (dMRI) is a crucial\nstrategy for white matter (WM) parcellation. Current methods primarily use the\ngeometric information of fibers (i.e., the spatial trajectories) to group\nsimilar fibers into clusters, overlooking the important functional signals\npresent along the fiber tracts. There is increasing evidence that neural\nactivity in the WM can be measured using functional MRI (fMRI), offering\npotentially valuable multimodal information for fiber clustering. In this\npaper, we develop a novel deep learning fiber clustering framework, namely Deep\nMulti-view Fiber Clustering (DMVFC), that uses joint dMRI and fMRI data to\nenable functionally consistent WM parcellation. DMVFC can effectively integrate\nthe geometric characteristics of the WM fibers with the fMRI BOLD signals along\nthe fiber tracts. It includes two major components: 1) a multi-view pretraining\nmodule to compute embedding features from fiber geometric information and\nfunctional signals separately, and 2) a collaborative fine-tuning module to\nsimultaneously refine the two kinds of embeddings. In the experiments, we\ncompare DMVFC with two state-of-the-art fiber clustering methods and\ndemonstrate superior performance in achieving functionally meaningful and\nconsistent WM parcellation results.\n", "date": "2024-11-04", "categories": []}
{"id": "2412.10923", "title": "Linear Programming based Approximation to Individually Fair k-Clustering\n  with Outliers", "abstract": "  Individual fairness guarantees are often desirable properties to have, but\nthey become hard to formalize when the dataset contains outliers. Here, we\ninvestigate the problem of developing an individually fair $k$-means clustering\nalgorithm for datasets that contain outliers. That is, given $n$ points and $k$\ncenters, we want that for each point which is not an outlier, there must be a\ncenter within the $\\frac{n}{k}$ nearest neighbours of the given point. While a\nfew of the recent works have looked into individually fair clustering, this is\nthe first work that explores this problem in the presence of outliers for\n$k$-means clustering.\n  For this purpose, we define and solve a linear program (LP) that helps us\nidentify the outliers. We exclude these outliers from the dataset and apply a\nrounding algorithm that computes the $k$ centers, such that the fairness\nconstraint of the remaining points is satisfied. We also provide theoretical\nguarantees that our method leads to a guaranteed approximation of the fair\nradius as well as the clustering cost. We also demonstrate our techniques\nempirically on real-world datasets.\n", "date": "2024-12-14", "categories": []}
{"id": "2412.11080", "title": "Deep Spectral Clustering via Joint Spectral Embedding and Kmeans", "abstract": "  Spectral clustering is a popular clustering method. It first maps data into\nthe spectral embedding space and then uses Kmeans to find clusters. However,\nthe two decoupled steps prohibit joint optimization for the optimal solution.\nIn addition, it needs to construct the similarity graph for samples, which\nsuffers from the curse of dimensionality when the data are high-dimensional. To\naddress these two challenges, we introduce \\textbf{D}eep \\textbf{S}pectral\n\\textbf{C}lustering (\\textbf{DSC}), which consists of two main modules: the\nspectral embedding module and the greedy Kmeans module. The former module\nlearns to efficiently embed raw samples into the spectral embedding space using\ndeep neural networks and power iteration. The latter module improves the\ncluster structures of Kmeans on the learned spectral embeddings by a greedy\noptimization strategy, which iteratively reveals the direction of the worst\ncluster structures and optimizes embeddings in this direction. To jointly\noptimize spectral embeddings and clustering, we seamlessly integrate the two\nmodules and optimize them in an end-to-end manner. Experimental results on\nseven real-world datasets demonstrate that DSC achieves state-of-the-art\nclustering performance.\n", "date": "2024-12-15", "categories": []}
{"id": "2412.04482", "title": "NLP Cluster Analysis of Common Core State Standards and NAEP Item\n  Specifications", "abstract": "  Camilli (2024) proposed a methodology using natural language processing (NLP)\nto map the relationship of a set of content standards to item specifications.\nThis study provided evidence that NLP can be used to improve the mapping\nprocess. As part of this investigation, the nominal classifications of\nstandards and items specifications were used to examine construct equivalence.\nIn the current paper, we determine the strength of empirical support for the\nsemantic distinctiveness of these classifications, which are known as \"domains\"\nfor Common Core standards, and \"strands\" for National Assessment of Educational\nProgress (NAEP) item specifications. This is accomplished by separate k-means\nclustering for standards and specifications of their corresponding embedding\nvectors. We then briefly illustrate an application of these findings.\n", "date": "2024-11-20", "categories": []}
{"id": "2412.09748", "title": "New Approach to Clustering Random Attributes", "abstract": "  This paper proposes a new method for similarity analysis and, consequently, a\nnew algorithm for clustering different types of random attributes, both\nnumerical and nominal. However, in order for nominal attributes to be\nclustered, their values must be properly encoded. In the encoding process,\nnominal attributes obtain a new representation in numerical form. Only the\nnumeric attributes can be subjected to factor analysis, which allows them to be\nclustered in terms of their similarity to factors. The proposed method was\ntested for several sample datasets. It was found that the proposed method is\nuniversal. On the one hand, the method allows clustering of numerical\nattributes. On the other hand, it provides the ability to cluster nominal\nattributes. It also allows simultaneous clustering of numerical attributes and\nnumerically encoded nominal attributes.\n", "date": "2024-12-12", "categories": []}
{"id": "2412.05305", "title": "AdaptiveMDL-GenClust: A Robust Clustering Framework Integrating\n  Normalized Mutual Information and Evolutionary Algorithms", "abstract": "  Clustering algorithms are pivotal in data analysis, enabling the organization\nof data into meaningful groups. However, individual clustering methods often\nexhibit inherent limitations and biases, preventing the development of a\nuniversal solution applicable to diverse datasets. To address these challenges,\nwe introduce a robust clustering framework that integrates the Minimum\nDescription Length (MDL) principle with a genetic optimization algorithm. The\nframework begins with an ensemble clustering approach to generate an initial\nclustering solution, which is then refined using MDL-guided evaluation\nfunctions and optimized through a genetic algorithm. This integration allows\nthe method to adapt to the dataset's intrinsic properties, minimizing\ndependency on the initial clustering input and ensuring a data-driven, robust\nclustering process. We evaluated the proposed method on thirteen benchmark\ndatasets using four established validation metrics: accuracy, normalized mutual\ninformation (NMI), Fisher score, and adjusted Rand index (ARI). Experimental\nresults demonstrate that our approach consistently outperforms traditional\nclustering methods, yielding higher accuracy, improved stability, and reduced\nbias. The methods adaptability makes it effective across datasets with diverse\ncharacteristics, highlighting its potential as a versatile and reliable tool\nfor complex clustering tasks. By combining the MDL principle with genetic\noptimization, this study offers a significant advancement in clustering\nmethodology, addressing key limitations and delivering superior performance in\nvaried applications.\n", "date": "2024-11-26", "categories": []}
{"id": "2412.08940", "title": "Deep Clustering using Dirichlet Process Gaussian Mixture and Alpha\n  Jensen-Shannon Divergence Clustering Loss", "abstract": "  Deep clustering is an emerging topic in deep learning where traditional\nclustering is performed in deep learning feature space. However, clustering and\ndeep learning are often mutually exclusive. In the autoencoder based deep\nclustering, the challenge is how to jointly optimize both clustering and\ndimension reduction together, so that the weights in the hidden layers are not\nonly guided by reconstruction loss, but also by a loss function associated with\nclustering. The current state-of-the-art has two fundamental flaws. First, they\nrely on the mathematical convenience of Kullback-Leibler divergence for the\nclustering loss function but the former is asymmetric. Secondly, they assume\nthe prior knowledge on the number of clusters is always available for their\ndataset of interest. This paper tries to improve on these problems. In the\nfirst problem, we use a Jensen-Shannon divergence to overcome the asymmetric\nissue, specifically using a closed form variant. Next, we introduce an infinite\ncluster representation using Dirichlet process Gaussian mixture model for joint\nclustering and model selection in the latent space which we called deep model\nselection. The number of clusters in the latent space are not fixed but instead\nvary accordingly as they gradually approach the optimal number during training.\nThus, prior knowledge is not required. We evaluate our proposed deep model\nselection method with traditional model selection on large class number\ndatasets such as MIT67 and CIFAR100 and also compare with both traditional\nvariational Bayes model and deep clustering method with convincing results.\n", "date": "2024-12-12", "categories": []}
{"id": "2412.09065", "title": "Multi-view Clustering via Unified Multi-kernel Learning and Matrix\n  Factorization", "abstract": "  Multi-view clustering has become increasingly important due to the\nmulti-source character of real-world data. Among existing multi-view clustering\nmethods, multi-kernel clustering and matrix factorization-based multi-view\nclustering have gained widespread attention as mainstream approaches. However,\nmulti-kernel clustering tends to learn an optimal kernel and then perform\neigenvalue decomposition on it, which leads to high computational complexity.\nMatrix factorization-based multi-view clustering methods impose orthogonal\nconstraints on individual views. This overly emphasizes the accuracy of\nclustering structures within single views and restricts the learning of\nindividual views. Based on this analysis, we propose a multi-view clustering\nmethod that integrates multi-kernel learning with matrix factorization. This\napproach combines the advantages of both multi-kernel learning and matrix\nfactorization. It removes the orthogonal constraints on individual views and\nimposes orthogonal constraints on the consensus matrix, resulting in an\naccurate final clustering structure. Ultimately, the method is unified into a\nsimple form of multi-kernel clustering, but avoids learning an optimal kernel,\nthus reducing the time complexity. Furthermore, we propose an efficient\nthree-step optimization algorithm to achieve a locally optimal solution.\nExperiments on widely-used real-world datasets demonstrate the effectiveness of\nour proposed method.\n", "date": "2024-12-12", "categories": []}
{"id": "2412.07789", "title": "Dynamic data summarization for hierarchical spatial clustering", "abstract": "  Hierarchical Density-Based Spatial Clustering of Applications with Noise\n(HDBSCAN) finds meaningful patterns in spatial data by considering density and\nspatial proximity. As the clustering algorithm is inherently designed for\nstatic applications, so have recent studies focused on accelerating the\nalgorithm for static applications using approximate or parallel methods.\nHowever, much less attention has been given to dynamic environments, where even\na single point insertion or deletion can require recomputing the clustering\nhierarchy from scratch due to the need of maintaining the minimum spanning tree\n(MST) over a complete graph. This paper addresses the challenge of enhancing\nthe clustering algorithm for dynamic data. We present an exact algorithm that\nmaintains density information and updates the clustering hierarchy of HDBSCAN\nduring point insertions and deletions. Considering the hardness of adapting the\nexact algorithm to dynamic data involving modern workloads, we propose an\nonline-offline framework. The online component efficiently summarizes dynamic\ndata using a tree structure, called Bubble-tree, while the offline step\nperforms the static clustering. Experimental results demonstrate that the data\nsummarization adapts well to fully dynamic environments, providing compression\nquality on par with existing techniques while significantly improving runtime\nperformance of the clustering algorithm in dynamic data workloads.\n", "date": "2024-11-26", "categories": []}
{"id": "2403.03349", "title": "A consensus-constrained parsimonious Gaussian mixture model for\n  clustering hyperspectral images", "abstract": "  The use of hyperspectral imaging to investigate food samples has grown due to\nthe improved performance and lower cost of instrumentation. Food engineers use\nhyperspectral images to classify the type and quality of a food sample,\ntypically using classification methods. In order to train these methods, every\npixel in each training image needs to be labelled. Typically, computationally\ncheap threshold-based approaches are used to label the pixels, and\nclassification methods are trained based on those labels. However,\nthreshold-based approaches are subjective and cannot be generalized across\nhyperspectral images taken in different conditions and of different foods. Here\na consensus-constrained parsimonious Gaussian mixture model (ccPGMM) is\nproposed to label pixels in hyperspectral images using a model-based clustering\napproach. The ccPGMM utilizes information that is available on some pixels and\nspecifies constraints on those pixels belonging to the same or different\nclusters while clustering the rest of the pixels in the image. A latent\nvariable model is used to represent the high-dimensional data in terms of a\nsmall number of underlying latent factors. To ensure computational feasibility,\na consensus clustering approach is employed, where the data are divided into\nmultiple randomly selected subsets of variables and constrained clustering is\napplied to each data subset; the clustering results are then consolidated\nacross all data subsets to provide a consensus clustering solution. The ccPGMM\napproach is applied to simulated datasets and real hyperspectral images of\nthree types of puffed cereal, corn, rice, and wheat. Improved clustering\nperformance and computational efficiency are demonstrated when compared to\nother current state-of-the-art approaches.\n", "date": "2024-03-05", "categories": []}
{"id": "2411.01115", "title": "Relax and Merge: A Simple Yet Effective Framework for Solving Fair\n  $k$-Means and $k$-sparse Wasserstein Barycenter Problems", "abstract": "  The fairness of clustering algorithms has gained widespread attention across\nvarious areas, including machine learning, In this paper, we study fair\n$k$-means clustering in Euclidean space. Given a dataset comprising several\ngroups, the fairness constraint requires that each cluster should contain a\nproportion of points from each group within specified lower and upper bounds.\nDue to these fairness constraints, determining the optimal locations of $k$\ncenters is a quite challenging task. We propose a novel ``Relax and Merge''\nframework that returns a $(1+4\\rho + O(\\epsilon))$-approximate solution, where\n$\\rho$ is the approximate ratio of an off-the-shelf vanilla $k$-means algorithm\nand $O(\\epsilon)$ can be an arbitrarily small positive number. If equipped with\na PTAS of $k$-means, our solution can achieve an approximation ratio of\n$(5+O(\\epsilon))$ with only a slight violation of the fairness constraints,\nwhich improves the current state-of-the-art approximation guarantee.\nFurthermore, using our framework, we can also obtain a $(1+4\\rho\n+O(\\epsilon))$-approximate solution for the $k$-sparse Wasserstein Barycenter\nproblem, which is a fundamental optimization problem in the field of optimal\ntransport, and a $(2+6\\rho)$-approximate solution for the strictly fair\n$k$-means clustering with no violation, both of which are better than the\ncurrent state-of-the-art methods. In addition, the empirical results\ndemonstrate that our proposed algorithm can significantly outperform baseline\napproaches in terms of clustering cost.\n", "date": "2024-11-02", "categories": []}
{"id": "2409.09304", "title": "Consistent Spectral Clustering in Hyperbolic Spaces", "abstract": "  Clustering, as an unsupervised technique, plays a pivotal role in various\ndata analysis applications. Among clustering algorithms, Spectral Clustering on\nEuclidean Spaces has been extensively studied. However, with the rapid\nevolution of data complexity, Euclidean Space is proving to be inefficient for\nrepresenting and learning algorithms. Although Deep Neural Networks on\nhyperbolic spaces have gained recent traction, clustering algorithms or\nnon-deep machine learning models on non-Euclidean Spaces remain underexplored.\nIn this paper, we propose a spectral clustering algorithm on Hyperbolic Spaces\nto address this gap. Hyperbolic Spaces offer advantages in representing complex\ndata structures like hierarchical and tree-like structures, which cannot be\nembedded efficiently in Euclidean Spaces. Our proposed algorithm replaces the\nEuclidean Similarity Matrix with an appropriate Hyperbolic Similarity Matrix,\ndemonstrating improved efficiency compared to clustering in Euclidean Spaces.\nOur contributions include the development of the spectral clustering algorithm\non Hyperbolic Spaces and the proof of its weak consistency. We show that our\nalgorithm converges at least as fast as Spectral Clustering on Euclidean\nSpaces. To illustrate the efficacy of our approach, we present experimental\nresults on the Wisconsin Breast Cancer Dataset, highlighting the superior\nperformance of Hyperbolic Spectral Clustering over its Euclidean counterpart.\nThis work opens up avenues for utilizing non-Euclidean Spaces in clustering\nalgorithms, offering new perspectives for handling complex data structures and\nimproving clustering efficiency.\n", "date": "2024-09-14", "categories": []}
{"id": "2403.15112", "title": "Text Clustering with Large Language Model Embeddings", "abstract": "  Text clustering is an important method for organising the increasing volume\nof digital content, aiding in the structuring and discovery of hidden patterns\nin uncategorised data. The effectiveness of text clustering largely depends on\nthe selection of textual embeddings and clustering algorithms. This study\nargues that recent advancements in large language models (LLMs) have the\npotential to enhance this task. The research investigates how different textual\nembeddings, particularly those utilised in LLMs, and various clustering\nalgorithms influence the clustering of text datasets. A series of experiments\nwere conducted to evaluate the impact of embeddings on clustering results, the\nrole of dimensionality reduction through summarisation, and the adjustment of\nmodel size. The findings indicate that LLM embeddings are superior at capturing\nsubtleties in structured language. OpenAI's GPT-3.5 Turbo model yields better\nresults in three out of five clustering metrics across most tested datasets.\nMost LLM embeddings show improvements in cluster purity and provide a more\ninformative silhouette score, reflecting a refined structural understanding of\ntext data compared to traditional methods. Among the more lightweight models,\nBERT demonstrates leading performance. Additionally, it was observed that\nincreasing model dimensionality and employing summarisation techniques do not\nconsistently enhance clustering efficiency, suggesting that these strategies\nrequire careful consideration for practical application. These results\nhighlight a complex balance between the need for refined text representation\nand computational feasibility in text clustering applications. This study\nextends traditional text clustering frameworks by integrating embeddings from\nLLMs, offering improved methodologies and suggesting new avenues for future\nresearch in various types of textual analysis.\n", "date": "2024-03-22", "categories": []}
{"id": "2412.03584", "title": "Resampled Mutual Information for Clustering and Community Detection", "abstract": "  We introduce resampled mutual information (ResMI), a novel measure of\nclustering similarity that combines insights from information theoretic and\npair counting approaches to clustering and community detection. Similar to\nchance-corrected measures, ResMI satisfies the constant baseline property, but\nit has the advantages of not requiring adjustment terms and being fully\ninterpretable in the language of information theory. Experiments on synthetic\ndatasets demonstrate that ResMI is robust to common biases exhibited by\nexisting measures, particularly in settings with high cluster counts and\nasymmetric cluster distributions. Additionally, we show that ResMI identifies\nmeaningful community structures in two real contact tracing networks.\n", "date": "2024-11-21", "categories": []}
{"id": "2412.03780", "title": "Community Detection with Heterogeneous Block Covariance Model", "abstract": "  Community detection is the task of clustering objects based on their pairwise\nrelationships. Most of the model-based community detection methods, such as the\nstochastic block model and its variants, are designed for networks with binary\n(yes/no) edges. In many practical scenarios, edges often possess continuous\nweights, spanning positive and negative values, which reflect varying levels of\nconnectivity. To address this challenge, we introduce the heterogeneous block\ncovariance model (HBCM) that defines a community structure within the\ncovariance matrix, where edges have signed and continuous weights. Furthermore,\nit takes into account the heterogeneity of objects when forming connections\nwith other objects within a community. A novel variational\nexpectation-maximization algorithm is proposed to estimate the group\nmembership. The HBCM provides provable consistent estimates of memberships, and\nits promising performance is observed in numerical simulations with different\nsetups. The model is applied to a single-cell RNA-seq dataset of a mouse embryo\nand a stock price dataset. Supplementary materials for this article are\navailable online.\n", "date": "2024-12-04", "categories": []}
{"id": "2412.04082", "title": "Learnable Similarity and Dissimilarity Guided Symmetric Non-Negative\n  Matrix Factorization", "abstract": "  Symmetric nonnegative matrix factorization (SymNMF) is a powerful tool for\nclustering, which typically uses the $k$-nearest neighbor ($k$-NN) method to\nconstruct similarity matrix. However, $k$-NN may mislead clustering since the\nneighbors may belong to different clusters, and its reliability generally\ndecreases as $k$ grows. In this paper, we construct the similarity matrix as a\nweighted $k$-NN graph with learnable weight that reflects the reliability of\neach $k$-th NN. This approach reduces the search space of the similarity matrix\nlearning to $n - 1$ dimension, as opposed to the $\\mathcal{O}(n^2)$ dimension\nof existing methods, where $n$ represents the number of samples. Moreover, to\nobtain a discriminative similarity matrix, we introduce a dissimilarity matrix\nwith a dual structure of the similarity matrix, and propose a new form of\northogonality regularization with discussions on its geometric interpretation\nand numerical stability. An efficient alternative optimization algorithm is\ndesigned to solve the proposed model, with theoretically guarantee that the\nvariables converge to a stationary point that satisfies the KKT conditions. The\nadvantage of the proposed model is demonstrated by the comparison with nine\nstate-of-the-art clustering methods on eight datasets. The code is available at\n\\url{https://github.com/lwl-learning/LSDGSymNMF}.\n", "date": "2024-12-05", "categories": []}
{"id": "2412.03471", "title": "Cluster Specific Representation Learning", "abstract": "  Representation learning aims to extract meaningful lower-dimensional\nembeddings from data, known as representations. Despite its widespread\napplication, there is no established definition of a ``good'' representation.\nTypically, the representation quality is evaluated based on its performance in\ndownstream tasks such as clustering, de-noising, etc. However, this\ntask-specific approach has a limitation where a representation that performs\nwell for one task may not necessarily be effective for another. This highlights\nthe need for a more agnostic formulation, which is the focus of our work. We\npropose a downstream-agnostic formulation: when inherent clusters exist in the\ndata, the representations should be specific to each cluster. Under this idea,\nwe develop a meta-algorithm that jointly learns cluster-specific\nrepresentations and cluster assignments. As our approach is easy to integrate\nwith any representation learning framework, we demonstrate its effectiveness in\nvarious setups, including Autoencoders, Variational Autoencoders, Contrastive\nlearning models, and Restricted Boltzmann Machines. We qualitatively compare\nour cluster-specific embeddings to standard embeddings and downstream tasks\nsuch as de-noising and clustering. While our method slightly increases runtime\nand parameters compared to the standard model, the experiments clearly show\nthat it extracts the inherent cluster structures in the data, resulting in\nimproved performance in relevant applications.\n", "date": "2024-12-04", "categories": []}
{"id": "2411.11421", "title": "Enabling DBSCAN for Very Large-Scale High-Dimensional Spaces", "abstract": "  DBSCAN is one of the most important non-parametric unsupervised data analysis\ntools. By applying DBSCAN to a dataset, two key analytical results can be\nobtained: (1) clustering data points based on density distribution and (2)\nidentifying outliers in the dataset. However, the time complexity of the DBSCAN\nalgorithm is $O(n^2 \\beta)$, where $n$ is the number of data points and $\\beta\n= O(D)$, with $D$ representing the dimensionality of the data space. As a\nresult, DBSCAN becomes computationally infeasible when both $n$ and $D$ are\nlarge. In this paper, we propose a DBSCAN method based on spectral data\ncompression, capable of efficiently processing datasets with a large number of\ndata points ($n$) and high dimensionality ($D$). By preserving only the most\ncritical structural information during the compression process, our method\neffectively removes substantial redundancy and noise. Consequently, the\nsolution quality of DBSCAN is significantly improved, enabling more accurate\nand reliable results.\n", "date": "2024-11-18", "categories": []}
{"id": "2412.02244", "title": "On Simplifying Large-Scale Spatial Vectors: Fast, Memory-Efficient, and\n  Cost-Predictable k-means", "abstract": "  The k-means algorithm can simplify large-scale spatial vectors, such as 2D\ngeo-locations and 3D point clouds, to support fast analytics and learning.\nHowever, when processing large-scale datasets, existing k-means algorithms have\nbeen developed to achieve high performance with significant computational\nresources, such as memory and CPU usage time. These algorithms, though\neffective, are not well-suited for resource-constrained devices. In this paper,\nwe propose a fast, memory-efficient, and cost-predictable k-means called\nDask-means. We first accelerate k-means by designing a memory-efficient\naccelerator, which utilizes an optimized nearest neighbor search over a\nmemory-tunable index to assign spatial vectors to clusters in batches. We then\ndesign a lightweight cost estimator to predict the memory cost and runtime of\nthe k-means task, allowing it to request appropriate memory from devices or\nadjust the accelerator's required space to meet memory constraints, and ensure\nsufficient CPU time for running k-means. Experiments show that when simplifying\ndatasets with scale such as $10^6$, Dask-means uses less than $30$MB of memory,\nachieves over $168$ times speedup compared to the widely-used Lloyd's\nalgorithm. We also validate Dask-means on mobile devices, where it demonstrates\nsignificant speedup and low memory cost compared to other state-of-the-art\n(SOTA) k-means algorithms. Our cost estimator estimates the memory cost with a\ndifference of less than $3\\%$ from the actual ones and predicts runtime with an\nMSE up to $33.3\\%$ lower than SOTA methods.\n", "date": "2024-12-03", "categories": []}
{"id": "2412.02292", "title": "Deep Matrix Factorization with Adaptive Weights for Multi-View\n  Clustering", "abstract": "  Recently, deep matrix factorization has been established as a powerful model\nfor unsupervised tasks, achieving promising results, especially for multi-view\nclustering. However, existing methods often lack effective feature selection\nmechanisms and rely on empirical hyperparameter selection. To address these\nissues, we introduce a novel Deep Matrix Factorization with Adaptive Weights\nfor Multi-View Clustering (DMFAW). Our method simultaneously incorporates\nfeature selection and generates local partitions, enhancing clustering results.\nNotably, the features weights are controlled and adjusted by a parameter that\nis dynamically updated using Control Theory inspired mechanism, which not only\nimproves the model's stability and adaptability to diverse datasets but also\naccelerates convergence. A late fusion approach is then proposed to align the\nweighted local partitions with the consensus partition. Finally, the\noptimization problem is solved via an alternating optimization algorithm with\ntheoretically guaranteed convergence. Extensive experiments on benchmark\ndatasets highlight that DMFAW outperforms state-of-the-art methods in terms of\nclustering performance.\n", "date": "2024-12-03", "categories": []}
{"id": "2212.03853", "title": "Clustering with Neural Network and Index", "abstract": "  A new model called Clustering with Neural Network and Index (CNNI) is\nintroduced. CNNI uses a Neural Network to cluster data points. Training of the\nNeural Network mimics supervised learning, with an internal clustering\nevaluation index acting as the loss function. An experiment is conducted to\ntest the feasibility of the new model, and compared with results of other\nclustering models like K-means and Gaussian Mixture Model (GMM). The result\nshows CNNI can work properly for clustering data; CNNI equipped with MMJ-SC,\nachieves the first parametric (inductive) clustering model that can deal with\nnon-convex shaped (non-flat geometry) data.\n", "date": "2022-12-05", "categories": []}
{"id": "2412.01296", "title": "I Spy With My Little Eye: A Minimum Cost Multicut Investigation of\n  Dataset Frames", "abstract": "  Visual framing analysis is a key method in social sciences for determining\ncommon themes and concepts in a given discourse. To reduce manual effort, image\nclustering can significantly speed up the annotation process. In this work, we\nphrase the clustering task as a Minimum Cost Multicut Problem [MP]. Solutions\nto the MP have been shown to provide clusterings that maximize the posterior\nprobability, solely from provided local, pairwise probabilities of two images\nbelonging to the same cluster. We discuss the efficacy of numerous embedding\nspaces to detect visual frames and show its superiority over other clustering\nmethods. To this end, we employ the climate change dataset \\textit{ClimateTV}\nwhich contains images commonly used for visual frame analysis. For broad visual\nframes, DINOv2 is a suitable embedding space, while ConvNeXt V2 returns a\nlarger number of clusters which contain fine-grain differences, i.e. speech and\nprotest. Our insights into embedding space differences in combination with the\noptimal clustering - by definition - advances automated visual frame detection.\nOur code can be found at https://github.com/KathPra/MP4VisualFrameDetection.\n", "date": "2024-12-02", "categories": []}
{"id": "2411.19496", "title": "An Approach Towards Learning K-means-friendly Deep Latent Representation", "abstract": "  Clustering is a long-standing problem area in data mining. The centroid-based\nclassical approaches to clustering mainly face difficulty in the case of high\ndimensional inputs such as images. With the advent of deep neural networks, a\ncommon approach to this problem is to map the data to some latent space of\ncomparatively lower dimensions and then do the clustering in that space.\nNetwork architectures adopted for this are generally autoencoders that\nreconstruct a given input in the output. To keep the input in some compact\nform, the encoder in AE's learns to extract useful features that get decoded at\nthe reconstruction end. A well-known centroid-based clustering algorithm is\nK-means. In the context of deep feature learning, recent works have empirically\nshown the importance of learning the representations and the cluster centroids\ntogether. However, in this aspect of joint learning, recently a continuous\nvariant of K-means has been proposed; where the softmax function is used in\nplace of argmax to learn the clustering and network parameters jointly using\nstochastic gradient descent (SGD). However, unlike K-means, where the input\nspace stays constant, here the learning of the centroid is done in parallel to\nthe learning of the latent space for every batch of data. Such batch updates\ndisagree with the concept of classical K-means, where the clustering space\nremains constant as it is the input space itself. To this end, we propose to\nalternatively learn a clustering-friendly data representation and K-means based\ncluster centers. Experiments on some benchmark datasets have shown improvements\nof our approach over the previous approaches.\n", "date": "2024-11-29", "categories": []}
{"id": "2411.19902", "title": "Noncommutative Model Selection for Data Clustering and Dimension\n  Reduction Using Relative von Neumann Entropy", "abstract": "  We propose a pair of completely data-driven algorithms for unsupervised\nclassification and dimension reduction, and we empirically study their\nperformance on a number of data sets, both simulated data in three-dimensions\nand images from the COIL-20 data set. The algorithms take as input a set of\npoints sampled from a uniform distribution supported on a metric space, the\nlatter embedded in an ambient metric space, and they output a clustering or\nreduction of dimension of the data. They work by constructing a natural family\nof graphs from the data and selecting the graph which maximizes the relative\nvon Neumann entropy of certain normalized heat operators constructed from the\ngraphs. Once the appropriate graph is selected, the eigenvectors of the graph\nLaplacian may be used to reduce the dimension of the data, and clusters in the\ndata may be identified with the kernel of the associated graph Laplacian.\nNotably, these algorithms do not require information about the size of a\nneighborhood or the desired number of clusters as input, in contrast to popular\nalgorithms such as $k$-means, and even more modern spectral methods such as\nLaplacian eigenmaps, among others.\n  In our computational experiments, our clustering algorithm outperforms\n$k$-means clustering on data sets with non-trivial geometry and topology, in\nparticular data whose clusters are not concentrated around a specific point,\nand our dimension reduction algorithm is shown to work well in several simple\nexamples.\n", "date": "2024-11-29", "categories": []}
{"id": "2408.10511", "title": "Single-cell Curriculum Learning-based Deep Graph Embedding Clustering", "abstract": "  The swift advancement of single-cell RNA sequencing (scRNA-seq) technologies\nenables the investigation of cellular-level tissue heterogeneity. Cell\nannotation significantly contributes to the extensive downstream analysis of\nscRNA-seq data. However, The analysis of scRNA-seq for biological inference\npresents challenges owing to its intricate and indeterminate data distribution,\ncharacterized by a substantial volume and a high frequency of dropout events.\nFurthermore, the quality of training samples varies greatly, and the\nperformance of the popular scRNA-seq data clustering solution GNN could be\nharmed by two types of low-quality training nodes: 1) nodes on the boundary; 2)\nnodes that contribute little additional information to the graph. To address\nthese problems, we propose a single-cell curriculum learning-based deep graph\nembedding clustering (scCLG). We first propose a Chebyshev graph convolutional\nautoencoder with multi-criteria (ChebAE) that combines three optimization\nobjectives, including topology reconstruction loss of cell graphs,\nzero-inflated negative binomial (ZINB) loss, and clustering loss, to learn\ncell-cell topology representation. Meanwhile, we employ a selective training\nstrategy to train GNN based on the features and entropy of nodes and prune the\ndifficult nodes based on the difficulty scores to keep the high-quality graph.\nEmpirical results on a variety of gene expression datasets show that our model\noutperforms state-of-the-art methods. The code of scCLG will be made publicly\navailable at https://github.com/LFD-byte/scCLG.\n", "date": "2024-08-20", "categories": []}
{"id": "2411.16701", "title": "A multi-dimensional unsupervised machine learning framework for\n  clustering residential heat load profiles", "abstract": "  Central to achieving the energy transition, heating systems provide essential\nspace heating and hot water in residential and industrial environments. A major\nchallenge lies in effectively profiling large clusters of buildings to improve\ndemand estimation and enable efficient Demand Response (DR) schemes. This paper\naddresses this challenge by introducing an unsupervised machine learning\nframework for clustering residential heating load profiles, focusing on natural\ngas space heating and hot water preparation boilers. The profiles are analyzed\nacross five dimensions: boiler usage, heating demand, weather conditions,\nbuilding characteristics, and user behavior. We apply three distance metrics:\nEuclidean Distance (ED), Dynamic Time Warping (DTW), and Derivative Dynamic\nTime Warping (DDTW), and evaluate their performance using established\nclustering indices. The proposed method is assessed considering 29 residential\nbuildings in Greece equipped with smart meters throughout a calendar heating\nseason (i.e., 210 days). Results indicate that DTW is the most suitable metric,\nuncovering strong correlations between boiler usage, heat demand, and\ntemperature, while ED highlights broader interrelations across dimensions and\nDDTW proves less effective, resulting in weaker clusters. These findings offer\nkey insights into heating load behavior, establishing a solid foundation for\ndeveloping more targeted and effective DR programs.\n", "date": "2024-11-11", "categories": []}
{"id": "2411.16972", "title": "Clustering Time Series Data with Gaussian Mixture Embeddings in a Graph\n  Autoencoder Framework", "abstract": "  Time series data analysis is prevalent across various domains, including\nfinance, healthcare, and environmental monitoring. Traditional time series\nclustering methods often struggle to capture the complex temporal dependencies\ninherent in such data. In this paper, we propose the Variational Mixture Graph\nAutoencoder (VMGAE), a graph-based approach for time series clustering that\nleverages the structural advantages of graphs to capture enriched data\nrelationships and produces Gaussian mixture embeddings for improved\nseparability. Comparisons with baseline methods are included with experimental\nresults, demonstrating that our method significantly outperforms\nstate-of-the-art time-series clustering techniques. We further validate our\nmethod on real-world financial data, highlighting its practical applications in\nfinance. By uncovering community structures in stock markets, our method\nprovides deeper insights into stock relationships, benefiting market\nprediction, portfolio optimization, and risk management.\n", "date": "2024-11-25", "categories": []}
{"id": "2411.17291", "title": "Interpretable label-free self-guided subspace clustering", "abstract": "  Majority subspace clustering (SC) algorithms depend on one or more\nhyperparameters that need to be carefully tuned for the SC algorithms to\nachieve high clustering performance. Hyperparameter optimization (HPO) is often\nperformed using grid-search, assuming that some labeled data is available. In\nsome domains, such as medicine, this assumption does not hold true in many\ncases. One avenue of research focuses on developing SC algorithms that are\ninherently free of hyperparameters. For hyperparameters-dependent SC\nalgorithms, one approach to label-independent HPO tuning is based on internal\nclustering quality metrics (if available), whose performance should ideally\nmatch that of external (label-dependent) clustering quality metrics. In this\npaper, we propose a novel approach to label-independent HPO that uses\nclustering quality metrics, such as accuracy (ACC) or normalized mutual\ninformation (NMI), that are computed based on pseudo-labels obtained from the\nSC algorithm across a predefined grid of hyperparameters. Assuming that ACC (or\nNMI) is a smooth function of hyperparameter values it is possible to select\nsubintervals of hyperparameters. These subintervals are then iteratively\nfurther split into halves or thirds until a relative error criterion is\nsatisfied. In principle, the hyperparameters of any SC algorithm can be tuned\nusing the proposed method. We demonstrate this approach on several single- and\nmulti-view SC algorithms, comparing the achieved performance with their oracle\nversions across six datasets representing digits, faces and objects. The\nproposed method typically achieves clustering performance that is 5% to 7%\nlower than that of the oracle versions. We also make our proposed method\ninterpretable by visualizing subspace bases, which are estimated from the\ncomputed clustering partitions. This aids in the initial selection of the\nhyperparameter search space.\n", "date": "2024-11-26", "categories": []}
{"id": "2402.01302", "title": "A Unified Framework for Center-based Clustering of Distributed Data", "abstract": "  We develop a family of distributed center-based clustering algorithms that\nwork over networks of users. In the proposed scenario, users contain a local\ndataset and communicate only with their immediate neighbours, with the aim of\nfinding a clustering of the full, joint data. The proposed family, termed\nDistributed Gradient Clustering (DGC-$\\mathcal{F}_\\rho$), is parametrized by\n$\\rho \\geq 1$, controling the proximity of users' center estimates, with\n$\\mathcal{F}$ determining the clustering loss. Our framework allows for a broad\nclass of smooth convex loss functions, including popular clustering losses like\n$K$-means and Huber loss. Specialized to popular clustering losses like\n$K$-means and Huber loss, DGC-$\\mathcal{F}_\\rho$ gives rise to novel\ndistributed clustering algorithms DGC-KM$_\\rho$ and DGC-HL$_\\rho$, while novel\nclustering losses based on Logistic and Fair functions lead to DGC-LL$_\\rho$\nand DGC-FL$_\\rho$. We provide a unified analysis and establish several strong\nresults, under mild assumptions. First, we show that the sequence of centers\ngenerated by the methods converges to a well-defined notion of fixed point,\nunder any center initialization and value of $\\rho$. Second, we prove that, as\n$\\rho$ increases, the family of fixed points produced by DGC-$\\mathcal{F}_\\rho$\nconverges to a notion of consensus fixed points. We show that consensus fixed\npoints of DGC-$\\mathcal{F}_{\\rho}$ are equivalent to fixed points of gradient\nclustering over the full data, guaranteeing a clustering of the full data is\nproduced. For the special case of Bregman losses, we show that our fixed points\nconverge to the set of Lloyd points. Extensive numerical experiments on\nsynthetic and real data confirm our theoretical findings, show strong\nperformance of our methods and demonstrate the usefulness and wide range of\npotential applications of our general framework, such as outlier detection.\n", "date": "2024-02-02", "categories": []}
{"id": "2402.09881", "title": "Explaining Kernel Clustering via Decision Trees", "abstract": "  Despite the growing popularity of explainable and interpretable machine\nlearning, there is still surprisingly limited work on inherently interpretable\nclustering methods. Recently, there has been a surge of interest in explaining\nthe classic k-means algorithm, leading to efficient algorithms that approximate\nk-means clusters using axis-aligned decision trees. However, interpretable\nvariants of k-means have limited applicability in practice, where more flexible\nclustering methods are often needed to obtain useful partitions of the data. In\nthis work, we investigate interpretable kernel clustering, and propose\nalgorithms that construct decision trees to approximate the partitions induced\nby kernel k-means, a nonlinear extension of k-means. We further build on\nprevious work on explainable k-means and demonstrate how a suitable choice of\nfeatures allows preserving interpretability without sacrificing approximation\nguarantees on the interpretable model.\n", "date": "2024-02-15", "categories": []}
{"id": "2405.02631", "title": "Unsupervised machine learning for data-driven rock mass classification:\n  addressing limitations in existing systems using drilling data", "abstract": "  Rock mass classification systems are crucial for assessing stability and risk\nin underground construction globally and guiding support and excavation design.\nHowever, these systems, developed primarily in the 1970s, lack access to modern\nhigh-resolution data and advanced statistical techniques, limiting their\neffectiveness as decision-support systems. We outline these limitations and\ndescribe how a data-driven system, based on drilling data, can overcome them.\nUsing statistical information extracted from thousands of MWD-data values in\none-meter sections of a tunnel profile, acting as a signature of the rock mass,\nwe demonstrate that well-defined clusters can form a foundational basis for\nvarious classification systems. Representation learning was used to reduce the\ndimensionality of 48-value vectors via a nonlinear manifold learning technique\n(UMAP) and linear principal component analysis (PCA) to enhance clustering.\nUnsupervised machine learning methods (HDBSCAN, Agglomerative Clustering,\nK-means) clustered the data, with hyperparameters optimised through\nmulti-objective Bayesian optimisation. Domain knowledge improved clustering by\nadding extra features to core MWD-data clusters. We structured and correlated\nthese clusters with physical rock properties, including rock type and quality,\nand analysed cumulative distributions of key MWD-parameters to determine if\nclusters meaningfully differentiate rock masses. The ability of MWD data to\nform distinct rock mass clusters suggests substantial potential for future\nclassification systems using this objective, data-driven methodology,\nminimising human bias.\n", "date": "2024-05-04", "categories": []}
{"id": "2411.14728", "title": "K-GBS3FCM -- KNN Graph-Based Safe Semi-Supervised Fuzzy C-Means", "abstract": "  Clustering data using prior domain knowledge, starting from a partially\nlabeled set, has recently been widely investigated. Often referred to as\nsemi-supervised clustering, this approach leverages labeled data to enhance\nclustering accuracy. To maximize algorithm performance, it is crucial to ensure\nthe safety of this prior knowledge. Methods addressing this concern are termed\nsafe semi-supervised clustering (S3C) algorithms. This paper introduces the KNN\ngraph-based safety-aware semi-supervised fuzzy c-means algorithm (K-GBS3FCM),\nwhich dynamically assesses neighborhood relationships between labeled and\nunlabeled data using the K-Nearest Neighbors (KNN) algorithm. This approach\naims to optimize the use of labeled data while minimizing the adverse effects\nof incorrect labels. Additionally, it is proposed a mechanism that adjusts the\ninfluence of labeled data on unlabeled ones through regularization parameters\nand the average safety degree. Experimental results on multiple benchmark\ndatasets demonstrate that the graph-based approach effectively leverages prior\nknowledge to enhance clustering accuracy. The proposed method was significantly\nsuperior in 64% of the 56 test configurations, obtaining higher levels of\nclustering accuracy when compared to other semi-supervised and traditional\nunsupervised methods. This research highlights the potential of integrating\ngraph-based approaches, such as KNN, with established techniques to develop\nadvanced clustering algorithms, offering significant applications in fields\nthat rely on both labeled and unlabeled data for more effective clustering.\n", "date": "2024-11-22", "categories": []}
{"id": "2406.00599", "title": "Robust Fair Clustering with Group Membership Uncertainty Sets", "abstract": "  We study the canonical fair clustering problem where each cluster is\nconstrained to have close to population-level representation of each group.\nDespite significant attention, the salient issue of having incomplete knowledge\nabout the group membership of each point has been superficially addressed. In\nthis paper, we consider a setting where the assigned group memberships are\nnoisy. We introduce a simple noise model that requires a small number of\nparameters to be given by the decision maker. We then present an algorithm for\nfair clustering with provable \\emph{robustness} guarantees. Our framework\nenables the decision maker to trade off between the robustness and the\nclustering quality. Unlike previous work, our algorithms are backed by\nworst-case theoretical guarantees. Finally, we empirically verify the\nperformance of our algorithm on real world datasets and show its superior\nperformance over existing baselines.\n", "date": "2024-06-02", "categories": []}
{"id": "2407.07128", "title": "Modularity aided consistent attributed graph clustering via coarsening", "abstract": "  Graph clustering is an important unsupervised learning technique for\npartitioning graphs with attributes and detecting communities. However, current\nmethods struggle to accurately capture true community structures and\nintra-cluster relations, be computationally efficient, and identify smaller\ncommunities. We address these challenges by integrating coarsening and\nmodularity maximization, effectively leveraging both adjacency and node\nfeatures to enhance clustering accuracy. We propose a loss function\nincorporating log-determinant, smoothness, and modularity components using a\nblock majorization-minimization technique, resulting in superior clustering\noutcomes. The method is theoretically consistent under the Degree-Corrected\nStochastic Block Model (DC-SBM), ensuring asymptotic error-free performance and\ncomplete label recovery. Our provably convergent and time-efficient algorithm\nseamlessly integrates with graph neural networks (GNNs) and variational graph\nautoencoders (VGAEs) to learn enhanced node features and deliver exceptional\nclustering performance. Extensive experiments on benchmark datasets demonstrate\nits superiority over existing state-of-the-art methods for both attributed and\nnon-attributed graphs.\n", "date": "2024-07-09", "categories": []}
{"id": "2411.11074", "title": "Spectral Subspace Clustering for Attributed Graphs", "abstract": "  Subspace clustering seeks to identify subspaces that segment a set of n data\npoints into k (k<<n) groups, which has emerged as a powerful tool for analyzing\ndata from various domains, especially images and videos. Recently, several\nstudies have demonstrated the great potential of subspace clustering models for\npartitioning vertices in attributed graphs, referred to as SCAG. However, these\nworks either demand significant computational overhead for constructing the nxn\nself-expressive matrix, or fail to incorporate graph topology and attribute\ndata into the subspace clustering framework effectively, and thus, compromise\nresult quality.\n  Motivated by this, this paper presents two effective and efficient\nalgorithms, S2CAG and M-S2CAG, for SCAG computation. Particularly, S2CAG\nobtains superb performance through three major contributions. First, we\nformulate a new objective function for SCAG with a refined representation model\nfor vertices and two non-trivial constraints. On top of that, an efficient\nlinear-time optimization solver is developed based on our theoretically\ngrounded problem transformation and well-thought-out adaptive strategy. We then\nconduct an in-depth analysis to disclose the theoretical connection of S2CAG to\nconductance minimization, which further inspires the design of M-S2CAG that\nmaximizes the modularity. Our extensive experiments, comparing S2CAG and\nM-S2CAG against 17 competitors over 8 benchmark datasets, exhibit that our\nsolutions outperform all baselines in terms of clustering quality measured\nagainst the ground truth while delivering high efficiency\n", "date": "2024-11-17", "categories": []}
{"id": "2411.11300", "title": "Accelerating spherical K-means clustering for large-scale sparse\n  document data", "abstract": "  This paper presents an accelerated spherical K-means clustering algorithm for\nlarge-scale and high-dimensional sparse document data sets. We design an\nalgorithm working in an architecture-friendly manner (AFM), which is a\nprocedure of suppressing performance-degradation factors such as the numbers of\ninstructions, branch mispredictions, and cache misses in CPUs of a modern\ncomputer system. For the AFM operation, we leverage unique universal\ncharacteristics (UCs) of a data-object and a cluster's mean set, which are\nskewed distributions on data relationships such as Zipf's law and a\nfeature-value concentration phenomenon. The UCs indicate that the most part of\nthe number of multiplications for similarity calculations is executed regarding\nterms with high document frequencies (df) and the most part of a similarity\nbetween an object- and a mean-feature vector is obtained by the multiplications\nregarding a few high mean-feature values. Our proposed algorithm applies an\ninverted-index data structure to a mean set, extracts the specific region with\nhigh-df terms and high mean-feature values in the mean-inverted index by newly\nintroduced two structural parameters, and exploits the index divided into three\nparts for efficient pruning. The algorithm determines the two structural\nparameters by minimizing the approximate number of multiplications related to\nthat of instructions, reduces the branch mispredictions by sharing the index\nstructure including the two parameters with all the objects, and suppressing\nthe cache misses by keeping in the caches the frequently used data in the\nforegoing specific region, resulting in working in the AFM. We experimentally\ndemonstrate that our algorithm efficiently achieves superior speed performance\nin large-scale documents compared with algorithms using the state-of-the-art\ntechniques.\n", "date": "2024-11-18", "categories": []}
{"id": "2411.09758", "title": "Partial Multi-View Clustering via Meta-Learning and Contrastive Feature\n  Alignment", "abstract": "  Partial multi-view clustering (PVC) presents significant challenges practical\nresearch problem for data analysis in real-world applications, especially when\nsome views of the data are partially missing. Existing clustering methods\nstruggle to handle incomplete views effectively, leading to suboptimal\nclustering performance. In this paper, we propose a novel dual optimization\nframework based on contrastive learning, which aims to maximize the consistency\nof latent features in incomplete multi-view data and improve clustering\nperformance through deep learning models. By combining a fine-tuned Vision\nTransformer and k-nearest neighbors (KNN), we fill in missing views and\ndynamically adjust view weights using self-supervised learning and\nmeta-learning. Experimental results demonstrate that our framework outperforms\nstate-of-the-art clustering models on the BDGP and HW datasets, particularly in\nhandling complex and incomplete multi-view data.\n", "date": "2024-11-14", "categories": []}
{"id": "2411.09853", "title": "KULCQ: An Unsupervised Keyword-based Utterance Level Clustering Quality\n  Metric", "abstract": "  Intent discovery is crucial for both building new conversational agents and\nimproving existing ones. While several approaches have been proposed for intent\ndiscovery, most rely on clustering to group similar utterances together.\nTraditional evaluation of these utterance clusters requires intent labels for\neach utterance, limiting scalability. Although some clustering quality metrics\nexist that do not require labeled data, they focus solely on cluster geometry\nwhile ignoring the linguistic nuances present in conversational transcripts. In\nthis paper, we introduce Keyword-based Utterance Level Clustering Quality\n(KULCQ), an unsupervised metric that leverages keyword analysis to evaluate\nclustering quality. We demonstrate KULCQ's effectiveness by comparing it with\nexisting unsupervised clustering metrics and validate its performance through\ncomprehensive ablation studies. Our results show that KULCQ better captures\nsemantic relationships in conversational data while maintaining consistency\nwith geometric clustering principles.\n", "date": "2024-11-15", "categories": []}
{"id": "2411.10290", "title": "The ParClusterers Benchmark Suite (PCBS): A Fine-Grained Analysis of\n  Scalable Graph Clustering", "abstract": "  We introduce the ParClusterers Benchmark Suite (PCBS) -- a collection of\nhighly scalable parallel graph clustering algorithms and benchmarking tools\nthat streamline comparing different graph clustering algorithms and\nimplementations.\n  The benchmark includes clustering algorithms that target a wide range of\nmodern clustering use cases, including community detection, classification, and\ndense subgraph mining.\n  The benchmark toolkit makes it easy to run and evaluate multiple instances of\ndifferent clustering algorithms, which can be useful for fine-tuning the\nperformance of clustering on a given task, and for comparing different\nclustering algorithms based on different metrics of interest, including\nclustering quality and running time.\n  Using PCBS, we evaluate a broad collection of real-world graph clustering\ndatasets. Somewhat surprisingly, we find that the best quality results are\nobtained by algorithms that not included in many popular graph clustering\ntoolkits. The PCBS provides a standardized way to evaluate and judge the\nquality-performance tradeoffs of the active research area of scalable graph\nclustering algorithms. We believe it will help enable fair, accurate, and\nnuanced evaluation of graph clustering algorithms in the future.\n", "date": "2024-11-15", "categories": []}
{"id": "2407.02538", "title": "CGRclust: Chaos Game Representation for Twin Contrastive Clustering of\n  Unlabelled DNA Sequences", "abstract": "  This study proposes CGRclust, a novel combination of unsupervised twin\ncontrastive clustering of Chaos Game Representations (CGR) of DNA sequences,\nwith convolutional neural networks (CNNs). To the best of our knowledge,\nCGRclust is the first method to use unsupervised learning for image\nclassification (herein applied to two-dimensional CGR images) for clustering\ndatasets of DNA sequences. CGRclust overcomes the limitations of traditional\nsequence classification methods by leveraging unsupervised twin contrastive\nlearning to detect distinctive sequence patterns, without requiring DNA\nsequence alignment or biological/taxonomic labels. CGRclust accurately\nclustered twenty-five diverse datasets, with sequence lengths ranging from 664\nbp to 100 kbp, including mitochondrial genomes of fish, fungi, and protists, as\nwell as viral whole genome assemblies and synthetic DNA sequences. Compared\nwith three recent clustering methods for DNA sequences (DeLUCS, iDeLUCS, and\nMeShClust v3.0.), CGRclust is the only method that surpasses 81.70% accuracy\nacross all four taxonomic levels tested for mitochondrial DNA genomes of fish.\nMoreover, CGRclust also consistently demonstrates superior performance across\nall the viral genomic datasets. The high clustering accuracy of CGRclust on\nthese twenty-five datasets, which vary significantly in terms of sequence\nlength, number of genomes, number of clusters, and level of taxonomy,\ndemonstrates its robustness, scalability, and versatility.\n", "date": "2024-07-01", "categories": []}
{"id": "2411.08371", "title": "Multiscale Graph Construction Using Non-local Cluster Features", "abstract": "  This paper presents a multiscale graph construction method using both graph\nand signal features. Multiscale graph is a hierarchical representation of the\ngraph, where a node at each level indicates a cluster in a finer resolution. To\nobtain the hierarchical clusters, existing methods often use graph clustering;\nhowever, they may ignore signal variations. As a result, these methods could\nfail to detect the clusters having similar features on nodes. In this paper, we\nconsider graph and node-wise features simultaneously for multiscale clustering\nof a graph. With given clusters of the graph, the clusters are merged\nhierarchically in three steps: 1) Feature vectors in the clusters are\nextracted. 2) Similarities among cluster features are calculated using optimal\ntransport. 3) A variable $k$-nearest neighbor graph (V$k$NNG) is constructed\nand graph spectral clustering is applied to the V$k$NNG to obtain clusters at a\ncoarser scale. Additionally, the multiscale graph in this paper has\n\\textit{non-local} characteristics: Nodes with similar features are merged even\nif they are spatially separated. In experiments on multiscale image and point\ncloud segmentation, we demonstrate the effectiveness of the proposed method.\n", "date": "2024-11-13", "categories": []}
{"id": "2411.07685", "title": "Fast Disentangled Slim Tensor Learning for Multi-view Clustering", "abstract": "  Tensor-based multi-view clustering has recently received significant\nattention due to its exceptional ability to explore cross-view high-order\ncorrelations. However, most existing methods still encounter some limitations.\n(1) Most of them explore the correlations among different affinity matrices,\nmaking them unscalable to large-scale data. (2) Although some methods address\nit by introducing bipartite graphs, they may result in sub-optimal solutions\ncaused by an unstable anchor selection process. (3) They generally ignore the\nnegative impact of latent semantic-unrelated information in each view. To\ntackle these issues, we propose a new approach termed fast Disentangled Slim\nTensor Learning (DSTL) for multi-view clustering . Instead of focusing on the\nmulti-view graph structures, DSTL directly explores the high-order correlations\namong multi-view latent semantic representations based on matrix factorization.\nTo alleviate the negative influence of feature redundancy, inspired by robust\nPCA, DSTL disentangles the latent low-dimensional representation into a\nsemantic-unrelated part and a semantic-related part for each view.\nSubsequently, two slim tensors are constructed with tensor-based\nregularization. To further enhance the quality of feature disentanglement, the\nsemantic-related representations are aligned across views through a consensus\nalignment indicator. Our proposed model is computationally efficient and can be\nsolved effectively. Extensive experiments demonstrate the superiority and\nefficiency of DSTL over state-of-the-art approaches. The code of DSTL is\navailable at https://github.com/dengxu-nju/DSTL.\n", "date": "2024-11-12", "categories": []}
{"id": "2411.05097", "title": "On the cohesion and separability of average-link for hierarchical\n  agglomerative clustering", "abstract": "  Average-link is widely recognized as one of the most popular and effective\nmethods for building hierarchical agglomerative clustering. The available\ntheoretical analyses show that this method has a much better approximation than\nother popular heuristics, as single-linkage and complete-linkage, regarding\nvariants of Dasgupta's cost function [STOC 2016]. However, these analyses do\nnot separate average-link from a random hierarchy and they are not appealing\nfor metric spaces since every hierarchical clustering has a 1/2 approximation\nwith regard to the variant of Dasgupta's function that is employed for\ndissimilarity measures [Moseley and Yang 2020]. In this paper, we present a\ncomprehensive study of the performance of average-link in metric spaces,\nregarding several natural criteria that capture separability and cohesion and\nare more interpretable than Dasgupta's cost function and its variants. We also\npresent experimental results with real datasets that, together with our\ntheoretical analyses, suggest that average-link is a better choice than other\nrelated methods when both cohesion and separability are important goals.\n", "date": "2024-11-07", "categories": []}
{"id": "2404.04940", "title": "Fuzzy K-Means Clustering without Cluster Centroids", "abstract": "  Fuzzy K-Means clustering is a critical technique in unsupervised data\nanalysis. Unlike traditional hard clustering algorithms such as K-Means, it\nallows data points to belong to multiple clusters with varying degrees of\nmembership, determined through iterative optimization to establish optimal\ncluster centers and memberships, thereby achieving fuzzy partitioning of data.\nHowever, the performance of popular Fuzzy K-Means algorithms is sensitive to\nthe selection of initial cluster centroids and is also affected by noise when\nupdating mean cluster centroids. To address these challenges, this paper\nproposes a novel Fuzzy \\textit{K}-Means clustering algorithm that entirely\neliminates the reliance on cluster centroids, obtaining membership metrics\nsolely through distance matrix computation. This innovation enhances\nflexibility in distance measurement between sample points, thus improving the\nalgorithm's performance and robustness. The paper also establishes theoretical\nconnections between the proposed model and popular Fuzzy K-Means clustering\ntechniques. Experimental results on several real datasets demonstrate the\neffectiveness of the algorithm.\n", "date": "2024-04-07", "categories": []}
{"id": "2405.16598", "title": "Regularized Projection Matrix Approximation with Applications to\n  Community Detection", "abstract": "  This paper introduces a regularized projection matrix approximation framework\ndesigned to recover cluster information from the affinity matrix. The model is\nformulated as a projection approximation problem, incorporating an entry-wise\npenalty function. We investigate three distinct penalty functions, each\nspecifically tailored to address bounded, positive, and sparse scenarios. To\nsolve this problem, we propose direct optimization on the Stiefel manifold,\nutilizing the Cayley transformation along with the Alternating Direction Method\nof Multipliers (ADMM) algorithm. Additionally, we provide a theoretical\nanalysis that establishes the convergence properties of ADMM, demonstrating\nthat the convergence point satisfies the KKT conditions of the original\nproblem. Numerical experiments conducted on both synthetic and real-world\ndatasets reveal that our regularized projection matrix approximation approach\nsignificantly outperforms state-of-the-art methods in clustering performance.\n", "date": "2024-05-26", "categories": []}
{"id": "2411.04397", "title": "A Bayesian Mixture Model of Temporal Point Processes with Determinantal\n  Point Process Prior", "abstract": "  Asynchronous event sequence clustering aims to group similar event sequences\nin an unsupervised manner. Mixture models of temporal point processes have been\nproposed to solve this problem, but they often suffer from overfitting, leading\nto excessive cluster generation with a lack of diversity. To overcome these\nlimitations, we propose a Bayesian mixture model of Temporal Point Processes\nwith Determinantal Point Process prior (TP$^2$DP$^2$) and accordingly an\nefficient posterior inference algorithm based on conditional Gibbs sampling.\nOur work provides a flexible learning framework for event sequence clustering,\nenabling automatic identification of the potential number of clusters and\naccurate grouping of sequences with similar features. It is applicable to a\nwide range of parametric temporal point processes, including neural\nnetwork-based models. Experimental results on both synthetic and real-world\ndata suggest that our framework could produce moderately fewer yet more diverse\nmixture components, and achieve outstanding results across multiple evaluation\nmetrics.\n", "date": "2024-11-07", "categories": []}
{"id": "2411.03978", "title": "Customized Multiple Clustering via Multi-Modal Subspace Proxy Learning", "abstract": "  Multiple clustering aims to discover various latent structures of data from\ndifferent aspects. Deep multiple clustering methods have achieved remarkable\nperformance by exploiting complex patterns and relationships in data. However,\nexisting works struggle to flexibly adapt to diverse user-specific needs in\ndata grouping, which may require manual understanding of each clustering. To\naddress these limitations, we introduce Multi-Sub, a novel end-to-end multiple\nclustering approach that incorporates a multi-modal subspace proxy learning\nframework in this work. Utilizing the synergistic capabilities of CLIP and\nGPT-4, Multi-Sub aligns textual prompts expressing user preferences with their\ncorresponding visual representations. This is achieved by automatically\ngenerating proxy words from large language models that act as subspace bases,\nthus allowing for the customized representation of data in terms specific to\nthe user's interests. Our method consistently outperforms existing baselines\nacross a broad set of datasets in visual multiple clustering tasks. Our code is\navailable at https://github.com/Alexander-Yao/Multi-Sub.\n", "date": "2024-11-06", "categories": []}
{"id": "2411.03186", "title": "Insights into Lunar Mineralogy: An Unsupervised Approach for Clustering\n  of the Moon Mineral Mapper (M3) spectral data", "abstract": "  This paper presents a novel method for mapping spectral features of the Moon\nusing machine learning-based clustering of hyperspectral data from the Moon\nMineral Mapper (M3) imaging spectrometer. The method uses a convolutional\nvariational autoencoder to reduce the dimensionality of the spectral data and\nextract features of the spectra. Then, a k-means algorithm is applied to\ncluster the latent variables into five distinct groups, corresponding to\ndominant spectral features, which are related to the mineral composition of the\nMoon's surface. The resulting global spectral cluster map shows the\ndistribution of the five clusters on the Moon, which consist of a mixture of,\namong others, plagioclase, pyroxene, olivine, and Fe-bearing minerals across\nthe Moon's surface. The clusters are compared to the mineral maps from the\nKaguya mission, which showed that the locations of the clusters overlap with\nthe locations of high wt% of minerals such as plagioclase, clinopyroxene, and\nolivine. The paper demonstrates the usefulness of unbiased unsupervised\nlearning for lunar mineral exploration and provides a comprehensive analysis of\nlunar mineralogy.\n", "date": "2024-11-05", "categories": []}
{"id": "2304.13917", "title": "Proportionally Representative Clustering", "abstract": "  In recent years, there has been a surge in effort to formalize notions of\nfairness in machine learning. We focus on centroid clustering--one of the\nfundamental tasks in unsupervised machine learning. We propose a new axiom\n``proportionally representative fairness'' (PRF) that is designed for\nclustering problems where the selection of centroids reflects the distribution\nof data points and how tightly they are clustered together. Our fairness\nconcept is not satisfied by existing fair clustering algorithms. We design\nefficient algorithms to achieve PRF both for unconstrained and discrete\nclustering problems. Our algorithm for the unconstrained setting is also the\nfirst known polynomial-time approximation algorithm for the well-studied\nProportional Fairness (PF) axiom. Our algorithm for the discrete setting also\nmatches the best known approximation factor for PF.\n", "date": "2023-04-27", "categories": []}
{"id": "2305.10356", "title": "Spectral Clustering via Orthogonalization-Free Methods", "abstract": "  While orthogonalization exists in current dimensionality reduction methods in\nspectral clustering on undirected graphs, it does not scale in parallel\ncomputing environments. We propose four orthogonalization-free methods for\nspectral clustering. Our methods optimize one of two objective functions with\nno spurious local minima. In theory, two methods converge to features\nisomorphic to the eigenvectors corresponding to the smallest eigenvalues of the\nsymmetric normalized Laplacian. The other two converge to features isomorphic\nto weighted eigenvectors weighting by the square roots of eigenvalues. We\nprovide numerical evidence on the synthetic graphs from the IEEE HPEC Graph\nChallenge to demonstrate the effectiveness of the orthogonalization-free\nmethods. Numerical results on the streaming graphs show that the\northogonalization-free methods are competitive in the streaming graph scenario\nsince they can take full advantage of the computed features of previous graphs\nand converge fast. Our methods are also more scalable in parallel computing\nenvironments because orthogonalization is unnecessary. Numerical results are\nprovided to demonstrate the scalability of our methods. Consequently, our\nmethods have advantages over other dimensionality reduction methods when\nhandling spectral clustering for large streaming graphs.\n", "date": "2023-05-16", "categories": []}
{"id": "2408.03765", "title": "Reliable Node Similarity Matrix Guided Contrastive Graph Clustering", "abstract": "  Graph clustering, which involves the partitioning of nodes within a graph\ninto disjoint clusters, holds significant importance for numerous subsequent\napplications. Recently, contrastive learning, known for utilizing supervisory\ninformation, has demonstrated encouraging results in deep graph clustering.\nThis methodology facilitates the learning of favorable node representations for\nclustering by attracting positively correlated node pairs and distancing\nnegatively correlated pairs within the representation space. Nevertheless, a\nsignificant limitation of existing methods is their inadequacy in thoroughly\nexploring node-wise similarity. For instance, some hypothesize that the node\nsimilarity matrix within the representation space is identical, ignoring the\ninherent semantic relationships among nodes. Given the fundamental role of\ninstance similarity in clustering, our research investigates contrastive graph\nclustering from the perspective of the node similarity matrix. We argue that an\nideal node similarity matrix within the representation space should accurately\nreflect the inherent semantic relationships among nodes, ensuring the\npreservation of semantic similarities in the learned representations. In\nresponse to this, we introduce a new framework, Reliable Node Similarity Matrix\nGuided Contrastive Graph Clustering (NS4GC), which estimates an approximately\nideal node similarity matrix within the representation space to guide\nrepresentation learning. Our method introduces node-neighbor alignment and\nsemantic-aware sparsification, ensuring the node similarity matrix is both\naccurate and efficiently sparse. Comprehensive experiments conducted on $8$\nreal-world datasets affirm the efficacy of learning the node similarity matrix\nand the superior performance of NS4GC.\n", "date": "2024-08-07", "categories": []}
{"id": "2411.00904", "title": "Similarity and Dissimilarity Guided Co-association Matrix Construction\n  for Ensemble Clustering", "abstract": "  Ensemble clustering aggregates multiple weak clusterings to achieve a more\naccurate and robust consensus result. The Co-Association matrix (CA matrix)\nbased method is the mainstream ensemble clustering approach that constructs the\nsimilarity relationships between sample pairs according the weak clustering\npartitions to generate the final clustering result. However, the existing\nmethods neglect that the quality of cluster is related to its size, i.e., a\ncluster with smaller size tends to higher accuracy. Moreover, they also do not\nconsider the valuable dissimilarity information in the base clusterings which\ncan reflect the varying importance of sample pairs that are completely\ndisconnected. To this end, we propose the Similarity and Dissimilarity Guided\nCo-association matrix (SDGCA) to achieve ensemble clustering. First, we\nintroduce normalized ensemble entropy to estimate the quality of each cluster,\nand construct a similarity matrix based on this estimation. Then, we employ the\nrandom walk to explore high-order proximity of base clusterings to construct a\ndissimilarity matrix. Finally, the adversarial relationship between the\nsimilarity matrix and the dissimilarity matrix is utilized to construct a\npromoted CA matrix for ensemble clustering. We compared our method with 13\nstate-of-the-art methods across 12 datasets, and the results demonstrated the\nsuperiority clustering ability and robustness of the proposed approach. The\ncode is available at https://github.com/xuz2019/SDGCA.\n", "date": "2024-11-01", "categories": []}
{"id": "2411.01250", "title": "Hierarchical and Density-based Causal Clustering", "abstract": "  Understanding treatment effect heterogeneity is vital for scientific and\npolicy research. However, identifying and evaluating heterogeneous treatment\neffects pose significant challenges due to the typically unknown subgroup\nstructure. Recently, a novel approach, causal k-means clustering, has emerged\nto assess heterogeneity of treatment effect by applying the k-means algorithm\nto unknown counterfactual regression functions. In this paper, we expand upon\nthis framework by integrating hierarchical and density-based clustering\nalgorithms. We propose plug-in estimators that are simple and readily\nimplementable using off-the-shelf algorithms. Unlike k-means clustering, which\nrequires the margin condition, our proposed estimators do not rely on strong\nstructural assumptions on the outcome process. We go on to study their rate of\nconvergence, and show that under the minimal regularity conditions, the\nadditional cost of causal clustering is essentially the estimation error of the\noutcome regression functions. Our findings significantly extend the\ncapabilities of the causal clustering framework, thereby contributing to the\nprogression of methodologies for identifying homogeneous subgroups in treatment\nresponse, consequently facilitating more nuanced and targeted interventions.\nThe proposed methods also open up new avenues for clustering with generic\npseudo-outcomes. We explore finite sample properties via simulation, and\nillustrate the proposed methods in voting and employment projection datasets.\n", "date": "2024-11-02", "categories": []}
{"id": "2411.01780", "title": "Clustering Based on Density Propagation and Subcluster Merging", "abstract": "  We propose the DPSM method, a density-based node clustering approach that\nautomatically determines the number of clusters and can be applied in both data\nspace and graph space. Unlike traditional density-based clustering methods,\nwhich necessitate calculating the distance between any two nodes, our proposed\ntechnique determines density through a propagation process, thereby making it\nsuitable for a graph space. In DPSM, nodes are partitioned into small clusters\nbased on propagated density. The partitioning technique has been proved to be\nsound and complete. We then extend the concept of spectral clustering from\nindividual nodes to these small clusters, while introducing the CluCut measure\nto guide cluster merging. This measure is modified in various ways to account\nfor cluster properties, thus provides guidance on when to terminate the merging\nprocess. Various experiments have validated the effectiveness of DOSM and the\naccuracy of these conclusions.\n", "date": "2024-11-04", "categories": []}
{"id": "2308.10505", "title": "A Clustering Algorithm to Organize Satellite Hotspot Data for the\n  Purpose of Tracking Bushfires Remotely", "abstract": "  This paper proposes a spatiotemporal clustering algorithm and its\nimplementation in the R package spotoroo. This work is motivated by the\ncatastrophic bushfires in Australia throughout the summer of 2019-2020 and made\npossible by the availability of satellite hotspot data. The algorithm is\ninspired by two existing spatiotemporal clustering algorithms but makes\nenhancements to cluster points spatially in conjunction with their movement\nacross consecutive time periods. It also allows for the adjustment of key\nparameters, if required, for different locations and satellite data sources.\nBushfire data from Victoria, Australia, is used to illustrate the algorithm and\nits use within the package.\n", "date": "2023-08-21", "categories": []}
{"id": "2411.00268", "title": "Clustering ensemble algorithm with high-order consistency learning", "abstract": "  Most of the research on clustering ensemble focuses on designing practical\nconsistency learning algorithms.To solve the problems that the quality of base\nclusters varies and the low-quality base clusters have an impact on the\nperformance of the clustering ensemble, from the perspective of data mining,\nthe intrinsic connections of data were mined based on the base clusters, and a\nhigh-order information fusion algorithm was proposed to represent the\nconnections between data from different dimensions, namely Clustering Ensemble\nwith High-order Consensus learning (HCLCE). Firstly, each high-order\ninformation was fused into a new structured consistency matrix. Then, the\nobtained multiple consistency matrices were fused together. Finally, multiple\ninformation was fused into a consistent result. Experimental results show that\nLCLCE algorithm has the clustering accuracy improved by an average of 7.22%,\nand the Normalized Mutual Information (NMI) improved by an average of 9.19%\ncompared with the suboptimal Locally Weighted Evidence Accumulation (LWEA)\nalgorithm. It can be seen that the proposed algorithm can obtain better\nclustering results compared with clustering ensemble algorithms and using one\ninformation alone.\n", "date": "2024-10-31", "categories": []}
{"id": "2410.24104", "title": "Clustering to Minimize Cluster-Aware Norm Objectives", "abstract": "  We initiate the study of the following general clustering problem. We seek to\npartition a given set $P$ of data points into $k$ clusters by finding a set $X$\nof $k$ centers and assigning each data point to one of the centers. The cost of\na cluster, represented by a center $x\\in X$, is a monotone, symmetric norm $f$\n(inner norm) of the vector of distances of points assigned to $x$. The goal is\nto minimize a norm $g$ (outer norm) of the vector of cluster costs. This\nproblem, which we call $(f,g)$-Clustering, generalizes many fundamental\nclustering problems such as $k$-Center, $k$-Median , Min-Sum of Radii, and\nMin-Load $k$-Clustering . A recent line of research (Chakrabarty, Swamy\n[STOC'19]) studies norm objectives that are oblivious to the cluster structure\nsuch as $k$-Median and $k$-Center. In contrast, our problem models\ncluster-aware objectives including Min-Sum of Radii and Min-Load\n$k$-Clustering.\n  Our main results are as follows. First, we design a constant-factor\napproximation algorithm for $(\\textsf{top}_\\ell,\\mathcal{L}_1)$-Clustering\nwhere the inner norm ($\\textsf{top}_\\ell$) sums over the $\\ell$ largest\ndistances. Second, we design a constant-factor approximation\\ for\n$(\\mathcal{L}_\\infty,\\textsf{Ord})$-Clustering where the outer norm is a convex\ncombination of $\\textsf{top}_\\ell$ norms (ordered weighted norm).\n", "date": "2024-10-31", "categories": []}
{"id": "2402.15688", "title": "Anchor-free Clustering based on Anchor Graph Factorization", "abstract": "  Anchor-based methods are a pivotal approach in handling clustering of\nlarge-scale data. However, these methods typically entail two distinct stages:\nselecting anchor points and constructing an anchor graph. This bifurcation,\nalong with the initialization of anchor points, significantly influences the\noverall performance of the algorithm. To mitigate these issues, we introduce a\nnovel method termed Anchor-free Clustering based on Anchor Graph Factorization\n(AFCAGF). AFCAGF innovates in learning the anchor graph, requiring only the\ncomputation of pairwise distances between samples. This process, achievable\nthrough straightforward optimization, circumvents the necessity for explicit\nselection of anchor points. More concretely, our approach enhances the Fuzzy\nk-means clustering algorithm (FKM), introducing a new manifold learning\ntechnique that obviates the need for initializing cluster centers.\nAdditionally, we evolve the concept of the membership matrix between cluster\ncenters and samples in FKM into an anchor graph encompassing multiple anchor\npoints and samples. Employing Non-negative Matrix Factorization (NMF) on this\nanchor graph allows for the direct derivation of cluster labels, thereby\neliminating the requirement for further post-processing steps. To solve the\nmethod proposed, we implement an alternating optimization algorithm that\nensures convergence. Empirical evaluations on various real-world datasets\nunderscore the superior efficacy of our algorithm compared to traditional\napproaches.\n", "date": "2024-02-24", "categories": []}
{"id": "2404.00883", "title": "Interpretable Multi-View Clustering Based on Anchor Graph Tensor\n  Factorization", "abstract": "  The clustering method based on the anchor graph has gained significant\nattention due to its exceptional clustering performance and ability to process\nlarge-scale data. One common approach is to learn bipartite graphs with\nK-connected components, helping avoid the need for post-processing. However,\nthis method has strict parameter requirements and may not always get\nK-connected components. To address this issue, an alternative approach is to\ndirectly obtain the cluster label matrix by performing non-negative matrix\nfactorization (NMF) on the anchor graph. Nevertheless, existing multi-view\nclustering methods based on anchor graph factorization lack adequate cluster\ninterpretability for the decomposed matrix and often overlook the inter-view\ninformation. We address this limitation by using non-negative tensor\nfactorization to decompose an anchor graph tensor that combines anchor graphs\nfrom multiple views. This approach allows us to consider inter-view information\ncomprehensively. The decomposed tensors, namely the sample indicator tensor and\nthe anchor indicator tensor, enhance the interpretability of the factorization.\nExtensive experiments validate the effectiveness of this method.\n", "date": "2024-04-01", "categories": []}
{"id": "2409.15887", "title": "Self-Supervised Graph Embedding Clustering", "abstract": "  The K-means one-step dimensionality reduction clustering method has made some\nprogress in addressing the curse of dimensionality in clustering tasks.\nHowever, it combines the K-means clustering and dimensionality reduction\nprocesses for optimization, leading to limitations in the clustering effect due\nto the introduced hyperparameters and the initialization of clustering centers.\nMoreover, maintaining class balance during clustering remains challenging. To\novercome these issues, we propose a unified framework that integrates manifold\nlearning with K-means, resulting in the self-supervised graph embedding\nframework. Specifically, we establish a connection between K-means and the\nmanifold structure, allowing us to perform K-means without explicitly defining\ncentroids. Additionally, we use this centroid-free K-means to generate labels\nin low-dimensional space and subsequently utilize the label information to\ndetermine the similarity between samples. This approach ensures consistency\nbetween the manifold structure and the labels. Our model effectively achieves\none-step clustering without the need for redundant balancing hyperparameters.\nNotably, we have discovered that maximizing the $\\ell_{2,1}$-norm naturally\nmaintains class balance during clustering, a result that we have theoretically\nproven. Finally, experiments on multiple datasets demonstrate that the\nclustering results of Our-LPP and Our-MFA exhibit excellent and reliable\nperformance.\n", "date": "2024-09-24", "categories": []}
{"id": "2410.23273", "title": "Proportional Fairness in Non-Centroid Clustering", "abstract": "  We revisit the recently developed framework of proportionally fair\nclustering, where the goal is to provide group fairness guarantees that become\nstronger for groups of data points (agents) that are large and cohesive. Prior\nwork applies this framework to centroid clustering, where the loss of an agent\nis its distance to the centroid assigned to its cluster. We expand the\nframework to non-centroid clustering, where the loss of an agent is a function\nof the other agents in its cluster, by adapting two proportional fairness\ncriteria -- the core and its relaxation, fully justified representation (FJR)\n-- to this setting.\n  We show that the core can be approximated only under structured loss\nfunctions, and even then, the best approximation we are able to establish,\nusing an adaptation of the GreedyCapture algorithm developed for centroid\nclustering [Chen et al., 2019; Micha and Shah, 2020], is unappealing for a\nnatural loss function. In contrast, we design a new (inefficient) algorithm,\nGreedyCohesiveClustering, which achieves the relaxation FJR exactly under\narbitrary loss functions, and show that the efficient GreedyCapture algorithm\nachieves a constant approximation of FJR. We also design an efficient auditing\nalgorithm, which estimates the FJR approximation of any given clustering\nsolution up to a constant factor. Our experiments on real data suggest that\ntraditional clustering algorithms are highly unfair, whereas GreedyCapture is\nconsiderably fairer and incurs only a modest loss in common clustering\nobjectives.\n", "date": "2024-10-30", "categories": []}
{"id": "2410.21711", "title": "Multi-view clustering integrating anchor attribute and structural\n  information", "abstract": "  Multisource data has spurred the development of advanced clustering\nalgorithms, such as multi-view clustering, which critically relies on\nconstructing similarity matrices. Traditional algorithms typically generate\nthese matrices from sample attributes alone. However, real-world networks often\ninclude pairwise directed topological structures critical for clustering. This\npaper introduces a novel multi-view clustering algorithm, AAS. It utilizes a\ntwo-step proximity approach via anchors in each view, integrating attribute and\ndirected structural information. This approach enhances the clarity of category\ncharacteristics in the similarity matrices. The anchor structural similarity\nmatrix leverages strongly connected components of directed graphs. The entire\nprocess-from similarity matrices construction to clustering - is consolidated\ninto a unified optimization framework. Comparative experiments on the modified\nAttribute SBM dataset against eight algorithms affirm the effectiveness and\nsuperiority of AAS.\n", "date": "2024-10-29", "categories": []}
{"id": "2309.16384", "title": "Multi-Swap $k$-Means++", "abstract": "  The $k$-means++ algorithm of Arthur and Vassilvitskii (SODA 2007) is often\nthe practitioners' choice algorithm for optimizing the popular $k$-means\nclustering objective and is known to give an $O(\\log k)$-approximation in\nexpectation. To obtain higher quality solutions, Lattanzi and Sohler (ICML\n2019) proposed augmenting $k$-means++ with $O(k \\log \\log k)$ local search\nsteps obtained through the $k$-means++ sampling distribution to yield a\n$c$-approximation to the $k$-means clustering problem, where $c$ is a large\nabsolute constant. Here we generalize and extend their local search algorithm\nby considering larger and more sophisticated local search neighborhoods hence\nallowing to swap multiple centers at the same time. Our algorithm achieves a $9\n+ \\varepsilon$ approximation ratio, which is the best possible for local\nsearch. Importantly we show that our approach yields substantial practical\nimprovements, we show significant quality improvements over the approach of\nLattanzi and Sohler (ICML 2019) on several datasets.\n", "date": "2023-09-28", "categories": []}
{"id": "2403.11087", "title": "Incorporating Higher-order Structural Information for Graph Clustering", "abstract": "  Clustering holds profound significance in data mining. In recent years, graph\nconvolutional network (GCN) has emerged as a powerful tool for deep clustering,\nintegrating both graph structural information and node attributes. However,\nmost existing methods ignore the higher-order structural information of the\ngraph. Evidently, nodes within the same cluster can establish distant\nconnections. Besides, recent deep clustering methods usually apply a\nself-supervised module to monitor the training process of their model, focusing\nsolely on node attributes without paying attention to graph structure. In this\npaper, we propose a novel graph clustering network to make full use of graph\nstructural information. To capture the higher-order structural information, we\ndesign a graph mutual infomax module, effectively maximizing mutual information\nbetween graph-level and node-level representations, and employ a trinary\nself-supervised module that includes modularity as a structural constraint. Our\nproposed model outperforms many state-of-the-art methods on various datasets,\ndemonstrating its superiority.\n", "date": "2024-03-17", "categories": []}
{"id": "2405.02688", "title": "Semi-supervised Symmetric Non-negative Matrix Factorization with\n  Low-Rank Tensor Representation", "abstract": "  Semi-supervised symmetric non-negative matrix factorization (SNMF) utilizes\nthe available supervisory information (usually in the form of pairwise\nconstraints) to improve the clustering ability of SNMF. The previous methods\nintroduce the pairwise constraints from the local perspective, i.e., they\neither directly refine the similarity matrix element-wisely or restrain the\ndistance of the decomposed vectors in pairs according to the pairwise\nconstraints, which overlook the global perspective, i.e., in the ideal case,\nthe pairwise constraint matrix and the ideal similarity matrix possess the same\nlow-rank structure. To this end, we first propose a novel semi-supervised SNMF\nmodel by seeking low-rank representation for the tensor synthesized by the\npairwise constraint matrix and a similarity matrix obtained by the product of\nthe embedding matrix and its transpose, which could strengthen those two\nmatrices simultaneously from a global perspective. We then propose an enhanced\nSNMF model, making the embedding matrix tailored to the above tensor low-rank\nrepresentation. We finally refine the similarity matrix by the strengthened\npairwise constraints. We repeat the above steps to continuously boost the\nsimilarity matrix and pairwise constraint matrix, leading to a high-quality\nembedding matrix. Extensive experiments substantiate the superiority of our\nmethod. The code is available at https://github.com/JinaLeejnl/TSNMF.\n", "date": "2024-05-04", "categories": []}
{"id": "2410.20383", "title": "Multiple kernel concept factorization algorithm based on global fusion", "abstract": "  Non-negative Matrix Factorization(NMF) algorithm can only be used to find low\nrank approximation of original non-negative data while Concept\nFactorization(CF) algorithm extends matrix factorization to single non-linear\nkernel space, improving learning ability and adaptability of matrix\nfactorization. In unsupervised environment, to design or select proper kernel\nfunction for specific dataset, a new algorithm called Globalized Multiple\nKernel CF(GMKCF)was proposed. Multiple candidate kernel functions were input in\nthe same time and learned in the CF framework based on global linear fusion,\nobtaining a clustering result with high quality and stability and solving the\nproblem of kernel function selection that the CF faced. The convergence of the\nproposed algorithm was verified by solving the model with alternate iteration.\nThe experimental results on several real databases show that the proposed\nalgorithm outperforms comparison algorithms in data clustering, such as Kernel\nK-Means(KKM), Spectral Clustering(SC), Kernel CF(KCF), Co-regularized\nmulti-view spectral clustering(Coreg), and Robust Multiple KKM(RMKKM).\n", "date": "2024-10-27", "categories": []}
{"id": "2410.20391", "title": "Hierarchical Multiple Kernel K-Means Algorithm Based on Sparse\n  Connectivity", "abstract": "  Multiple kernel learning (MKL) aims to find an optimal, consistent kernel\nfunction. In the hierarchical multiple kernel clustering (HMKC) algorithm,\nsample features are extracted layer by layer from a high-dimensional space to\nmaximize the retention of effective information. However, information\ninteraction between layers is often ignored. In this model, only corresponding\nnodes in adjacent layers exchange information; other nodes remain isolated, and\nif full connectivity is adopted, the diversity of the final consistency matrix\nis reduced. Therefore, this paper proposes a hierarchical multiple kernel\nK-Means (SCHMKKM) algorithm based on sparse connectivity, which controls the\nassignment matrix to achieve sparse connections through a sparsity rate,\nthereby locally fusing the features obtained by distilling information between\nlayers. Finally, we conduct cluster analysis on multiple datasets and compare\nit with the fully connected hierarchical multiple kernel K-Means (FCHMKKM)\nalgorithm in experiments. It is shown that more discriminative information\nfusion is beneficial for learning a better consistent partition matrix, and the\nfusion strategy based on sparse connection outperforms the full connection\nstrategy.\n", "date": "2024-10-27", "categories": []}
{"id": "2410.17256", "title": "Inference with K-means", "abstract": "  This thesis aims to invent new approaches for making inferences with the\nk-means algorithm. k-means is an iterative clustering algorithm that randomly\nassigns k centroids, then assigns data points to the nearest centroid, and\nupdates centroids based on the mean of assigned points. This process continues\nuntil convergence, forming k clusters where each point belongs to the closest\ncentroid. This research investigates the prediction of the last component of\ndata points obtained from a distribution of clustered data using the online\nbalanced k-means approach. Through extensive experimentation and analysis, key\nfindings have emerged. It is observed that a larger number of clusters or\npartitions tends to yield lower errors while increasing the number of assigned\ndata points does not significantly improve inference errors. Reducing losses in\nthe learning process does not significantly impact overall inference errors.\nIndicating that as learning is going on inference errors remain unchanged.\nRecommendations include the need for specialized inference techniques to\nestimate better data points derived from multi-clustered data and exploring\nmethods that yield improved results with larger assigned datasets. By\naddressing these recommendations, this research advances the accuracy and\nreliability of inferences made with the k-means algorithm, bridging the gap\nbetween clustering and non-parametric density estimation and inference.\n", "date": "2024-10-04", "categories": []}
{"id": "2410.15117", "title": "Accelerating k-Means Clustering with Cover Trees", "abstract": "  The k-means clustering algorithm is a popular algorithm that partitions data\ninto k clusters. There are many improvements to accelerate the standard\nalgorithm. Most current research employs upper and lower bounds on\npoint-to-cluster distances and the triangle inequality to reduce the number of\ndistance computations, with only arrays as underlying data structures. These\napproaches cannot exploit that nearby points are likely assigned to the same\ncluster. We propose a new k-means algorithm based on the cover tree index, that\nhas relatively low overhead and performs well, for a wider parameter range,\nthan previous approaches based on the k-d tree. By combining this with upper\nand lower bounds, as in state-of-the-art approaches, we obtain a hybrid\nalgorithm that combines the benefits of tree aggregation and bounds-based\nfiltering.\n", "date": "2024-10-19", "categories": []}
{"id": "2410.15233", "title": "A Semidefinite Relaxation Approach for Fair Graph Clustering", "abstract": "  Fair graph clustering is crucial for ensuring equitable representation and\ntreatment of diverse communities in network analysis. Traditional methods often\nignore disparities among social, economic, and demographic groups, perpetuating\nbiased outcomes and reinforcing inequalities. This study introduces fair graph\nclustering within the framework of the disparate impact doctrine, treating it\nas a joint optimization problem integrating clustering quality and fairness\nconstraints. Given the NP-hard nature of this problem, we employ a semidefinite\nrelaxation approach to approximate the underlying optimization problem. For up\nto medium-sized graphs, we utilize a singular value decomposition-based\nalgorithm, while for larger graphs, we propose a novel algorithm based on the\nalternative direction method of multipliers. Unlike existing methods, our\nformulation allows for tuning the trade-off between clustering quality and\nfairness. Experimental results on graphs generated from the standard stochastic\nblock model demonstrate the superiority of our approach in achieving an optimal\naccuracy-fairness trade-off compared to state-of-the-art methods.\n", "date": "2024-10-19", "categories": []}
{"id": "2410.15304", "title": "Multiple Kernel Clustering via Local Regression Integration", "abstract": "  Multiple kernel methods less consider the intrinsic manifold structure of\nmultiple kernel data and estimate the consensus kernel matrix with quadratic\nnumber of variables, which makes it vulnerable to the noise and outliers within\nmultiple candidate kernels. This paper first presents the clustering method via\nkernelized local regression (CKLR). It captures the local structure of kernel\ndata and employs kernel regression on the local region to predict the\nclustering results. Moreover, this paper further extends it to perform\nclustering via the multiple kernel local regression (CMKLR). We construct the\nkernel level local regression sparse coefficient matrix for each candidate\nkernel, which well characterizes the kernel level manifold structure. We then\naggregate all the kernel level local regression coefficients via linear weights\nand generate the consensus sparse local regression coefficient, which largely\nreduces the number of candidate variables and becomes more robust against\nnoises and outliers within multiple kernel data. Thus, the proposed method\nCMKLR avoids the above two limitations. It only contains one additional\nhyperparameter for tuning. Extensive experimental results show that the\nclustering performance of the proposed method on benchmark datasets is better\nthan that of 10 state-of-the-art multiple kernel clustering methods.\n", "date": "2024-10-20", "categories": []}
{"id": "2410.16124", "title": "MNIST-Nd: a set of naturalistic datasets to benchmark clustering across\n  dimensions", "abstract": "  Driven by advances in recording technology, large-scale high-dimensional\ndatasets have emerged across many scientific disciplines. Especially in\nbiology, clustering is often used to gain insights into the structure of such\ndatasets, for instance to understand the organization of different cell types.\nHowever, clustering is known to scale poorly to high dimensions, even though\nthe exact impact of dimensionality is unclear as current benchmark datasets are\nmostly two-dimensional. Here we propose MNIST-Nd, a set of synthetic datasets\nthat share a key property of real-world datasets, namely that individual\nsamples are noisy and clusters do not perfectly separate. MNIST-Nd is obtained\nby training mixture variational autoencoders with 2 to 64 latent dimensions on\nMNIST, resulting in six datasets with comparable structure but varying\ndimensionality. It thus offers the chance to disentangle the impact of\ndimensionality on clustering. Preliminary common clustering algorithm\nbenchmarks on MNIST-Nd suggest that Leiden is the most robust for growing\ndimensions.\n", "date": "2024-10-21", "categories": []}
{"id": "2212.14437", "title": "An algorithm for clustering with confidence-based must-link and\n  cannot-link constraints", "abstract": "  We study here the semi-supervised $k$-clustering problem where information is\navailable on whether pairs of objects are in the same or in different clusters.\nThis information is either available with certainty or with a limited level of\nconfidence. We introduce the PCCC (Pairwise-Confidence-Constraints-Clustering)\nalgorithm, which iteratively assigns objects to clusters while accounting for\nthe information provided on the pairs of objects. Our algorithm uses integer\nprogramming for the assignment of objects which allows to include relationships\nas hard constraints that are guaranteed to be satisfied or as soft constraints\nthat can be violated subject to a penalty. This flexibility distinguishes our\nalgorithm from the state-of-the-art in which all pairwise constraints are\neither considered hard, or all are considered soft. We developed an enhanced\nmulti-start approach and a model-size reduction technique for the integer\nprogram that contributes to the effectiveness and the efficiency of the\nalgorithm. Unlike existing algorithms, our algorithm scales to large-scale\ninstances with up to 60,000 objects, 100 clusters, and millions of cannot-link\nconstraints (which are the most challenging constraints to incorporate). We\ncompare the PCCC algorithm with state-of-the-art approaches in an extensive\ncomputational study. Even though the PCCC algorithm is more general than the\nstate-of-the-art approaches in its applicability, it outperforms the\nstate-of-the-art approaches on instances with all hard or all soft constraints\nboth in terms of runtime and various metrics of solution quality. The code of\nthe PCCC algorithm is publicly available on GitHub.\n", "date": "2022-12-29", "categories": []}
{"id": "2410.14269", "title": "On time series clustering with k-means", "abstract": "  There is a long history of research into time series clustering using\ndistance-based partitional clustering. Many of the most popular algorithms\nadapt k-means (also known as Lloyd's algorithm) to exploit time dependencies in\nthe data by specifying a time series distance function. However, these\nalgorithms are often presented with k-means configured in various ways,\naltering key parameters such as the initialisation strategy. This variability\nmakes it difficult to compare studies because k-means is known to be highly\nsensitive to its configuration. To address this, we propose a standard\nLloyd's-based model for TSCL that adopts an end-to-end approach, incorporating\na specialised distance function not only in the assignment step but also in the\ninitialisation and stopping criteria. By doing so, we create a unified\nstructure for comparing seven popular Lloyd's-based TSCL algorithms. This\ncommon framework enables us to more easily attribute differences in clustering\nperformance to the distance function itself, rather than variations in the\nk-means configuration.\n", "date": "2024-10-18", "categories": []}
{"id": "2410.14548", "title": "Boosting K-means for Big Data by Fusing Data Streaming with Global\n  Optimization", "abstract": "  K-means clustering is a cornerstone of data mining, but its efficiency\ndeteriorates when confronted with massive datasets. To address this limitation,\nwe propose a novel heuristic algorithm that leverages the Variable Neighborhood\nSearch (VNS) metaheuristic to optimize K-means clustering for big data. Our\napproach is based on the sequential optimization of the partial objective\nfunction landscapes obtained by restricting the Minimum Sum-of-Squares\nClustering (MSSC) formulation to random samples from the original big dataset.\nWithin each landscape, systematically expanding neighborhoods of the currently\nbest (incumbent) solution are explored by reinitializing all degenerate and a\nvarying number of additional centroids. Extensive and rigorous experimentation\non a large number of real-world datasets reveals that by transforming the\ntraditional local search into a global one, our algorithm significantly\nenhances the accuracy and efficiency of K-means clustering in big data\nenvironments, becoming the new state of the art in the field.\n", "date": "2024-10-18", "categories": []}
{"id": "2410.12913", "title": "Fair Clustering for Data Summarization: Improved Approximation\n  Algorithms and Complexity Insights", "abstract": "  Data summarization tasks are often modeled as $k$-clustering problems, where\nthe goal is to choose $k$ data points, called cluster centers, that best\nrepresent the dataset by minimizing a clustering objective. A popular objective\nis to minimize the maximum distance between any data point and its nearest\ncenter, which is formalized as the $k$-center problem. While in some\napplications all data points can be chosen as centers, in the general setting,\ncenters must be chosen from a predefined subset of points, referred as\nfacilities or suppliers; this is known as the $k$-supplier problem. In this\nwork, we focus on fair data summarization modeled as the fair $k$-supplier\nproblem, where data consists of several groups, and a minimum number of centers\nmust be selected from each group while minimizing the $k$-supplier objective.\nThe groups can be disjoint or overlapping, leading to two distinct problem\nvariants each with different computational complexity.\n  We present $3$-approximation algorithms for both variants, improving the\npreviously known factor of $5$. For disjoint groups, our algorithm runs in\npolynomial time, while for overlapping groups, we present a fixed-parameter\ntractable algorithm, where the exponential runtime depends only on the number\nof groups and centers. We show that these approximation factors match the\ntheoretical lower bounds, assuming standard complexity theory conjectures.\nFinally, using an open-source implementation, we demonstrate the scalability of\nour algorithms on large synthetic datasets and assess the price of fairness on\nreal-world data, comparing solution quality with and without fairness\nconstraints.\n", "date": "2024-10-16", "categories": []}
{"id": "2302.14599", "title": "Scalable Clustering: Large Scale Unsupervised Learning of Gaussian\n  Mixture Models with Outliers", "abstract": "  Clustering is a widely used technique with a long and rich history in a\nvariety of areas. However, most existing algorithms do not scale well to large\ndatasets, or are missing theoretical guarantees of convergence. This paper\nintroduces a provably robust clustering algorithm based on loss minimization\nthat performs well on Gaussian mixture models with outliers. It provides\ntheoretical guarantees that the algorithm obtains high accuracy with high\nprobability under certain assumptions. Moreover, it can also be used as an\ninitialization strategy for $k$-means clustering. Experiments on real-world\nlarge-scale datasets demonstrate the effectiveness of the algorithm when\nclustering a large number of clusters, and a $k$-means algorithm initialized by\nthe algorithm outperforms many of the classic clustering methods in both speed\nand accuracy, while scaling well to large datasets such as ImageNet.\n", "date": "2023-02-28", "categories": []}
{"id": "2410.09484", "title": "Bridging Gaps: Federated Multi-View Clustering in Heterogeneous Hybrid\n  Views", "abstract": "  Recently, federated multi-view clustering (FedMVC) has emerged to explore\ncluster structures in multi-view data distributed on multiple clients. Existing\napproaches often assume that clients are isomorphic and all of them belong to\neither single-view clients or multi-view clients. Despite their success, these\nmethods also present limitations when dealing with practical FedMVC scenarios\ninvolving heterogeneous hybrid views, where a mixture of both single-view and\nmulti-view clients exhibit varying degrees of heterogeneity. In this paper, we\npropose a novel FedMVC framework, which concurrently addresses two challenges\nassociated with heterogeneous hybrid views, i.e., client gap and view gap. To\naddress the client gap, we design a local-synergistic contrastive learning\napproach that helps single-view clients and multi-view clients achieve\nconsistency for mitigating heterogeneity among all clients. To address the view\ngap, we develop a global-specific weighting aggregation method, which\nencourages global models to learn complementary features from hybrid views. The\ninterplay between local-synergistic contrastive learning and global-specific\nweighting aggregation mutually enhances the exploration of the data cluster\nstructures distributed on multiple clients. Theoretical analysis and extensive\nexperiments demonstrate that our method can handle the heterogeneous hybrid\nviews in FedMVC and outperforms state-of-the-art methods. The code is available\nat \\url{https://github.com/5Martina5/FMCSC}.\n", "date": "2024-10-12", "categories": []}
{"id": "2410.09491", "title": "Dying Clusters Is All You Need -- Deep Clustering With an Unknown Number\n  of Clusters", "abstract": "  Finding meaningful groups, i.e., clusters, in high-dimensional data such as\nimages or texts without labeled data at hand is an important challenge in data\nmining. In recent years, deep clustering methods have achieved remarkable\nresults in these tasks. However, most of these methods require the user to\nspecify the number of clusters in advance. This is a major limitation since the\nnumber of clusters is typically unknown if labeled data is unavailable. Thus,\nan area of research has emerged that addresses this problem. Most of these\napproaches estimate the number of clusters separated from the clustering\nprocess. This results in a strong dependency of the clustering result on the\nquality of the initial embedding. Other approaches are tailored to specific\nclustering processes, making them hard to adapt to other scenarios. In this\npaper, we propose UNSEEN, a general framework that, starting from a given upper\nbound, is able to estimate the number of clusters. To the best of our\nknowledge, it is the first method that can be easily combined with various deep\nclustering algorithms. We demonstrate the applicability of our approach by\ncombining UNSEEN with the popular deep clustering algorithms DCN, DEC, and DKM\nand verify its effectiveness through an extensive experimental evaluation on\nseveral image and tabular datasets. Moreover, we perform numerous ablations to\nanalyze our approach and show the importance of its components. The code is\navailable at: https://github.com/collinleiber/UNSEEN\n", "date": "2024-10-12", "categories": []}
{"id": "2306.01890", "title": "Mixed-type Distance Shrinkage and Selection for Clustering via Kernel\n  Metric Learning", "abstract": "  Distance-based clustering and classification are widely used in various\nfields to group mixed numeric and categorical data. In many algorithms, a\npredefined distance measurement is used to cluster data points based on their\ndissimilarity. While there exist numerous distance-based measures for data with\npure numerical attributes and several ordered and unordered categorical\nmetrics, an efficient and accurate distance for mixed-type data that utilizes\nthe continuous and discrete properties simulatenously is an open problem. Many\nmetrics convert numerical attributes to categorical ones or vice versa. They\nhandle the data points as a single attribute type or calculate a distance\nbetween each attribute separately and add them up. We propose a metric called\nKDSUM that uses mixed kernels to measure dissimilarity, with cross-validated\noptimal bandwidth selection. We demonstrate that KDSUM is a shrinkage method\nfrom existing mixed-type metrics to a uniform dissimilarity metric, and\nimproves clustering accuracy when utilized in existing distance-based\nclustering algorithms on simulated and real-world datasets containing\ncontinuous-only, categorical-only, and mixed-type data.\n", "date": "2023-06-02", "categories": []}
{"id": "2307.04904", "title": "Fast dynamic time warping and clustering in C++", "abstract": "  We present an approach for computationally efficient dynamic time warping\n(DTW) and clustering of time-series data. The method frames the dynamic warping\nof time series datasets as an optimisation problem solved using dynamic\nprogramming, and then clusters time series data by solving a second\noptimisation problem using mixed-integer programming (MIP). There is also an\noption to use k-medoids clustering for increased speed, when a certificate for\nglobal optimality is not essential. The improved efficiency of our approach is\ndue to task-level parallelisation of the clustering alongside DTW. Our approach\nwas tested using the UCR Time Series Archive, and was found to be, on average,\n33% faster than the next fastest option when using the same clustering method.\nThis increases to 64% faster when considering only larger datasets (with more\nthan 1000 time series). The MIP clustering is most effective on small numbers\nof longer time series, because the DTW computation is faster than other\napproaches, but the clustering problem becomes increasingly computationally\nexpensive as the number of time series to be clustered increases.\n", "date": "2023-07-10", "categories": []}
{"id": "2410.05902", "title": "Mini-Batch Kernel $k$-means", "abstract": "  We present the first mini-batch kernel $k$-means algorithm, offering an order\nof magnitude improvement in running time compared to the full batch algorithm.\nA single iteration of our algorithm takes $\\widetilde{O}(kb^2)$ time,\nsignificantly faster than the $O(n^2)$ time required by the full batch kernel\n$k$-means, where $n$ is the dataset size and $b$ is the batch size. Extensive\nexperiments demonstrate that our algorithm consistently achieves a 10-100x\nspeedup with minimal loss in quality, addressing the slow runtime that has\nlimited kernel $k$-means adoption in practice. We further complement these\nresults with a theoretical analysis under an early stopping condition, proving\nthat with a batch size of $\\widetilde{\\Omega}(\\max \\{\\gamma^{4}, \\gamma^{2}\\}\n\\cdot \\epsilon^{-2})$, the algorithm terminates in $O(\\gamma^2/\\epsilon)$\niterations with high probability, where $\\gamma$ bounds the norm of points in\nfeature space and $\\epsilon$ is a termination threshold. Our analysis holds for\nany reasonable center initialization, and when using $k$-means++\ninitialization, the algorithm achieves an approximation ratio of $O(\\log k)$ in\nexpectation. For normalized kernels, such as Gaussian or Laplacian it holds\nthat $\\gamma=1$. Taking $\\epsilon = O(1)$ and $b=\\Theta(\\log n)$, the algorithm\nterminates in $O(1)$ iterations, with each iteration running in\n$\\widetilde{O}(k)$ time.\n", "date": "2024-10-08", "categories": []}
{"id": "2410.06265", "title": "SHADE: Deep Density-based Clustering", "abstract": "  Detecting arbitrarily shaped clusters in high-dimensional noisy data is\nchallenging for current clustering methods. We introduce SHADE\n(Structure-preserving High-dimensional Analysis with Density-based\nExploration), the first deep clustering algorithm that incorporates\ndensity-connectivity into its loss function. Similar to existing deep\nclustering algorithms, SHADE supports high-dimensional and large data sets with\nthe expressive power of a deep autoencoder. In contrast to most existing deep\nclustering methods that rely on a centroid-based clustering objective, SHADE\nincorporates a novel loss function that captures density-connectivity. SHADE\nthereby learns a representation that enhances the separation of\ndensity-connected clusters. SHADE detects a stable clustering and noise points\nfully automatically without any user input. It outperforms existing methods in\nclustering quality, especially on data that contain non-Gaussian clusters, such\nas video data. Moreover, the embedded space of SHADE is suitable for\nvisualization and interpretation of the clustering results as the individual\nshapes of the clusters are preserved.\n", "date": "2024-10-08", "categories": []}
{"id": "2408.05459", "title": "A Versatile Framework for Attributed Network Clustering via K-Nearest\n  Neighbor Augmentation", "abstract": "  Attributed networks containing entity-specific information in node attributes\nare ubiquitous in modeling social networks, e-commerce, bioinformatics, etc.\nTheir inherent network topology ranges from simple graphs to hypergraphs with\nhigh-order interactions and multiplex graphs with separate layers. An important\ngraph mining task is node clustering, aiming to partition the nodes of an\nattributed network into k disjoint clusters such that intra-cluster nodes are\nclosely connected and share similar attributes, while inter-cluster nodes are\nfar apart and dissimilar. It is highly challenging to capture multi-hop\nconnections via nodes or attributes for effective clustering on multiple types\nof attributed networks. In this paper, we first present AHCKA as an efficient\napproach to attributed hypergraph clustering (AHC). AHCKA includes a\ncarefully-crafted K-nearest neighbor augmentation strategy for the optimized\nexploitation of attribute information on hypergraphs, a joint hypergraph random\nwalk model to devise an effective AHC objective, and an efficient solver with\nspeedup techniques for the objective optimization. The proposed techniques are\nextensible to various types of attributed networks, and thus, we develop ANCKA\nas a versatile attributed network clustering framework, capable of attributed\ngraph clustering (AGC), attributed multiplex graph clustering (AMGC), and AHC.\nMoreover, we devise ANCKA with algorithmic designs tailored for GPU\nacceleration to boost efficiency. We have conducted extensive experiments to\ncompare our methods with 19 competitors on 8 attributed hypergraphs, 16\ncompetitors on 6 attributed graphs, and 16 competitors on 3 attributed\nmultiplex graphs, all demonstrating the superb clustering quality and\nefficiency of our methods.\n", "date": "2024-08-10", "categories": []}
{"id": "2410.03937", "title": "Clustering Alzheimer's Disease Subtypes via Similarity Learning and\n  Graph Diffusion", "abstract": "  Alzheimer's disease (AD) is a complex neurodegenerative disorder that affects\nmillions of people worldwide. Due to the heterogeneous nature of AD, its\ndiagnosis and treatment pose critical challenges. Consequently, there is a\ngrowing research interest in identifying homogeneous AD subtypes that can\nassist in addressing these challenges in recent years. In this study, we aim to\nidentify subtypes of AD that represent distinctive clinical features and\nunderlying pathology by utilizing unsupervised clustering with graph diffusion\nand similarity learning. We adopted SIMLR, a multi-kernel similarity learning\nframework, and graph diffusion to perform clustering on a group of 829 patients\nwith AD and mild cognitive impairment (MCI, a prodromal stage of AD) based on\ntheir cortical thickness measurements extracted from magnetic resonance imaging\n(MRI) scans. Although the clustering approach we utilized has not been explored\nfor the task of AD subtyping before, it demonstrated significantly better\nperformance than several commonly used clustering methods. Specifically, we\nshowed the power of graph diffusion in reducing the effects of noise in the\nsubtype detection. Our results revealed five subtypes that differed remarkably\nin their biomarkers, cognitive status, and some other clinical features. To\nevaluate the resultant subtypes further, a genetic association study was\ncarried out and successfully identified potential genetic underpinnings of\ndifferent AD subtypes. Our source code is available at:\nhttps://github.com/PennShenLab/AD-SIMLR.\n", "date": "2024-10-04", "categories": []}
{"id": "2410.03596", "title": "SiMilarity-Enhanced Homophily for Multi-View Heterophilous Graph\n  Clustering", "abstract": "  With the increasing prevalence of graph-structured data, multi-view graph\nclustering has been widely used in various downstream applications. Existing\napproaches primarily rely on a unified message passing mechanism, which\nsignificantly enhances clustering performance. Nevertheless, this mechanism\nlimits its applicability to heterophilous situations, as it is fundamentally\npredicated on the assumption of homophily, i.e., the connected nodes often\nbelong to the same class. In reality, this assumption does not always hold; a\nmoderately or even mildly homophilous graph is more common than a fully\nhomophilous one due to inevitable heterophilous information in the graph. To\naddress this issue, in this paper, we propose a novel SiMilarity-enhanced\nHomophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By\nanalyzing the relationship between similarity and graph homophily, we propose\nto enhance the homophily by introducing three similarity terms, i.e., neighbor\npattern similarity, node feature similarity, and multi-view global similarity,\nin a label-free manner. Then, a consensus-based inter- and intra-view fusion\nparadigm is proposed to fuse the improved homophilous graph from different\nviews and utilize them for clustering. The state-of-the-art experimental\nresults on both multi-view heterophilous and homophilous datasets collectively\ndemonstrate the strong capacity of similarity for unsupervised multi-view\nheterophilous graph learning. Additionally, the consistent performance across\nsemi-synthetic datasets with varying levels of homophily serves as further\nevidence of SMHGC's resilience to heterophily.\n", "date": "2024-10-04", "categories": []}
{"id": "2309.03487", "title": "Privacy-preserving Continual Federated Clustering via Adaptive Resonance\n  Theory", "abstract": "  With the increasing importance of data privacy protection, various\nprivacy-preserving machine learning methods have been proposed. In the\nclustering domain, various algorithms with a federated learning framework\n(i.e., federated clustering) have been actively studied and showed high\nclustering performance while preserving data privacy. However, most of the base\nclusterers (i.e., clustering algorithms) used in existing federated clustering\nalgorithms need to specify the number of clusters in advance. These algorithms,\ntherefore, are unable to deal with data whose distributions are unknown or\ncontinually changing. To tackle this problem, this paper proposes a\nprivacy-preserving continual federated clustering algorithm. In the proposed\nalgorithm, an adaptive resonance theory-based clustering algorithm capable of\ncontinual learning is used as a base clusterer. Therefore, the proposed\nalgorithm inherits the ability of continual learning. Experimental results with\nsynthetic and real-world datasets show that the proposed algorithm has superior\nclustering performance to state-of-the-art federated clustering algorithms\nwhile realizing data privacy protection and continual learning ability. The\nsource code is available at \\url{https://github.com/Masuyama-lab/FCAC}.\n", "date": "2023-09-07", "categories": []}
{"id": "2410.02290", "title": "Density based Spatial Clustering of Lines via Probabilistic Generation\n  of Neighbourhood", "abstract": "  Density based spatial clustering of points in $\\mathbb{R}^n$ has a myriad of\napplications in a variety of industries. We generalise this problem to the\ndensity based clustering of lines in high-dimensional spaces, keeping in mind\nthere exists no valid distance measure that follows the triangle inequality for\nlines. In this paper, we design a clustering algorithm that generates a\ncustomised neighbourhood for a line of a fixed volume (given as a parameter),\nbased on an optional parameter as a continuous probability density function.\nThis algorithm is not sensitive to the outliers and can effectively identify\nthe noise in the data using a cardinality parameter. One of the pivotal\napplications of this algorithm is clustering data points in $\\mathbb{R}^n$ with\nmissing entries, while utilising the domain knowledge of the respective data.\nIn particular, the proposed algorithm is able to cluster $n$-dimensional data\npoints that contain at least $(n-1)$-dimensional information. We illustrate the\nneighbourhoods for the standard probability distributions with continuous\nprobability density functions and demonstrate the effectiveness of our\nalgorithm on various synthetic and real-world datasets (e.g., rail and road\nnetworks). The experimental results also highlight its application in\nclustering incomplete data.\n", "date": "2024-10-03", "categories": []}
{"id": "2301.11405", "title": "Discriminative Entropy Clustering and its Relation to K-means and SVM", "abstract": "  Maximization of mutual information between the model's input and output is\nformally related to \"decisiveness\" and \"fairness\" of the softmax predictions,\nmotivating these unsupervised entropy-based criteria for clustering. First, in\nthe context of linear softmax models, we discuss some general properties of\nentropy-based clustering. Disproving some earlier claims, we point out\nfundamental differences with K-means. On the other hand, we prove the margin\nmaximizing property for decisiveness establishing a relation to SVM-based\nclustering. Second, we propose a new self-labeling formulation of entropy\nclustering for general softmax models. The pseudo-labels are introduced as\nauxiliary variables \"splitting\" the fairness and decisiveness. The derived\nself-labeling loss includes the reverse cross-entropy robust to pseudo-label\nerrors and allows an efficient EM solver for pseudo-labels. Our algorithm\nimproves the state of the art on several standard benchmarks for deep\nclustering.\n", "date": "2023-01-26", "categories": []}
{"id": "2309.00834", "title": "Approximating Fair $k$-Min-Sum-Radii in Euclidean Space", "abstract": "  The $k$-center problem is a classical clustering problem in which one is\nasked to find a partitioning of a point set $P$ into $k$ clusters such that the\nmaximum radius of any cluster is minimized. It is well-studied. But what if we\nadd up the radii of the clusters instead of only considering the cluster with\nmaximum radius? This natural variant is called the $k$-min-sum-radii problem.\nIt has become the subject of more and more interest in recent years, inspiring\nthe development of approximation algorithms for the $k$-min-sum-radii problem\nin its plain version as well as in constrained settings.\n  We study the problem for Euclidean spaces $\\mathbb{R}^d$ of arbitrary\ndimension but assume the number $k$ of clusters to be constant. In this case, a\nPTAS for the problem is known (see Bandyapadhyay, Lochet and Saurabh, SoCG,\n2023). Our aim is to extend the knowledge base for $k$-min-sum-radii to the\ndomain of fair clustering. We study several group fairness constraints, such as\nthe one introduced by Chierichetti et al. (NeurIPS, 2017). In this model, input\npoints have an additional attribute (e.g., colors such as red and blue), and\nclusters have to preserve the ratio between different attribute values (e.g.,\nhave the same fraction of red and blue points as the ground set). Different\nvariants of this general idea have been studied in the literature. To the best\nof our knowledge, no approximative results for the fair $k$-min-sum-radii\nproblem are known, despite the immense amount of work on the related fair\n$k$-center problem.\n  We propose a PTAS for the fair $k$-min-sum-radii problem in Euclidean spaces\nof arbitrary dimension for the case of constant $k$. To the best of our\nknowledge, this is the first PTAS for the problem. It works for different\nnotions of group fairness.\n", "date": "2023-09-02", "categories": []}
{"id": "2409.16904", "title": "Discriminative Anchor Learning for Efficient Multi-view Clustering", "abstract": "  Multi-view clustering aims to study the complementary information across\nviews and discover the underlying structure. For solving the relatively high\ncomputational cost for the existing approaches, works based on anchor have been\npresented recently. Even with acceptable clustering performance, these methods\ntend to map the original representation from multiple views into a fixed shared\ngraph based on the original dataset. However, most studies ignore the\ndiscriminative property of the learned anchors, which ruin the representation\ncapability of the built model. Moreover, the complementary information among\nanchors across views is neglected to be ensured by simply learning the shared\nanchor graph without considering the quality of view-specific anchors. In this\npaper, we propose discriminative anchor learning for multi-view clustering\n(DALMC) for handling the above issues. We learn discriminative view-specific\nfeature representations according to the original dataset and build anchors\nfrom different views based on these representations, which increase the quality\nof the shared anchor graph. The discriminative feature learning and consensus\nanchor graph construction are integrated into a unified framework to improve\neach other for realizing the refinement. The optimal anchors from multiple\nviews and the consensus anchor graph are learned with the orthogonal\nconstraints. We give an iterative algorithm to deal with the formulated\nproblem. Extensive experiments on different datasets show the effectiveness and\nefficiency of our method compared with other methods.\n", "date": "2024-09-25", "categories": []}
{"id": "2409.17090", "title": "Locally Regularized Sparse Graph by Fast Proximal Gradient Descent", "abstract": "  Sparse graphs built by sparse representation has been demonstrated to be\neffective in clustering high-dimensional data. Albeit the compelling empirical\nperformance, the vanilla sparse graph ignores the geometric information of the\ndata by performing sparse representation for each datum separately. In order to\nobtain a sparse graph aligned with the local geometric structure of data, we\npropose a novel Support Regularized Sparse Graph, abbreviated as SRSG, for data\nclustering. SRSG encourages local smoothness on the neighborhoods of nearby\ndata points by a well-defined support regularization term. We propose a fast\nproximal gradient descent method to solve the non-convex optimization problem\nof SRSG with the convergence matching the Nesterov's optimal convergence rate\nof first-order methods on smooth and convex objective function with Lipschitz\ncontinuous gradient. Extensive experimental results on various real data sets\ndemonstrate the superiority of SRSG over other competing clustering methods.\n", "date": "2024-09-25", "categories": []}
{"id": "2409.14455", "title": "A High-Performance External Validity Index for Clustering with a Large\n  Number of Clusters", "abstract": "  This paper introduces the Stable Matching Based Pairing (SMBP) algorithm, a\nhigh-performance external validity index for clustering evaluation in\nlarge-scale datasets with a large number of clusters. SMBP leverages the stable\nmatching framework to pair clusters across different clustering methods,\nsignificantly reducing computational complexity to $O(N^2)$, compared to\ntraditional Maximum Weighted Matching (MWM) with $O(N^3)$ complexity. Through\ncomprehensive evaluations on real-world and synthetic datasets, SMBP\ndemonstrates comparable accuracy to MWM and superior computational efficiency.\nIt is particularly effective for balanced, unbalanced, and large-scale datasets\nwith a large number of clusters, making it a scalable and practical solution\nfor modern clustering tasks. Additionally, SMBP is easily implementable within\nmachine learning frameworks like PyTorch and TensorFlow, offering a robust tool\nfor big data applications. The algorithm is validated through extensive\nexperiments, showcasing its potential as a powerful alternative to existing\nmethods such as Maximum Match Measure (MMM) and Centroid Ratio (CR).\n", "date": "2024-09-22", "categories": []}
{"id": "2409.14882", "title": "Probabilistically Aligned View-unaligned Clustering with Adaptive\n  Template Selection", "abstract": "  In most existing multi-view modeling scenarios, cross-view correspondence\n(CVC) between instances of the same target from different views, like paired\nimage-text data, is a crucial prerequisite for effortlessly deriving a\nconsistent representation. Nevertheless, this premise is frequently compromised\nin certain applications, where each view is organized and transmitted\nindependently, resulting in the view-unaligned problem (VuP). Restoring CVC of\nunaligned multi-view data is a challenging and highly demanding task that has\nreceived limited attention from the research community. To tackle this\npractical challenge, we propose to integrate the permutation derivation\nprocedure into the bipartite graph paradigm for view-unaligned clustering,\ntermed Probabilistically Aligned View-unaligned Clustering with Adaptive\nTemplate Selection (PAVuC-ATS). Specifically, we learn consistent anchors and\nview-specific graphs by the bipartite graph, and derive permutations applied to\nthe unaligned graphs by reformulating the alignment between two latent\nrepresentations as a 2-step transition of a Markov chain with adaptive template\nselection, thereby achieving the probabilistic alignment. The convergence of\nthe resultant optimization problem is validated both experimentally and\ntheoretically. Extensive experiments on six benchmark datasets demonstrate the\nsuperiority of the proposed PAVuC-ATS over the baseline methods.\n", "date": "2024-09-23", "categories": []}
{"id": "2401.13581", "title": "Towards Efficient and Effective Deep Clustering with Dynamic Grouping\n  and Prototype Aggregation", "abstract": "  Previous contrastive deep clustering methods mostly focus on instance-level\ninformation while overlooking the member relationship within groups/clusters,\nwhich may significantly undermine their representation learning and clustering\ncapability. Recently, some group-contrastive methods have been developed,\nwhich, however, typically rely on the samples of the entire dataset to obtain\npseudo labels and lack the ability to efficiently update the group assignments\nin a batch-wise manner. To tackle these critical issues, we present a novel\nend-to-end deep clustering framework with dynamic grouping and prototype\naggregation, termed as DigPro. Specifically, the proposed dynamic grouping\nextends contrastive learning from instance-level to group-level, which is\neffective and efficient for timely updating groups. Meanwhile, we perform\ncontrastive learning on prototypes in a spherical feature space, termed as\nprototype aggregation, which aims to maximize the inter-cluster distance.\nNotably, with an expectation-maximization framework, DigPro simultaneously\ntakes advantage of compact intra-cluster connections, well-separated clusters,\nand efficient group updating during the self-supervised training. Extensive\nexperiments on six image benchmarks demonstrate the superior performance of our\napproach over the state-of-the-art. Code is available at\nhttps://github.com/Regan-Zhang/DigPro.\n", "date": "2024-01-24", "categories": []}
{"id": "2401.14038", "title": "Deep Clustering with Diffused Sampling and Hardness-aware\n  Self-distillation", "abstract": "  Deep clustering has gained significant attention due to its capability in\nlearning clustering-friendly representations without labeled data. However,\nprevious deep clustering methods tend to treat all samples equally, which\nneglect the variance in the latent distribution and the varying difficulty in\nclassifying or clustering different samples. To address this, this paper\nproposes a novel end-to-end deep clustering method with diffused sampling and\nhardness-aware self-distillation (HaDis). Specifically, we first align one view\nof instances with another view via diffused sampling alignment (DSA), which\nhelps improve the intra-cluster compactness. To alleviate the sampling bias, we\npresent the hardness-aware self-distillation (HSD) mechanism to mine the\nhardest positive and negative samples and adaptively adjust their weights in a\nself-distillation fashion, which is able to deal with the potential imbalance\nin sample contributions during optimization. Further, the prototypical\ncontrastive learning is incorporated to simultaneously enhance the\ninter-cluster separability and intra-cluster compactness. Experimental results\non five challenging image datasets demonstrate the superior clustering\nperformance of our HaDis method over the state-of-the-art. Source code is\navailable at https://github.com/Regan-Zhang/HaDis.\n", "date": "2024-01-25", "categories": []}
{"id": "2409.04561", "title": "Dual-Level Cross-Modal Contrastive Clustering", "abstract": "  Image clustering, which involves grouping images into different clusters\nwithout labels, is a key task in unsupervised learning. Although previous deep\nclustering methods have achieved remarkable results, they only explore the\nintrinsic information of the image itself but overlook external supervision\nknowledge to improve the semantic understanding of images. Recently,\nvisual-language pre-trained model on large-scale datasets have been used in\nvarious downstream tasks and have achieved great results. However, there is a\ngap between visual representation learning and textual semantic learning, and\nhow to properly utilize the representation of two different modalities for\nclustering is still a big challenge. To tackle the challenges, we propose a\nnovel image clustering framwork, named Dual-level Cross-Modal Contrastive\nClustering (DXMC). Firstly, external textual information is introduced for\nconstructing a semantic space which is adopted to generate image-text pairs.\nSecondly, the image-text pairs are respectively sent to pre-trained image and\ntext encoder to obtain image and text embeddings which subsquently are fed into\nfour well-designed networks. Thirdly, dual-level cross-modal contrastive\nlearning is conducted between discriminative representations of different\nmodalities and distinct level. Extensive experimental results on five benchmark\ndatasets demonstrate the superiority of our proposed method.\n", "date": "2024-09-06", "categories": []}
{"id": "2306.06124", "title": "Unsupervised clustering of disturbances in power systems via deep\n  convolutional autoencoders", "abstract": "  Power quality (PQ) events are recorded by PQ meters whenever anomalous events\nare detected on the power grid. Using neural networks with machine learning can\naid in accurately classifying the recorded waveforms and help power system\nengineers diagnose and rectify the root causes of problems. However, many of\nthe waveforms captured during a disturbance in the power system need to be\nlabeled for supervised learning, leaving a large number of data recordings for\nengineers to process manually or go unseen. This paper presents an autoencoder\nand K-means clustering-based unsupervised technique that can be used to cluster\nPQ events into categories like sag, interruption, transients, normal, and\nharmonic distortion to enable filtering of anomalous waveforms from recurring\nor normal waveforms. The method is demonstrated using three-phase,\nfield-obtained voltage waveforms recorded in a distribution grid. First, a\nconvolutional autoencoder compresses the input signals into a set of lower\nfeature dimensions which, after further processing, is passed to the K-means\nalgorithm to identify data clusters. Using a small, labeled dataset, numerical\nlabels are then assigned to events based on a cosine similarity analysis.\nFinally, the study analyzes the clusters using the t-distributed stochastic\nneighbor embedding (t-SNE) visualization tool, demonstrating that the technique\ncan help investigate a large number of captured events in a quick manner.\n", "date": "2023-06-08", "categories": []}
{"id": "2407.12214", "title": "VideoClusterNet: Self-Supervised and Adaptive Face Clustering For Videos", "abstract": "  With the rise of digital media content production, the need for analyzing\nmovies and TV series episodes to locate the main cast of characters precisely\nis gaining importance.Specifically, Video Face Clustering aims to group\ntogether detected video face tracks with common facial identities. This problem\nis very challenging due to the large range of pose, expression, appearance, and\nlighting variations of a given face across video frames. Generic pre-trained\nFace Identification (ID) models fail to adapt well to the video production\ndomain, given its high dynamic range content and also unique cinematic style.\nFurthermore, traditional clustering algorithms depend on hyperparameters\nrequiring individual tuning across datasets. In this paper, we present a novel\nvideo face clustering approach that learns to adapt a generic face ID model to\nnew video face tracks in a fully self-supervised fashion. We also propose a\nparameter-free clustering algorithm that is capable of automatically adapting\nto the finetuned model's embedding space for any input video. Due to the lack\nof comprehensive movie face clustering benchmarks, we also present a\nfirst-of-kind movie dataset: MovieFaceCluster. Our dataset is handpicked by\nfilm industry professionals and contains extremely challenging face ID\nscenarios. Experiments show our method's effectiveness in handling difficult\nmainstream movie scenes on our benchmark dataset and state-of-the-art\nperformance on traditional TV series datasets.\n", "date": "2024-07-16", "categories": []}
{"id": "2305.07316", "title": "Parameterized Approximation for Robust Clustering in Discrete Geometric\n  Spaces", "abstract": "  We consider the well-studied Robust $(k, z)$-Clustering problem, which\ngeneralizes the classic $k$-Median, $k$-Means, and $k$-Center problems. Given a\nconstant $z\\ge 1$, the input to Robust $(k, z)$-Clustering is a set $P$ of $n$\nweighted points in a metric space $(M,\\delta)$ and a positive integer $k$.\nFurther, each point belongs to one (or more) of the $m$ many different groups\n$S_1,S_2,\\ldots,S_m$. Our goal is to find a set $X$ of $k$ centers such that\n$\\max_{i \\in [m]} \\sum_{p \\in S_i} w(p) \\delta(p,X)^z$ is minimized.\n  This problem arises in the domains of robust optimization [Anthony, Goyal,\nGupta, Nagarajan, Math. Oper. Res. 2010] and in algorithmic fairness. For\npolynomial time computation, an approximation factor of $O(\\log m/\\log\\log m)$\nis known [Makarychev, Vakilian, COLT $2021$], which is tight under a plausible\ncomplexity assumption even in the line metrics. For FPT time, there is a\n$(3^z+\\epsilon)$-approximation algorithm, which is tight under GAP-ETH [Goyal,\nJaiswal, Inf. Proc. Letters, 2023].\n  Motivated by the tight lower bounds for general discrete metrics, we focus on\n\\emph{geometric} spaces such as the (discrete) high-dimensional Euclidean\nsetting and metrics of low doubling dimension, which play an important role in\ndata analysis applications. First, for a universal constant $\\eta_0 >0.0006$,\nwe devise a $3^z(1-\\eta_{0})$-factor FPT approximation algorithm for discrete\nhigh-dimensional Euclidean spaces thereby bypassing the lower bound for general\nmetrics. We complement this result by showing that even the special case of\n$k$-Center in dimension $\\Theta(\\log n)$ is $(\\sqrt{3/2}- o(1))$-hard to\napproximate for FPT algorithms. Finally, we complete the FPT approximation\nlandscape by designing an FPT $(1+\\epsilon)$-approximation scheme (EPAS) for\nthe metric of sub-logarithmic doubling dimension.\n", "date": "2023-05-12", "categories": []}
{"id": "2409.09418", "title": "Distributed Clustering based on Distributional Kernel", "abstract": "  This paper introduces a new framework for clustering in a distributed network\ncalled Distributed Clustering based on Distributional Kernel (K) or KDC that\nproduces the final clusters based on the similarity with respect to the\ndistributions of initial clusters, as measured by K. It is the only framework\nthat satisfies all three of the following properties. First, KDC guarantees\nthat the combined clustering outcome from all sites is equivalent to the\nclustering outcome of its centralized counterpart from the combined dataset\nfrom all sites. Second, the maximum runtime cost of any site in distributed\nmode is smaller than the runtime cost in centralized mode. Third, it is\ndesigned to discover clusters of arbitrary shapes, sizes and densities. To the\nbest of our knowledge, this is the first distributed clustering framework that\nemploys a distributional kernel. The distribution-based clustering leads\ndirectly to significantly better clustering outcomes than existing methods of\ndistributed clustering. In addition, we introduce a new clustering algorithm\ncalled Kernel Bounded Cluster Cores, which is the best clustering algorithm\napplied to KDC among existing clustering algorithms. We also show that KDC is a\ngeneric framework that enables a quadratic time clustering algorithm to deal\nwith large datasets that would otherwise be impossible.\n", "date": "2024-09-14", "categories": []}
{"id": "2409.08396", "title": "Federated One-Shot Ensemble Clustering", "abstract": "  Cluster analysis across multiple institutions poses significant challenges\ndue to data-sharing restrictions. To overcome these limitations, we introduce\nthe Federated One-shot Ensemble Clustering (FONT) algorithm, a novel solution\ntailored for multi-site analyses under such constraints. FONT requires only a\nsingle round of communication between sites and ensures privacy by exchanging\nonly fitted model parameters and class labels. The algorithm combines locally\nfitted clustering models into a data-adaptive ensemble, making it broadly\napplicable to various clustering techniques and robust to differences in\ncluster proportions across sites. Our theoretical analysis validates the\neffectiveness of the data-adaptive weights learned by FONT, and simulation\nstudies demonstrate its superior performance compared to existing benchmark\nmethods. We applied FONT to identify subgroups of patients with rheumatoid\narthritis across two health systems, revealing improved consistency of patient\nclusters across sites, while locally fitted clusters proved less transferable.\nFONT is particularly well-suited for real-world applications with stringent\ncommunication and privacy constraints, offering a scalable and practical\nsolution for multi-site clustering.\n", "date": "2024-09-12", "categories": []}
{"id": "2409.08867", "title": "Establish seedling quality classification standard for Chrysanthemum\n  efficiently with help of deep clustering algorithm", "abstract": "  Establishing reasonable standards for edible chrysanthemum seedlings helps\npromote seedling development, thereby improving plant quality. However, current\ngrading methods have the several issues. The limitation that only support a few\nindicators causes information loss, and indicators selected to evaluate\nseedling level have a narrow applicability. Meanwhile, some methods misuse\nmathematical formulas. Therefore, we propose a simple, efficient, and generic\nframework, SQCSEF, for establishing seedling quality classification standards\nwith flexible clustering modules, applicable to most plant species. In this\nstudy, we introduce the state-of-the-art deep clustering algorithm CVCL, using\nfactor analysis to divide indicators into several perspectives as inputs for\nthe CVCL method, resulting in more reasonable clusters and ultimately a grading\nstandard $S_{cvcl}$ for edible chrysanthemum seedlings. Through conducting\nextensive experiments, we validate the correctness and efficiency of the\nproposed SQCSEF framework.\n", "date": "2024-09-12", "categories": []}
{"id": "2409.08954", "title": "A Bayesian Approach to Clustering via the Proper Bayesian Bootstrap: the\n  Bayesian Bagged Clustering (BBC) algorithm", "abstract": "  The paper presents a novel approach for unsupervised techniques in the field\nof clustering. A new method is proposed to enhance existing literature models\nusing the proper Bayesian bootstrap to improve results in terms of robustness\nand interpretability. Our approach is organized in two steps: k-means\nclustering is used for prior elicitation, then proper Bayesian bootstrap is\napplied as resampling method in an ensemble clustering approach. Results are\nanalyzed introducing measures of uncertainty based on Shannon entropy. The\nproposal provides clear indication on the optimal number of clusters, as well\nas a better representation of the clustered data. Empirical results are\nprovided on simulated data showing the methodological and empirical advances\nobtained.\n", "date": "2024-09-13", "categories": []}
{"id": "2409.06938", "title": "k-MLE, k-Bregman, k-VARs: Theory, Convergence, Computation", "abstract": "  We develop hard clustering based on likelihood rather than distance and prove\nconvergence. We also provide simulations and real data examples.\n", "date": "2024-09-11", "categories": []}
{"id": "2409.03938", "title": "Deep Clustering of Remote Sensing Scenes through Heterogeneous Transfer\n  Learning", "abstract": "  This paper proposes a method for unsupervised whole-image clustering of a\ntarget dataset of remote sensing scenes with no labels. The method consists of\nthree main steps: (1) finetuning a pretrained deep neural network (DINOv2) on a\nlabelled source remote sensing imagery dataset and using it to extract a\nfeature vector from each image in the target dataset, (2) reducing the\ndimension of these deep features via manifold projection into a low-dimensional\nEuclidean space, and (3) clustering the embedded features using a Bayesian\nnonparametric technique to infer the number and membership of clusters\nsimultaneously. The method takes advantage of heterogeneous transfer learning\nto cluster unseen data with different feature and label distributions. We\ndemonstrate the performance of this approach outperforming state-of-the-art\nzero-shot classification methods on several remote sensing scene classification\ndatasets.\n", "date": "2024-09-05", "categories": []}
{"id": "2312.14763", "title": "Enhanced Latent Multi-view Subspace Clustering", "abstract": "  Latent multi-view subspace clustering has been demonstrated to have desirable\nclustering performance. However, the original latent representation method\nvertically concatenates the data matrices from multiple views into a single\nmatrix along the direction of dimensionality to recover the latent\nrepresentation matrix, which may result in an incomplete information recovery.\nTo fully recover the latent space representation, we in this paper propose an\nEnhanced Latent Multi-view Subspace Clustering (ELMSC) method. The ELMSC method\ninvolves constructing an augmented data matrix that enhances the representation\nof multi-view data. Specifically, we stack the data matrices from various views\ninto the block-diagonal locations of the augmented matrix to exploit the\ncomplementary information. Meanwhile, the non-block-diagonal entries are\ncomposed based on the similarity between different views to capture the\nconsistent information. In addition, we enforce a sparse regularization for the\nnon-diagonal blocks of the augmented self-representation matrix to avoid\nredundant calculations of consistency information. Finally, a novel iterative\nalgorithm based on the framework of Alternating Direction Method of Multipliers\n(ADMM) is developed to solve the optimization problem for ELMSC. Extensive\nexperiments on real-world datasets demonstrate that our proposed ELMSC is able\nto achieve higher clustering performance than some state-of-art multi-view\nclustering methods.\n", "date": "2023-12-22", "categories": []}
{"id": "2402.02051", "title": "Nonlinear subspace clustering by functional link neural networks", "abstract": "  Nonlinear subspace clustering based on a feed-forward neural network has been\ndemonstrated to provide better clustering accuracy than some advanced subspace\nclustering algorithms. While this approach demonstrates impressive outcomes, it\ninvolves a balance between effectiveness and computational cost. In this study,\nwe employ a functional link neural network to transform data samples into a\nnonlinear domain. Subsequently, we acquire a self-representation matrix through\na learning mechanism that builds upon the mapped samples. As the functional\nlink neural network is a single-layer neural network, our proposed method\nachieves high computational efficiency while ensuring desirable clustering\nperformance. By incorporating the local similarity regularization to enhance\nthe grouping effect, our proposed method further improves the quality of the\nclustering results. Additionally, we introduce a convex combination subspace\nclustering scheme, which combining a linear subspace clustering method with the\nfunctional link neural network subspace clustering approach. This combination\napproach allows for a dynamic balance between linear and nonlinear\nrepresentations. Extensive experiments confirm the advancement of our methods.\nThe source code will be released on https://lshi91.github.io/ soon.\n", "date": "2024-02-03", "categories": []}
{"id": "2408.14119", "title": "Contrastive Learning Subspace for Text Clustering", "abstract": "  Contrastive learning has been frequently investigated to learn effective\nrepresentations for text clustering tasks. While existing contrastive\nlearning-based text clustering methods only focus on modeling instance-wise\nsemantic similarity relationships, they ignore contextual information and\nunderlying relationships among all instances that needs to be clustered. In\nthis paper, we propose a novel text clustering approach called Subspace\nContrastive Learning (SCL) which models cluster-wise relationships among\ninstances. Specifically, the proposed SCL consists of two main modules: (1) a\nself-expressive module that constructs virtual positive samples and (2) a\ncontrastive learning module that further learns a discriminative subspace to\ncapture task-specific cluster-wise relationships among texts. Experimental\nresults show that the proposed SCL method not only has achieved superior\nresults on multiple task clustering datasets but also has less complexity in\npositive sample construction.\n", "date": "2024-08-26", "categories": []}
{"id": "2408.13189", "title": "Accelerating the k-means++ Algorithm by Using Geometric Information", "abstract": "  In this paper, we propose an acceleration of the exact k-means++ algorithm\nusing geometric information, specifically the Triangle Inequality and\nadditional norm filters, along with a two-step sampling procedure. Our\nexperiments demonstrate that the accelerated version outperforms the standard\nk-means++ version in terms of the number of visited points and distance\ncalculations, achieving greater speedup as the number of clusters increases.\nThe version utilizing the Triangle Inequality is particularly effective for\nlow-dimensional data, while the additional norm-based filter enhances\nperformance in high-dimensional instances with greater norm variance among\npoints. Additional experiments show the behavior of our algorithms when\nexecuted concurrently across multiple jobs and examine how memory performance\nimpacts practical speedup.\n", "date": "2024-08-23", "categories": []}
{"id": "2304.13886", "title": "Improving the Utility of Differentially Private Clustering through\n  Dynamical Processing", "abstract": "  This study aims to alleviate the trade-off between utility and privacy of\ndifferentially private clustering. Existing works focus on simple methods,\nwhich show poor performance for non-convex clusters. To fit complex cluster\ndistributions, we propose sophisticated dynamical processing inspired by Morse\ntheory, with which we hierarchically connect the Gaussian sub-clusters obtained\nthrough existing methods. Our theoretical results imply that the proposed\ndynamical processing introduces little to no additional privacy loss.\nExperiments show that our framework can improve the clustering performance of\nexisting methods at the same privacy level.\n", "date": "2023-04-27", "categories": []}
{"id": "2407.00429", "title": "Time Series Clustering with General State Space Models via Stochastic\n  Variational Inference", "abstract": "  In this paper, we propose a novel method of model-based time series\nclustering with mixtures of general state space models (MSSMs). Each component\nof MSSMs is associated with each cluster. An advantage of the proposed method\nis that it enables the use of time series models appropriate to the specific\ntime series. This not only improves clustering and prediction accuracy but also\nenhances the interpretability of the estimated parameters. The parameters of\nthe MSSMs are estimated using stochastic variational inference, a subtype of\nvariational inference. The proposed method estimates the latent variables of an\narbitrary state space model by using neural networks with a normalizing flow as\na variational estimator. The number of clusters can be estimated using the\nBayesian information criterion. In addition, to prevent MSSMs from converging\nto the local optimum, we propose several optimization tricks, including an\nadditional penalty term called entropy annealing. To our best knowledge, the\nproposed method is the first computationally feasible one for time series\nclustering based on general (possibly nonlinear, non-Gaussian) state space\nmodels. Experiments on simulated datasets show that the proposed method is\neffective for clustering, parameter estimation, and estimating the number of\nclusters.\n", "date": "2024-06-29", "categories": []}
{"id": "2307.02969", "title": "DPM: Clustering Sensitive Data through Separation", "abstract": "  Clustering is an important tool for data exploration where the goal is to\nsubdivide a data set into disjoint clusters that fit well into the underlying\ndata structure. When dealing with sensitive data, privacy-preserving algorithms\naim to approximate the non-private baseline while minimising the leakage of\nsensitive information. State-of-the-art privacy-preserving clustering\nalgorithms tend to output clusters that are good in terms of the standard\nmetrics, inertia, silhouette score, and clustering accuracy, however, the\nclustering result strongly deviates from the non-private KMeans baseline. In\nthis work, we present a privacy-preserving clustering algorithm called DPM that\nrecursively separates a data set into clusters based on a geometrical\nclustering approach. In addition, DPM estimates most of the data-dependent\nhyper-parameters in a privacy-preserving way. We prove that DPM preserves\nDifferential Privacy and analyse the utility guarantees of DPM. Finally, we\nconduct an extensive empirical evaluation for synthetic and real-life data\nsets. We show that DPM achieves state-of-the-art utility on the standard\nclustering metrics and yields a clustering result much closer to that of the\npopular non-private KMeans algorithm without requiring the number of classes.\n", "date": "2023-07-06", "categories": []}
{"id": "2408.10340", "title": "Can an unsupervised clustering algorithm reproduce a categorization\n  system?", "abstract": "  Peer analysis is a critical component of investment management, often relying\non expert-provided categorization systems. These systems' consistency is\nquestioned when they do not align with cohorts from unsupervised clustering\nalgorithms optimized for various metrics. We investigate whether unsupervised\nclustering can reproduce ground truth classes in a labeled dataset, showing\nthat success depends on feature selection and the chosen distance metric. Using\ntoy datasets and fund categorization as real-world examples we demonstrate that\naccurately reproducing ground truth classes is challenging. We also highlight\nthe limitations of standard clustering evaluation metrics in identifying the\noptimal number of clusters relative to the ground truth classes. We then show\nthat if appropriate features are available in the dataset, and a proper\ndistance metric is known (e.g., using a supervised Random Forest-based distance\nmetric learning method), then an unsupervised clustering can indeed reproduce\nthe ground truth classes as distinct clusters.\n", "date": "2024-08-19", "categories": []}
{"id": "2209.10545", "title": "SGC: A semi-supervised pipeline for gene clustering using self-training\n  approach in gene co-expression networks", "abstract": "  A widely used approach for extracting information from gene expression data\nemploy the construction of a gene co-expression network and the subsequent\napplication of algorithms that discover network structure. In particular, a\ncommon goal is the computational discovery of gene clusters, commonly called\nmodules. When applied on a novel gene expression dataset, the quality of the\ncomputed modules can be evaluated automatically, using Gene Ontology\nenrichment, a method that measures the frequencies of Gene Ontology terms in\nthe computed modules and evaluates their statistical likelihood. In this work\nwe propose SGC a novel pipeline for gene clustering based on relatively recent\nseminal work in the mathematics of spectral network theory. SGC consists of\nmultiple novel steps that enable the computation of highly enriched modules in\nan unsupervised manner. But unlike all existing frameworks, it further\nincorporates a novel step that leverages Gene Ontology information in a\nsemi-supervised clustering method that further improves the quality of the\ncomputed modules. Comparing with already well-known existing frameworks, we\nshow that SGC results in higher enrichment in real data. In particular, in 12\nreal gene expression datasets, SGC outperforms in all except one.\n", "date": "2022-09-21", "categories": []}
{"id": "2211.11114", "title": "Graph-based Semi-supervised Local Clustering with Few Labeled Nodes", "abstract": "  Local clustering aims at extracting a local structure inside a graph without\nthe necessity of knowing the entire graph structure. As the local structure is\nusually small in size compared to the entire graph, one can think of it as a\ncompressive sensing problem where the indices of target cluster can be thought\nas a sparse solution to a linear system. In this paper, we apply this idea\nbased on two pioneering works under the same framework and propose a new\nsemi-supervised local clustering approach using only few labeled nodes. Our\napproach improves the existing works by making the initial cut to be the entire\ngraph and hence overcomes a major limitation of the existing works, which is\nthe low quality of initial cut. Extensive experimental results on various\ndatasets demonstrate the effectiveness of our approach.\n", "date": "2022-11-20", "categories": []}
{"id": "2408.07956", "title": "RandomNet: Clustering Time Series Using Untrained Deep Neural Networks", "abstract": "  Neural networks are widely used in machine learning and data mining.\nTypically, these networks need to be trained, implying the adjustment of\nweights (parameters) within the network based on the input data. In this work,\nwe propose a novel approach, RandomNet, that employs untrained deep neural\nnetworks to cluster time series. RandomNet uses different sets of random\nweights to extract diverse representations of time series and then ensembles\nthe clustering relationships derived from these different representations to\nbuild the final clustering results. By extracting diverse representations, our\nmodel can effectively handle time series with different characteristics. Since\nall parameters are randomly generated, no training is required during the\nprocess. We provide a theoretical analysis of the effectiveness of the method.\nTo validate its performance, we conduct extensive experiments on all of the 128\ndatasets in the well-known UCR time series archive and perform statistical\nanalysis of the results. These datasets have different sizes, sequence lengths,\nand they are from diverse fields. The experimental results show that the\nproposed method is competitive compared with existing state-of-the-art methods.\n", "date": "2024-08-15", "categories": []}
{"id": "2408.10002", "title": "The Fairness-Quality Trade-off in Clustering", "abstract": "  Fairness in clustering has been considered extensively in the past; however,\nthe trade-off between the two objectives -- e.g., can we sacrifice just a\nlittle in the quality of the clustering to significantly increase fairness, or\nvice-versa? -- has rarely been addressed. We introduce novel algorithms for\ntracing the complete trade-off curve, or Pareto front, between quality and\nfairness in clustering problems; that is, computing all clusterings that are\nnot dominated in both objectives by other clusterings. Unlike previous work\nthat deals with specific objectives for quality and fairness, we deal with all\nobjectives for fairness and quality in two general classes encompassing most of\nthe special cases addressed in previous work. Our algorithm must take\nexponential time in the worst case as the Pareto front itself can be\nexponential. Even when the Pareto front is polynomial, our algorithm may take\nexponential time, and we prove that this is inevitable unless P = NP. However,\nwe also present a new polynomial-time algorithm for computing the entire Pareto\nfront when the cluster centers are fixed, and for perhaps the most natural\nfairness objective: minimizing the sum, over all clusters, of the imbalance\nbetween the two groups in each cluster.\n", "date": "2024-08-19", "categories": []}
{"id": "2305.07307", "title": "Self-Learning Symmetric Multi-view Probabilistic Clustering", "abstract": "  Multi-view Clustering (MVC) has achieved significant progress, with many\nefforts dedicated to learn knowledge from multiple views. However, most\nexisting methods are either not applicable or require additional steps for\nincomplete MVC. Such a limitation results in poor-quality clustering\nperformance and poor missing view adaptation. Besides, noise or outliers might\nsignificantly degrade the overall clustering performance, which are not handled\nwell by most existing methods. In this paper, we propose a novel unified\nframework for incomplete and complete MVC named self-learning symmetric\nmulti-view probabilistic clustering (SLS-MPC). SLS-MPC proposes a novel\nsymmetric multi-view probability estimation and equivalently transforms\nmulti-view pairwise posterior matching probability into composition of each\nview's individual distribution, which tolerates data missing and might extend\nto any number of views. Then, SLS-MPC proposes a novel self-learning\nprobability function without any prior knowledge and hyper-parameters to learn\neach view's individual distribution. Next, graph-context-aware refinement with\npath propagation and co-neighbor propagation is used to refine pairwise\nprobability, which alleviates the impact of noise and outliers. Finally,\nSLS-MPC proposes a probabilistic clustering algorithm to adjust clustering\nassignments by maximizing the joint probability iteratively without category\ninformation. Extensive experiments on multiple benchmarks show that SLS-MPC\noutperforms previous state-of-the-art methods.\n", "date": "2023-05-12", "categories": []}
{"id": "2401.13913", "title": "Spectral Clustering for Discrete Distributions", "abstract": "  The discrete distribution is often used to describe complex instances in\nmachine learning, such as images, sequences, and documents. Traditionally,\nclustering of discrete distributions (D2C) has been approached using\nWasserstein barycenter methods. These methods operate under the assumption that\nclusters can be well-represented by barycenters, which is seldom true in many\nreal-world applications. Additionally, these methods are not scalable for large\ndatasets due to the high computational cost of calculating Wasserstein\nbarycenters. In this work, we explore the feasibility of using spectral\nclustering combined with distribution affinity measures (e.g., maximum mean\ndiscrepancy and Wasserstein distance) to cluster discrete distributions. We\ndemonstrate that these methods can be more accurate and efficient than\nbarycenter methods. To further enhance scalability, we propose using linear\noptimal transport to construct affinity matrices efficiently for large\ndatasets. We provide theoretical guarantees for the success of our methods in\nclustering distributions. Experiments on both synthetic and real data show that\nour methods outperform existing baselines.\n", "date": "2024-01-25", "categories": []}
{"id": "2408.07763", "title": "Data Clustering and Visualization with Recursive Goemans-Williamson\n  MaxCut Algorithm", "abstract": "  In this article, we introduce a novel recursive modification to the classical\nGoemans-Williamson MaxCut algorithm, offering improved performance in\nvectorized data clustering tasks. Focusing on the clustering of medical\npublications, we employ recursive iterations in conjunction with a dimension\nrelaxation method to significantly enhance density of clustering results.\nFurthermore, we propose a unique vectorization technique for articles,\nleveraging conditional probabilities for more effective clustering. Our methods\nprovide advantages in both computational efficiency and clustering accuracy,\nsubstantiated through comprehensive experiments.\n", "date": "2024-08-14", "categories": []}
{"id": "2408.07558", "title": "Sonic: Fast and Transferable Data Poisoning on Clustering Algorithms", "abstract": "  Data poisoning attacks on clustering algorithms have received limited\nattention, with existing methods struggling to scale efficiently as dataset\nsizes and feature counts increase. These attacks typically require\nre-clustering the entire dataset multiple times to generate predictions and\nassess the attacker's objectives, significantly hindering their scalability.\nThis paper addresses these limitations by proposing Sonic, a novel genetic data\npoisoning attack that leverages incremental and scalable clustering algorithms,\ne.g., FISHDBC, as surrogates to accelerate poisoning attacks against\ngraph-based and density-based clustering methods, such as HDBSCAN. We\nempirically demonstrate the effectiveness and efficiency of Sonic in poisoning\nthe target clustering algorithms. We then conduct a comprehensive analysis of\nthe factors affecting the scalability and transferability of poisoning attacks\nagainst clustering algorithms, and we conclude by examining the robustness of\nhyperparameters in our attack strategy Sonic.\n", "date": "2024-08-14", "categories": []}
{"id": "2408.01920", "title": "Image Clustering Algorithm Based on Self-Supervised Pretrained Models\n  and Latent Feature Distribution Optimization", "abstract": "  In the face of complex natural images, existing deep clustering algorithms\nfall significantly short in terms of clustering accuracy when compared to\nsupervised classification methods, making them less practical. This paper\nintroduces an image clustering algorithm based on self-supervised pretrained\nmodels and latent feature distribution optimization, substantially enhancing\nclustering performance. It is found that: (1) For complex natural images, we\neffectively enhance the discriminative power of latent features by leveraging\nself-supervised pretrained models and their fine-tuning, resulting in improved\nclustering performance. (2) In the latent feature space, by searching for\nk-nearest neighbor images for each training sample and shortening the distance\nbetween the training sample and its nearest neighbor, the discriminative power\nof latent features can be further enhanced, and clustering performance can be\nimproved. (3) In the latent feature space, reducing the distance between sample\nfeatures and the nearest predefined cluster centroids can optimize the\ndistribution of latent features, therefore further improving clustering\nperformance. Through experiments on multiple datasets, our approach outperforms\nthe latest clustering algorithms and achieves state-of-the-art clustering\nresults. When the number of categories in the datasets is small, such as\nCIFAR-10 and STL-10, and there are significant differences between categories,\nour clustering algorithm has similar accuracy to supervised methods without\nusing pretrained models, slightly lower than supervised methods using\npre-trained models. The code linked algorithm is\nhttps://github.com/LihengHu/semi.\n", "date": "2024-08-04", "categories": []}
{"id": "2408.02932", "title": "Doubly Stochastic Adaptive Neighbors Clustering via the Marcus Mapping", "abstract": "  Clustering is a fundamental task in machine learning and data science, and\nsimilarity graph-based clustering is an important approach within this domain.\nDoubly stochastic symmetric similarity graphs provide numerous benefits for\nclustering problems and downstream tasks, yet learning such graphs remains a\nsignificant challenge. Marcus theorem states that a strictly positive symmetric\nmatrix can be transformed into a doubly stochastic symmetric matrix by diagonal\nmatrices. However, in clustering, learning sparse matrices is crucial for\ncomputational efficiency. We extend Marcus theorem by proposing the Marcus\nmapping, which indicates that certain sparse matrices can also be transformed\ninto doubly stochastic symmetric matrices via diagonal matrices. Additionally,\nwe introduce rank constraints into the clustering problem and propose the\nDoubly Stochastic Adaptive Neighbors Clustering algorithm based on the Marcus\nMapping (ANCMM). This ensures that the learned graph naturally divides into the\ndesired number of clusters. We validate the effectiveness of our algorithm\nthrough extensive comparisons with state-of-the-art algorithms. Finally, we\nexplore the relationship between the Marcus mapping and optimal transport. We\nprove that the Marcus mapping solves a specific type of optimal transport\nproblem and demonstrate that solving this problem through Marcus mapping is\nmore efficient than directly applying optimal transport methods.\n", "date": "2024-08-06", "categories": []}
{"id": "2408.05258", "title": "scASDC: Attention Enhanced Structural Deep Clustering for Single-cell\n  RNA-seq Data", "abstract": "  Single-cell RNA sequencing (scRNA-seq) data analysis is pivotal for\nunderstanding cellular heterogeneity. However, the high sparsity and complex\nnoise patterns inherent in scRNA-seq data present significant challenges for\ntraditional clustering methods. To address these issues, we propose a deep\nclustering method, Attention-Enhanced Structural Deep Embedding Graph\nClustering (scASDC), which integrates multiple advanced modules to improve\nclustering accuracy and robustness.Our approach employs a multi-layer graph\nconvolutional network (GCN) to capture high-order structural relationships\nbetween cells, termed as the graph autoencoder module. To mitigate the\noversmoothing issue in GCNs, we introduce a ZINB-based autoencoder module that\nextracts content information from the data and learns latent representations of\ngene expression. These modules are further integrated through an attention\nfusion mechanism, ensuring effective combination of gene expression and\nstructural information at each layer of the GCN. Additionally, a\nself-supervised learning module is incorporated to enhance the robustness of\nthe learned embeddings. Extensive experiments demonstrate that scASDC\noutperforms existing state-of-the-art methods, providing a robust and effective\nsolution for single-cell clustering tasks. Our method paves the way for more\naccurate and meaningful analysis of single-cell RNA sequencing data,\ncontributing to better understanding of cellular heterogeneity and biological\nprocesses. All code and public datasets used in this paper are available at\n\\url{https://github.com/wenwenmin/scASDC} and\n\\url{https://zenodo.org/records/12814320}.\n", "date": "2024-08-09", "categories": []}
{"id": "2408.05707", "title": "Fast and Scalable Semi-Supervised Learning for Multi-View Subspace\n  Clustering", "abstract": "  In this paper, we introduce a Fast and Scalable Semi-supervised Multi-view\nSubspace Clustering (FSSMSC) method, a novel solution to the high computational\ncomplexity commonly found in existing approaches. FSSMSC features linear\ncomputational and space complexity relative to the size of the data. The method\ngenerates a consensus anchor graph across all views, representing each data\npoint as a sparse linear combination of chosen landmarks. Unlike traditional\nmethods that manage the anchor graph construction and the label propagation\nprocess separately, this paper proposes a unified optimization model that\nfacilitates simultaneous learning of both. An effective alternating update\nalgorithm with convergence guarantees is proposed to solve the unified\noptimization model. Additionally, the method employs the obtained anchor graph\nand landmarks' low-dimensional representations to deduce low-dimensional\nrepresentations for raw data. Following this, a straightforward clustering\napproach is conducted on these low-dimensional representations to achieve the\nfinal clustering results. The effectiveness and efficiency of FSSMSC are\nvalidated through extensive experiments on multiple benchmark datasets of\nvarying scales.\n", "date": "2024-08-11", "categories": []}
{"id": "2408.05765", "title": "Scalable and Adaptive Spectral Embedding for Attributed Graph Clustering", "abstract": "  Attributed graph clustering, which aims to group the nodes of an attributed\ngraph into disjoint clusters, has made promising advancements in recent years.\nHowever, most existing methods face challenges when applied to large graphs due\nto the expensive computational cost and high memory usage. In this paper, we\nintroduce Scalable and Adaptive Spectral Embedding (SASE), a simple attributed\ngraph clustering method devoid of parameter learning. SASE comprises three main\ncomponents: node features smoothing via $k$-order simple graph convolution,\nscalable spectral clustering using random Fourier features, and adaptive order\nselection. With these designs, SASE not only effectively captures global\ncluster structures but also exhibits linear time and space complexity relative\nto the graph size. Empirical results demonstrate the superiority of SASE. For\nexample, on the ArXiv dataset with 169K nodes and 1.17M edges, SASE achieves a\n6.9\\% improvement in ACC and a $5.87\\times$ speedup compared to the runner-up,\nS3GC.\n", "date": "2024-08-11", "categories": []}
{"id": "2408.06029", "title": "Graph Clustering with Cross-View Feature Propagation", "abstract": "  Graph clustering is a fundamental and challenging learning task, which is\nconventionally approached by grouping similar vertices based on edge structure\nand feature similarity.In contrast to previous methods, in this paper, we\ninvestigate how multi-view feature propagation can influence cluster discovery\nin graph data.To this end, we present Graph Clustering With Cross-View Feature\nPropagation (GCCFP), a novel method that leverages multi-view feature\npropagation to enhance cluster identification in graph data.GCCFP employs a\nunified objective function that utilizes graph topology and multi-view vertex\nfeatures to determine vertex cluster membership, regularized by a module that\nsupports key latent feature propagation. We derive an iterative algorithm to\noptimize this function, prove model convergence within a finite number of\niterations, and analyze its computational complexity. Our experiments on\nvarious real-world graphs demonstrate the superior clustering performance of\nGCCFP compared to well-established methods, manifesting its effectiveness\nacross different scenarios.\n", "date": "2024-08-12", "categories": []}
{"id": "2408.04891", "title": "Clustering-friendly Representation Learning for Enhancing Salient\n  Features", "abstract": "  Recently, representation learning with contrastive learning algorithms has\nbeen successfully applied to challenging unlabeled datasets. However, these\nmethods are unable to distinguish important features from unimportant ones\nunder simply unsupervised settings, and definitions of importance vary\naccording to the type of downstream task or analysis goal, such as the\nidentification of objects or backgrounds. In this paper, we focus on\nunsupervised image clustering as the downstream task and propose a\nrepresentation learning method that enhances features critical to the\nclustering task. We extend a clustering-friendly contrastive learning method\nand incorporate a contrastive analysis approach, which utilizes a reference\ndataset to separate important features from unimportant ones, into the design\nof loss functions. Conducting an experimental evaluation of image clustering\nfor three datasets with characteristic backgrounds, we show that for all\ndatasets, our method achieves higher clustering scores compared with\nconventional contrastive analysis and deep clustering methods.\n", "date": "2024-08-09", "categories": []}
{"id": "2408.04339", "title": "Self-Supervised Contrastive Graph Clustering Network via Structural\n  Information Fusion", "abstract": "  Graph clustering, a classical task in graph learning, involves partitioning\nthe nodes of a graph into distinct clusters. This task has applications in\nvarious real-world scenarios, such as anomaly detection, social network\nanalysis, and community discovery. Current graph clustering methods commonly\nrely on module pre-training to obtain a reliable prior distribution for the\nmodel, which is then used as the optimization objective. However, these methods\noften overlook deeper supervised signals, leading to sub-optimal reliability of\nthe prior distribution. To address this issue, we propose a novel deep graph\nclustering method called CGCN. Our approach introduces contrastive signals and\ndeep structural information into the pre-training process. Specifically, CGCN\nutilizes a contrastive learning mechanism to foster information\ninteroperability among multiple modules and allows the model to adaptively\nadjust the degree of information aggregation for different order structures.\nOur CGCN method has been experimentally validated on multiple real-world graph\ndatasets, showcasing its ability to boost the dependability of prior clustering\ndistributions acquired through pre-training. As a result, we observed notable\nenhancements in the performance of the model.\n", "date": "2024-08-08", "categories": []}
{"id": "2408.03407", "title": "Deep Clustering via Distribution Learning", "abstract": "  Distribution learning finds probability density functions from a set of data\nsamples, whereas clustering aims to group similar data points to form clusters.\nAlthough there are deep clustering methods that employ distribution learning\nmethods, past work still lacks theoretical analysis regarding the relationship\nbetween clustering and distribution learning. Thus, in this work, we provide a\ntheoretical analysis to guide the optimization of clustering via distribution\nlearning. To achieve better results, we embed deep clustering guided by a\ntheoretical analysis. Furthermore, the distribution learning method cannot\nalways be directly applied to data. To overcome this issue, we introduce a\nclustering-oriented distribution learning method called Monte-Carlo\nMarginalization for Clustering. We integrate Monte-Carlo Marginalization for\nClustering into Deep Clustering, resulting in Deep Clustering via Distribution\nLearning (DCDL). Eventually, the proposed DCDL achieves promising results\ncompared to state-of-the-art methods on popular datasets. Considering a\nclustering task, the new distribution learning method outperforms previous\nmethods as well.\n", "date": "2024-08-06", "categories": []}
{"id": "2408.02250", "title": "Hierarchical Clustering using Reversible Binary Cellular Automata for\n  High-Dimensional Data", "abstract": "  This work proposes a hierarchical clustering algorithm for high-dimensional\ndatasets using the cyclic space of reversible finite cellular automata. In\ncellular automaton (CA) based clustering, if two objects belong to the same\ncycle, they are closely related and considered as part of the same cluster.\nHowever, if a high-dimensional dataset is clustered using the cycles of one CA,\nclosely related objects may belong to different cycles. This paper identifies\nthe relationship between objects in two different cycles based on the median of\nall elements in each cycle so that they can be grouped in the next stage.\nFurther, to minimize the number of intermediate clusters which in turn reduces\nthe computational cost, a rule selection strategy is taken to find the best\nrules based on information propagation and cycle structure. After encoding the\ndataset using frequency-based encoding such that the consecutive data elements\nmaintain a minimum hamming distance in encoded form, our proposed clustering\nalgorithm iterates over three stages to finally cluster the data elements into\nthe desired number of clusters given by user. This algorithm can be applied to\nvarious fields, including healthcare, sports, chemical research, agriculture,\netc. When verified over standard benchmark datasets with various performance\nmetrics, our algorithm is at par with the existing algorithms with quadratic\ntime complexity.\n", "date": "2024-08-05", "categories": []}
{"id": "2407.20119", "title": "Adaptive Self-supervised Robust Clustering for Unstructured Data with\n  Unknown Cluster Number", "abstract": "  We introduce a novel self-supervised deep clustering approach tailored for\nunstructured data without requiring prior knowledge of the number of clusters,\ntermed Adaptive Self-supervised Robust Clustering (ASRC). In particular, ASRC\nadaptively learns the graph structure and edge weights to capture both local\nand global structural information. The obtained graph enables us to learn\nclustering-friendly feature representations by an enhanced graph auto-encoder\nwith contrastive learning technique. It further leverages the clustering\nresults adaptively obtained by robust continuous clustering (RCC) to generate\nprototypes for negative sampling, which can further contribute to promoting\nconsistency among positive pairs and enlarging the gap between positive and\nnegative samples. ASRC obtains the final clustering results by applying RCC to\nthe learned feature representations with their consistent graph structure and\nedge weights. Extensive experiments conducted on seven benchmark datasets\ndemonstrate the efficacy of ASRC, demonstrating its superior performance over\nother popular clustering models. Notably, ASRC even outperforms methods that\nrely on prior knowledge of the number of clusters, highlighting its\neffectiveness in addressing the challenges of clustering unstructured data.\n", "date": "2024-07-29", "categories": []}
{"id": "2407.20246", "title": "From A-to-Z Review of Clustering Validation Indices", "abstract": "  Data clustering involves identifying latent similarities within a dataset and\norganizing them into clusters or groups. The outcomes of various clustering\nalgorithms differ as they are susceptible to the intrinsic characteristics of\nthe original dataset, including noise and dimensionality. The effectiveness of\nsuch clustering procedures directly impacts the homogeneity of clusters,\nunderscoring the significance of evaluating algorithmic outcomes. Consequently,\nthe assessment of clustering quality presents a significant and complex\nendeavor. A pivotal aspect affecting clustering validation is the cluster\nvalidity metric, which aids in determining the optimal number of clusters. The\nmain goal of this study is to comprehensively review and explain the\nmathematical operation of internal and external cluster validity indices, but\nnot all, to categorize these indices and to brainstorm suggestions for future\nadvancement of clustering validation research. In addition, we review and\nevaluate the performance of internal and external clustering validation indices\non the most common clustering algorithms, such as the evolutionary clustering\nalgorithm star (ECA*). Finally, we suggest a classification framework for\nexamining the functionality of both internal and external clustering validation\nmeasures regarding their ideal values, user-friendliness, responsiveness to\ninput data, and appropriateness across various fields. This classification aids\nresearchers in selecting the appropriate clustering validation measure to suit\ntheir specific requirements.\n", "date": "2024-07-18", "categories": []}
{"id": "2407.19199", "title": "A simulation study of cluster search algorithms in data set generated by\n  Gaussian mixture models", "abstract": "  Determining the number of clusters is a fundamental issue in data clustering.\nSeveral algorithms have been proposed, including centroid-based algorithms\nusing the Euclidean distance and model-based algorithms using a mixture of\nprobability distributions. Among these, greedy algorithms for searching the\nnumber of clusters by repeatedly splitting or merging clusters have advantages\nin terms of computation time for problems with large sample sizes. However,\nstudies comparing these methods in systematic evaluation experiments still need\nto be included. This study examines centroid- and model-based cluster search\nalgorithms in various cases that Gaussian mixture models (GMMs) can generate.\nThe cases are generated by combining five factors: dimensionality, sample size,\nthe number of clusters, cluster overlap, and covariance type. The results show\nthat some cluster-splitting criteria based on Euclidean distance make\nunreasonable decisions when clusters overlap. The results also show that\nmodel-based algorithms are insensitive to covariance type and cluster overlap\ncompared to the centroid-based method if the sample size is sufficient. Our\ncluster search implementation codes are available at\nhttps://github.com/lipryou/searchClustK\n", "date": "2024-07-27", "categories": []}
{"id": "2407.18287", "title": "Estimating the number of clusters of a Block Markov Chain", "abstract": "  Clustering algorithms frequently require the number of clusters to be chosen\nin advance, but it is usually not clear how to do this. To tackle this\nchallenge when clustering within sequential data, we present a method for\nestimating the number of clusters when the data is a trajectory of a Block\nMarkov Chain. Block Markov Chains are Markov Chains that exhibit a block\nstructure in their transition matrix. The method considers a matrix that counts\nthe number of transitions between different states within the trajectory, and\ntransforms this into a spectral embedding whose dimension is set via singular\nvalue thresholding. The number of clusters is subsequently estimated via\ndensity-based clustering of this spectral embedding, an approach inspired by\nliterature on the Stochastic Block Model. By leveraging and augmenting recent\nresults on the spectral concentration of random matrices with Markovian\ndependence, we show that the method is asymptotically consistent - in spite of\nthe dependencies between the count matrix's entries, and even when the count\nmatrix is sparse. We also present a numerical evaluation of our method, and\ncompare it to alternatives.\n", "date": "2024-07-25", "categories": []}
{"id": "2402.02290", "title": "Goodness-of-Fit and Clustering of Spherical Data: the QuadratiK package\n  in R and Python", "abstract": "  We introduce the QuadratiK package that incorporates innovative data analysis\nmethodologies. The presented software, implemented in both R and Python, offers\na comprehensive set of goodness-of-fit tests and clustering techniques using\nkernel-based quadratic distances, thereby bridging the gap between the\nstatistical and machine learning literatures. Our software implements one, two\nand k-sample tests for goodness of fit, providing an efficient and\nmathematically sound way to assess the fit of probability distributions.\nExpanded capabilities of our software include supporting tests for uniformity\non the d-dimensional Sphere based on Poisson kernel densities. Particularly\nnoteworthy is the incorporation of a unique clustering algorithm specifically\ntailored for spherical data that leverages a mixture of Poisson kernel-based\ndensities on the sphere. Alongside this, our software includes additional\ngraphical functions, aiding the users in validating, as well as visualizing and\nrepresenting clustering results. This enhances interpretability and usability\nof the analysis. In summary, our R and Python packages serve as a powerful\nsuite of tools, offering researchers and practitioners the means to delve\ndeeper into their data, draw robust inference, and conduct potentially\nimpactful analyses and inference across a wide array of disciplines.\n", "date": "2024-02-03", "categories": []}
{"id": "2407.17744", "title": "Balancing Complementarity and Consistency via Delayed Activation in\n  Incomplete Multi-view Clustering", "abstract": "  This paper study one challenging issue in incomplete multi-view clustering,\nwhere valuable complementary information from other views is always ignored. To\nbe specific, we propose a framework that effectively balances Complementarity\nand Consistency information in Incomplete Multi-view Clustering (CoCo-IMC).\nSpecifically, we design a dual network of delayed activation, which achieves a\nbalance of complementarity and consistency among different views. The delayed\nactivation could enriches the complementarity information that was ignored\nduring consistency learning. Then, we recover the incomplete information and\nenhance the consistency learning by minimizing the conditional entropy and\nmaximizing the mutual information across different views. This could be the\nfirst theoretical attempt to incorporate delayed activation into incomplete\ndata recovery and the balance of complementarity and consistency. We have\nproved the effectiveness of CoCo-IMC in extensive comparative experiments with\n12 state-of-the-art baselines on four publicly available datasets.\n", "date": "2024-07-25", "categories": []}
{"id": "2407.06782", "title": "Fuzzy color model and clustering algorithm for color clustering problem", "abstract": "  The research interest of this paper is focused on the efficient clustering\ntask for an arbitrary color data. In order to tackle this problem, we have\ntried to model the inherent uncertainty and vagueness of color data using fuzzy\ncolor model. By taking fuzzy approach to color modeling, we could make a soft\ndecision for the vague regions between neighboring colors. The proposed fuzzy\ncolor model defined a three dimensional fuzzy color ball and color membership\ncomputation method with two inter-color distances. With the fuzzy color model,\nwe developed a new fuzzy clustering algorithm for an efficient partition of\ncolor data. Each fuzzy cluster set has a cluster prototype which is represented\nby fuzzy color centroid.\n", "date": "2024-07-09", "categories": []}
{"id": "2407.16863", "title": "Balanced Multi-Relational Graph Clustering", "abstract": "  Multi-relational graph clustering has demonstrated remarkable success in\nuncovering underlying patterns in complex networks. Representative methods\nmanage to align different views motivated by advances in contrastive learning.\nOur empirical study finds the pervasive presence of imbalance in real-world\ngraphs, which is in principle contradictory to the motivation of alignment. In\nthis paper, we first propose a novel metric, the Aggregation Class Distance, to\nempirically quantify structural disparities among different graphs. To address\nthe challenge of view imbalance, we propose Balanced Multi-Relational Graph\nClustering (BMGC), comprising unsupervised dominant view mining and dual\nsignals guided representation learning. It dynamically mines the dominant view\nthroughout the training process, synergistically improving clustering\nperformance with representation learning. Theoretical analysis ensures the\neffectiveness of dominant view mining. Extensive experiments and in-depth\nanalysis on real-world and synthetic datasets showcase that BMGC achieves\nstate-of-the-art performance, underscoring its superiority in addressing the\nview imbalance inherent in multi-relational graphs. The source code and\ndatasets are available at https://github.com/zxlearningdeep/BMGC.\n", "date": "2024-07-23", "categories": []}
{"id": "2407.16984", "title": "scGHSOM: Hierarchical clustering and visualization of single-cell and\n  CRISPR data using growing hierarchical SOM", "abstract": "  High-dimensional single-cell data poses significant challenges in identifying\nunderlying biological patterns due to the complexity and heterogeneity of\ncellular states. We propose a comprehensive gene-cell dependency visualization\nvia unsupervised clustering, Growing Hierarchical Self-Organizing Map (GHSOM),\nspecifically designed for analyzing high-dimensional single-cell data like\nsingle-cell sequencing and CRISPR screens. GHSOM is applied to cluster samples\nin a hierarchical structure such that the self-growth structure of clusters\nsatisfies the required variations between and within. We propose a novel\nSignificant Attributes Identification Algorithm to identify features that\ndistinguish clusters. This algorithm pinpoints attributes with minimal\nvariation within a cluster but substantial variation between clusters. These\nkey attributes can then be used for targeted data retrieval and downstream\nanalysis. Furthermore, we present two innovative visualization tools: Cluster\nFeature Map and Cluster Distribution Map. The Cluster Feature Map highlights\nthe distribution of specific features across the hierarchical structure of\nGHSOM clusters. This allows for rapid visual assessment of cluster uniqueness\nbased on chosen features. The Cluster Distribution Map depicts leaf clusters as\ncircles on the GHSOM grid, with circle size reflecting cluster data size and\ncolor customizable to visualize features like cell type or other attributes. We\napply our analysis to three single-cell datasets and one CRISPR dataset\n(cell-gene database) and evaluate clustering methods with internal and external\nCH and ARI scores. GHSOM performs well, being the best performer in internal\nevaluation (CH=4.2). In external evaluation, GHSOM has the third-best\nperformance of all methods.\n", "date": "2024-07-24", "categories": []}
{"id": "2407.17423", "title": "On selection of centroids of fuzzy clusters for color classification", "abstract": "  A novel initialization method in the fuzzy c-means (FCM) algorithm is\nproposed for the color clustering problem. Given a set of color points, the\nproposed initialization extracts dominant colors that are the most vivid and\ndistinguishable colors. Color points closest to the dominant colors are\nselected as initial centroids in the FCM. To obtain the dominant colors and\ntheir closest color points, we introduce reference colors and define a fuzzy\nmembership model between a color point and a reference color.\n", "date": "2024-07-09", "categories": []}
{"id": "2407.11084", "title": "A Survey of Distance-Based Vessel Trajectory Clustering: Data\n  Pre-processing, Methodologies, Applications, and Experimental Evaluation", "abstract": "  Vessel trajectory clustering, a crucial component of the maritime intelligent\ntransportation systems, provides valuable insights for applications such as\nanomaly detection and trajectory prediction. This paper presents a\ncomprehensive survey of the most prevalent distance-based vessel trajectory\nclustering methods, which encompass two main steps: trajectory similarity\nmeasurement and clustering. Initially, we conducted a thorough literature\nreview using relevant keywords to gather and summarize pertinent research\npapers and datasets. Then, this paper discussed the principal methods of data\npre-processing that prepare data for further analysis. The survey progresses to\ndetail the leading algorithms for measuring vessel trajectory similarity and\nthe main clustering techniques used in the field today. Furthermore, the\nvarious applications of trajectory clustering within the maritime context are\nexplored. Finally, the paper evaluates the effectiveness of different algorithm\ncombinations and pre-processing methods through experimental analysis, focusing\non their impact on the performance of distance-based trajectory clustering\nalgorithms. The experimental results demonstrate the effectiveness of various\ntrajectory clustering algorithms and notably highlight the significant\nimprovements that trajectory compression techniques contribute to the\nefficiency and accuracy of trajectory clustering. This comprehensive approach\nensures a deep understanding of current capabilities and future directions in\nvessel trajectory clustering.\n", "date": "2024-07-13", "categories": []}
{"id": "2407.14259", "title": "Voices in a Crowd: Searching for Clusters of Unique Perspectives", "abstract": "  Language models have been shown to reproduce underlying biases existing in\ntheir training data, which is the majority perspective by default. Proposed\nsolutions aim to capture minority perspectives by either modelling annotator\ndisagreements or grouping annotators based on shared metadata, both of which\nface significant challenges. We propose a framework that trains models without\nencoding annotator metadata, extracts latent embeddings informed by annotator\nbehaviour, and creates clusters of similar opinions, that we refer to as\nvoices. Resulting clusters are validated post-hoc via internal and external\nquantitative metrics, as well a qualitative analysis to identify the type of\nvoice that each cluster represents. Our results demonstrate the strong\ngeneralisation capability of our framework, indicated by resulting clusters\nbeing adequately robust, while also capturing minority perspectives based on\ndifferent demographic factors throughout two distinct datasets.\n", "date": "2024-07-19", "categories": []}
{"id": "2302.03391", "title": "Sparse and geometry-aware generalisation of the mutual information for\n  joint discriminative clustering and feature selection", "abstract": "  Feature selection in clustering is a hard task which involves simultaneously\nthe discovery of relevant clusters as well as relevant variables with respect\nto these clusters. While feature selection algorithms are often model-based\nthrough optimised model selection or strong assumptions on the data\ndistribution, we introduce a discriminative clustering model trying to maximise\na geometry-aware generalisation of the mutual information called GEMINI with a\nsimple l1 penalty: the Sparse GEMINI. This algorithm avoids the burden of\ncombinatorial feature subset exploration and is easily scalable to\nhigh-dimensional data and large amounts of samples while only designing a\ndiscriminative clustering model. We demonstrate the performances of Sparse\nGEMINI on synthetic datasets and large-scale datasets. Our results show that\nSparse GEMINI is a competitive algorithm and has the ability to select relevant\nsubsets of variables with respect to the clustering without using relevance\ncriteria or prior hypotheses.\n", "date": "2023-02-07", "categories": []}
{"id": "2402.15432", "title": "Universal Lower Bounds and Optimal Rates: Achieving Minimax Clustering\n  Error in Sub-Exponential Mixture Models", "abstract": "  Clustering is a pivotal challenge in unsupervised machine learning and is\noften investigated through the lens of mixture models. The optimal error rate\nfor recovering cluster labels in Gaussian and sub-Gaussian mixture models\ninvolves ad hoc signal-to-noise ratios. Simple iterative algorithms, such as\nLloyd's algorithm, attain this optimal error rate. In this paper, we first\nestablish a universal lower bound for the error rate in clustering any mixture\nmodel, expressed through a Chernoff divergence, a more versatile measure of\nmodel information than signal-to-noise ratios. We then demonstrate that\niterative algorithms attain this lower bound in mixture models with\nsub-exponential tails, notably emphasizing location-scale mixtures featuring\nLaplace-distributed errors. Additionally, for datasets better modelled by\nPoisson or Negative Binomial mixtures, we study mixture models whose\ndistributions belong to an exponential family. In such mixtures, we establish\nthat Bregman hard clustering, a variant of Lloyd's algorithm employing a\nBregman divergence, is rate optimal.\n", "date": "2024-02-23", "categories": []}
{"id": "2407.12764", "title": "Jigsaw Game: Federated Clustering", "abstract": "  Federated learning has recently garnered significant attention, especially\nwithin the domain of supervised learning. However, despite the abundance of\nunlabeled data on end-users, unsupervised learning problems such as clustering\nin the federated setting remain underexplored. In this paper, we investigate\nthe federated clustering problem, with a focus on federated k-means. We outline\nthe challenge posed by its non-convex objective and data heterogeneity in the\nfederated framework. To tackle these challenges, we adopt a new perspective by\nstudying the structures of local solutions in k-means and propose a one-shot\nalgorithm called FeCA (Federated Centroid Aggregation). FeCA adaptively refines\nlocal solutions on clients, then aggregates these refined solutions to recover\nthe global solution of the entire dataset in a single round. We empirically\ndemonstrate the robustness of FeCA under various federated scenarios on both\nsynthetic and real-world data. Additionally, we extend FeCA to representation\nlearning and present DeepFeCA, which combines DeepCluster and FeCA for\nunsupervised feature learning in the federated setting.\n", "date": "2024-07-17", "categories": []}
{"id": "2310.11989", "title": "Image Clustering with External Guidance", "abstract": "  The core of clustering is incorporating prior knowledge to construct\nsupervision signals. From classic k-means based on data compactness to recent\ncontrastive clustering guided by self-supervision, the evolution of clustering\nmethods intrinsically corresponds to the progression of supervision signals. At\npresent, substantial efforts have been devoted to mining internal supervision\nsignals from data. Nevertheless, the abundant external knowledge such as\nsemantic descriptions, which naturally conduces to clustering, is regrettably\noverlooked. In this work, we propose leveraging external knowledge as a new\nsupervision signal to guide clustering, even though it seems irrelevant to the\ngiven data. To implement and validate our idea, we design an externally guided\nclustering method (Text-Aided Clustering, TAC), which leverages the textual\nsemantics of WordNet to facilitate image clustering. Specifically, TAC first\nselects and retrieves WordNet nouns that best distinguish images to enhance the\nfeature discriminability. Then, to improve image clustering performance, TAC\ncollaborates text and image modalities by mutually distilling cross-modal\nneighborhood information. Experiments demonstrate that TAC achieves\nstate-of-the-art performance on five widely used and three more challenging\nimage clustering benchmarks, including the full ImageNet-1K dataset.\n", "date": "2023-10-18", "categories": []}
{"id": "2407.05246", "title": "Deep Online Probability Aggregation Clustering", "abstract": "  Combining machine clustering with deep models has shown remarkable\nsuperiority in deep clustering. It modifies the data processing pipeline into\ntwo alternating phases: feature clustering and model training. However, such\nalternating schedule may lead to instability and computational burden issues.\nWe propose a centerless clustering algorithm called Probability Aggregation\nClustering (PAC) to proactively adapt deep learning technologies, enabling easy\ndeployment in online deep clustering. PAC circumvents the cluster center and\naligns the probability space and distribution space by formulating clustering\nas an optimization problem with a novel objective function. Based on the\ncomputation mechanism of the PAC, we propose a general online probability\naggregation module to perform stable and flexible feature clustering over\nmini-batch data and further construct a deep visual clustering framework deep\nPAC (DPAC). Extensive experiments demonstrate that PAC has superior clustering\nrobustness and performance and DPAC remarkably outperforms the state-of-the-art\ndeep clustering methods.\n", "date": "2024-07-07", "categories": []}
{"id": "2407.10196", "title": "A3S: A General Active Clustering Method with Pairwise Constraints", "abstract": "  Active clustering aims to boost the clustering performance by integrating\nhuman-annotated pairwise constraints through strategic querying. Conventional\napproaches with semi-supervised clustering schemes encounter high query costs\nwhen applied to large datasets with numerous classes. To address these\nlimitations, we propose a novel Adaptive Active Aggregation and Splitting (A3S)\nframework, falling within the cluster-adjustment scheme in active clustering.\nA3S features strategic active clustering adjustment on the initial cluster\nresult, which is obtained by an adaptive clustering algorithm. In particular,\nour cluster adjustment is inspired by the quantitative analysis of Normalized\nmutual information gain under the information theory framework and can provably\nimprove the clustering quality. The proposed A3S framework significantly\nelevates the performance and scalability of active clustering. In extensive\nexperiments across diverse real-world datasets, A3S achieves desired results\nwith significantly fewer human queries compared with existing methods.\n", "date": "2024-07-14", "categories": []}
{"id": "2407.04302", "title": "Fair Federated Data Clustering through Personalization: Bridging the Gap\n  between Diverse Data Distributions", "abstract": "  The rapid growth of data from edge devices has catalyzed the performance of\nmachine learning algorithms. However, the data generated resides at client\ndevices thus there are majorly two challenge faced by traditional machine\nlearning paradigms - centralization of data for training and secondly for most\nthe generated data the class labels are missing and there is very poor\nincentives to clients to manually label their data owing to high cost and lack\nof expertise. To overcome these issues, there have been initial attempts to\nhandle unlabelled data in a privacy preserving distributed manner using\nunsupervised federated data clustering. The goal is partition the data\navailable on clients into $k$ partitions (called clusters) without actual\nexchange of data. Most of the existing algorithms are highly dependent on data\ndistribution patterns across clients or are computationally expensive.\nFurthermore, due to presence of skewed nature of data across clients in most of\npractical scenarios existing models might result in clients suffering high\nclustering cost making them reluctant to participate in federated process. To\nthis, we are first to introduce the idea of personalization in federated\nclustering. The goal is achieve balance between achieving lower clustering cost\nand at same time achieving uniform cost across clients. We propose p-FClus that\naddresses these goal in a single round of communication between server and\nclients. We validate the efficacy of p-FClus against variety of federated\ndatasets showcasing it's data independence nature, applicability to any finite\n$\\ell$-norm, while simultaneously achieving lower cost and variance.\n", "date": "2024-07-05", "categories": []}
{"id": "2407.09055", "title": "Advanced Graph Clustering Methods: A Comprehensive and In-Depth Analysis", "abstract": "  Graph clustering, which aims to divide a graph into several homogeneous\ngroups, is a critical area of study with applications that span various fields\nsuch as social network analysis, bioinformatics, and image segmentation. This\npaper explores both traditional and more recent approaches to graph clustering.\nFirstly, key concepts and definitions in graph theory are introduced. The\nbackground section covers essential topics, including graph Laplacians and the\nintegration of Deep Learning in graph analysis. The paper then delves into\ntraditional clustering methods, including Spectral Clustering and the Leiden\nalgorithm. Following this, state-of-the-art clustering techniques that leverage\ndeep learning are examined. A comprehensive comparison of these methods is made\nthrough experiments. The paper concludes with a discussion of the practical\napplications of graph clustering and potential future research directions.\n", "date": "2024-07-12", "categories": []}
{"id": "2407.09120", "title": "URRL-IMVC: Unified and Robust Representation Learning for Incomplete\n  Multi-View Clustering", "abstract": "  Incomplete multi-view clustering (IMVC) aims to cluster multi-view data that\nare only partially available. This poses two main challenges: effectively\nleveraging multi-view information and mitigating the impact of missing views.\nPrevailing solutions employ cross-view contrastive learning and missing view\nrecovery techniques. However, they either neglect valuable complementary\ninformation by focusing only on consensus between views or provide unreliable\nrecovered views due to the absence of supervision. To address these\nlimitations, we propose a novel Unified and Robust Representation Learning for\nIncomplete Multi-View Clustering (URRL-IMVC). URRL-IMVC directly learns a\nunified embedding that is robust to view missing conditions by integrating\ninformation from multiple views and neighboring samples. Firstly, to overcome\nthe limitations of cross-view contrastive learning, URRL-IMVC incorporates an\nattention-based auto-encoder framework to fuse multi-view information and\ngenerate unified embeddings. Secondly, URRL-IMVC directly enhances the\nrobustness of the unified embedding against view-missing conditions through KNN\nimputation and data augmentation techniques, eliminating the need for explicit\nmissing view recovery. Finally, incremental improvements are introduced to\nfurther enhance the overall performance, such as the Clustering Module and the\ncustomization of the Encoder. We extensively evaluate the proposed URRL-IMVC\nframework on various benchmark datasets, demonstrating its state-of-the-art\nperformance. Furthermore, comprehensive ablation studies are performed to\nvalidate the effectiveness of our design.\n", "date": "2024-07-12", "categories": []}
{"id": "2407.08340", "title": "SLRL: Structured Latent Representation Learning for Multi-view\n  Clustering", "abstract": "  In recent years, Multi-View Clustering (MVC) has attracted increasing\nattention for its potential to reduce the annotation burden associated with\nlarge datasets. The aim of MVC is to exploit the inherent consistency and\ncomplementarity among different views, thereby integrating information from\nmultiple perspectives to improve clustering outcomes.\n  Despite extensive research in MVC, most existing methods focus predominantly\non harnessing complementary information across views to enhance clustering\neffectiveness, often neglecting the structural information among samples, which\nis crucial for exploring sample correlations. To address this gap, we introduce\na novel framework, termed Structured Latent Representation Learning based\nMulti-View Clustering method (SLRL). SLRL leverages both the complementary and\nstructural information. Initially, it learns a common latent representation for\nall views. Subsequently, to exploit the structural information among samples, a\nk-nearest neighbor graph is constructed from this common latent representation.\nThis graph facilitates enhanced sample interaction through graph learning\ntechniques, leading to a structured latent representation optimized for\nclustering. Extensive experiments demonstrate that SLRL not only competes well\nwith existing methods but also sets new benchmarks in various multi-view\ndatasets.\n", "date": "2024-07-11", "categories": []}
{"id": "2406.19300", "title": "scTree: Discovering Cellular Hierarchies in the Presence of Batch\n  Effects in scRNA-seq Data", "abstract": "  We propose a novel method, scTree, for single-cell Tree Variational\nAutoencoders, extending a hierarchical clustering approach to single-cell RNA\nsequencing data. scTree corrects for batch effects while simultaneously\nlearning a tree-structured data representation. This VAE-based method allows\nfor a more in-depth understanding of complex cellular landscapes independently\nof the biasing effects of batches. We show empirically on seven datasets that\nscTree discovers the underlying clusters of the data and the hierarchical\nrelations between them, as well as outperforms established baseline methods\nacross these datasets. Additionally, we analyze the learned hierarchy to\nunderstand its biological relevance, thus underpinning the importance of\nintegrating batch correction directly into the clustering procedure.\n", "date": "2024-06-27", "categories": []}
{"id": "2407.07222", "title": "SPINEX-Clustering: Similarity-based Predictions with Explainable\n  Neighbors Exploration for Clustering Problems", "abstract": "  This paper presents a novel clustering algorithm from the SPINEX\n(Similarity-based Predictions with Explainable Neighbors Exploration)\nalgorithmic family. The newly proposed clustering variant leverages the concept\nof similarity and higher-order interactions across multiple subspaces to group\ndata into clusters. To showcase the merit of SPINEX, a thorough set of\nbenchmarking experiments was carried out against 13 algorithms, namely,\nAffinity Propagation, Agglomerative, Birch, DBSCAN, Gaussian Mixture, HDBSCAN,\nK-Means, KMedoids, Mean Shift, MiniBatch K-Means, OPTICS, Spectral Clustering,\nand Ward Hierarchical. Then, the performance of all algorithms was examined\nacross 51 synthetic and real datasets from various domains, dimensions, and\ncomplexities. Furthermore, we present a companion complexity analysis to\ncompare the complexity of SPINEX to that of the aforementioned algorithms. Our\nresults demonstrate that SPINEX can outperform commonly adopted clustering\nalgorithms by ranking within the top-5 best performing algorithms and has\nmoderate complexity. Finally, a demonstration of the explainability\ncapabilities of SPINEX, along with future research needs, is presented.\n", "date": "2024-07-09", "categories": []}
{"id": "2407.06774", "title": "A new validity measure for fuzzy c-means clustering", "abstract": "  A new cluster validity index is proposed for fuzzy clusters obtained from\nfuzzy c-means algorithm. The proposed validity index exploits inter-cluster\nproximity between fuzzy clusters. Inter-cluster proximity is used to measure\nthe degree of overlap between clusters. A low proximity value refers to\nwell-partitioned clusters. The best fuzzy c-partition is obtained by minimizing\ninter-cluster proximity with respect to c. Well-known data sets are tested to\nshow the effectiveness and reliability of the proposed index.\n", "date": "2024-07-09", "categories": []}
{"id": "2404.04970", "title": "How to characterize imprecision in multi-view clustering?", "abstract": "  It is still challenging to cluster multi-view data since existing methods can\nonly assign an object to a specific (singleton) cluster when combining\ndifferent view information. As a result, it fails to characterize imprecision\nof objects in overlapping regions of different clusters, thus leading to a high\nrisk of errors. In this paper, we thereby want to answer the question: how to\ncharacterize imprecision in multi-view clustering? Correspondingly, we propose\na multi-view low-rank evidential c-means based on entropy constraint (MvLRECM).\nThe proposed MvLRECM can be considered as a multi-view version of evidential\nc-means based on the theory of belief functions. In MvLRECM, each object is\nallowed to belong to different clusters with various degrees of support (masses\nof belief) to characterize uncertainty when decision-making. Moreover, if an\nobject is in the overlapping region of several singleton clusters, it can be\nassigned to a meta-cluster, defined as the union of these singleton clusters,\nto characterize the local imprecision in the result. In addition,\nentropy-weighting and low-rank constraints are employed to reduce imprecision\nand improve accuracy. Compared to state-of-the-art methods, the effectiveness\nof MvLRECM is demonstrated based on several toy and UCI real datasets.\n", "date": "2024-04-07", "categories": []}
{"id": "2407.03574", "title": "An Axiomatic Definition of Hierarchical Clustering", "abstract": "  In this paper, we take an axiomatic approach to defining a population\nhierarchical clustering for piecewise constant densities, and in a similar\nmanner to Lebesgue integration, extend this definition to more general\ndensities. When the density satisfies some mild conditions, e.g., when it has\nconnected support, is continuous, and vanishes only at infinity, or when the\nconnected components of the density satisfy these conditions, our axiomatic\ndefinition results in Hartigan's definition of cluster tree.\n", "date": "2024-07-04", "categories": []}
{"id": "2407.02863", "title": "Fast maneuver recovery from aerial observation: trajectory clustering\n  and outliers rejection", "abstract": "  The implementation of road user models that realistically reproduce a\ncredible behavior in a multi-agentsimulation is still an open problem. A\ndata-driven approach consists on to deduce behaviors that may exist in real\nsituation to obtain different types of trajectories from a large set of\nobservations. The data, and its classification, could then be used to train\nmodels capable to extrapolate such behavior. Cars and two different types of\nVulnerable Road Users (VRU) will be considered by the trajectory clustering\nmethods proposed: pedestrians and cyclists. The results reported here evaluate\nmethods to extract well-defined trajectory classes from raw data without the\nuse of map information while also separating ''eccentric'' or incomplete\ntrajectories from the ones that are complete and representative in any\nscenario. Two environments will serve as test for the methods develop, three\ndifferent intersections and one roundabout. The resulting clusters of\ntrajectories can then be used for prediction or learning tasks or discarded if\nit is composed by outliers.\n", "date": "2024-07-03", "categories": []}
{"id": "2301.05994", "title": "Min-Max-Jump distance and its applications", "abstract": "  We explore three applications of Min-Max-Jump distance (MMJ distance).\nMMJ-based K-means revises K-means with MMJ distance. MMJ-based Silhouette\ncoefficient revises Silhouette coefficient with MMJ distance. We also tested\nthe Clustering with Neural Network and Index (CNNI) model with MMJ-based\nSilhouette coefficient. In the last application, we tested using Min-Max-Jump\ndistance for predicting labels of new points, after a clustering analysis of\ndata. Result shows Min-Max-Jump distance achieves good performances in all the\nthree proposed applications. In addition, we devise several algorithms for\ncalculating or estimating the distance.\n", "date": "2023-01-15", "categories": []}
{"id": "2208.00287", "title": "Simplex Clustering via sBeta with Applications to Online Adjustment of\n  Black-Box Predictions", "abstract": "  We explore clustering the softmax predictions of deep neural networks and\nintroduce a novel probabilistic clustering method, referred to as k-sBetas. In\nthe general context of clustering discrete distributions, the existing methods\nfocused on exploring distortion measures tailored to simplex data, such as the\nKL divergence, as alternatives to the standard Euclidean distance. We provide a\ngeneral maximum a posteriori (MAP) perspective of clustering distributions,\nemphasizing that the statistical models underlying the existing\ndistortion-based methods may not be descriptive enough. Instead, we optimize a\nmixed-variable objective measuring data conformity within each cluster to the\nintroduced sBeta density function, whose parameters are constrained and\nestimated jointly with binary assignment variables. Our versatile formulation\napproximates various parametric densities for modeling simplex data and enables\nthe control of the cluster-balance bias. This yields highly competitive\nperformances for the unsupervised adjustment of black-box model predictions in\nvarious scenarios. Our code and comparisons with the existing\nsimplex-clustering approaches and our introduced softmax-prediction benchmarks\nare publicly available:\nhttps://github.com/fchiaroni/Clustering_Softmax_Predictions.\n", "date": "2022-07-30", "categories": []}
{"id": "2406.19602", "title": "A Survey on Deep Clustering: From the Prior Perspective", "abstract": "  Facilitated by the powerful feature extraction ability of neural networks,\ndeep clustering has achieved great success in analyzing high-dimensional and\ncomplex real-world data. The performance of deep clustering methods is affected\nby various factors such as network structures and learning objectives. However,\nas pointed out in this survey, the essence of deep clustering lies in the\nincorporation and utilization of prior knowledge, which is largely ignored by\nexisting works. From pioneering deep clustering methods based on data structure\nassumptions to recent contrastive clustering methods based on data augmentation\ninvariances, the development of deep clustering intrinsically corresponds to\nthe evolution of prior knowledge. In this survey, we provide a comprehensive\nreview of deep clustering methods by categorizing them into six types of prior\nknowledge. We find that in general the prior innovation follows two trends,\nnamely, i) from mining to constructing, and ii) from internal to external.\nBesides, we provide a benchmark on five widely-used datasets and analyze the\nperformance of methods with diverse priors. By providing a novel prior\nknowledge perspective, we hope this survey could provide some novel insights\nand inspire future research in the deep clustering community.\n", "date": "2024-06-28", "categories": []}
{"id": "2311.04517", "title": "High-Performance Hybrid Algorithm for Minimum Sum-of-Squares Clustering\n  of Infinitely Tall Data", "abstract": "  This paper introduces a novel formulation of the clustering problem, namely\nthe Minimum Sum-of-Squares Clustering of Infinitely Tall Data (MSSC-ITD), and\npresents HPClust, an innovative set of hybrid parallel approaches for its\neffective solution. By utilizing modern high-performance computing techniques,\nHPClust enhances key clustering metrics: effectiveness, computational\nefficiency, and scalability. In contrast to vanilla data parallelism, which\nonly accelerates processing time through the MapReduce framework, our approach\nunlocks superior performance by leveraging the multi-strategy\ncompetitive-cooperative parallelism and intricate properties of the objective\nfunction landscape. Unlike other available algorithms that struggle to scale,\nour algorithm is inherently parallel in nature, improving solution quality\nthrough increased scalability and parallelism, and outperforming even advanced\nalgorithms designed for small and medium-sized datasets. Our evaluation of\nHPClust, featuring four parallel strategies, demonstrates its superiority over\ntraditional and cutting-edge methods by offering better performance in the key\nmetrics. These results also show that parallel processing not only enhances the\nclustering efficiency, but the accuracy as well. Additionally, we explore the\nbalance between computational efficiency and clustering quality, providing\ninsights into optimal parallel strategies based on dataset specifics and\nresource availability. This research advances our understanding of parallelism\nin clustering algorithms, demonstrating that a judicious hybridization of\nadvanced parallel approaches yields optimal results for MSSC-ITD. Experiments\non synthetic data further confirm HPClust's exceptional scalability and\nrobustness to noise.\n", "date": "2023-11-08", "categories": []}
{"id": "2305.01539", "title": "Jacobian-Scaled K-means Clustering for Physics-Informed Segmentation of\n  Reacting Flows", "abstract": "  This work introduces Jacobian-scaled K-means (JSK-means) clustering, which is\na physics-informed clustering strategy centered on the K-means framework. The\nmethod allows for the injection of underlying physical knowledge into the\nclustering procedure through a distance function modification: instead of\nleveraging conventional Euclidean distance vectors, the JSK-means procedure\noperates on distance vectors scaled by matrices obtained from dynamical system\nJacobians evaluated at the cluster centroids. The goal of this work is to show\nhow the JSK-means algorithm -- without modifying the input dataset -- produces\nclusters that capture regions of dynamical similarity, in that the clusters are\nredistributed towards high-sensitivity regions in phase space and are described\nby similarity in the source terms of samples instead of the samples themselves.\nThe algorithm is demonstrated on a complex reacting flow simulation dataset (a\nchannel detonation configuration), where the dynamics in the thermochemical\ncomposition space are known through the highly nonlinear and stiff\nArrhenius-based chemical source terms. Interpretations of cluster partitions in\nboth physical space and composition space reveal how JSK-means shifts clusters\nproduced by standard K-means towards regions of high chemical sensitivity\n(e.g., towards regions of peak heat release rate near the detonation reaction\nzone). The findings presented here illustrate the benefits of utilizing\nJacobian-scaled distances in clustering techniques, and the JSK-means method in\nparticular displays promising potential for improving former partition-based\nmodeling strategies in reacting flow (and other multi-physics) applications.\n", "date": "2023-05-02", "categories": []}
{"id": "2401.05831", "title": "Revisiting Silhouette Aggregation", "abstract": "  Silhouette coefficient is an established internal clustering evaluation\nmeasure that produces a score per data point, assessing the quality of its\nclustering assignment. To assess the quality of the clustering of the whole\ndataset, the scores of all the points in the dataset are typically (micro)\naveraged into a single value. An alternative path, however, that is rarely\nemployed, is to average first at the cluster level and then (macro) average\nacross clusters. As we illustrate in this work with a synthetic example, the\ntypical micro-averaging strategy is sensitive to cluster imbalance while the\noverlooked macro-averaging strategy is far more robust. By investigating\nmacro-Silhouette further, we find that uniform sub-sampling, the only available\nstrategy in existing libraries, harms the measure's robustness against\nimbalance. We address this issue by proposing a per-cluster sampling method. An\nexperimental study on eight real-world datasets is then used to analyse both\ncoefficients in two clustering tasks.\n", "date": "2024-01-11", "categories": []}
{"id": "2406.15960", "title": "Fair Clustering: Critique, Caveats, and Future Directions", "abstract": "  Clustering is a fundamental problem in machine learning and operations\nresearch. Therefore, given the fact that fairness considerations have become of\nparamount importance in algorithm design, fairness in clustering has received\nsignificant attention from the research community. The literature on fair\nclustering has resulted in a collection of interesting fairness notions and\nelaborate algorithms. In this paper, we take a critical view of fair\nclustering, identifying a collection of ignored issues such as the lack of a\nclear utility characterization and the difficulty in accounting for the\ndownstream effects of a fair clustering algorithm in machine learning settings.\nIn some cases, we demonstrate examples where the application of a fair\nclustering algorithm can have significant negative impacts on social welfare.\nWe end by identifying a collection of steps that would lead towards more\nimpactful research in fair clustering.\n", "date": "2024-06-22", "categories": []}
{"id": "2406.16557", "title": "Efficient k-means with Individual Fairness via Exponential Tilting", "abstract": "  In location-based resource allocation scenarios, the distances between each\nindividual and the facility are desired to be approximately equal, thereby\nensuring fairness. Individually fair clustering is often employed to achieve\nthe principle of treating all points equally, which can be applied in these\nscenarios. This paper proposes a novel algorithm, tilted k-means (TKM), aiming\nto achieve individual fairness in clustering. We integrate the exponential\ntilting into the sum of squared errors (SSE) to formulate a novel objective\nfunction called tilted SSE. We demonstrate that the tilted SSE can generalize\nto SSE and employ the coordinate descent and first-order gradient method for\noptimization. We propose a novel fairness metric, the variance of the distances\nwithin each cluster, which can alleviate the Matthew Effect typically caused by\nexisting fairness metrics. Our theoretical analysis demonstrates that the\nwell-known k-means++ incurs a multiplicative error of O(k log k), and we\nestablish the convergence of TKM under mild conditions. In terms of fairness,\nwe prove that the variance generated by TKM decreases with a scaled\nhyperparameter. In terms of efficiency, we demonstrate the time complexity is\nlinear with the dataset size. Our experiments demonstrate that TKM outperforms\nstate-of-the-art methods in effectiveness, fairness, and efficiency.\n", "date": "2024-06-24", "categories": []}
{"id": "2404.07112", "title": "Unfolding ADMM for Enhanced Subspace Clustering of Hyperspectral Images", "abstract": "  Deep subspace clustering methods are now prominent in clustering, typically\nusing fully connected networks and a self-representation loss function.\nHowever, these methods often struggle with overfitting and lack\ninterpretability. In this paper, we explore an alternative clustering approach\nbased on deep unfolding. By unfolding iterative optimization methods into\nneural networks, this approach offers enhanced interpretability and reliability\ncompared to data-driven deep learning methods, and greater adaptability and\ngeneralization than model-based approaches. Hence, unfolding has become widely\nused in inverse imaging problems, such as image restoration, reconstruction,\nand super-resolution, but has not been sufficiently explored yet in the context\nof clustering. In this work, we introduce an innovative clustering architecture\nfor hyperspectral images (HSI) by unfolding an iterative solver based on the\nAlternating Direction Method of Multipliers (ADMM) for sparse subspace\nclustering. To our knowledge, this is the first attempt to apply unfolding ADMM\nfor computing the self-representation matrix in subspace clustering. Moreover,\nour approach captures well the structural characteristics of HSI data by\nemploying the K nearest neighbors algorithm as part of a structure preservation\nmodule. Experimental evaluation of three established HSI datasets shows clearly\nthe potential of the unfolding approach in HSI clustering and even demonstrates\nsuperior performance compared to state-of-the-art techniques.\n", "date": "2024-04-10", "categories": []}
{"id": "2406.14288", "title": "Revisiting Modularity Maximization for Graph Clustering: A Contrastive\n  Learning Perspective", "abstract": "  Graph clustering, a fundamental and challenging task in graph mining, aims to\nclassify nodes in a graph into several disjoint clusters. In recent years,\ngraph contrastive learning (GCL) has emerged as a dominant line of research in\ngraph clustering and advances the new state-of-the-art. However, GCL-based\nmethods heavily rely on graph augmentations and contrastive schemes, which may\npotentially introduce challenges such as semantic drift and scalability issues.\nAnother promising line of research involves the adoption of modularity\nmaximization, a popular and effective measure for community detection, as the\nguiding principle for clustering tasks. Despite the recent progress, the\nunderlying mechanism of modularity maximization is still not well understood.\nIn this work, we dig into the hidden success of modularity maximization for\ngraph clustering. Our analysis reveals the strong connections between\nmodularity maximization and graph contrastive learning, where positive and\nnegative examples are naturally defined by modularity. In light of our results,\nwe propose a community-aware graph clustering framework, coined MAGI, which\nleverages modularity maximization as a contrastive pretext task to effectively\nuncover the underlying information of communities in graphs, while avoiding the\nproblem of semantic drift. Extensive experiments on multiple graph datasets\nverify the effectiveness of MAGI in terms of scalability and clustering\nperformance compared to state-of-the-art graph clustering methods. Notably,\nMAGI easily scales a sufficiently large graph with 100M nodes while\noutperforming strong baselines.\n", "date": "2024-06-20", "categories": []}
{"id": "2406.12297", "title": "Faithful Density-Peaks Clustering via Matrix Computations on MPI\n  Parallelization System", "abstract": "  Density peaks clustering (DP) has the ability of detecting clusters of\narbitrary shape and clustering non-Euclidean space data, but its quadratic\ncomplexity in both computing and storage makes it difficult to scale for big\ndata. Various approaches have been proposed in this regard, including MapReduce\nbased distribution computing, multi-core parallelism, presentation\ntransformation (e.g., kd-tree, Z-value), granular computing, and so forth.\nHowever, most of these existing methods face two limitations. One is their\ntarget datasets are mostly constrained to be in Euclidian space, the other is\nthey emphasize only on local neighbors while ignoring global data distribution\ndue to restriction to cut-off kernel when computing density. To address the two\nissues, we present a faithful and parallel DP method that makes use of two\ntypes of vector-like distance matrices and an inverse leading-node-finding\npolicy. The method is implemented on a message passing interface (MPI) system.\nExtensive experiments showed that our method is capable of clustering\nnon-Euclidean data such as in community detection, while outperforming the\nstate-of-the-art counterpart methods in accuracy when clustering large\nEuclidean data. Our code is publicly available at\nhttps://github.com/alanxuji/FaithPDP.\n", "date": "2024-06-18", "categories": []}
{"id": "2207.01294", "title": "A New Index for Clustering Evaluation Based on Density Estimation", "abstract": "  A new index for internal evaluation of clustering is introduced. The index is\ndefined as a mixture of two sub-indices. The first sub-index $ I_a $ is called\nthe Ambiguous Index; the second sub-index $ I_s $ is called the Similarity\nIndex. Calculation of the two sub-indices is based on density estimation to\neach cluster of a partition of the data. An experiment is conducted to test the\nperformance of the new index, and compared with six other internal clustering\nevaluation indices -- Calinski-Harabasz index, Silhouette coefficient,\nDavies-Bouldin index, CDbw, DBCV, and VIASCKDE, on a set of 145 datasets. The\nresult shows the new index significantly improves other internal clustering\nevaluation indices.\n", "date": "2022-07-04", "categories": []}
{"id": "2406.11485", "title": "Active clustering with bandit feedback", "abstract": "  We investigate the Active Clustering Problem (ACP). A learner interacts with\nan $N$-armed stochastic bandit with $d$-dimensional subGaussian feedback. There\nexists a hidden partition of the arms into $K$ groups, such that arms within\nthe same group, share the same mean vector. The learner's task is to uncover\nthis hidden partition with the smallest budget - i.e., the least number of\nobservation - and with a probability of error smaller than a prescribed\nconstant $\\delta$. In this paper, (i) we derive a non-asymptotic lower bound\nfor the budget, and (ii) we introduce the computationally efficient ACB\nalgorithm, whose budget matches the lower bound in most regimes. We improve on\nthe performance of a uniform sampling strategy. Importantly, contrary to the\nbatch setting, we establish that there is no computation-information gap in the\nactive setting.\n", "date": "2024-06-17", "categories": []}
{"id": "2406.11649", "title": "Making Old Things New: A Unified Algorithm for Differentially Private\n  Clustering", "abstract": "  As a staple of data analysis and unsupervised learning, the problem of\nprivate clustering has been widely studied under various privacy models.\nCentralized differential privacy is the first of them, and the problem has also\nbeen studied for the local and the shuffle variation. In each case, the goal is\nto design an algorithm that computes privately a clustering, with the smallest\npossible error. The study of each variation gave rise to new algorithms: the\nlandscape of private clustering algorithms is therefore quite intricate.\n  In this paper, we show that a 20-year-old algorithm can be slightly modified\nto work for any of these models. This provides a unified picture: while\nmatching almost all previously known results, it allows us to improve some of\nthem and extend it to a new privacy model, the continual observation setting,\nwhere the input is changing over time and the algorithm must output a new\nsolution at each time step.\n", "date": "2024-06-17", "categories": []}
{"id": "2406.10061", "title": "TACCO: Task-guided Co-clustering of Clinical Concepts and Patient Visits\n  for Disease Subtyping based on EHR Data", "abstract": "  The growing availability of well-organized Electronic Health Records (EHR)\ndata has enabled the development of various machine learning models towards\ndisease risk prediction. However, existing risk prediction methods overlook the\nheterogeneity of complex diseases, failing to model the potential disease\nsubtypes regarding their corresponding patient visits and clinical concept\nsubgroups. In this work, we introduce TACCO, a novel framework that jointly\ndiscovers clusters of clinical concepts and patient visits based on a\nhypergraph modeling of EHR data. Specifically, we develop a novel\nself-supervised co-clustering framework that can be guided by the risk\nprediction task of specific diseases. Furthermore, we enhance the hypergraph\nmodel of EHR data with textual embeddings and enforce the alignment between the\nclusters of clinical concepts and patient visits through a contrastive\nobjective. Comprehensive experiments conducted on the public MIMIC-III dataset\nand Emory internal CRADLE dataset over the downstream clinical tasks of\nphenotype classification and cardiovascular risk prediction demonstrate an\naverage 31.25% performance improvement compared to traditional ML baselines and\na 5.26% improvement on top of the vanilla hypergraph model without our\nco-clustering mechanism. In-depth model analysis, clustering results analysis,\nand clinical case studies further validate the improved utilities and\ninsightful interpretations delivered by TACCO. Code is available at\nhttps://github.com/PericlesHat/TACCO.\n", "date": "2024-06-14", "categories": []}
{"id": "2406.09137", "title": "Dynamic Correlation Clustering in Sublinear Update Time", "abstract": "  We study the classic problem of correlation clustering in dynamic node\nstreams. In this setting, nodes are either added or randomly deleted over time,\nand each node pair is connected by a positive or negative edge. The objective\nis to continuously find a partition which minimizes the sum of positive edges\ncrossing clusters and negative edges within clusters. We present an algorithm\nthat maintains an $O(1)$-approximation with $O$(polylog $n$) amortized update\ntime. Prior to our work, Behnezhad, Charikar, Ma, and L. Tan achieved a\n$5$-approximation with $O(1)$ expected update time in edge streams which\ntranslates in node streams to an $O(D)$-update time where $D$ is the maximum\npossible degree. Finally we complement our theoretical analysis with\nexperiments on real world data.\n", "date": "2024-06-13", "categories": []}
{"id": "2306.04785", "title": "Interpretable Deep Clustering for Tabular Data", "abstract": "  Clustering is a fundamental learning task widely used as a first step in data\nanalysis. For example, biologists use cluster assignments to analyze genome\nsequences, medical records, or images. Since downstream analysis is typically\nperformed at the cluster level, practitioners seek reliable and interpretable\nclustering models. We propose a new deep-learning framework for general domain\ntabular data that predicts interpretable cluster assignments at the instance\nand cluster levels. First, we present a self-supervised procedure to identify\nthe subset of the most informative features from each data point. Then, we\ndesign a model that predicts cluster assignments and a gate matrix that\nprovides cluster-level feature selection. Overall, our model provides cluster\nassignments with an indication of the driving feature for each sample and each\ncluster. We show that the proposed method can reliably predict cluster\nassignments in biological, text, image, and physics tabular datasets.\nFurthermore, using previously proposed metrics, we verify that our model leads\nto interpretable results at a sample and cluster level. Our code is available\nat https://github.com/jsvir/idc.\n", "date": "2023-06-07", "categories": []}
{"id": "2406.05545", "title": "Privacy-Preserving Optimal Parameter Selection for Collaborative\n  Clustering", "abstract": "  This study investigates the optimal selection of parameters for collaborative\nclustering while ensuring data privacy. We focus on key clustering algorithms\nwithin a collaborative framework, where multiple data owners combine their\ndata. A semi-trusted server assists in recommending the most suitable\nclustering algorithm and its parameters. Our findings indicate that the privacy\nparameter ($\\epsilon$) minimally impacts the server's recommendations, but an\nincrease in $\\epsilon$ raises the risk of membership inference attacks, where\nsensitive information might be inferred. To mitigate these risks, we implement\ndifferential privacy techniques, particularly the Randomized Response\nmechanism, to add noise and protect data privacy. Our approach demonstrates\nthat high-quality clustering can be achieved while maintaining data\nconfidentiality, as evidenced by metrics such as the Adjusted Rand Index and\nSilhouette Score. This study contributes to privacy-aware data sharing, optimal\nalgorithm and parameter selection, and effective communication between data\nowners and the server.\n", "date": "2024-06-08", "categories": []}
{"id": "2406.04857", "title": "A Near-Linear Time Approximation Algorithm for Beyond-Worst-Case Graph\n  Clustering", "abstract": "  We consider the semi-random graph model of [Makarychev, Makarychev and\nVijayaraghavan, STOC'12], where, given a random bipartite graph with $\\alpha$\nedges and an unknown bipartition $(A, B)$ of the vertex set, an adversary can\nadd arbitrary edges inside each community and remove arbitrary edges from the\ncut $(A, B)$ (i.e. all adversarial changes are \\textit{monotone} with respect\nto the bipartition). For this model, a polynomial time algorithm is known to\napproximate the Balanced Cut problem up to value $O(\\alpha)$ [MMV'12] as long\nas the cut $(A, B)$ has size $\\Omega(\\alpha)$. However, it consists of slow\nsubroutines requiring optimal solutions for logarithmically many semidefinite\nprograms. We study the fine-grained complexity of the problem and present the\nfirst near-linear time algorithm that achieves similar performances to that of\n[MMV'12]. Our algorithm runs in time $O(|V(G)|^{1+o(1)} + |E(G)|^{1+o(1)})$ and\nfinds a balanced cut of value $O(\\alpha)$. Our approach appears easily\nextendible to related problem, such as Sparsest Cut, and also yields an\nnear-linear time $O(1)$-approximation to Dagupta's objective function for\nhierarchical clustering [Dasgupta, STOC'16] for the semi-random hierarchical\nstochastic block model inputs of [Cohen-Addad, Kanade, Mallmann-Trenn, Mathieu,\nJACM'19].\n", "date": "2024-06-07", "categories": []}
{"id": "2406.04860", "title": "Multi-View Stochastic Block Models", "abstract": "  Graph clustering is a central topic in unsupervised learning with a multitude\nof practical applications. In recent years, multi-view graph clustering has\ngained a lot of attention for its applicability to real-world instances where\none has access to multiple data sources. In this paper we formalize a new\nfamily of models, called \\textit{multi-view stochastic block models} that\ncaptures this setting.\n  For this model, we first study efficient algorithms that naively work on the\nunion of multiple graphs. Then, we introduce a new efficient algorithm that\nprovably outperforms previous approaches by analyzing the structure of each\ngraph separately. Furthermore, we complement our results with an\ninformation-theoretic lower bound studying the limits of what can be done in\nthis model. Finally, we corroborate our results with experimental evaluations.\n", "date": "2024-06-07", "categories": []}
{"id": "2402.14490", "title": "Imbalanced Data Clustering using Equilibrium K-Means", "abstract": "  Centroid-based clustering algorithms, such as hard K-means (HKM) and fuzzy\nK-means (FKM), have suffered from learning bias towards large clusters. Their\ncentroids tend to be crowded in large clusters, compromising performance when\nthe true underlying data groups vary in size (i.e., imbalanced data). To\naddress this, we propose a new clustering objective function based on the\nBoltzmann operator, which introduces a novel centroid repulsion mechanism,\nwhere data points surrounding the centroids repel other centroids. Larger\nclusters repel more, effectively mitigating the issue of large cluster learning\nbias. The proposed new algorithm, called equilibrium K-means (EKM), is simple,\nalternating between two steps; resource-saving, with the same time and space\ncomplexity as FKM; and scalable to large datasets via batch learning. We\nsubstantially evaluate the performance of EKM on synthetic and real-world\ndatasets. The results show that EKM performs competitively on balanced data and\nsignificantly outperforms benchmark algorithms on imbalanced data. Deep\nclustering experiments demonstrate that EKM is a better alternative to HKM and\nFKM on imbalanced data as more discriminative representation can be obtained.\nAdditionally, we reformulate HKM, FKM, and EKM in a general form of gradient\ndescent and demonstrate how this general form facilitates a uniform study of\nK-means algorithms.\n", "date": "2024-02-22", "categories": []}
{"id": "2406.03653", "title": "Equivalence Set Restricted Latent Class Models (ESRLCM)", "abstract": "  Latent Class Models (LCMs) are used to cluster multivariate categorical data,\ncommonly used to interpret survey responses. We propose a novel Bayesian model\ncalled the Equivalence Set Restricted Latent Class Model (ESRLCM). This model\nidentifies clusters who have common item response probabilities, and does so\nmore generically than traditional restricted latent attribute models. We verify\nthe identifiability of ESRLCMs, and demonstrate the effectiveness in both\nsimulations and real-world applications.\n", "date": "2024-06-05", "categories": []}
{"id": "2406.03819", "title": "Subspace Clustering in Wavelet Packets Domain", "abstract": "  Subspace clustering (SC) algorithms utilize the union of subspaces model to\ncluster data points according to the subspaces from which they are drawn. To\nbetter address separability of subspaces and robustness to noise we propose a\nwavelet packet (WP) based transform domain subspace clustering. Depending on\nthe number of resolution levels, WP yields several representations instantiated\nin terms of subbands. The first approach combines original and subband data\ninto one complementary multi-view representation. Afterward, we formulate joint\nrepresentation learning as a low-rank MERA tensor network approximation\nproblem. That is motivated by the strong representation power of the MERA\nnetwork to capture complex intra/inter-view dependencies in corresponding\nself-representation tensor. In the second approach, we use a self-stopping\ncomputationally efficient method to select the subband with the smallest\nclustering error on the validation set. When existing SC algorithms are applied\nto the chosen subband, their performance is expected to improve. Consequently,\nboth approaches enable the re-use of SC algorithms developed so far. Improved\nclustering performance is due to the dual nature of subbands as representations\nand filters, which is essential for noise suppression. We exemplify the\nproposed WP domain approach to SC on the MERA tensor network and eight other\nwell-known linear SC algorithms using six well-known image datasets\nrepresenting faces, digits, and objects. Although WP domain-based SC is a\nlinear method, it achieved clustering performance comparable with some best\ndeep SC algorithms and outperformed many other deep SC algorithms by a\nsignificant margin. That is in particular case for the WP MERA SC algorithm. On\nthe COIL100 dataset, it achieves an accuracy of 87.45% and outperforms the best\ndeep SC competitor in the amount of 14.75%.\n", "date": "2024-06-06", "categories": []}
{"id": "2406.03152", "title": "Dynamic Spectral Clustering with Provable Approximation Guarantee", "abstract": "  This paper studies clustering algorithms for dynamically evolving graphs\n$\\{G_t\\}$, in which new edges (and potential new vertices) are added into a\ngraph, and the underlying cluster structure of the graph can gradually change.\nThe paper proves that, under some mild condition on the cluster-structure, the\nclusters of the final graph $G_T$ of $n_T$ vertices at time $T$ can be well\napproximated by a dynamic variant of the spectral clustering algorithm. The\nalgorithm runs in amortised update time $O(1)$ and query time $o(n_T)$.\nExperimental studies on both synthetic and real-world datasets further confirm\nthe practicality of our designed algorithm.\n", "date": "2024-06-05", "categories": []}
{"id": "2406.01203", "title": "Scaling Up Deep Clustering Methods Beyond ImageNet-1K", "abstract": "  Deep image clustering methods are typically evaluated on small-scale balanced\nclassification datasets while feature-based $k$-means has been applied on\nproprietary billion-scale datasets. In this work, we explore the performance of\nfeature-based deep clustering approaches on large-scale benchmarks whilst\ndisentangling the impact of the following data-related factors: i) class\nimbalance, ii) class granularity, iii) easy-to-recognize classes, and iv) the\nability to capture multiple classes. Consequently, we develop multiple new\nbenchmarks based on ImageNet21K. Our experimental analysis reveals that\nfeature-based $k$-means is often unfairly evaluated on balanced datasets.\nHowever, deep clustering methods outperform $k$-means across most large-scale\nbenchmarks. Interestingly, $k$-means underperforms on easy-to-classify\nbenchmarks by large margins. The performance gap, however, diminishes on the\nhighest data regimes such as ImageNet21K. Finally, we find that non-primary\ncluster predictions capture meaningful classes (i.e. coarser classes).\n", "date": "2024-06-03", "categories": []}
{"id": "2211.03894", "title": "visClust: A visual clustering algorithm based on orthogonal projections", "abstract": "  We present a novel clustering algorithm, visClust, that is based on lower\ndimensional data representations and visual interpretation. Thereto, we design\na transformation that allows the data to be represented by a binary integer\narray enabling the use of image processing methods to select a partition.\nQualitative and quantitative analyses measured in accuracy and an adjusted\nRand-Index show that the algorithm performs well while requiring low runtime\nand RAM. We compare the results to 6 state-of-the-art algorithms with available\ncode, confirming the quality of visClust by superior performance in most\nexperiments. Moreover, the algorithm asks for just one obligatory input\nparameter while allowing optimization via optional parameters. The code is made\navailable on GitHub and straightforward to use.\n", "date": "2022-11-07", "categories": []}
{"id": "2405.19559", "title": "Clustering Mixtures of Discrete Distributions: A Note on Mitra's\n  Algorithm", "abstract": "  In this note, we provide a refined analysis of Mitra's algorithm\n\\cite{mitra2008clustering} for classifying general discrete mixture\ndistribution models. Built upon spectral clustering\n\\cite{mcsherry2001spectral}, this algorithm offers compelling conditions for\nprobability distributions. We enhance this analysis by tailoring the model to\nbipartite stochastic block models, resulting in more refined conditions.\nCompared to those derived in \\cite{mitra2008clustering}, our improved\nseparation conditions are obtained.\n", "date": "2024-05-29", "categories": []}
{"id": "2401.01558", "title": "One-Step Late Fusion Multi-view Clustering with Compressed Subspace", "abstract": "  Late fusion multi-view clustering (LFMVC) has become a rapidly growing class\nof methods in the multi-view clustering (MVC) field, owing to its excellent\ncomputational speed and clustering performance. One bottleneck faced by\nexisting late fusion methods is that they are usually aligned to the average\nkernel function, which makes the clustering performance highly dependent on the\nquality of datasets. Another problem is that they require subsequent k-means\nclustering after obtaining the consensus partition matrix to get the final\ndiscrete labels, and the resulting separation of the label learning and cluster\nstructure optimization processes limits the integrity of these models. To\naddress the above issues, we propose an integrated framework named One-Step\nLate Fusion Multi-view Clustering with Compressed Subspace (OS-LFMVC-CS).\nSpecifically, we use the consensus subspace to align the partition matrix while\noptimizing the partition fusion, and utilize the fused partition matrix to\nguide the learning of discrete labels. A six-step iterative optimization\napproach with verified convergence is proposed. Sufficient experiments on\nmultiple datasets validate the effectiveness and efficiency of our proposed\nmethod.\n", "date": "2024-01-03", "categories": []}
{"id": "2402.12302", "title": "Asymptotic Gaussian Fluctuations of Eigenvectors in Spectral Clustering", "abstract": "  The performance of spectral clustering relies on the fluctuations of the\nentries of the eigenvectors of a similarity matrix, which has been left\nuncharacterized until now. In this letter, it is shown that the signal $+$\nnoise structure of a general spike random matrix model is transferred to the\neigenvectors of the corresponding Gram kernel matrix and the fluctuations of\ntheir entries are Gaussian in the large-dimensional regime. This CLT-like\nresult was the last missing piece to precisely predict the classification\nperformance of spectral clustering. The proposed proof is very general and\nrelies solely on the rotational invariance of the noise. Numerical experiments\non synthetic and real data illustrate the universality of this phenomenon.\n", "date": "2024-02-19", "categories": []}
{"id": "2405.15882", "title": "Risk Factor Identification In Osteoporosis Using Unsupervised Machine\n  Learning Techniques", "abstract": "  In this study, the reliability of identified risk factors associated with\nosteoporosis is investigated using a new clustering-based method on electronic\nmedical records. This study proposes utilizing a new CLustering Iterations\nFramework (CLIF) that includes an iterative clustering framework that can adapt\nany of the following three components: clustering, feature selection, and\nprincipal feature identification. The study proposes using Wasserstein distance\nto identify principal features, borrowing concepts from the optimal transport\ntheory. The study also suggests using a combination of ANOVA and ablation tests\nto select influential features from a data set. Some risk factors presented in\nexisting works are endorsed by our identified significant clusters, while the\nreliability of some other risk factors is weakened.\n", "date": "2024-05-24", "categories": []}
{"id": "2405.15983", "title": "Hierarchical Clustering via Local Search", "abstract": "  In this paper, we introduce a local search algorithm for hierarchical\nclustering. For the local step, we consider a tree re-arrangement operation,\nknown as the {\\em interchange}, which involves swapping two closely positioned\nsub-trees within a tree hierarchy. The interchange operation has been\npreviously used in the context of phylogenetic trees. As the objective function\nfor evaluating the resulting hierarchies, we utilize the revenue function\nproposed by Moseley and Wang (NIPS 2017.)\n  In our main result, we show that any locally optimal tree guarantees a\nrevenue of at least $\\frac{n-2}{3}\\sum_{i < j}w(i,j)$ where is $n$ the number\nof objects and $w: [n] \\times [n] \\rightarrow \\mathbb{R}^+$ is the associated\nsimilarity function. This finding echoes the previously established bound for\nthe average link algorithm as analyzed by Moseley and Wang. We demonstrate that\nthis alignment is not coincidental, as the average link trees enjoy the\nproperty of being locally optimal with respect to the interchange operation.\nConsequently, our study provides an alternative insight into the average link\nalgorithm and reveals the existence of a broader range of hierarchies with\nrelatively high revenue achievable through a straightforward local search\nalgorithm.\n  Furthermore, we present an implementation of the local search framework,\nwhere each local step requires $O(n)$ computation time. Our empirical results\nindicate that the proposed method, used as post-processing step, can\neffectively generate a hierarchical clustering with substantial revenue.\n", "date": "2024-05-24", "categories": []}
{"id": "2405.16447", "title": "Fast Asymmetric Factorization for Large Scale Multiple Kernel Clustering", "abstract": "  Kernel methods are extensively employed for nonlinear data clustering, yet\ntheir effectiveness heavily relies on selecting suitable kernels and associated\nparameters, posing challenges in advance determination. In response, Multiple\nKernel Clustering (MKC) has emerged as a solution, allowing the fusion of\ninformation from multiple base kernels for clustering. However, both early\nfusion and late fusion methods for large-scale MKC encounter challenges in\nmemory and time constraints, necessitating simultaneous optimization of both\naspects. To address this issue, we propose Efficient Multiple Kernel Concept\nFactorization (EMKCF), which constructs a new sparse kernel matrix inspired by\nlocal regression to achieve memory efficiency. EMKCF learns consensus and\nindividual representations by extending orthogonal concept factorization to\nhandle multiple kernels for time efficiency. Experimental results demonstrate\nthe efficiency and effectiveness of EMKCF on benchmark datasets compared to\nstate-of-the-art methods. The proposed method offers a straightforward,\nscalable, and effective solution for large-scale MKC tasks.\n", "date": "2024-05-26", "categories": []}
{"id": "2310.18162", "title": "Proportional Fairness in Clustering: A Social Choice Perspective", "abstract": "  We study the proportional clustering problem of Chen et al. [ICML'19] and\nrelate it to the area of multiwinner voting in computational social choice. We\nshow that any clustering satisfying a weak proportionality notion of Brill and\nPeters [EC'23] simultaneously obtains the best known approximations to the\nproportional fairness notion of Chen et al. [ICML'19], but also to individual\nfairness [Jung et al., FORC'20] and the \"core\" [Li et al. ICML'21]. In fact, we\nshow that any approximation to proportional fairness is also an approximation\nto individual fairness and vice versa. Finally, we also study stronger notions\nof proportional representation, in which deviations do not only happen to\nsingle, but multiple candidate centers, and show that stronger proportionality\nnotions of Brill and Peters [EC'23] imply approximations to these stronger\nguarantees.\n", "date": "2023-10-27", "categories": []}
{"id": "2405.13427", "title": "Adaptive Fuzzy C-Means with Graph Embedding", "abstract": "  Fuzzy clustering algorithms can be roughly categorized into two main groups:\nFuzzy C-Means (FCM) based methods and mixture model based methods. However, for\nalmost all existing FCM based methods, how to automatically selecting proper\nmembership degree hyper-parameter values remains a challenging and unsolved\nproblem. Mixture model based methods, while circumventing the difficulty of\nmanually adjusting membership degree hyper-parameters inherent in FCM based\nmethods, often have a preference for specific distributions, such as the\nGaussian distribution. In this paper, we propose a novel FCM based clustering\nmodel that is capable of automatically learning an appropriate membership\ndegree hyper-parameter value and handling data with non-Gaussian clusters.\nMoreover, by removing the graph embedding regularization, the proposed FCM\nmodel can degenerate into the simplified generalized Gaussian mixture model.\nTherefore, the proposed FCM model can be also seen as the generalized Gaussian\nmixture model with graph embedding. Extensive experiments are conducted on both\nsynthetic and real-world datasets to demonstrate the effectiveness of the\nproposed model.\n", "date": "2024-05-22", "categories": []}
{"id": "2405.12237", "title": "EKM: An exact, polynomial-time algorithm for the $K$-medoids problem", "abstract": "  The $K$-medoids problem is a challenging combinatorial clustering task,\nwidely used in data analysis applications. While numerous algorithms have been\nproposed to solve this problem, none of these are able to obtain an exact\n(globally optimal) solution for the problem in polynomial time. In this paper,\nwe present EKM: a novel algorithm for solving this problem exactly with\nworst-case $O\\left(N^{K+1}\\right)$ time complexity. EKM is developed according\nto recent advances in transformational programming and combinatorial\ngeneration, using formal program derivation steps. The derived algorithm is\nprovably correct by construction. We demonstrate the effectiveness of our\nalgorithm by comparing it against various approximate methods on numerous\nreal-world datasets. We show that the wall-clock run time of our algorithm\nmatches the worst-case time complexity analysis on synthetic datasets, clearly\noutperforming the exponential time complexity of benchmark branch-and-bound\nbased MIP solvers. To our knowledge, this is the first, rigorously-proven\npolynomial time, practical algorithm for this ubiquitous problem.\n", "date": "2024-05-16", "categories": []}
{"id": "2405.12775", "title": "Unsupervised Multimodal Clustering for Semantics Discovery in Multimodal\n  Utterances", "abstract": "  Discovering the semantics of multimodal utterances is essential for\nunderstanding human language and enhancing human-machine interactions. Existing\nmethods manifest limitations in leveraging nonverbal information for discerning\ncomplex semantics in unsupervised scenarios. This paper introduces a novel\nunsupervised multimodal clustering method (UMC), making a pioneering\ncontribution to this field. UMC introduces a unique approach to constructing\naugmentation views for multimodal data, which are then used to perform\npre-training to establish well-initialized representations for subsequent\nclustering. An innovative strategy is proposed to dynamically select\nhigh-quality samples as guidance for representation learning, gauged by the\ndensity of each sample's nearest neighbors. Besides, it is equipped to\nautomatically determine the optimal value for the top-$K$ parameter in each\ncluster to refine sample selection. Finally, both high- and low-quality samples\nare used to learn representations conducive to effective clustering. We build\nbaselines on benchmark multimodal intent and dialogue act datasets. UMC shows\nremarkable improvements of 2-6\\% scores in clustering metrics over\nstate-of-the-art methods, marking the first successful endeavor in this domain.\nThe complete code and data are available at https://github.com/thuiar/UMC.\n", "date": "2024-05-21", "categories": []}
{"id": "2305.16656", "title": "Clustering Method for Time-Series Images Using Quantum-Inspired\n  Computing Technology", "abstract": "  Time-series clustering serves as a powerful data mining technique for\ntime-series data in the absence of prior knowledge about clusters. A large\namount of time-series data with large size has been acquired and used in\nvarious research fields. Hence, clustering method with low computational cost\nis required. Given that a quantum-inspired computing technology, such as a\nsimulated annealing machine, surpasses conventional computers in terms of fast\nand accurately solving combinatorial optimization problems, it holds promise\nfor accomplishing clustering tasks that are challenging to achieve using\nexisting methods. This study proposes a novel time-series clustering method\nthat leverages an annealing machine. The proposed method facilitates an even\nclassification of time-series data into clusters close to each other while\nmaintaining robustness against outliers. Moreover, its applicability extends to\ntime-series images. We compared the proposed method with a standard existing\nmethod for clustering an online distributed dataset. In the existing method,\nthe distances between each data are calculated based on the Euclidean distance\nmetric, and the clustering is performed using the k-means++ method. We found\nthat both methods yielded comparable results. Furthermore, the proposed method\nwas applied to a flow measurement image dataset containing noticeable noise\nwith a signal-to-noise ratio of approximately 1. Despite a small signal\nvariation of approximately 2%, the proposed method effectively classified the\ndata without any overlap among the clusters. In contrast, the clustering\nresults by the standard existing method and the conditional image sampling\n(CIS) method, a specialized technique for flow measurement data, displayed\noverlapping clusters. Consequently, the proposed method provides better results\nthan the other two methods, demonstrating its potential as a superior\nclustering method.\n", "date": "2023-05-26", "categories": []}
{"id": "2310.09819", "title": "Comparative Analysis of Optimization Strategies for K-means Clustering\n  in Big Data Contexts: A Review", "abstract": "  This paper presents a comparative analysis of different optimization\ntechniques for the K-means algorithm in the context of big data. K-means is a\nwidely used clustering algorithm, but it can suffer from scalability issues\nwhen dealing with large datasets. The paper explores different approaches to\novercome these issues, including parallelization, approximation, and sampling\nmethods. The authors evaluate the performance of various clustering techniques\non a large number of benchmark datasets, comparing them according to the\ndominance criterion provided by the \"less is more\" approach (LIMA), i.e.,\nsimultaneously along the dimensions of speed, clustering quality, and\nsimplicity. The results show that different techniques are more suitable for\ndifferent types of datasets and provide insights into the trade-offs between\nspeed and accuracy in K-means clustering for big data. Overall, the paper\noffers a comprehensive guide for practitioners and researchers on how to\noptimize K-means for big data applications.\n", "date": "2023-10-15", "categories": []}
{"id": "2405.10987", "title": "Manifold-based Incomplete Multi-view Clustering via Bi-Consistency\n  Guidance", "abstract": "  Incomplete multi-view clustering primarily focuses on dividing unlabeled data\ninto corresponding categories with missing instances, and has received\nintensive attention due to its superiority in real applications. Considering\nthe influence of incomplete data, the existing methods mostly attempt to\nrecover data by adding extra terms. However, for the unsupervised methods, a\nsimple recovery strategy will cause errors and outlying value accumulations,\nwhich will affect the performance of the methods. Broadly, the previous methods\nhave not taken the effectiveness of recovered instances into consideration, or\ncannot flexibly balance the discrepancies between recovered data and original\ndata. To address these problems, we propose a novel method termed\nManifold-based Incomplete Multi-view clustering via Bi-consistency guidance\n(MIMB), which flexibly recovers incomplete data among various views, and\nattempts to achieve biconsistency guidance via reverse regularization. In\nparticular, MIMB adds reconstruction terms to representation learning by\nrecovering missing instances, which dynamically examines the latent consensus\nrepresentation. Moreover, to preserve the consistency information among\nmultiple views, MIMB implements a biconsistency guidance strategy with reverse\nregularization of the consensus representation and proposes a manifold\nembedding measure for exploring the hidden structure of the recovered data.\nNotably, MIMB aims to balance the importance of different views, and introduces\nan adaptive weight term for each view. Finally, an optimization algorithm with\nan alternating iteration optimization strategy is designed for final\nclustering. Extensive experimental results on 6 benchmark datasets are provided\nto confirm that MIMB can significantly obtain superior results as compared with\nseveral state-of-the-art baselines.\n", "date": "2024-05-16", "categories": []}
{"id": "2405.11801", "title": "LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph\n  Clustering", "abstract": "  Graph clustering is a fundamental problem in machine learning. Deep learning\nmethods achieve the state-of-the-art results in recent years, but they still\ncannot work without predefined cluster numbers. Such limitation motivates us to\npose a more challenging problem of graph clustering with unknown cluster\nnumber. We propose to address this problem from a fresh perspective of graph\ninformation theory (i.e., structural information). In the literature,\nstructural information has not yet been introduced to deep clustering, and its\nclassic definition falls short of discrete formulation and modeling node\nfeatures. In this work, we first formulate a differentiable structural\ninformation (DSI) in the continuous realm, accompanied by several theoretical\nresults. By minimizing DSI, we construct the optimal partitioning tree where\ndensely connected nodes in the graph tend to have the same assignment,\nrevealing the cluster structure. DSI is also theoretically presented as a new\ngraph clustering objective, not requiring the predefined cluster number.\nFurthermore, we design a neural LSEnet in the Lorentz model of hyperbolic\nspace, where we integrate node features to structural information via\nmanifold-valued graph convolution. Extensive empirical results on real graphs\nshow the superiority of our approach.\n", "date": "2024-05-20", "categories": []}
{"id": "2405.11922", "title": "Effective Clustering on Large Attributed Bipartite Graphs", "abstract": "  Attributed bipartite graphs (ABGs) are an expressive data model for\ndescribing the interactions between two sets of heterogeneous nodes that are\nassociated with rich attributes, such as customer-product purchase networks and\nauthor-paper authorship graphs. Partitioning the target node set in such graphs\ninto k disjoint clusters (referred to as k-ABGC) finds widespread use in\nvarious domains, including social network analysis, recommendation systems,\ninformation retrieval, and bioinformatics. However, the majority of existing\nsolutions towards k-ABGC either overlook attribute information or fail to\ncapture bipartite graph structures accurately, engendering severely compromised\nresult quality. The severity of these issues is accentuated in real ABGs, which\noften encompass millions of nodes and a sheer volume of attribute data,\nrendering effective k-ABGC over such graphs highly challenging.\n  In this paper, we propose TPO, an effective and efficient approach to k-ABGC\nthat achieves superb clustering performance on multiple real datasets. TPO\nobtains high clustering quality through two major contributions: (i) a novel\nformulation and transformation of the k-ABGC problem based on multi-scale\nattribute affinity specialized for capturing attribute affinities between nodes\nwith the consideration of their multi-hop connections in ABGs, and (ii) a\nhighly efficient solver that includes a suite of carefully-crafted\noptimizations for sidestepping explicit affinity matrix construction and\nfacilitating faster convergence. Extensive experiments, comparing TPO against\n19 baselines over 5 real ABGs, showcase the superior clustering quality of TPO\nmeasured against ground-truth labels. Moreover, compared to the state of the\narts, TPO is often more than 40x faster over both small and large ABGs.\n", "date": "2024-05-20", "categories": []}
{"id": "2405.12052", "title": "Parallelization of the K-Means Algorithm with Applications to Big Data\n  Clustering", "abstract": "  The K-Means clustering using LLoyd's algorithm is an iterative approach to\npartition the given dataset into K different clusters. The algorithm assigns\neach point to the cluster based on the following objective function\n  \\[\\ \\min \\Sigma_{i=1}^{n}||x_i-\\mu_{x_i}||^2\\] The serial algorithm involves\niterative steps where we compute the distance of each datapoint from the\ncentroids and assign the datapoint to the nearest centroid. This approach is\nessentially known as the expectation-maximization step. Clustering involves\nextensive computations to calculate distances at each iteration, which\nincreases as the number of data points increases. This provides scope for\nparallelism. However, we must ensure that in a parallel process, each thread\nhas access to the updated centroid value and no racing condition exists on any\ncentroid values. We will compare two different approaches in this project. The\nfirst approach is an OpenMP flat synchronous method where all processes are run\nin parallel, and we use synchronization to ensure safe updates of clusters. The\nsecond approach we adopt is a GPU based parallelization approach using OpenACC\nwherein we will try to make use of GPU architecture to parallelize chunks of\nthe algorithm to observe decreased computation time. We will analyze metrics\nsuch as speed up, efficiency,time taken with varying data points, and number of\nprocesses to compare the two approaches and understand the relative performance\nimprovement we can get.\n", "date": "2024-05-20", "categories": []}
{"id": "2405.12183", "title": "Multi-order Graph Clustering with Adaptive Node-level Weight Learning", "abstract": "  Current graph clustering methods emphasize individual node and edge con\nnections, while ignoring higher-order organization at the level of motif. Re\ncently, higher-order graph clustering approaches have been designed by motif\nbased hypergraphs. However, these approaches often suffer from hypergraph\nfragmentation issue seriously, which degrades the clustering performance\ngreatly. Moreover, real-world graphs usually contain diverse motifs, with nodes\nparticipating in multiple motifs. A key challenge is how to achieve precise\nclustering results by integrating information from multiple motifs at the node\nlevel. In this paper, we propose a multi-order graph clustering model (MOGC) to\nintegrate multiple higher-order structures and edge connections at node level.\nMOGC employs an adaptive weight learning mechanism to au tomatically adjust the\ncontributions of different motifs for each node. This not only tackles\nhypergraph fragmentation issue but enhances clustering accuracy. MOGC is\nefficiently solved by an alternating minimization algo rithm. Experiments on\nseven real-world datasets illustrate the effectiveness of MOGC.\n", "date": "2024-05-20", "categories": []}
{"id": "2301.00802", "title": "Deep Clustering of Tabular Data by Weighted Gaussian Distribution\n  Learning", "abstract": "  Deep learning methods are primarily proposed for supervised learning of\nimages or text with limited applications to clustering problems. In contrast,\ntabular data with heterogeneous features pose unique challenges in\nrepresentation learning, where deep learning has yet to replace traditional\nmachine learning. This paper addresses these challenges in developing one of\nthe first deep clustering methods for tabular data: Gaussian Cluster Embedding\nin Autoencoder Latent Space (G-CEALS). G-CEALS is an unsupervised deep\nclustering framework for learning the parameters of multivariate Gaussian\ncluster distributions by iteratively updating individual cluster weights. The\nG-CEALS method presents average rank orderings of 2.9(1.7) and 2.8(1.7) based\non clustering accuracy and adjusted Rand index (ARI) scores on sixteen tabular\ndata sets, respectively, and outperforms nine state-of-the-art clustering\nmethods. G-CEALS substantially improves clustering performance compared to\ntraditional K-means and GMM, which are still de facto methods for clustering\ntabular data. Similar computationally efficient and high-performing deep\nclustering frameworks are imperative to reap the myriad benefits of deep\nlearning on tabular data over traditional machine learning.\n", "date": "2023-01-02", "categories": []}
{"id": "2405.05619", "title": "Rectified Gaussian kernel multi-view k-means clustering", "abstract": "  In this paper, we show two new variants of multi-view k-means (MVKM)\nalgorithms to address multi-view data. The general idea is to outline the\ndistance between $h$-th view data points $x_i^h$ and $h$-th view cluster\ncenters $a_k^h$ in a different manner of centroid-based approach. Unlike other\nmethods, our proposed methods learn the multi-view data by calculating the\nsimilarity using Euclidean norm in the space of Gaussian-kernel, namely as\nmulti-view k-means with exponent distance (MVKM-ED). By simultaneously aligning\nthe stabilizer parameter $p$ and kernel coefficients $\\beta^h$, the compression\nof Gaussian-kernel based weighted distance in Euclidean norm reduce the\nsensitivity of MVKM-ED. To this end, this paper designated as Gaussian-kernel\nmulti-view k-means (GKMVKM) clustering algorithm. Numerical evaluation of five\nreal-world multi-view data demonstrates the robustness and efficiency of our\nproposed MVKM-ED and GKMVKM approaches.\n", "date": "2024-05-09", "categories": []}
{"id": "2403.05778", "title": "Spatial Clustering Approach for Vessel Path Identification", "abstract": "  This paper addresses the challenge of identifying the paths for vessels with\noperating routes of repetitive paths, partially repetitive paths, and new\npaths. We propose a spatial clustering approach for labeling the vessel paths\nby using only position information. We develop a path clustering framework\nemploying two methods: a distance-based path modeling and a likelihood\nestimation method. The former enhances the accuracy of path clustering through\nthe integration of unsupervised machine learning techniques, while the latter\nfocuses on likelihood-based path modeling and introduces segmentation for a\nmore detailed analysis. The result findings highlight the superior performance\nand efficiency of the developed approach, as both methods for clustering vessel\npaths into five classes achieve a perfect F1-score. The approach aims to offer\nvaluable insights for route planning, ultimately contributing to improving\nsafety and efficiency in maritime transportation.\n", "date": "2024-03-09", "categories": []}
{"id": "2405.04854", "title": "Explaining Clustering of Ecological Momentary Assessment Data Through\n  Temporal and Feature Attention", "abstract": "  In the field of psychopathology, Ecological Momentary Assessment (EMA)\nstudies offer rich individual data on psychopathology-relevant variables (e.g.,\naffect, behavior, etc) in real-time. EMA data is collected dynamically,\nrepresented as complex multivariate time series (MTS). Such information is\ncrucial for a better understanding of mental disorders at the individual- and\ngroup-level. More specifically, clustering individuals in EMA data facilitates\nuncovering and studying the commonalities as well as variations of groups in\nthe population. Nevertheless, since clustering is an unsupervised task and true\nEMA grouping is not commonly available, the evaluation of clustering is quite\nchallenging. An important aspect of evaluation is clustering explainability.\nThus, this paper proposes an attention-based interpretable framework to\nidentify the important time-points and variables that play primary roles in\ndistinguishing between clusters. A key part of this study is to examine ways to\nanalyze, summarize, and interpret the attention weights as well as evaluate the\npatterns underlying the important segments of the data that differentiate\nacross clusters. To evaluate the proposed approach, an EMA dataset of 187\nindividuals grouped in 3 clusters is used for analyzing the derived\nattention-based importance attributes. More specifically, this analysis\nprovides the distinct characteristics at the cluster-, feature- and individual\nlevel. Such clustering explanations could be beneficial for generalizing\nexisting concepts of mental disorders, discovering new insights, and even\nenhancing our knowledge at an individual level.\n", "date": "2024-05-08", "categories": []}
{"id": "2405.04881", "title": "G\\\"odel Number based Clustering Algorithm with Decimal First Degree\n  Cellular Automata", "abstract": "  In this paper, a decimal first degree cellular automata (FDCA) based\nclustering algorithm is proposed where clusters are created based on\nreachability. Cyclic spaces are created and configurations which are in the\nsame cycle are treated as the same cluster. Here, real-life data objects are\nencoded into decimal strings using G\\\"odel number based encoding. The benefits\nof the scheme is, it reduces the encoded string length while maintaining the\nfeatures properties. Candidate CA rules are identified based on some\ntheoretical criteria such as self-replication and information flow. An\niterative algorithm is developed to generate the desired number of clusters\nover three stages. The results of the clustering are evaluated based on\nbenchmark clustering metrics such as Silhouette score, Davis Bouldin, Calinski\nHarabasz and Dunn Index. In comparison with the existing state-of-the-art\nclustering algorithms, our proposed algorithm gives better performance.\n", "date": "2024-05-08", "categories": []}
{"id": "2405.05015", "title": "Concrete Dense Network for Long-Sequence Time Series Clustering", "abstract": "  Time series clustering is fundamental in data analysis for discovering\ntemporal patterns. Despite recent advancements, learning cluster-friendly\nrepresentations is still challenging, particularly with long and complex time\nseries. Deep temporal clustering methods have been trying to integrate the\ncanonical k-means into end-to-end training of neural networks but fall back on\nsurrogate losses due to the non-differentiability of the hard cluster\nassignment, yielding sub-optimal solutions. In addition, the autoregressive\nstrategy used in the state-of-the-art RNNs is subject to error accumulation and\nslow training, while recent research findings have revealed that Transformers\nare less effective due to time points lacking semantic meaning, to the\npermutation invariance of attention that discards the chronological order and\nhigh computation cost. In light of these observations, we present LoSTer which\nis a novel dense autoencoder architecture for the long-sequence time series\nclustering problem (LSTC) capable of optimizing the k-means objective via the\nGumbel-softmax reparameterization trick and designed specifically for accurate\nand fast clustering of long time series. Extensive experiments on numerous\nbenchmark datasets and two real-world applications prove the effectiveness of\nLoSTer over state-of-the-art RNNs and Transformer-based deep clustering\nmethods.\n", "date": "2024-05-08", "categories": []}
{"id": "2405.03327", "title": "Clustering of Disease Trajectories with Explainable Machine Learning: A\n  Case Study on Postoperative Delirium Phenotypes", "abstract": "  The identification of phenotypes within complex diseases or syndromes is a\nfundamental component of precision medicine, which aims to adapt healthcare to\nindividual patient characteristics. Postoperative delirium (POD) is a complex\nneuropsychiatric condition with significant heterogeneity in its clinical\nmanifestations and underlying pathophysiology. We hypothesize that POD\ncomprises several distinct phenotypes, which cannot be directly observed in\nclinical practice. Identifying these phenotypes could enhance our understanding\nof POD pathogenesis and facilitate the development of targeted prevention and\ntreatment strategies. In this paper, we propose an approach that combines\nsupervised machine learning for personalized POD risk prediction with\nunsupervised clustering techniques to uncover potential POD phenotypes. We\nfirst demonstrate our approach using synthetic data, where we simulate patient\ncohorts with predefined phenotypes based on distinct sets of informative\nfeatures. We aim to mimic any clinical disease with our synthetic data\ngeneration method. By training a predictive model and applying SHAP, we show\nthat clustering patients in the SHAP feature importance space successfully\nrecovers the true underlying phenotypes, outperforming clustering in the raw\nfeature space. We then present a case study using real-world data from a cohort\nof elderly surgical patients. The results showcase the utility of our approach\nin uncovering clinically relevant subtypes of complex disorders like POD,\npaving the way for more precise and personalized treatment strategies.\n", "date": "2024-05-06", "categories": []}
{"id": "2405.00937", "title": "New bounds on the cohesion of complete-link and other linkage methods\n  for agglomeration clustering", "abstract": "  Linkage methods are among the most popular algorithms for hierarchical\nclustering. Despite their relevance the current knowledge regarding the quality\nof the clustering produced by these methods is limited. Here, we improve the\ncurrently available bounds on the maximum diameter of the clustering obtained\nby complete-link for metric spaces.\n  One of our new bounds, in contrast to the existing ones, allows us to\nseparate complete-link from single-link in terms of approximation for the\ndiameter, which corroborates the common perception that the former is more\nsuitable than the latter when the goal is producing compact clusters.\n  We also show that our techniques can be employed to derive upper bounds on\nthe cohesion of a class of linkage methods that includes the quite popular\naverage-link.\n", "date": "2024-05-02", "categories": []}
{"id": "2405.00988", "title": "Context-Aware Clustering using Large Language Models", "abstract": "  Despite the remarkable success of Large Language Models (LLMs) in text\nunderstanding and generation, their potential for text clustering tasks remains\nunderexplored. We observed that powerful closed-source LLMs provide good\nquality clusterings of entity sets but are not scalable due to the massive\ncompute power required and the associated costs. Thus, we propose CACTUS\n(Context-Aware ClusTering with aUgmented triplet losS), a systematic approach\nthat leverages open-source LLMs for efficient and effective supervised\nclustering of entity subsets, particularly focusing on text-based entities.\nExisting text clustering methods fail to effectively capture the context\nprovided by the entity subset. Moreover, though there are several language\nmodeling based approaches for clustering, very few are designed for the task of\nsupervised clustering. This paper introduces a novel approach towards\nclustering entity subsets using LLMs by capturing context via a scalable\ninter-entity attention mechanism. We propose a novel augmented triplet loss\nfunction tailored for supervised clustering, which addresses the inherent\nchallenges of directly applying the triplet loss to this problem. Furthermore,\nwe introduce a self-supervised clustering task based on text augmentation\ntechniques to improve the generalization of our model. For evaluation, we\ncollect ground truth clusterings from a closed-source LLM and transfer this\nknowledge to an open-source LLM under the supervised clustering framework,\nallowing a faster and cheaper open-source model to perform the same task.\nExperiments on various e-commerce query and product clustering datasets\ndemonstrate that our proposed approach significantly outperforms existing\nunsupervised and supervised baselines under various external clustering\nevaluation metrics.\n", "date": "2024-05-02", "categories": []}
{"id": "2310.12153", "title": "Probabilistic Sampling of Balanced K-Means using Adiabatic Quantum\n  Computing", "abstract": "  Adiabatic quantum computing (AQC) is a promising approach for discrete and\noften NP-hard optimization problems. Current AQCs allow to implement problems\nof research interest, which has sparked the development of quantum\nrepresentations for many computer vision tasks. Despite requiring multiple\nmeasurements from the noisy AQC, current approaches only utilize the best\nmeasurement, discarding information contained in the remaining ones. In this\nwork, we explore the potential of using this information for probabilistic\nbalanced k-means clustering. Instead of discarding non-optimal solutions, we\npropose to use them to compute calibrated posterior probabilities with little\nadditional compute cost. This allows us to identify ambiguous solutions and\ndata points, which we demonstrate on a D-Wave AQC on synthetic tasks and real\nvisual data.\n", "date": "2023-10-18", "categories": []}
{"id": "2304.06145", "title": "R-Shiny Applications for Local Clustering to be Included in the\n  growclusters for R Package", "abstract": "  growclusters for R is a package that estimates a partition structure for\nmultivariate data. It does this by implementing a hierarchical version of\nk-means clustering that accounts for possible known dependencies in a\ncollection of datasets, where each set draws its cluster means from a single,\nglobal partition. Each component data set in the collection corresponds to a\nknown group in the data. This paper focuses on R Shiny applications that\nimplement the clustering methodology and simulate data sets with known group\nstructures. These Shiny applications implement novel ways of visualizing the\nresults of the clustering. These visualizations include scatterplots of\nindividual data sets in the context of the entire collection and cluster\ndistributions versus component (or sub-domain) datasets. Data obtained from a\ncollection of 2000-2013 articles from the Bureau of Labor Statistics (BLS)\nMonthly Labor Review (MLR) will be used to illustrate the R-Shiny applications.\nHere, the known grouping in the collection is the year of publication.\n", "date": "2023-04-12", "categories": []}
{"id": "2404.19134", "title": "Evaluating Deep Clustering Algorithms on Non-Categorical 3D CAD Models", "abstract": "  We introduce the first work on benchmarking and evaluating deep clustering\nalgorithms on large-scale non-categorical 3D CAD models. We first propose a\nworkflow to allow expert mechanical engineers to efficiently annotate 252,648\ncarefully sampled pairwise CAD model similarities, from a subset of the ABC\ndataset with 22,968 shapes. Using seven baseline deep clustering methods, we\nthen investigate the fundamental challenges of evaluating clustering methods\nfor non-categorical data. Based on these challenges, we propose a novel and\nviable ensemble-based clustering comparison approach. This work is the first to\ndirectly target the underexplored area of deep clustering algorithms for 3D\nshapes, and we believe it will be an important building block to analyze and\nutilize the massive 3D shape collections that are starting to appear in deep\ngeometric computing.\n", "date": "2024-04-29", "categories": []}
{"id": "2404.01341", "title": "Block-Diagonal Guided DBSCAN Clustering", "abstract": "  Cluster analysis plays a crucial role in database mining, and one of the most\nwidely used algorithms in this field is DBSCAN. However, DBSCAN has several\nlimitations, such as difficulty in handling high-dimensional large-scale data,\nsensitivity to input parameters, and lack of robustness in producing clustering\nresults. This paper introduces an improved version of DBSCAN that leverages the\nblock-diagonal property of the similarity graph to guide the clustering\nprocedure of DBSCAN. The key idea is to construct a graph that measures the\nsimilarity between high-dimensional large-scale data points and has the\npotential to be transformed into a block-diagonal form through an unknown\npermutation, followed by a cluster-ordering procedure to generate the desired\npermutation. The clustering structure can be easily determined by identifying\nthe diagonal blocks in the permuted graph. We propose a gradient descent-based\nmethod to solve the proposed problem. Additionally, we develop a DBSCAN-based\npoints traversal algorithm that identifies clusters with high densities in the\ngraph and generates an augmented ordering of clusters. The block-diagonal\nstructure of the graph is then achieved through permutation based on the\ntraversal order, providing a flexible foundation for both automatic and\ninteractive cluster analysis. We introduce a split-and-refine algorithm to\nautomatically search for all diagonal blocks in the permuted graph with\ntheoretically optimal guarantees under specific cases. We extensively evaluate\nour proposed approach on twelve challenging real-world benchmark clustering\ndatasets and demonstrate its superior performance compared to the\nstate-of-the-art clustering method on every dataset.\n", "date": "2024-03-31", "categories": []}
{"id": "2404.17894", "title": "Unpaired Multi-view Clustering via Reliable View Guidance", "abstract": "  This paper focuses on unpaired multi-view clustering (UMC), a challenging\nproblem where paired observed samples are unavailable across multiple views.\nThe goal is to perform effective joint clustering using the unpaired observed\nsamples in all views. In incomplete multi-view clustering, existing methods\ntypically rely on sample pairing between views to capture their complementary.\nHowever, that is not applicable in the case of UMC. Hence, we aim to extract\nthe consistent cluster structure across views. In UMC, two challenging issues\narise: uncertain cluster structure due to lack of label and uncertain pairing\nrelationship due to absence of paired samples. We assume that the view with a\ngood cluster structure is the reliable view, which acts as a supervisor to\nguide the clustering of the other views. With the guidance of reliable views, a\nmore certain cluster structure of these views is obtained while achieving\nalignment between reliable views and other views. Then we propose Reliable view\nGuidance with one reliable view (RG-UMC) and multiple reliable views (RGs-UMC)\nfor UMC. Specifically, we design alignment modules with one reliable view and\nmultiple reliable views, respectively, to adaptively guide the optimization\nprocess. Also, we utilize the compactness module to enhance the relationship of\nsamples within the same cluster. Meanwhile, an orthogonal constraint is applied\nto latent representation to obtain discriminate features. Extensive experiments\nshow that both RG-UMC and RGs-UMC outperform the best state-of-the-art method\nby an average of 24.14\\% and 29.42\\% in NMI, respectively.\n", "date": "2024-04-27", "categories": []}
{"id": "2306.05272", "title": "Image Clustering via the Principle of Rate Reduction in the Age of\n  Pretrained Models", "abstract": "  The advent of large pre-trained models has brought about a paradigm shift in\nboth visual representation learning and natural language processing. However,\nclustering unlabeled images, as a fundamental and classic machine learning\nproblem, still lacks an effective solution, particularly for large-scale\ndatasets. In this paper, we propose a novel image clustering pipeline that\nleverages the powerful feature representation of large pre-trained models such\nas CLIP and cluster images effectively and efficiently at scale. We first\ndeveloped a novel algorithm to estimate the number of clusters in a given\ndataset. We then show that the pre-trained features are significantly more\nstructured by further optimizing the rate reduction objective. The resulting\nfeatures may significantly improve the clustering accuracy, e.g., from 57\\% to\n66\\% on ImageNet-1k. Furthermore, by leveraging CLIP's multimodality bridge\nbetween image and text, we develop a simple yet effective self-labeling\nalgorithm that produces meaningful captions for the clusters. Through extensive\nexperiments, we show that our pipeline works well on standard datasets such as\nCIFAR-10, CIFAR-100, and ImageNet-1k. It also extends to datasets that are not\ncurated for clustering, such as LAION-Aesthetics and WikiArts. We released the\ncode in https://github.com/LeslieTrue/CPP.\n", "date": "2023-06-08", "categories": []}
{"id": "2307.09055", "title": "Robust Data Clustering with Outliers via Transformed Tensor Low-Rank\n  Representation", "abstract": "  Recently, tensor low-rank representation (TLRR) has become a popular tool for\ntensor data recovery and clustering, due to its empirical success and\ntheoretical guarantees. However, existing TLRR methods consider Gaussian or\ngross sparse noise, inevitably leading to performance degradation when the\ntensor data are contaminated by outliers or sample-specific corruptions. This\npaper develops an outlier-robust tensor low-rank representation (OR-TLRR)\nmethod that provides outlier detection and tensor data clustering\nsimultaneously based on the t-SVD framework. For tensor observations with\narbitrary outlier corruptions, OR-TLRR has provable performance guarantee for\nexactly recovering the row space of clean data and detecting outliers under\nmild conditions. Moreover, an extension of OR-TLRR is proposed to handle the\ncase when parts of the data are missing. Finally, extensive experimental\nresults on synthetic and real data demonstrate the effectiveness of the\nproposed algorithms. We release our code at\nhttps://github.com/twugithub/2024-AISTATS-ORTLRR.\n", "date": "2023-07-18", "categories": []}
{"id": "2404.15967", "title": "Interpretable Clustering with the Distinguishability Criterion", "abstract": "  Cluster analysis is a popular unsupervised learning tool used in many\ndisciplines to identify heterogeneous sub-populations within a sample. However,\nvalidating cluster analysis results and determining the number of clusters in a\ndata set remains an outstanding problem. In this work, we present a global\ncriterion called the Distinguishability criterion to quantify the separability\nof identified clusters and validate inferred cluster configurations. Our\ncomputational implementation of the Distinguishability criterion corresponds to\nthe Bayes risk of a randomized classifier under the 0-1 loss. We propose a\ncombined loss function-based computational framework that integrates the\nDistinguishability criterion with many commonly used clustering procedures,\nsuch as hierarchical clustering, k-means, and finite mixture models. We present\nthese new algorithms as well as the results from comprehensive data analysis\nbased on simulation studies and real data applications.\n", "date": "2024-04-24", "categories": []}
{"id": "2404.16131", "title": "Combinatorial Approximations for Cluster Deletion: Simpler, Faster, and\n  Better", "abstract": "  Cluster deletion is an NP-hard graph clustering objective with applications\nin computational biology and social network analysis, where the goal is to\ndelete a minimum number of edges to partition a graph into cliques. We first\nprovide a tighter analysis of two previous approximation algorithms, improving\ntheir approximation guarantees from 4 to 3. Moreover, we show that both\nalgorithms can be derandomized in a surprisingly simple way, by greedily taking\na vertex of maximum degree in an auxiliary graph and forming a cluster around\nit. One of these algorithms relies on solving a linear program. Our final\ncontribution is to design a new and purely combinatorial approach for doing so\nthat is far more scalable in theory and practice.\n", "date": "2024-04-24", "categories": []}
{"id": "2404.15655", "title": "Multi-Modal Proxy Learning Towards Personalized Visual Multiple\n  Clustering", "abstract": "  Multiple clustering has gained significant attention in recent years due to\nits potential to reveal multiple hidden structures of data from different\nperspectives. The advent of deep multiple clustering techniques has notably\nadvanced the performance by uncovering complex patterns and relationships\nwithin large datasets. However, a major challenge arises as users often do not\nneed all the clusterings that algorithms generate, and figuring out the one\nneeded requires a substantial understanding of each clustering result.\nTraditionally, aligning a user's brief keyword of interest with the\ncorresponding vision components was challenging, but the emergence of\nmulti-modal and large language models (LLMs) has begun to bridge this gap. In\nresponse, given unlabeled target visual data, we propose Multi-MaP, a novel\nmethod employing a multi-modal proxy learning process. It leverages CLIP\nencoders to extract coherent text and image embeddings, with GPT-4 integrating\nusers' interests to formulate effective textual contexts. Moreover, reference\nword constraint and concept-level constraint are designed to learn the optimal\ntext proxy according to the user's interest. Multi-MaP not only adeptly\ncaptures a user's interest via a keyword but also facilitates identifying\nrelevant clusterings. Our extensive experiments show that Multi-MaP\nconsistently outperforms state-of-the-art methods in all benchmark\nmulti-clustering vision tasks. Our code is available at\nhttps://github.com/Alexander-Yao/Multi-MaP.\n", "date": "2024-04-24", "categories": []}
{"id": "2310.19454", "title": "MMM and MMMSynth: Clustering of heterogeneous tabular data, and\n  synthetic data generation", "abstract": "  We provide new algorithms for two tasks relating to heterogeneous tabular\ndatasets: clustering, and synthetic data generation. Tabular datasets typically\nconsist of heterogeneous data types (numerical, ordinal, categorical) in\ncolumns, but may also have hidden cluster structure in their rows: for example,\nthey may be drawn from heterogeneous (geographical, socioeconomic,\nmethodological) sources, such that the outcome variable they describe (such as\nthe presence of a disease) may depend not only on the other variables but on\nthe cluster context. Moreover, sharing of biomedical data is often hindered by\npatient confidentiality laws, and there is current interest in algorithms to\ngenerate synthetic tabular data from real data, for example via deep learning.\n  We demonstrate a novel EM-based clustering algorithm, MMM (``Madras Mixture\nModel''), that outperforms standard algorithms in determining clusters in\nsynthetic heterogeneous data, and recovers structure in real data. Based on\nthis, we demonstrate a synthetic tabular data generation algorithm, MMMsynth,\nthat pre-clusters the input data, and generates cluster-wise synthetic data\nassuming cluster-specific data distributions for the input columns. We\nbenchmark this algorithm by testing the performance of standard ML algorithms\nwhen they are trained on synthetic data and tested on real published datasets.\nOur synthetic data generation algorithm outperforms other literature\ntabular-data generators, and approaches the performance of training purely with\nreal data.\n", "date": "2023-10-30", "categories": []}
{"id": "2312.02407", "title": "Robust Clustering using Hyperdimensional Computing", "abstract": "  This paper addresses the clustering of data in the hyperdimensional computing\n(HDC) domain. In prior work, an HDC-based clustering framework, referred to as\nHDCluster, has been proposed. However, the performance of the existing\nHDCluster is not robust. The performance of HDCluster is degraded as the\nhypervectors for the clusters are chosen at random during the initialization\nstep. To overcome this bottleneck, we assign the initial cluster hypervectors\nby exploring the similarity of the encoded data, referred to as \\textit{query}\nhypervectors. Intra-cluster hypervectors have a higher similarity than\ninter-cluster hypervectors. Harnessing the similarity results among query\nhypervectors, this paper proposes four HDC-based clustering algorithms:\nsimilarity-based k-means, equal bin-width histogram, equal bin-height\nhistogram, and similarity-based affinity propagation. Experimental results\nillustrate that: (i) Compared to the existing HDCluster, our proposed HDC-based\nclustering algorithms can achieve better accuracy, more robust performance,\nfewer iterations, and less execution time. Similarity-based affinity\npropagation outperforms the other three HDC-based clustering algorithms on\neight datasets by 2~38% in clustering accuracy. (ii) Even for one-pass\nclustering, i.e., without any iterative update of the cluster hypervectors, our\nproposed algorithms can provide more robust clustering accuracy than HDCluster.\n(iii) Over eight datasets, five out of eight can achieve higher or comparable\naccuracy when projected onto the hyperdimensional space. Traditional clustering\nis more desirable than HDC when the number of clusters, $k$, is large.\n", "date": "2023-12-05", "categories": []}
{"id": "2404.12246", "title": "Blind Localization and Clustering of Anomalies in Textures", "abstract": "  Anomaly detection and localization in images is a growing field in computer\nvision. In this area, a seemingly understudied problem is anomaly clustering,\ni.e., identifying and grouping different types of anomalies in a fully\nunsupervised manner. In this work, we propose a novel method for clustering\nanomalies in largely stationary images (textures) in a blind setting. That is,\nthe input consists of normal and anomalous images without distinction and\nwithout labels. What contributes to the difficulty of the task is that\nanomalous regions are often small and may present only subtle changes in\nappearance, which can be easily overshadowed by the genuine variance in the\ntexture. Moreover, each anomaly type may have a complex appearance\ndistribution. We introduce a novel scheme for solving this task using a\ncombination of blind anomaly localization and contrastive learning. By\nidentifying the anomalous regions with high fidelity, we can restrict our focus\nto those regions of interest; then, contrastive learning is employed to\nincrease the separability of different anomaly types and reduce the intra-class\nvariation. Our experiments show that the proposed solution yields significantly\nbetter results compared to prior work, setting a new state of the art. Project\npage: https://reality.tf.fau.de/pub/ardelean2024blind.html.\n", "date": "2024-04-18", "categories": []}
{"id": "2211.05337", "title": "Spatiotemporal k-means", "abstract": "  Spatiotemporal data is increasingly available due to emerging sensor and data\nacquisition technologies that track moving objects. Spatiotemporal clustering\naddresses the need to efficiently discover patterns and trends in moving object\nbehavior without human supervision. One application of interest is the\ndiscovery of moving clusters, where clusters have a static identity, but their\nlocation and content can change over time. We propose a two phase\nspatiotemporal clustering method called spatiotemporal k-means (STkM) that is\nable to analyze the multi-scale relationships within spatiotemporal data. By\noptimizing an objective function that is unified over space and time, the\nmethod can track dynamic clusters at both short and long timescales with\nminimal parameter tuning and no post-processing. We begin by proposing a\ntheoretical generating model for spatiotemporal data and prove the efficacy of\nSTkM in this setting. We then evaluate STkM on a recently developed collective\nanimal behavior benchmark dataset and show that STkM outperforms baseline\nmethods in the low-data limit, which is a critical regime of consideration in\nmany emerging applications. Finally, we showcase how STkM can be extended to\nmore complex machine learning tasks, particularly unsupervised region of\ninterest detection and tracking in videos.\n", "date": "2022-11-10", "categories": []}
{"id": "2305.18436", "title": "Statistically Optimal K-means Clustering via Nonnegative Low-rank\n  Semidefinite Programming", "abstract": "  $K$-means clustering is a widely used machine learning method for identifying\npatterns in large datasets. Recently, semidefinite programming (SDP)\nrelaxations have been proposed for solving the $K$-means optimization problem,\nwhich enjoy strong statistical optimality guarantees. However, the prohibitive\ncost of implementing an SDP solver renders these guarantees inaccessible to\npractical datasets. In contrast, nonnegative matrix factorization (NMF) is a\nsimple clustering algorithm widely used by machine learning practitioners, but\nit lacks a solid statistical underpinning and theoretical guarantees. In this\npaper, we consider an NMF-like algorithm that solves a nonnegative low-rank\nrestriction of the SDP-relaxed $K$-means formulation using a nonconvex\nBurer--Monteiro factorization approach. The resulting algorithm is as simple\nand scalable as state-of-the-art NMF algorithms while also enjoying the same\nstrong statistical optimality guarantees as the SDP. In our experiments, we\nobserve that our algorithm achieves significantly smaller mis-clustering errors\ncompared to the existing state-of-the-art while maintaining scalability.\n", "date": "2023-05-29", "categories": []}
{"id": "2404.09115", "title": "GCC: Generative Calibration Clustering", "abstract": "  Deep clustering as an important branch of unsupervised representation\nlearning focuses on embedding semantically similar samples into the identical\nfeature space. This core demand inspires the exploration of contrastive\nlearning and subspace clustering. However, these solutions always rely on the\nbasic assumption that there are sufficient and category-balanced samples for\ngenerating valid high-level representation. This hypothesis actually is too\nstrict to be satisfied for real-world applications. To overcome such a\nchallenge, the natural strategy is utilizing generative models to augment\nconsiderable instances. How to use these novel samples to effectively fulfill\nclustering performance improvement is still difficult and under-explored. In\nthis paper, we propose a novel Generative Calibration Clustering (GCC) method\nto delicately incorporate feature learning and augmentation into clustering\nprocedure. First, we develop a discriminative feature alignment mechanism to\ndiscover intrinsic relationship across real and generated samples. Second, we\ndesign a self-supervised metric learning to generate more reliable cluster\nassignment to boost the conditional diffusion generation. Extensive\nexperimental results on three benchmarks validate the effectiveness and\nadvantage of our proposed method over the state-of-the-art methods.\n", "date": "2024-04-14", "categories": []}
{"id": "2404.09451", "title": "Contrastive Mean-Shift Learning for Generalized Category Discovery", "abstract": "  We address the problem of generalized category discovery (GCD) that aims to\npartition a partially labeled collection of images; only a small part of the\ncollection is labeled and the total number of target classes is unknown. To\naddress this generalized image clustering problem, we revisit the mean-shift\nalgorithm, i.e., a classic, powerful technique for mode seeking, and\nincorporate it into a contrastive learning framework. The proposed method,\ndubbed Contrastive Mean-Shift (CMS) learning, trains an image encoder to\nproduce representations with better clustering properties by an iterative\nprocess of mean shift and contrastive update. Experiments demonstrate that our\nmethod, both in settings with and without the total number of clusters being\nknown, achieves state-of-the-art performance on six public GCD benchmarks\nwithout bells and whistles.\n", "date": "2024-04-15", "categories": []}
{"id": "2305.10738", "title": "Deep Temporal Graph Clustering", "abstract": "  Deep graph clustering has recently received significant attention due to its\nability to enhance the representation learning capabilities of models in\nunsupervised scenarios. Nevertheless, deep clustering for temporal graphs,\nwhich could capture crucial dynamic interaction information, has not been fully\nexplored. It means that in many clustering-oriented real-world scenarios,\ntemporal graphs can only be processed as static graphs. This not only causes\nthe loss of dynamic information but also triggers huge computational\nconsumption. To solve the problem, we propose a general framework for deep\nTemporal Graph Clustering called TGC, which introduces deep clustering\ntechniques to suit the interaction sequence-based batch-processing pattern of\ntemporal graphs. In addition, we discuss differences between temporal graph\nclustering and static graph clustering from several levels. To verify the\nsuperiority of the proposed framework TGC, we conduct extensive experiments.\nThe experimental results show that temporal graph clustering enables more\nflexibility in finding a balance between time and space requirements, and our\nframework can effectively improve the performance of existing temporal graph\nlearning methods. The code is released:\nhttps://github.com/MGitHubL/Deep-Temporal-Graph-Clustering.\n", "date": "2023-05-18", "categories": []}
{"id": "2403.09107", "title": "S^2MVTC: a Simple yet Efficient Scalable Multi-View Tensor Clustering", "abstract": "  Anchor-based large-scale multi-view clustering has attracted considerable\nattention for its effectiveness in handling massive datasets. However, current\nmethods mainly seek the consensus embedding feature for clustering by exploring\nglobal correlations between anchor graphs or projection matrices.In this paper,\nwe propose a simple yet efficient scalable multi-view tensor clustering\n(S^2MVTC) approach, where our focus is on learning correlations of embedding\nfeatures within and across views. Specifically, we first construct the\nembedding feature tensor by stacking the embedding features of different views\ninto a tensor and rotating it. Additionally, we build a novel tensor\nlow-frequency approximation (TLFA) operator, which incorporates graph\nsimilarity into embedding feature learning, efficiently achieving smooth\nrepresentation of embedding features within different views. Furthermore,\nconsensus constraints are applied to embedding features to ensure inter-view\nsemantic consistency. Experimental results on six large-scale multi-view\ndatasets demonstrate that S^2MVTC significantly outperforms state-of-the-art\nalgorithms in terms of clustering performance and CPU execution time,\nespecially when handling massive data. The code of S^2MVTC is publicly\navailable at https://github.com/longzhen520/S2MVTC.\n", "date": "2024-03-14", "categories": []}
{"id": "2404.07962", "title": "Live and Learn: Continual Action Clustering with Incremental Views", "abstract": "  Multi-view action clustering leverages the complementary information from\ndifferent camera views to enhance the clustering performance. Although existing\napproaches have achieved significant progress, they assume all camera views are\navailable in advance, which is impractical when the camera view is incremental\nover time. Besides, learning the invariant information among multiple camera\nviews is still a challenging issue, especially in continual learning scenario.\nAiming at these problems, we propose a novel continual action clustering (CAC)\nmethod, which is capable of learning action categories in a continual learning\nmanner. To be specific, we first devise a category memory library, which\ncaptures and stores the learned categories from historical views. Then, as a\nnew camera view arrives, we only need to maintain a consensus partition matrix,\nwhich can be updated by leveraging the incoming new camera view rather than\nkeeping all of them. Finally, a three-step alternate optimization is proposed,\nin which the category memory library and consensus partition matrix are\noptimized. The empirical experimental results on 6 realistic multi-view action\ncollections demonstrate the excellent clustering performance and time/space\nefficiency of the CAC compared with 15 state-of-the-art baselines.\n", "date": "2024-03-23", "categories": []}
{"id": "2310.07166", "title": "Anchor-based Multi-view Subspace Clustering with Hierarchical Feature\n  Descent", "abstract": "  Multi-view clustering has attracted growing attention owing to its\ncapabilities of aggregating information from various sources and its promising\nhorizons in public affairs. Up till now, many advanced approaches have been\nproposed in recent literature. However, there are several ongoing difficulties\nto be tackled. One common dilemma occurs while attempting to align the features\nof different views. {Moreover, due to the fact that many existing multi-view\nclustering algorithms stem from spectral clustering, this results to cubic time\ncomplexity w.r.t. the number of dataset. However, we propose Anchor-based\nMulti-view Subspace Clustering with Hierarchical Feature Descent(MVSC-HFD) to\ntackle the discrepancy among views through hierarchical feature descent and\nproject to a common subspace( STAGE 1), which reveals dependency of different\nviews. We further reduce the computational complexity to linear time cost\nthrough a unified sampling strategy in the common subspace( STAGE 2), followed\nby anchor-based subspace clustering to learn the bipartite graph collectively(\nSTAGE 3). }Extensive experimental results on public benchmark datasets\ndemonstrate that our proposed model consistently outperforms the\nstate-of-the-art techniques.\n", "date": "2023-10-11", "categories": []}
{"id": "2402.15731", "title": "Clustering in Dynamic Environments: A Framework for Benchmark Dataset\n  Generation With Heterogeneous Changes", "abstract": "  Clustering in dynamic environments is of increasing importance, with broad\napplications ranging from real-time data analysis and online unsupervised\nlearning to dynamic facility location problems. While meta-heuristics have\nshown promising effectiveness in static clustering tasks, their application for\ntracking optimal clustering solutions or robust clustering over time in dynamic\nenvironments remains largely underexplored. This is partly due to a lack of\ndynamic datasets with diverse, controllable, and realistic dynamic\ncharacteristics, hindering systematic performance evaluations of clustering\nalgorithms in various dynamic scenarios. This deficiency leads to a gap in our\nunderstanding and capability to effectively design algorithms for clustering in\ndynamic environments. To bridge this gap, this paper introduces the Dynamic\nDataset Generator (DDG). DDG features multiple dynamic Gaussian components\nintegrated with a range of heterogeneous, local, and global changes. These\nchanges vary in spatial and temporal severity, patterns, and domain of\ninfluence, providing a comprehensive tool for simulating a wide range of\ndynamic scenarios.\n", "date": "2024-02-24", "categories": []}
{"id": "2404.04403", "title": "Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow\n  Modeling", "abstract": "  Tensor clustering has become an important topic, specifically in\nspatio-temporal modeling, due to its ability to cluster spatial modes (e.g.,\nstations or road segments) and temporal modes (e.g., time of the day or day of\nthe week). Our motivating example is from subway passenger flow modeling, where\nsimilarities between stations are commonly found. However, the challenges lie\nin the innate high-dimensionality of tensors and also the potential existence\nof anomalies. This is because the three tasks, i.e., dimension reduction,\nclustering, and anomaly decomposition, are inter-correlated to each other, and\ntreating them in a separate manner will render a suboptimal performance. Thus,\nin this work, we design a tensor-based subspace clustering and anomaly\ndecomposition technique for simultaneously outlier-robust dimension reduction\nand clustering for high-dimensional tensors. To achieve this, a novel low-rank\nrobust subspace clustering decomposition model is proposed by combining Tucker\ndecomposition, sparse anomaly decomposition, and subspace clustering. An\neffective algorithm based on Block Coordinate Descent is proposed to update the\nparameters. Prudent experiments prove the effectiveness of the proposed\nframework via the simulation study, with a gain of +25% clustering accuracy\nthan benchmark methods in a hard case. The interrelations of the three tasks\nare also analyzed via ablation studies, validating the interrelation\nassumption. Moreover, a case study in the station clustering based on real\npassenger flow data is conducted, with quite valuable insights discovered.\n", "date": "2024-04-05", "categories": []}
{"id": "2404.05211", "title": "Multi-level Graph Subspace Contrastive Learning for Hyperspectral Image\n  Clustering", "abstract": "  Hyperspectral image (HSI) clustering is a challenging task due to its high\ncomplexity. Despite subspace clustering shows impressive performance for HSI,\ntraditional methods tend to ignore the global-local interaction in HSI data. In\nthis study, we proposed a multi-level graph subspace contrastive learning\n(MLGSC) for HSI clustering. The model is divided into the following main parts.\nGraph convolution subspace construction: utilizing spectral and texture\nfeautures to construct two graph convolution views. Local-global graph\nrepresentation: local graph representations were obtained by step-by-step\nconvolutions and a more representative global graph representation was obtained\nusing an attention-based pooling strategy. Multi-level graph subspace\ncontrastive learning: multi-level contrastive learning was conducted to obtain\nlocal-global joint graph representations, to improve the consistency of the\npositive samples between views, and to obtain more robust graph embeddings.\nSpecifically, graph-level contrastive learning is used to better learn global\nrepresentations of HSI data. Node-level intra-view and inter-view contrastive\nlearning is designed to learn joint representations of local regions of HSI.\nThe proposed model is evaluated on four popular HSI datasets: Indian Pines,\nPavia University, Houston, and Xu Zhou. The overall accuracies are 97.75%,\n99.96%, 92.28%, and 95.73%, which significantly outperforms the current\nstate-of-the-art clustering methods.\n", "date": "2024-04-08", "categories": []}
{"id": "2404.05363", "title": "A parameter-free clustering algorithm for missing datasets", "abstract": "  Missing datasets, in which some objects have missing values in certain\ndimensions, are prevalent in the Real-world. Existing clustering algorithms for\nmissing datasets first impute the missing values and then perform clustering.\nHowever, both the imputation and clustering processes require input parameters.\nToo many input parameters inevitably increase the difficulty of obtaining\naccurate clustering results. Although some studies have shown that decision\ngraphs can replace the input parameters of clustering algorithms, current\ndecision graphs require equivalent dimensions among objects and are therefore\nnot suitable for missing datasets. To this end, we propose a Single-Dimensional\nClustering algorithm, i.e., SDC. SDC, which removes the imputation process and\nadapts the decision graph to the missing datasets by splitting dimension and\npartition intersection fusion, can obtain valid clustering results on the\nmissing datasets without input parameters. Experiments demonstrate that, across\nthree evaluation metrics, SDC outperforms baseline algorithms by at least\n13.7%(NMI), 23.8%(ARI), and 8.1%(Purity).\n", "date": "2024-04-08", "categories": []}
{"id": "2404.03012", "title": "Spectral Clustering in Convex and Constrained Settings", "abstract": "  Spectral clustering methods have gained widespread recognition for their\neffectiveness in clustering high-dimensional data. Among these techniques,\nconstrained spectral clustering has emerged as a prominent approach,\ndemonstrating enhanced performance by integrating pairwise constraints.\nHowever, the application of such constraints to semidefinite spectral\nclustering, a variant that leverages semidefinite programming to optimize\nclustering objectives, remains largely unexplored. In this paper, we introduce\na novel framework for seamlessly integrating pairwise constraints into\nsemidefinite spectral clustering. Our methodology systematically extends the\ncapabilities of semidefinite spectral clustering to capture complex data\nstructures, thereby addressing real-world clustering challenges more\neffectively. Additionally, we extend this framework to encompass both active\nand self-taught learning scenarios, further enhancing its versatility and\napplicability. Empirical studies conducted on well-known datasets demonstrate\nthe superiority of our proposed framework over existing spectral clustering\nmethods, showcasing its robustness and scalability across diverse datasets and\nlearning settings. By bridging the gap between constrained learning and\nsemidefinite spectral clustering, our work contributes to the advancement of\nspectral clustering techniques, offering researchers and practitioners a\nversatile tool for addressing complex clustering challenges in various\nreal-world applications. Access to the data, code, and experimental results is\nprovided for further exploration (https://github.com/swarupbehera/SCCCS).\n", "date": "2024-04-03", "categories": []}
{"id": "2404.01936", "title": "Settling Time vs. Accuracy Tradeoffs for Clustering Big Data", "abstract": "  We study the theoretical and practical runtime limits of k-means and k-median\nclustering on large datasets. Since effectively all clustering methods are\nslower than the time it takes to read the dataset, the fastest approach is to\nquickly compress the data and perform the clustering on the compressed\nrepresentation. Unfortunately, there is no universal best choice for\ncompressing the number of points - while random sampling runs in sublinear time\nand coresets provide theoretical guarantees, the former does not enforce\naccuracy while the latter is too slow as the numbers of points and clusters\ngrow. Indeed, it has been conjectured that any sensitivity-based coreset\nconstruction requires super-linear time in the dataset size. We examine this\nrelationship by first showing that there does exist an algorithm that obtains\ncoresets via sensitivity sampling in effectively linear time - within\nlog-factors of the time it takes to read the data. Any approach that\nsignificantly improves on this must then resort to practical heuristics,\nleading us to consider the spectrum of sampling strategies across both real and\nartificial datasets in the static and streaming settings. Through this, we show\nthe conditions in which coresets are necessary for preserving cluster validity\nas well as the settings in which faster, cruder sampling strategies are\nsufficient. As a result, we provide a comprehensive theoretical and practical\nblueprint for effective clustering regardless of data size. Our code is\npublicly available and has scripts to recreate the experiments.\n", "date": "2024-04-02", "categories": []}
{"id": "2403.19514", "title": "CDIMC-net: Cognitive Deep Incomplete Multi-view Clustering Network", "abstract": "  In recent years, incomplete multi-view clustering, which studies the\nchallenging multi-view clustering problem on missing views, has received\ngrowing research interests. Although a series of methods have been proposed to\naddress this issue, the following problems still exist: 1) Almost all of the\nexisting methods are based on shallow models, which is difficult to obtain\ndiscriminative common representations. 2) These methods are generally sensitive\nto noise or outliers since the negative samples are treated equally as the\nimportant samples. In this paper, we propose a novel incomplete multi-view\nclustering network, called Cognitive Deep Incomplete Multi-view Clustering\nNetwork (CDIMC-net), to address these issues. Specifically, it captures the\nhigh-level features and local structure of each view by incorporating the\nview-specific deep encoders and graph embedding strategy into a framework.\nMoreover, based on the human cognition, i.e., learning from easy to hard, it\nintroduces a self-paced strategy to select the most confident samples for model\ntraining, which can reduce the negative influence of outliers. Experimental\nresults on several incomplete datasets show that CDIMC-net outperforms the\nstate-of-the-art incomplete multi-view clustering methods.\n", "date": "2024-03-28", "categories": []}
{"id": "2403.18101", "title": "Towards Explainable Clustering: A Constrained Declarative based Approach", "abstract": "  The domain of explainable AI is of interest in all Machine Learning fields,\nand it is all the more important in clustering, an unsupervised task whose\nresult must be validated by a domain expert. We aim at finding a clustering\nthat has high quality in terms of classic clustering criteria and that is\nexplainable, and we argue that these two dimensions must be considered when\nbuilding the clustering. We consider that a good global explanation of a\nclustering should give the characteristics of each cluster taking into account\ntheir abilities to describe its objects (coverage) while distinguishing it from\nthe other clusters (discrimination). Furthermore, we aim at leveraging expert\nknowledge, at different levels, on the structure of the expected clustering or\non its explanations. In our framework an explanation of a cluster is a set of\npatterns, and we propose a novel interpretable constrained clustering method\ncalled ECS for declarative clustering with Explainabilty-driven Cluster\nSelection that integrates structural or domain expert knowledge expressed by\nmeans of constraints. It is based on the notion of coverage and discrimination\nthat are formalized at different levels (cluster / clustering), each allowing\nfor exceptions through parameterized thresholds. Our method relies on four\nsteps: generation of a set of partitions, computation of frequent patterns for\neach cluster, pruning clusters that violates some constraints, and selection of\nclusters and associated patterns to build an interpretable clustering. This\nlast step is combinatorial and we have developed a Constraint-Programming (CP)\nmodel to solve it. The method can integrate prior knowledge in the form of user\nconstraints, both before or in the CP model.\n", "date": "2024-03-26", "categories": []}
{"id": "2403.18766", "title": "Superior Parallel Big Data Clustering through Competitive Stochastic\n  Sample Size Optimization in Big-means", "abstract": "  This paper introduces a novel K-means clustering algorithm, an advancement on\nthe conventional Big-means methodology. The proposed method efficiently\nintegrates parallel processing, stochastic sampling, and competitive\noptimization to create a scalable variant designed for big data applications.\nIt addresses scalability and computation time challenges typically faced with\ntraditional techniques. The algorithm adjusts sample sizes dynamically for each\nworker during execution, optimizing performance. Data from these sample sizes\nare continually analyzed, facilitating the identification of the most efficient\nconfiguration. By incorporating a competitive element among workers using\ndifferent sample sizes, efficiency within the Big-means algorithm is further\nstimulated. In essence, the algorithm balances computational time and\nclustering quality by employing a stochastic, competitive sampling strategy in\na parallel computing setting.\n", "date": "2024-03-27", "categories": []}
{"id": "2403.17409", "title": "Neural Clustering based Visual Representation Learning", "abstract": "  We investigate a fundamental aspect of machine vision: the measurement of\nfeatures, by revisiting clustering, one of the most classic approaches in\nmachine learning and data analysis. Existing visual feature extractors,\nincluding ConvNets, ViTs, and MLPs, represent an image as rectangular regions.\nThough prevalent, such a grid-style paradigm is built upon engineering practice\nand lacks explicit modeling of data distribution. In this work, we propose\nfeature extraction with clustering (FEC), a conceptually elegant yet\nsurprisingly ad-hoc interpretable neural clustering framework, which views\nfeature extraction as a process of selecting representatives from data and thus\nautomatically captures the underlying data distribution. Given an image, FEC\nalternates between grouping pixels into individual clusters to abstract\nrepresentatives and updating the deep features of pixels with current\nrepresentatives. Such an iterative working mechanism is implemented in the form\nof several neural layers and the final representatives can be used for\ndownstream tasks. The cluster assignments across layers, which can be viewed\nand inspected by humans, make the forward process of FEC fully transparent and\nempower it with promising ad-hoc interpretability. Extensive experiments on\nvarious visual recognition models and tasks verify the effectiveness,\ngenerality, and interpretability of FEC. We expect this work will provoke a\nrethink of the current de facto grid-style paradigm.\n", "date": "2024-03-26", "categories": []}
{"id": "2303.17245", "title": "Investigating and Mitigating the Side Effects of Noisy Views for\n  Self-Supervised Clustering Algorithms in Practical Multi-View Scenarios", "abstract": "  Multi-view clustering (MVC) aims at exploring category structures among\nmulti-view data in self-supervised manners. Multiple views provide more\ninformation than single views and thus existing MVC methods can achieve\nsatisfactory performance. However, their performance might seriously degenerate\nwhen the views are noisy in practical multi-view scenarios. In this paper, we\nformally investigate the drawback of noisy views and then propose a\ntheoretically grounded deep MVC method (namely MVCAN) to address this issue.\nSpecifically, we propose a novel MVC objective that enables un-shared\nparameters and inconsistent clustering predictions across multiple views to\nreduce the side effects of noisy views. Furthermore, a two-level multi-view\niterative optimization is designed to generate robust learning targets for\nrefining individual views' representation learning. Theoretical analysis\nreveals that MVCAN works by achieving the multi-view consistency,\ncomplementarity, and noise robustness. Finally, experiments on extensive public\ndatasets demonstrate that MVCAN outperforms state-of-the-art methods and is\nrobust against the existence of noisy views.\n", "date": "2023-03-30", "categories": []}
{"id": "2403.15681", "title": "Differentiable Information Bottleneck for Deterministic Multi-view\n  Clustering", "abstract": "  In recent several years, the information bottleneck (IB) principle provides\nan information-theoretic framework for deep multi-view clustering (MVC) by\ncompressing multi-view observations while preserving the relevant information\nof multiple views. Although existing IB-based deep MVC methods have achieved\nhuge success, they rely on variational approximation and distribution\nassumption to estimate the lower bound of mutual information, which is a\nnotoriously hard and impractical problem in high-dimensional multi-view spaces.\nIn this work, we propose a new differentiable information bottleneck (DIB)\nmethod, which provides a deterministic and analytical MVC solution by fitting\nthe mutual information without the necessity of variational approximation.\nSpecifically, we first propose to directly fit the mutual information of\nhigh-dimensional spaces by leveraging normalized kernel Gram matrix, which does\nnot require any auxiliary neural estimator to estimate the lower bound of\nmutual information. Then, based on the new mutual information measurement, a\ndeterministic multi-view neural network with analytical gradients is explicitly\ntrained to parameterize IB principle, which derives a deterministic compression\nof input variables from different views. Finally, a triplet consistency\ndiscovery mechanism is devised, which is capable of mining the feature\nconsistency, cluster consistency and joint consistency based on the\ndeterministic and compact representations. Extensive experimental results show\nthe superiority of our DIB method on 6 benchmarks compared with 13\nstate-of-the-art baselines.\n", "date": "2024-03-23", "categories": []}
{"id": "2403.16201", "title": "From Discrete to Continuous: Deep Fair Clustering With Transferable\n  Representations", "abstract": "  We consider the problem of deep fair clustering, which partitions data into\nclusters via the representations extracted by deep neural networks while hiding\nsensitive data attributes. To achieve fairness, existing methods present a\nvariety of fairness-related objective functions based on the group fairness\ncriterion. However, these works typically assume that the sensitive attributes\nare discrete and do not work for continuous sensitive variables, such as the\nproportion of the female population in an area. Besides, the potential of the\nrepresentations learned from clustering tasks to improve performance on other\ntasks is ignored by existing works. In light of these limitations, we propose a\nflexible deep fair clustering method that can handle discrete and continuous\nsensitive attributes simultaneously. Specifically, we design an information\nbottleneck style objective function to learn fair and clustering-friendly\nrepresentations. Furthermore, we explore for the first time the transferability\nof the extracted representations to other downstream tasks. Unlike existing\nworks, we impose fairness at the representation level, which could guarantee\nfairness for the transferred task regardless of clustering results. To verify\nthe effectiveness of the proposed method, we perform extensive experiments on\ndatasets with discrete and continuous sensitive attributes, demonstrating the\nadvantage of our method in comparison with state-of-the-art methods.\n", "date": "2024-03-24", "categories": []}
{"id": "2403.14830", "title": "Deep Clustering Evaluation: How to Validate Internal Clustering\n  Validation Measures", "abstract": "  Deep clustering, a method for partitioning complex, high-dimensional data\nusing deep neural networks, presents unique evaluation challenges. Traditional\nclustering validation measures, designed for low-dimensional spaces, are\nproblematic for deep clustering, which involves projecting data into\nlower-dimensional embeddings before partitioning. Two key issues are\nidentified: 1) the curse of dimensionality when applying these measures to raw\ndata, and 2) the unreliable comparison of clustering results across different\nembedding spaces stemming from variations in training procedures and parameter\nsettings in different clustering models. This paper addresses these challenges\nin evaluating clustering quality in deep learning. We present a theoretical\nframework to highlight ineffectiveness arising from using internal validation\nmeasures on raw and embedded data and propose a systematic approach to applying\nclustering validity indices in deep clustering contexts. Experiments show that\nthis framework aligns better with external validation measures, effectively\nreducing the misguidance from the improper use of clustering validity indices\nin deep learning.\n", "date": "2024-03-21", "categories": []}
{"id": "2209.05812", "title": "A Non-Parametric Bootstrap for Spectral Clustering", "abstract": "  Finite mixture modelling is a popular method in the field of clustering and\nis beneficial largely due to its soft cluster membership probabilities. A\ncommon method for fitting finite mixture models is to employ spectral\nclustering, which can utilize the expectation-maximization (EM) algorithm.\nHowever, the EM algorithm falls victim to a number of issues, including\nconvergence to sub-optimal solutions. We address this issue by developing two\nnovel algorithms that incorporate the spectral decomposition of the data matrix\nand a non-parametric bootstrap sampling scheme. Simulations display the\nvalidity of our algorithms and demonstrate not only their flexibility, but also\ntheir computational efficiency and ability to avoid poor solutions when\ncompared to other clustering algorithms for estimating finite mixture models.\nOur techniques are more consistent in their convergence when compared to other\nbootstrapped algorithms that fit finite mixture models.\n", "date": "2022-09-13", "categories": []}
{"id": "2401.12648", "title": "Consistency Enhancement-Based Deep Multiview Clustering via Contrastive\n  Learning", "abstract": "  Multiview clustering (MVC) segregates data samples into meaningful clusters\nby synthesizing information across multiple views. Moreover, deep\nlearning-based methods have demonstrated their strong feature learning\ncapabilities in MVC scenarios. However, effectively generalizing feature\nrepresentations while maintaining consistency is still an intractable problem.\nIn addition, most existing deep clustering methods based on contrastive\nlearning overlook the consistency of the clustering representations during the\nclustering process. In this paper, we show how the above problems can be\novercome and propose a consistent enhancement-based deep MVC method via\ncontrastive learning (CCEC). Specifically, semantic connection blocks are\nincorporated into a feature representation to preserve the consistent\ninformation among multiple views. Furthermore, the representation process for\nclustering is enhanced through spectral clustering, and the consistency across\nmultiple views is improved. Experiments conducted on five datasets demonstrate\nthe effectiveness and superiority of our method in comparison with the\nstate-of-the-art (SOTA) methods. The code for this method can be accessed at\nhttps://anonymous.4open.science/r/CCEC-E84E/.\n", "date": "2024-01-23", "categories": []}
{"id": "2403.14332", "title": "A Differentially Private Clustering Algorithm for Well-Clustered Graphs", "abstract": "  We study differentially private (DP) algorithms for recovering clusters in\nwell-clustered graphs, which are graphs whose vertex set can be partitioned\ninto a small number of sets, each inducing a subgraph of high inner conductance\nand small outer conductance. Such graphs have widespread application as a\nbenchmark in the theoretical analysis of spectral clustering. We provide an\nefficient ($\\epsilon$,$\\delta$)-DP algorithm tailored specifically for such\ngraphs. Our algorithm draws inspiration from the recent work of Chen et al.,\nwho developed DP algorithms for recovery of stochastic block models in cases\nwhere the graph comprises exactly two nearly-balanced clusters. Our algorithm\nworks for well-clustered graphs with $k$ nearly-balanced clusters, and the\nmisclassification ratio almost matches the one of the best-known non-private\nalgorithms. We conduct experimental evaluations on datasets with known ground\ntruth clusters to substantiate the prowess of our algorithm. We also show that\nany (pure) $\\epsilon$-DP algorithm would result in substantial error.\n", "date": "2024-03-21", "categories": []}
{"id": "2403.13376", "title": "Correlation Clustering of Organoid Images", "abstract": "  In biological and medical research, scientists now routinely acquire\nmicroscopy images of hundreds of morphologically heterogeneous organoids and\nare then faced with the task of finding patterns in the image collection, i.e.,\nsubsets of organoids that appear similar and potentially represent the same\nmorphological class. We adopt models and algorithms for correlating organoid\nimages, i.e., for quantifying the similarity in appearance and geometry of the\norganoids they depict, and for clustering organoid images by consolidating\nconflicting correlations. For correlating organoid images, we adopt and compare\ntwo alternatives, a partial quadratic assignment problem and a twin network.\nFor clustering organoid images, we employ the correlation clustering problem.\nEmpirically, we learn the parameters of these models, infer a clustering of\norganoid images, and quantify the accuracy of the inferred clusters, with\nrespect to a training set and a test set we contribute of state-of-the-art\nlight microscopy images of organoids clustered manually by biologists.\n", "date": "2024-03-20", "categories": []}
{"id": "2403.08838", "title": "Predictive Clustering of Vessel Behavior Based on Hierarchical\n  Trajectory Representation", "abstract": "  Vessel trajectory clustering, which aims to find similar trajectory patterns,\nhas been widely leveraged in overwater applications. Most traditional methods\nuse predefined rules and thresholds to identify discrete vessel behaviors. They\naim for high-quality clustering and conduct clustering on entire sequences,\nwhether the original trajectory or its sub-trajectories, failing to represent\ntheir evolution. To resolve this problem, we propose a Predictive Clustering of\nHierarchical Vessel Behavior (PC-HiV). PC-HiV first uses hierarchical\nrepresentations to transform every trajectory into a behavioral sequence. Then,\nit predicts evolution at each timestamp of the sequence based on the\nrepresentations. By applying predictive clustering and latent encoding, PC-HiV\nimproves clustering and predictions simultaneously. Experiments on real AIS\ndatasets demonstrate PC-HiV's superiority over existing methods, showcasing its\neffectiveness in capturing behavioral evolution discrepancies between vessel\ntypes (tramp vs. liner) and within emission control areas. Results show that\nour method outperforms NN-Kmeans and Robust DAA by 3.9% and 6.4% of the purity\nscore.\n", "date": "2024-03-13", "categories": []}
{"id": "2403.10365", "title": "Scalable Algorithms for Individual Preference Stable Clustering", "abstract": "  In this paper, we study the individual preference (IP) stability, which is an\nnotion capturing individual fairness and stability in clustering. Within this\nsetting, a clustering is $\\alpha$-IP stable when each data point's average\ndistance to its cluster is no more than $\\alpha$ times its average distance to\nany other cluster. In this paper, we study the natural local search algorithm\nfor IP stable clustering. Our analysis confirms a $O(\\log n)$-IP stability\nguarantee for this algorithm, where $n$ denotes the number of points in the\ninput. Furthermore, by refining the local search approach, we show it runs in\nan almost linear time, $\\tilde{O}(nk)$.\n", "date": "2024-03-15", "categories": []}
{"id": "2211.02680", "title": "Climbing Routes Clustering Using Energy-Efficient Accelerometers\n  Attached to the Quickdraws", "abstract": "  One of the challenges for climbing gyms is to find out popular routes for the\nclimbers to improve their services and optimally use their infrastructure. This\nproblem must be addressed preserving both the privacy and convenience of the\nclimbers and the costs of the gyms. To this aim, a hardware prototype is\ndeveloped to collect data using accelerometer sensors attached to a piece of\nclimbing equipment mounted on the wall, called quickdraw, that connects the\nclimbing rope to the bolt anchors. The corresponding sensors are configured to\nbe energy-efficient, hence becoming practical in terms of expenses and time\nconsumption for replacement when used in large quantities in a climbing gym.\nThis paper describes hardware specifications, studies data measured by the\nsensors in ultra-low power mode, detect patterns in data during climbing\ndifferent routes, and develops an unsupervised approach for route clustering.\n", "date": "2022-11-04", "categories": []}
{"id": "2403.08787", "title": "Multi-view Subspace Clustering via An Adaptive Consensus Graph Filter", "abstract": "  Multiview subspace clustering (MVSC) has attracted an increasing amount of\nattention in recent years. Most existing MVSC methods first collect\ncomplementary information from different views and consequently derive a\nconsensus reconstruction coefficient matrix to indicate the subspace structure\nof a multi-view data set. In this paper, we initially assume the existence of a\nconsensus reconstruction coefficient matrix and then use it to build a\nconsensus graph filter. In each view, the filter is employed for smoothing the\ndata and designing a regularizer for the reconstruction coefficient matrix.\nFinally, the obtained reconstruction coefficient matrices from different views\nare used to create constraints for the consensus reconstruction coefficient\nmatrix. Therefore, in the proposed method, the consensus reconstruction\ncoefficient matrix, the consensus graph filter, and the reconstruction\ncoefficient matrices from different views are interdependent. We provide an\noptimization algorithm to obtain their optimal values. Extensive experiments on\ndiverse multi-view data sets demonstrate that our approach outperforms some\nstate-of-the-art methods.\n", "date": "2024-01-30", "categories": []}
{"id": "2303.16521", "title": "Hard Regularization to Prevent Deep Online Clustering Collapse without\n  Data Augmentation", "abstract": "  Online deep clustering refers to the joint use of a feature extraction\nnetwork and a clustering model to assign cluster labels to each new data point\nor batch as it is processed. While faster and more versatile than offline\nmethods, online clustering can easily reach the collapsed solution where the\nencoder maps all inputs to the same point and all are put into a single\ncluster. Successful existing models have employed various techniques to avoid\nthis problem, most of which require data augmentation or which aim to make the\naverage soft assignment across the dataset the same for each cluster. We\npropose a method that does not require data augmentation, and that, differently\nfrom existing methods, regularizes the hard assignments. Using a Bayesian\nframework, we derive an intuitive optimization objective that can be\nstraightforwardly included in the training of the encoder network. Tested on\nfour image datasets and one human-activity recognition dataset, it consistently\navoids collapse more robustly than other methods and leads to more accurate\nclustering. We also conduct further experiments and analyses justifying our\nchoice to regularize the hard cluster assignments. Code is available at\nhttps://github.com/Lou1sM/online_hard_clustering.\n", "date": "2023-03-29", "categories": []}
{"id": "2403.07137", "title": "Exploring Cluster Analysis in Nelore Cattle Visual Score Attribution", "abstract": "  Assessing the biotype of cattle through human visual inspection is a very\ncommon and important practice in precision cattle breeding. This paper presents\nthe results of a correlation analysis between scores produced by humans for\nNelore cattle and a variety of measurements that can be derived from images or\nother instruments. It also presents a study using the k-means algorithm to\ngenerate new ways of clustering a batch of cattle using the measurements that\nmost correlate with the animal's body weight and visual scores.\n", "date": "2024-03-11", "categories": []}
{"id": "2403.05669", "title": "Spectral Clustering of Categorical and Mixed-type Data via Extra Graph\n  Nodes", "abstract": "  Clustering data objects into homogeneous groups is one of the most important\ntasks in data mining. Spectral clustering is arguably one of the most important\nalgorithms for clustering, as it is appealing for its theoretical soundness and\nis adaptable to many real-world data settings. For example, mixed data, where\nthe data is composed of numerical and categorical features, is typically\nhandled via numerical discretization, dummy coding, or similarity computation\nthat takes into account both data types. This paper explores a more natural way\nto incorporate both numerical and categorical information into the spectral\nclustering algorithm, avoiding the need for data preprocessing or the use of\nsophisticated similarity functions. We propose adding extra nodes corresponding\nto the different categories the data may belong to and show that it leads to an\ninterpretable clustering objective function. Furthermore, we demonstrate that\nthis simple framework leads to a linear-time spectral clustering algorithm for\ncategorical-only data. Finally, we compare the performance of our algorithms\nagainst other related methods and show that it provides a competitive\nalternative to them in terms of performance and runtime.\n", "date": "2024-03-08", "categories": []}
{"id": "2403.05768", "title": "Deep Contrastive Multi-view Clustering under Semantic Feature Guidance", "abstract": "  Contrastive learning has achieved promising performance in the field of\nmulti-view clustering recently. However, the positive and negative sample\nconstruction mechanisms ignoring semantic consistency lead to false negative\npairs, limiting the performance of existing algorithms from further\nimprovement. To solve this problem, we propose a multi-view clustering\nframework named Deep Contrastive Multi-view Clustering under Semantic feature\nguidance (DCMCS) to alleviate the influence of false negative pairs.\nSpecifically, view-specific features are firstly extracted from raw features\nand fused to obtain fusion view features according to view importance. To\nmitigate the interference of view-private information, specific view and fusion\nview semantic features are learned by cluster-level contrastive learning and\nconcatenated to measure the semantic similarity of instances. By minimizing\ninstance-level contrastive loss weighted by semantic similarity, DCMCS\nadaptively weakens contrastive leaning between false negative pairs.\nExperimental results on several public datasets demonstrate the proposed\nframework outperforms the state-of-the-art methods.\n", "date": "2024-03-09", "categories": []}
{"id": "2403.06671", "title": "Untangling Gaussian Mixtures", "abstract": "  Tangles were originally introduced as a concept to formalize regions of high\nconnectivity in graphs. In recent years, they have also been discovered as a\nlink between structural graph theory and data science: when interpreting\nsimilarity in data sets as connectivity between points, finding clusters in the\ndata essentially amounts to finding tangles in the underlying graphs. This\npaper further explores the potential of tangles in data sets as a means for a\nformal study of clusters. Real-world data often follow a normal distribution.\nAccounting for this, we develop a quantitative theory of tangles in data sets\ndrawn from Gaussian mixtures. To this end, we equip the data with a graph\nstructure that models similarity between the points and allows us to apply\ntangle theory to the data. We provide explicit conditions under which tangles\nassociated with the marginal Gaussian distributions exist asymptotically almost\nsurely. This can be considered as a sufficient formal criterion for the\nseparabability of clusters in the data.\n", "date": "2024-03-11", "categories": []}
{"id": "2403.03448", "title": "Kernel Correlation-Dissimilarity for Multiple Kernel k-Means Clustering", "abstract": "  The main objective of the Multiple Kernel k-Means (MKKM) algorithm is to\nextract non-linear information and achieve optimal clustering by optimizing\nbase kernel matrices. Current methods enhance information diversity and reduce\nredundancy by exploiting interdependencies among multiple kernels based on\ncorrelations or dissimilarities. Nevertheless, relying solely on a single\nmetric, such as correlation or dissimilarity, to define kernel relationships\nintroduces bias and incomplete characterization. Consequently, this limitation\nhinders efficient information extraction, ultimately compromising clustering\nperformance. To tackle this challenge, we introduce a novel method that\nsystematically integrates both kernel correlation and dissimilarity. Our\napproach comprehensively captures kernel relationships, facilitating more\nefficient classification information extraction and improving clustering\nperformance. By emphasizing the coherence between kernel correlation and\ndissimilarity, our method offers a more objective and transparent strategy for\nextracting non-linear information and significantly improving clustering\nprecision, supported by theoretical rationale. We assess the performance of our\nalgorithm on 13 challenging benchmark datasets, demonstrating its superiority\nover contemporary state-of-the-art MKKM techniques.\n", "date": "2024-03-06", "categories": []}
{"id": "2309.15135", "title": "Contrastive Continual Multi-view Clustering with Filtered Structural\n  Fusion", "abstract": "  Multi-view clustering thrives in applications where views are collected in\nadvance by extracting consistent and complementary information among views.\nHowever, it overlooks scenarios where data views are collected sequentially,\ni.e., real-time data. Due to privacy issues or memory burden, previous views\nare not available with time in these situations. Some methods are proposed to\nhandle it but are trapped in a stability-plasticity dilemma. In specific, these\nmethods undergo a catastrophic forgetting of prior knowledge when a new view is\nattained. Such a catastrophic forgetting problem (CFP) would cause the\nconsistent and complementary information hard to get and affect the clustering\nperformance. To tackle this, we propose a novel method termed Contrastive\nContinual Multi-view Clustering with Filtered Structural Fusion (CCMVC-FSF).\nPrecisely, considering that data correlations play a vital role in clustering\nand prior knowledge ought to guide the clustering process of a new view, we\ndevelop a data buffer with fixed size to store filtered structural information\nand utilize it to guide the generation of a robust partition matrix via\ncontrastive learning. Furthermore, we theoretically connect CCMVC-FSF with\nsemi-supervised learning and knowledge distillation. Extensive experiments\nexhibit the excellence of the proposed method.\n", "date": "2023-09-26", "categories": []}
{"id": "2310.08031", "title": "Local Graph Clustering with Noisy Labels", "abstract": "  The growing interest in machine learning problems over graphs with additional\nnode information such as texts, images, or labels has popularized methods that\nrequire the costly operation of processing the entire graph. Yet, little effort\nhas been made to the development of fast local methods (i.e. without accessing\nthe entire graph) that extract useful information from such data. To that end,\nwe propose a study of local graph clustering using noisy node labels as a proxy\nfor additional node information. In this setting, nodes receive initial binary\nlabels based on cluster affiliation: 1 if they belong to the target cluster and\n0 otherwise. Subsequently, a fraction of these labels is flipped. We\ninvestigate the benefits of incorporating noisy labels for local graph\nclustering. By constructing a weighted graph with such labels, we study the\nperformance of graph diffusion-based local clustering method on both the\noriginal and the weighted graphs. From a theoretical perspective, we consider\nrecovering an unknown target cluster with a single seed node in a random graph\nwith independent noisy node labels. We provide sufficient conditions on the\nlabel noise under which, with high probability, using diffusion in the weighted\ngraph yields a more accurate recovery of the target cluster. This approach\nproves more effective than using the given labels alone or using diffusion in\nthe label-free original graph. Empirically, we show that reliable node labels\ncan be obtained with just a few samples from an attributed graph. Moreover,\nutilizing these labels via diffusion in the weighted graph leads to\nsignificantly better local clustering performance across several real-world\ndatasets, improving F1 scores by up to 13%.\n", "date": "2023-10-12", "categories": []}
{"id": "2312.07806", "title": "Contextually Affinitive Neighborhood Refinery for Deep Clustering", "abstract": "  Previous endeavors in self-supervised learning have enlightened the research\nof deep clustering from an instance discrimination perspective. Built upon this\nfoundation, recent studies further highlight the importance of grouping\nsemantically similar instances. One effective method to achieve this is by\npromoting the semantic structure preserved by neighborhood consistency.\nHowever, the samples in the local neighborhood may be limited due to their\nclose proximity to each other, which may not provide substantial and diverse\nsupervision signals. Inspired by the versatile re-ranking methods in the\ncontext of image retrieval, we propose to employ an efficient online re-ranking\nprocess to mine more informative neighbors in a Contextually Affinitive\n(ConAff) Neighborhood, and then encourage the cross-view neighborhood\nconsistency. To further mitigate the intrinsic neighborhood noises near cluster\nboundaries, we propose a progressively relaxed boundary filtering strategy to\ncircumvent the issues brought by noisy neighbors. Our method can be easily\nintegrated into the generic self-supervised frameworks and outperforms the\nstate-of-the-art methods on several popular benchmarks.\n", "date": "2023-12-12", "categories": []}
{"id": "2403.01460", "title": "One-Step Multi-View Clustering Based on Transition Probability", "abstract": "  The large-scale multi-view clustering algorithms, based on the anchor graph,\nhave shown promising performance and efficiency and have been extensively\nexplored in recent years. Despite their successes, current methods lack\ninterpretability in the clustering process and do not sufficiently consider the\ncomplementary information across different views. To address these\nshortcomings, we introduce the One-Step Multi-View Clustering Based on\nTransition Probability (OSMVC-TP). This method adopts a probabilistic approach,\nwhich leverages the anchor graph, representing the transition probabilities\nfrom samples to anchor points. Our method directly learns the transition\nprobabilities from anchor points to categories, and calculates the transition\nprobabilities from samples to categories, thus obtaining soft label matrices\nfor samples and anchor points, enhancing the interpretability of clustering.\nFurthermore, to maintain consistency in labels across different views, we apply\na Schatten p-norm constraint on the tensor composed of the soft labels. This\napproach effectively harnesses the complementary information among the views.\nExtensive experiments have confirmed the effectiveness and robustness of\nOSMVC-TP.\n", "date": "2024-03-03", "categories": []}
{"id": "2403.01465", "title": "Multiview Subspace Clustering of Hyperspectral Images based on Graph\n  Convolutional Networks", "abstract": "  High-dimensional and complex spectral structures make clustering of\nhy-perspectral images (HSI) a challenging task. Subspace clustering has been\nshown to be an effective approach for addressing this problem. However, current\nsubspace clustering algorithms are mainly designed for a single view and do not\nfully exploit spatial or texture feature information in HSI. This study\nproposed a multiview subspace clustering of HSI based on graph convolutional\nnetworks. (1) This paper uses the powerful classification ability of graph\nconvolutional network and the learning ability of topologi-cal relationships\nbetween nodes to analyze and express the spatial relation-ship of HSI. (2)\nPixel texture and pixel neighbor spatial-spectral infor-mation were sent to\nconstruct two graph convolutional subspaces. (3) An attention-based fusion\nmodule was used to adaptively construct a more discriminative feature map. The\nmodel was evaluated on three popular HSI datasets, including Indian Pines,\nPavia University, and Houston. It achieved overall accuracies of 92.38%,\n93.43%, and 83.82%, respectively and significantly outperformed the\nstate-of-the-art clustering methods. In conclusion, the proposed model can\neffectively improve the clustering ac-curacy of HSI.\n", "date": "2024-03-03", "categories": []}
{"id": "2305.15022", "title": "Hierarchical clustering with dot products recovers hidden tree structure", "abstract": "  In this paper we offer a new perspective on the well established\nagglomerative clustering algorithm, focusing on recovery of hierarchical\nstructure. We recommend a simple variant of the standard algorithm, in which\nclusters are merged by maximum average dot product and not, for example, by\nminimum distance or within-cluster variance. We demonstrate that the tree\noutput by this algorithm provides a bona fide estimate of generative\nhierarchical structure in data, under a generic probabilistic graphical model.\nThe key technical innovations are to understand how hierarchical information in\nthis model translates into tree geometry which can be recovered from data, and\nto characterise the benefits of simultaneously growing sample size and data\ndimension. We demonstrate superior tree recovery performance with real data\nover existing approaches such as UPGMA, Ward's method, and HDBSCAN.\n", "date": "2023-05-24", "categories": []}
{"id": "2402.16544", "title": "Label Learning Method Based on Tensor Projection", "abstract": "  Multi-view clustering method based on anchor graph has been widely concerned\ndue to its high efficiency and effectiveness. In order to avoid\npost-processing, most of the existing anchor graph-based methods learn\nbipartite graphs with connected components. However, such methods have high\nrequirements on parameters, and in some cases it may not be possible to obtain\nbipartite graphs with clear connected components. To end this, we propose a\nlabel learning method based on tensor projection (LLMTP). Specifically, we\nproject anchor graph into the label space through an orthogonal projection\nmatrix to obtain cluster labels directly. Considering that the spatial\nstructure information of multi-view data may be ignored to a certain extent\nwhen projected in different views separately, we extend the matrix projection\ntransformation to tensor projection, so that the spatial structure information\nbetween views can be fully utilized. In addition, we introduce the tensor\nSchatten $p$-norm regularization to make the clustering label matrices of\ndifferent views as consistent as possible. Extensive experiments have proved\nthe effectiveness of the proposed method.\n", "date": "2024-02-26", "categories": []}
{"id": "2402.15146", "title": "Convergence Analysis of Blurring Mean Shift", "abstract": "  Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm,\nis a kernel-based iterative method for data clustering, where data points are\nclustered according to their convergent points via iterative blurring. In this\npaper, we analyze convergence properties of the BMS algorithm by leveraging its\ninterpretation as an optimization procedure, which is known but has been\nunderutilized in existing convergence studies. Whereas existing results on\nconvergence properties applicable to multi-dimensional data only cover the case\nwhere all the blurred data point sequences converge to a single point, this\nstudy provides a convergence guarantee even when those sequences can converge\nto multiple points, yielding multiple clusters. This study also shows that the\nconvergence of the BMS algorithm is fast by further leveraging geometrical\ncharacterization of the convergent points.\n", "date": "2024-02-23", "categories": []}
{"id": "2212.06691", "title": "Quantum Clustering with k-Means: a Hybrid Approach", "abstract": "  Quantum computing is a promising paradigm based on quantum theory for\nperforming fast computations. Quantum algorithms are expected to surpass their\nclassical counterparts in terms of computational complexity for certain tasks,\nincluding machine learning. In this paper, we design, implement, and evaluate\nthree hybrid quantum k-Means algorithms, exploiting different degree of\nparallelism. Indeed, each algorithm incrementally leverages quantum parallelism\nto reduce the complexity of the cluster assignment step up to a constant cost.\nIn particular, we exploit quantum phenomena to speed up the computation of\ndistances. The core idea is that the computation of distances between records\nand centroids can be executed simultaneously, thus saving time, especially for\nbig datasets. We show that our hybrid quantum k-Means algorithms can be more\nefficient than the classical version, still obtaining comparable clustering\nresults.\n", "date": "2022-12-13", "categories": []}
{"id": "2402.11773", "title": "Dynamic Multi-Network Mining of Tensor Time Series", "abstract": "  Subsequence clustering of time series is an essential task in data mining,\nand interpreting the resulting clusters is also crucial since we generally do\nnot have prior knowledge of the data. Thus, given a large collection of tensor\ntime series consisting of multiple modes, including timestamps, how can we\nachieve subsequence clustering for tensor time series and provide interpretable\ninsights? In this paper, we propose a new method, Dynamic Multi-network Mining\n(DMM), that converts a tensor time series into a set of segment groups of\nvarious lengths (i.e., clusters) characterized by a dependency network\nconstrained with l1-norm. Our method has the following properties. (a)\nInterpretable: it characterizes the cluster with multiple networks, each of\nwhich is a sparse dependency network of a corresponding non-temporal mode, and\nthus provides visible and interpretable insights into the key relationships.\n(b) Accurate: it discovers the clusters with distinct networks from tensor time\nseries according to the minimum description length (MDL). (c) Scalable: it\nscales linearly in terms of the input data size when solving a non-convex\nproblem to optimize the number of segments and clusters, and thus it is\napplicable to long-range and high-dimensional tensors. Extensive experiments\nwith synthetic datasets confirm that our method outperforms the\nstate-of-the-art methods in terms of clustering accuracy. We then use real\ndatasets to demonstrate that DMM is useful for providing interpretable insights\nfrom tensor time series.\n", "date": "2024-02-19", "categories": []}
{"id": "2402.14621", "title": "latrend: A Framework for Clustering Longitudinal Data", "abstract": "  Clustering of longitudinal data is used to explore common trends among\nsubjects over time for a numeric measurement of interest. Various R packages\nhave been introduced throughout the years for identifying clusters of\nlongitudinal patterns, summarizing the variability in trajectories between\nsubject in terms of one or more trends. We introduce the R package \"latrend\" as\na framework for the unified application of methods for longitudinal clustering,\nenabling comparisons between methods with minimal coding. The package also\nserves as an interface to commonly used packages for clustering longitudinal\ndata, including \"dtwclust\", \"flexmix\", \"kml\", \"lcmm\", \"mclust\", \"mixAK\", and\n\"mixtools\". This enables researchers to easily compare different approaches,\nimplementations, and method specifications. Furthermore, researchers can build\nupon the standard tools provided by the framework to quickly implement new\ncluster methods, enabling rapid prototyping. We demonstrate the functionality\nand application of the latrend package on a synthetic dataset based on the\ntherapy adherence patterns of patients with sleep apnea.\n", "date": "2024-02-22", "categories": []}
{"id": "2401.16708", "title": "Multivariate Beta Mixture Model: Probabilistic Clustering With Flexible\n  Cluster Shapes", "abstract": "  This paper introduces the multivariate beta mixture model (MBMM), a new\nprobabilistic model for soft clustering. MBMM adapts to diverse cluster shapes\nbecause of the flexible probability density function of the multivariate beta\ndistribution. We introduce the properties of MBMM, describe the parameter\nlearning procedure, and present the experimental results, showing that MBMM\nfits diverse cluster shapes on synthetic and real datasets. The code is\nreleased anonymously at https://github.com/hhchen1105/mbmm/.\n", "date": "2024-01-30", "categories": []}
{"id": "2402.13595", "title": "A cutting plane algorithm for globally solving low dimensional k-means\n  clustering problems", "abstract": "  Clustering is one of the most fundamental tools in data science and machine\nlearning, and k-means clustering is one of the most common such methods. There\nis a variety of approximate algorithms for the k-means problem, but computing\nthe globally optimal solution is in general NP-hard. In this paper we consider\nthe k-means problem for instances with low dimensional data and formulate it as\na structured concave assignment problem. This allows us to exploit the low\ndimensional structure and solve the problem to global optimality within\nreasonable time for large data sets with several clusters. The method builds on\niteratively solving a small concave problem and a large linear programming\nproblem. This gives a sequence of feasible solutions along with bounds which we\nshow converges to zero optimality gap. The paper combines methods from global\noptimization theory to accelerate the procedure, and we provide numerical\nresults on their performance.\n", "date": "2024-02-21", "categories": []}
{"id": "2402.12852", "title": "CCFC++: Enhancing Federated Clustering through Feature Decorrelation", "abstract": "  In federated clustering, multiple data-holding clients collaboratively group\ndata without exchanging raw data. This field has seen notable advancements\nthrough its marriage with contrastive learning, exemplified by\nCluster-Contrastive Federated Clustering (CCFC). However, CCFC suffers from\nheterogeneous data across clients, leading to poor and unrobust performance.\nOur study conducts both empirical and theoretical analyses to understand the\nimpact of heterogeneous data on CCFC. Findings indicate that increased data\nheterogeneity exacerbates dimensional collapse in CCFC, evidenced by increased\ncorrelations across multiple dimensions of the learned representations. To\naddress this, we introduce a decorrelation regularizer to CCFC. Benefiting from\nthe regularizer, the improved method effectively mitigates the detrimental\neffects of data heterogeneity, and achieves superior performance, as evidenced\nby a marked increase in NMI scores, with the gain reaching as high as 0.32 in\nthe most pronounced case.\n", "date": "2024-02-20", "categories": []}
{"id": "2402.02996", "title": "Text-Guided Image Clustering", "abstract": "  Image clustering divides a collection of images into meaningful groups,\ntypically interpreted post-hoc via human-given annotations. Those are usually\nin the form of text, begging the question of using text as an abstraction for\nimage clustering. Current image clustering methods, however, neglect the use of\ngenerated textual descriptions. We, therefore, propose Text-Guided Image\nClustering, i.e., generating text using image captioning and visual\nquestion-answering (VQA) models and subsequently clustering the generated text.\nFurther, we introduce a novel approach to inject task- or domain knowledge for\nclustering by prompting VQA models. Across eight diverse image clustering\ndatasets, our results show that the obtained text representations often\noutperform image features. Additionally, we propose a counting-based cluster\nexplainability method. Our evaluations show that the derived keyword-based\nexplanations describe clusters better than the respective cluster accuracy\nsuggests. Overall, this research challenges traditional approaches and paves\nthe way for a paradigm shift in image clustering, using generated text.\n", "date": "2024-02-05", "categories": []}
{"id": "2402.11066", "title": "Towards Financially Inclusive Credit Products Through Financial Time\n  Series Clustering", "abstract": "  Financial inclusion ensures that individuals have access to financial\nproducts and services that meet their needs. As a key contributing factor to\neconomic growth and investment opportunity, financial inclusion increases\nconsumer spending and consequently business development. It has been shown that\ninstitutions are more profitable when they provide marginalised social groups\naccess to financial services. Customer segmentation based on consumer\ntransaction data is a well-known strategy used to promote financial inclusion.\nWhile the required data is available to modern institutions, the challenge\nremains that segment annotations are usually difficult and/or expensive to\nobtain. This prevents the usage of time series classification models for\ncustomer segmentation based on domain expert knowledge. As a result, clustering\nis an attractive alternative to partition customers into homogeneous groups\nbased on the spending behaviour encoded within their transaction data. In this\npaper, we present a solution to one of the key challenges preventing modern\nfinancial institutions from providing financially inclusive credit, savings and\ninsurance products: the inability to understand consumer financial behaviour,\nand hence risk, without the introduction of restrictive conventional credit\nscoring techniques. We present a novel time series clustering algorithm that\nallows institutions to understand the financial behaviour of their customers.\nThis enables unique product offerings to be provided based on the needs of the\ncustomer, without reliance on restrictive credit practices.\n", "date": "2024-02-16", "categories": []}
{"id": "2402.12008", "title": "Cluster Metric Sensitivity to Irrelevant Features", "abstract": "  Clustering algorithms are used extensively in data analysis for data\nexploration and discovery. Technological advancements lead to continually\ngrowth of data in terms of volume, dimensionality and complexity. This provides\ngreat opportunities in data analytics as the data can be interrogated for many\ndifferent purposes. This however leads challenges, such as identification of\nrelevant features for a given task. In supervised tasks, one can utilise a\nnumber of methods to optimise the input features for the task objective (e.g.\nclassification accuracy). In unsupervised problems, such tools are not readily\navailable, in part due to an inability to quantify feature relevance in\nunlabeled tasks. In this paper, we investigate the sensitivity of clustering\nperformance noisy uncorrelated variables iteratively added to baseline datasets\nwith well defined clusters. We show how different types of irrelevant variables\ncan impact the outcome of a clustering result from $k$-means in different ways.\nWe observe a resilience to very high proportions of irrelevant features for\nadjusted rand index (ARI) and normalised mutual information (NMI) when the\nirrelevant features are Gaussian distributed. For Uniformly distributed\nirrelevant features, we notice the resilience of ARI and NMI is dependent on\nthe dimensionality of the data and exhibits tipping points between high scores\nand near zero. Our results show that the Silhouette Coefficient and the\nDavies-Bouldin score are the most sensitive to irrelevant added features\nexhibiting large changes in score for comparably low proportions of irrelevant\nfeatures regardless of underlying distribution or data scaling. As such the\nSilhouette Coefficient and the Davies-Bouldin score are good candidates for\noptimising feature selection in unsupervised clustering tasks.\n", "date": "2024-02-19", "categories": []}
{"id": "2402.12232", "title": "Kernel KMeans clustering splits for end-to-end unsupervised decision\n  trees", "abstract": "  Trees are convenient models for obtaining explainable predictions on\nrelatively small datasets. Although there are many proposals for the end-to-end\nconstruction of such trees in supervised learning, learning a tree end-to-end\nfor clustering without labels remains an open challenge. As most works focus on\ninterpreting with trees the result of another clustering algorithm, we present\nhere a novel end-to-end trained unsupervised binary tree for clustering: Kauri.\nThis method performs a greedy maximisation of the kernel KMeans objective\nwithout requiring the definition of centroids. We compare this model on\nmultiple datasets with recent unsupervised trees and show that Kauri performs\nidentically when using a linear kernel. For other kernels, Kauri often\noutperforms the concatenation of kernel KMeans and a CART decision tree.\n", "date": "2024-02-19", "categories": []}
{"id": "2402.10229", "title": "Mixture-Models: a one-stop Python Library for Model-based Clustering\n  using various Mixture Models", "abstract": "  \\texttt{Mixture-Models} is an open-source Python library for fitting Gaussian\nMixture Models (GMM) and their variants, such as Parsimonious GMMs, Mixture of\nFactor Analyzers, MClust models, Mixture of Student's t distributions, etc. It\nstreamlines the implementation and analysis of these models using various\nfirst/second order optimization routines such as Gradient Descent and Newton-CG\nthrough automatic differentiation (AD) tools. This helps in extending these\nmodels to high-dimensional data, which is first of its kind among Python\nlibraries. The library provides user-friendly model evaluation tools, such as\nBIC, AIC, and log-likelihood estimation. The source-code is licensed under MIT\nlicense and can be accessed at \\url{https://github.com/kasakh/Mixture-Models}.\nThe package is highly extensible, allowing users to incorporate new\ndistributions and optimization techniques with ease. We conduct a large scale\nsimulation to compare the performance of various gradient based approaches\nagainst Expectation Maximization on a wide range of settings and identify the\ncorresponding best suited approach.\n", "date": "2024-02-08", "categories": []}
{"id": "2402.10756", "title": "Towards Cohesion-Fairness Harmony: Contrastive Regularization in\n  Individual Fair Graph Clustering", "abstract": "  Conventional fair graph clustering methods face two primary challenges: i)\nThey prioritize balanced clusters at the expense of cluster cohesion by\nimposing rigid constraints, ii) Existing methods of both individual and\ngroup-level fairness in graph partitioning mostly rely on eigen decompositions\nand thus, generally lack interpretability. To address these issues, we propose\niFairNMTF, an individual Fairness Nonnegative Matrix Tri-Factorization model\nwith contrastive fairness regularization that achieves balanced and cohesive\nclusters. By introducing fairness regularization, our model allows for\ncustomizable accuracy-fairness trade-offs, thereby enhancing user autonomy\nwithout compromising the interpretability provided by nonnegative matrix\ntri-factorization. Experimental evaluations on real and synthetic datasets\ndemonstrate the superior flexibility of iFairNMTF in achieving fairness and\nclustering performance.\n", "date": "2024-02-16", "categories": []}
{"id": "2211.15118", "title": "A Faster $k$-means++ Algorithm", "abstract": "  $k$-means++ is an important algorithm for choosing initial cluster centers\nfor the $k$-means clustering algorithm. In this work, we present a new\nalgorithm that can solve the $k$-means++ problem with nearly optimal running\ntime. Given $n$ data points in $\\mathbb{R}^d$, the current state-of-the-art\nalgorithm runs in $\\widetilde{O}(k )$ iterations, and each iteration takes\n$\\widetilde{O}(nd k)$ time. The overall running time is thus $\\widetilde{O}(n d\nk^2)$. We propose a new algorithm \\textsc{FastKmeans++} that only takes in\n$\\widetilde{O}(nd + nk^2)$ time, in total.\n", "date": "2022-11-28", "categories": []}
{"id": "2212.03188", "title": "An Unsupervised Machine Learning Approach for Ground-Motion Spectra\n  Clustering and Selection", "abstract": "  Clustering analysis of sequence data continues to address many applications\nin engineering design, aided with the rapid growth of machine learning in\napplied science. This paper presents an unsupervised machine learning algorithm\nto extract defining characteristics of earthquake ground-motion spectra, also\ncalled latent features, to aid in ground-motion selection (GMS). In this\ncontext, a latent feature is a low-dimensional machine-discovered spectral\ncharacteristic learned through nonlinear relationships of a neural network\nautoencoder. Machine discovered latent features can be combined with\ntraditionally defined intensity measures and clustering can be performed to\nselect a representative subgroup from a large ground-motion suite. The\nobjective of efficient GMS is to choose characteristic records representative\nof what the structure will probabilistically experience in its lifetime. Three\nexamples are presented to validate this approach, including the use of\nsynthetic and field recorded ground-motion datasets. The presented deep\nembedding clustering of ground-motion spectra has three main advantages: 1.\ndefining characteristics the represent the sparse spectral content of\nground-motions are discovered efficiently through training of the autoencoder,\n2. domain knowledge is incorporated into the machine learning framework with\nconditional variables in the deep embedding scheme, and 3. method exhibits\nexcellent performance when compared to a benchmark seismic hazard analysis.\n", "date": "2022-12-06", "categories": []}
{"id": "2310.09196", "title": "A 4-approximation algorithm for min max correlation clustering", "abstract": "  We introduce a lower bounding technique for the min max correlation\nclustering problem and, based on this technique, a combinatorial\n4-approximation algorithm for complete graphs. This improves upon the previous\nbest known approximation guarantees of 5, using a linear program formulation\n(Kalhan et al., 2019), and 40, for a combinatorial algorithm (Davies et al.,\n2023a). We extend this algorithm by a greedy joining heuristic and show\nempirically that it improves the state of the art in solution quality and\nruntime on several benchmark datasets.\n", "date": "2023-10-13", "categories": []}
{"id": "2402.08687", "title": "Fuzzy clustering of circular time series based on a new dependence\n  measure with applications to wind data", "abstract": "  Time series clustering is an essential machine learning task with\napplications in many disciplines. While the majority of the methods focus on\ntime series taking values on the real line, very few works consider time series\ndefined on the unit circle, although the latter objects frequently arise in\nmany applications. In this paper, the problem of clustering circular time\nseries is addressed. To this aim, a distance between circular series is\nintroduced and used to construct a clustering procedure. The metric relies on a\nnew measure of serial dependence considering circular arcs, thus taking\nadvantage of the directional character inherent to the series range. Since the\ndynamics of the series may vary over the time, we adopt a fuzzy approach, which\nenables the procedure to locate each series into several clusters with\ndifferent membership degrees. The resulting clustering algorithm is able to\ngroup series generated from similar stochastic processes, reaching accurate\nresults with series coming from a broad variety of models. An extensive\nsimulation study shows that the proposed method outperforms several alternative\ntechniques, besides being computationally efficient. Two interesting\napplications involving time series of wind direction in Saudi Arabia highlight\nthe potential of the proposed approach.\n", "date": "2024-01-26", "categories": []}
{"id": "2402.09167", "title": "Evolving Restricted Boltzmann Machine-Kohonen Network for Online\n  Clustering", "abstract": "  A novel online clustering algorithm is presented where an Evolving Restricted\nBoltzmann Machine (ERBM) is embedded with a Kohonen Network called ERBM-KNet.\nThe proposed ERBM-KNet efficiently handles streaming data in a single-pass mode\nusing the ERBM, employing a bias-variance strategy for neuron growing and\npruning, as well as online clustering based on a cluster update strategy for\ncluster prediction and cluster center update using KNet. Initially, ERBM\nevolves its architecture while processing unlabeled image data, effectively\ndisentangling the data distribution in the latent space. Subsequently, the KNet\nutilizes the feature extracted from ERBM to predict the number of clusters and\nupdates the cluster centers. By overcoming the common challenges associated\nwith clustering algorithms, such as prior initialization of the number of\nclusters and subpar clustering accuracy, the proposed ERBM-KNet offers\nsignificant improvements. Extensive experimental evaluations on four benchmarks\nand one industry dataset demonstrate the superiority of ERBM-KNet compared to\nstate-of-the-art approaches.\n", "date": "2024-02-14", "categories": []}
{"id": "2402.06730", "title": "A Scalable Algorithm for Individually Fair K-means Clustering", "abstract": "  We present a scalable algorithm for the individually fair ($p$,\n$k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$\npoints $P$ in a metric space, let $\\delta(x)$ for $x\\in P$ be the radius of the\nsmallest ball around $x$ containing at least $n / k$ points. A clustering is\nthen called individually fair if it has centers within distance $\\delta(x)$ of\n$x$ for each $x\\in P$. While good approximation algorithms are known for this\nproblem no efficient practical algorithms with good theoretical guarantees have\nbeen presented. We design the first fast local-search algorithm that runs in\n~$O(nk^2)$ time and obtains a bicriteria $(O(1), 6)$ approximation. Then we\nshow empirically that not only is our algorithm much faster than prior work,\nbut it also produces lower-cost solutions.\n", "date": "2024-02-09", "categories": []}
{"id": "2402.06759", "title": "A Methodology for Questionnaire Analysis: Insights through Cluster\n  Analysis of an Investor Competition Data", "abstract": "  In this paper, we propose a methodology for the analysis of questionnaire\ndata along with its application on discovering insights from investor data\nmotivated by a day trading competition. The questionnaire includes categorical\nquestions, which are reduced to binary questions, 'yes' or 'no'. The\nmethodology reduces dimensionality by grouping questions and participants with\nsimilar responses using clustering analysis. Rule discovery was performed by\nusing a conversion rate metric. Innovative visual representations were proposed\nto validate the cluster analysis and the relation discovery between questions.\nWhen crossing with financial data, additional insights were revealed related to\nthe recognized clusters.\n", "date": "2024-02-09", "categories": []}
{"id": "2402.06921", "title": "Clustering Techniques Selection for a Hybrid Regression Model: A Case\n  Study Based on a Solar Thermal System", "abstract": "  This work addresses the performance comparison between four clustering\ntechniques with the objective of achieving strong hybrid models in supervised\nlearning tasks. A real dataset from a bio-climatic house named Sotavento placed\non experimental wind farm and located in Xermade (Lugo) in Galicia (Spain) has\nbeen collected. Authors have chosen the thermal solar generation system in\norder to study how works applying several cluster methods followed by a\nregression technique to predict the output temperature of the system. With the\nobjective of defining the quality of each clustering method two possible\nsolutions have been implemented. The first one is based on three unsupervised\nlearning metrics (Silhouette, Calinski-Harabasz and Davies-Bouldin) while the\nsecond one, employs the most common error measurements for a regression\nalgorithm such as Multi Layer Perceptron.\n", "date": "2024-02-10", "categories": []}
{"id": "2402.05310", "title": "Dual-disentangled Deep Multiple Clustering", "abstract": "  Multiple clustering has gathered significant attention in recent years due to\nits potential to reveal multiple hidden structures of the data from different\nperspectives. Most of multiple clustering methods first derive feature\nrepresentations by controlling the dissimilarity among them, subsequently\nemploying traditional clustering methods (e.g., k-means) to achieve the final\nmultiple clustering outcomes. However, the learned feature representations can\nexhibit a weak relevance to the ultimate goal of distinct clustering. Moreover,\nthese features are often not explicitly learned for the purpose of clustering.\nTherefore, in this paper, we propose a novel Dual-Disentangled deep Multiple\nClustering method named DDMC by learning disentangled representations.\nSpecifically, DDMC is achieved by a variational Expectation-Maximization (EM)\nframework. In the E-step, the disentanglement learning module employs\ncoarse-grained and fine-grained disentangled representations to obtain a more\ndiverse set of latent factors from the data. In the M-step, the cluster\nassignment module utilizes a cluster objective function to augment the\neffectiveness of the cluster output. Our extensive experiments demonstrate that\nDDMC consistently outperforms state-of-the-art methods across seven commonly\nused tasks. Our code is available at https://github.com/Alexander-Yao/DDMC.\n", "date": "2024-02-07", "categories": []}
{"id": "2402.03813", "title": "NK Hybrid Genetic Algorithm for Clustering", "abstract": "  The NK hybrid genetic algorithm for clustering is proposed in this paper. In\norder to evaluate the solutions, the hybrid algorithm uses the NK clustering\nvalidation criterion 2 (NKCV2). NKCV2 uses information about the disposition of\n$N$ small groups of objects. Each group is composed of $K+1$ objects of the\ndataset. Experimental results show that density-based regions can be identified\nby using NKCV2 with fixed small $K$. In NKCV2, the relationship between\ndecision variables is known, which in turn allows us to apply gray box\noptimization. Mutation operators, a partition crossover, and a local search\nstrategy are proposed, all using information about the relationship between\ndecision variables. In partition crossover, the evaluation function is\ndecomposed into $q$ independent components; partition crossover then\ndeterministically returns the best among $2^q$ possible offspring with\ncomputational complexity $O(N)$. The NK hybrid genetic algorithm allows the\ndetection of clusters with arbitrary shapes and the automatic estimation of the\nnumber of clusters. In the experiments, the NK hybrid genetic algorithm\nproduced very good results when compared to another genetic algorithm approach\nand to state-of-art clustering algorithms.\n", "date": "2024-02-06", "categories": []}
{"id": "2402.04103", "title": "An Exploration of Clustering Algorithms for Customer Segmentation in the\n  UK Retail Market", "abstract": "  Recently, peoples awareness of online purchases has significantly risen. This\nhas given rise to online retail platforms and the need for a better\nunderstanding of customer purchasing behaviour. Retail companies are pressed\nwith the need to deal with a high volume of customer purchases, which requires\nsophisticated approaches to perform more accurate and efficient customer\nsegmentation. Customer segmentation is a marketing analytical tool that aids\ncustomer-centric service and thus enhances profitability. In this paper, we aim\nto develop a customer segmentation model to improve decision-making processes\nin the retail market industry. To achieve this, we employed a UK-based online\nretail dataset obtained from the UCI machine learning repository. The retail\ndataset consists of 541,909 customer records and eight features. Our study\nadopted the RFM (recency, frequency, and monetary) framework to quantify\ncustomer values. Thereafter, we compared several state-of-the-art (SOTA)\nclustering algorithms, namely, K-means clustering, the Gaussian mixture model\n(GMM), density-based spatial clustering of applications with noise (DBSCAN),\nagglomerative clustering, and balanced iterative reducing and clustering using\nhierarchies (BIRCH). The results showed the GMM outperformed other approaches,\nwith a Silhouette Score of 0.80.\n", "date": "2024-02-06", "categories": []}
{"id": "2302.02450", "title": "Regularization and Optimization in Model-Based Clustering", "abstract": "  Due to their conceptual simplicity, k-means algorithm variants have been\nextensively used for unsupervised cluster analysis. However, one main\nshortcoming of these algorithms is that they essentially fit a mixture of\nidentical spherical Gaussians to data that vastly deviates from such a\ndistribution. In comparison, general Gaussian Mixture Models (GMMs) can fit\nricher structures but require estimating a quadratic number of parameters per\ncluster to represent the covariance matrices. This poses two main issues: (i)\nthe underlying optimization problems are challenging due to their larger number\nof local minima, and (ii) their solutions can overfit the data. In this work,\nwe design search strategies that circumvent both issues. We develop more\neffective optimization algorithms for general GMMs, and we combine these\nalgorithms with regularization strategies that avoid overfitting. Through\nextensive computational analyses, we observe that optimization or\nregularization in isolation does not substantially improve cluster recovery.\nHowever, combining these techniques permits a completely new level of\nperformance previously unachieved by k-means algorithm variants, unraveling\nvastly different cluster structures. These results shed new light on the\ncurrent status quo between GMM and k-means methods and suggest the more\nfrequent use of general GMMs for data exploration. To facilitate such\napplications, we provide open-source code as well as Julia packages\n(UnsupervisedClustering.jl and RegularizedCovarianceMatrices.jl) implementing\nthe proposed techniques.\n", "date": "2023-02-05", "categories": []}
{"id": "2402.01050", "title": "Distributed MCMC inference for Bayesian Non-Parametric Latent Block\n  Model", "abstract": "  In this paper, we introduce a novel Distributed Markov Chain Monte Carlo\n(MCMC) inference method for the Bayesian Non-Parametric Latent Block Model\n(DisNPLBM), employing the Master/Worker architecture. Our non-parametric\nco-clustering algorithm divides observations and features into partitions using\nlatent multivariate Gaussian block distributions. The workload on rows is\nevenly distributed among workers, who exclusively communicate with the master\nand not among themselves. DisNPLBM demonstrates its impact on cluster labeling\naccuracy and execution times through experimental results. Moreover, we present\na real-use case applying our approach to co-cluster gene expression data. The\ncode source is publicly available at\nhttps://github.com/redakhoufache/Distributed-NPLBM.\n", "date": "2024-02-01", "categories": []}
{"id": "2402.00608", "title": "Deep Clustering Using the Soft Silhouette Score: Towards Compact and\n  Well-Separated Clusters", "abstract": "  Unsupervised learning has gained prominence in the big data era, offering a\nmeans to extract valuable insights from unlabeled datasets. Deep clustering has\nemerged as an important unsupervised category, aiming to exploit the non-linear\nmapping capabilities of neural networks in order to enhance clustering\nperformance. The majority of deep clustering literature focuses on minimizing\nthe inner-cluster variability in some embedded space while keeping the learned\nrepresentation consistent with the original high-dimensional dataset. In this\nwork, we propose soft silhoutte, a probabilistic formulation of the silhouette\ncoefficient. Soft silhouette rewards compact and distinctly separated\nclustering solutions like the conventional silhouette coefficient. When\noptimized within a deep clustering framework, soft silhouette guides the\nlearned representations towards forming compact and well-separated clusters. In\naddition, we introduce an autoencoder-based deep learning architecture that is\nsuitable for optimizing the soft silhouette objective function. The proposed\ndeep clustering method has been tested and compared with several well-studied\ndeep clustering methods on various benchmark datasets, yielding very\nsatisfactory clustering results.\n", "date": "2024-02-01", "categories": []}
{"id": "2301.13530", "title": "Domain-Generalizable Multiple-Domain Clustering", "abstract": "  This work generalizes the problem of unsupervised domain generalization to\nthe case in which no labeled samples are available (completely unsupervised).\nWe are given unlabeled samples from multiple source domains, and we aim to\nlearn a shared predictor that assigns examples to semantically related\nclusters. Evaluation is done by predicting cluster assignments in previously\nunseen domains. Towards this goal, we propose a two-stage training framework:\n(1) self-supervised pre-training for extracting domain invariant semantic\nfeatures. (2) multi-head cluster prediction with pseudo labels, which rely on\nboth the feature space and cluster head prediction, further leveraging a novel\nprediction-based label smoothing scheme. We demonstrate empirically that our\nmodel is more accurate than baselines that require fine-tuning using samples\nfrom the target domain or some level of supervision. Our code is available at\nhttps://github.com/AmitRozner/domain-generalizable-multiple-domain-clustering.\n", "date": "2023-01-31", "categories": []}
{"id": "2401.17033", "title": "Multilayer Graph Approach to Deep Subspace Clustering", "abstract": "  Deep subspace clustering (DSC) networks based on self-expressive model learn\nrepresentation matrix, often implemented in terms of fully connected network,\nin the embedded space. After the learning is finished, representation matrix is\nused by spectral clustering module to assign labels to clusters. However, such\napproach ignores complementary information that exist in other layers of the\nencoder (including the input data themselves). Herein, we apply selected linear\nsubspace clustering algorithm to learn representation matrices from\nrepresentations learned by all layers of encoder network including the input\ndata. Afterward, we learn a multilayer graph that in a multi-view like manner\nintegrates information from graph Laplacians of all used layers. That improves\nfurther performance of selected DSC network. Furthermore, we also provide\nformulation of our approach to cluster out-of-sample/test data points. We\nvalidate proposed approach on four well-known datasets with two DSC networks as\nbaseline models. In almost all the cases, proposed approach achieved\nstatistically significant improvement in three performance metrics. MATLAB code\nof proposed algorithm is posted on https://github.com/lovro-sinda/MLG-DSC.\n", "date": "2024-01-30", "categories": []}
{"id": "2401.17035", "title": "Robust Kernel Sparse Subspace Clustering", "abstract": "  Kernel methods are applied to many problems in pattern recognition, including\nsubspace clustering (SC). That way, nonlinear problems in the input data space\nbecome linear in mapped high-dimensional feature space. Thereby,\ncomputationally tractable nonlinear algorithms are enabled through implicit\nmapping by the virtue of kernel trick. However, kernelization of linear\nalgorithms is possible only if square of the Froebenious norm of the error term\nis used in related optimization problem. That, however, implies normal\ndistribution of the error. That is not appropriate for non-Gaussian errors such\nas gross sparse corruptions that are modeled by -norm. Herein, to the best of\nour knowledge, we propose for the first time robust kernel sparse SC (RKSSC)\nalgorithm for data with gross sparse corruptions. The concept, in principle,\ncan be applied to other SC algorithms to achieve robustness to the presence of\nsuch type of corruption. We validated proposed approach on two well-known\ndatasets with linear robust SSC algorithm as a baseline model. According to\nWilcoxon test, clustering performance obtained by the RKSSC algorithm is\nstatistically significantly better than corresponding performance obtained by\nthe robust SSC algorithm. MATLAB code of proposed RKSSC algorithm is posted on\nhttps://github.com/ikopriva/RKSSC.\n", "date": "2024-01-30", "categories": []}
{"id": "2304.10769", "title": "Deep Multiview Clustering by Contrasting Cluster Assignments", "abstract": "  Multiview clustering (MVC) aims to reveal the underlying structure of\nmultiview data by categorizing data samples into clusters. Deep learning-based\nmethods exhibit strong feature learning capabilities on large-scale datasets.\nFor most existing deep MVC methods, exploring the invariant representations of\nmultiple views is still an intractable problem. In this paper, we propose a\ncross-view contrastive learning (CVCL) method that learns view-invariant\nrepresentations and produces clustering results by contrasting the cluster\nassignments among multiple views. Specifically, we first employ deep\nautoencoders to extract view-dependent features in the pretraining stage. Then,\na cluster-level CVCL strategy is presented to explore consistent semantic label\ninformation among the multiple views in the fine-tuning stage. Thus, the\nproposed CVCL method is able to produce more discriminative cluster assignments\nby virtue of this learning strategy. Moreover, we provide a theoretical\nanalysis of soft cluster assignment alignment. Extensive experimental results\nobtained on several datasets demonstrate that the proposed CVCL method\noutperforms several state-of-the-art approaches.\n", "date": "2023-04-21", "categories": []}
{"id": "2401.15691", "title": "One for all: A novel Dual-space Co-training baseline for Large-scale\n  Multi-View Clustering", "abstract": "  In this paper, we propose a novel multi-view clustering model, named\nDual-space Co-training Large-scale Multi-view Clustering (DSCMC). The main\nobjective of our approach is to enhance the clustering performance by\nleveraging co-training in two distinct spaces. In the original space, we learn\na projection matrix to obtain latent consistent anchor graphs from different\nviews. This process involves capturing the inherent relationships and\nstructures between data points within each view. Concurrently, we employ a\nfeature transformation matrix to map samples from various views to a shared\nlatent space. This transformation facilitates the alignment of information from\nmultiple views, enabling a comprehensive understanding of the underlying data\ndistribution. We jointly optimize the construction of the latent consistent\nanchor graph and the feature transformation to generate a discriminative anchor\ngraph. This anchor graph effectively captures the essential characteristics of\nthe multi-view data and serves as a reliable basis for subsequent clustering\nanalysis. Moreover, the element-wise method is proposed to avoid the impact of\ndiverse information between different views. Our algorithm has an approximate\nlinear computational complexity, which guarantees its successful application on\nlarge-scale datasets. Through experimental validation, we demonstrate that our\nmethod significantly reduces computational complexity while yielding superior\nclustering performance compared to existing approaches.\n", "date": "2024-01-28", "categories": []}
{"id": "2401.15773", "title": "Evaluation of k-means time series clustering based on z-normalization\n  and NP-Free", "abstract": "  Despite the widespread use of k-means time series clustering in various\ndomains, there exists a gap in the literature regarding its comprehensive\nevaluation with different time series normalization approaches. This paper\nseeks to fill this gap by conducting a thorough performance evaluation of\nk-means time series clustering on real-world open-source time series datasets.\nThe evaluation focuses on two distinct normalization techniques:\nz-normalization and NP-Free. The former is one of the most commonly used\nnormalization approach for time series. The latter is a real-time time series\nrepresentation approach, which can serve as a time series normalization\napproach. The primary objective of this paper is to assess the impact of these\ntwo normalization techniques on k-means time series clustering in terms of its\nclustering quality. The experiments employ the silhouette score, a\nwell-established metric for evaluating the quality of clusters in a dataset. By\nsystematically investigating the performance of k-means time series clustering\nwith these two normalization techniques, this paper addresses the current gap\nin k-means time series clustering evaluation and contributes valuable insights\nto the development of time series clustering.\n", "date": "2024-01-28", "categories": []}
{"id": "2401.15989", "title": "Deep Embedding Clustering Driven by Sample Stability", "abstract": "  Deep clustering methods improve the performance of clustering tasks by\njointly optimizing deep representation learning and clustering. While numerous\ndeep clustering algorithms have been proposed, most of them rely on\nartificially constructed pseudo targets for performing clustering. This\nconstruction process requires some prior knowledge, and it is challenging to\ndetermine a suitable pseudo target for clustering. To address this issue, we\npropose a deep embedding clustering algorithm driven by sample stability\n(DECS), which eliminates the requirement of pseudo targets. Specifically, we\nstart by constructing the initial feature space with an autoencoder and then\nlearn the cluster-oriented embedding feature constrained by sample stability.\nThe sample stability aims to explore the deterministic relationship between\nsamples and all cluster centroids, pulling samples to their respective clusters\nand keeping them away from other clusters with high determinacy. We analyzed\nthe convergence of the loss using Lipschitz continuity in theory, which\nverifies the validity of the model. The experimental results on five datasets\nillustrate that the proposed method achieves superior performance compared to\nstate-of-the-art clustering approaches.\n", "date": "2024-01-29", "categories": []}
{"id": "2401.14439", "title": "Incremental Affinity Propagation based on Cluster Consolidation and\n  Stratification", "abstract": "  Modern data mining applications require to perform incremental clustering\nover dynamic datasets by tracing temporal changes over the resulting clusters.\nIn this paper, we propose A-Posteriori affinity Propagation (APP), an\nincremental extension of Affinity Propagation (AP) based on cluster\nconsolidation and cluster stratification to achieve faithfulness and\nforgetfulness. APP enforces incremental clustering where i) new arriving\nobjects are dynamically consolidated into previous clusters without the need to\nre-execute clustering over the entire dataset of objects, and ii) a faithful\nsequence of clustering results is produced and maintained over time, while\nallowing to forget obsolete clusters with decremental learning functionalities.\nFour popular labeled datasets are used to test the performance of APP with\nrespect to benchmark clustering performances obtained by conventional AP and\nIncremental Affinity Propagation based on Nearest neighbor Assignment (IAPNA)\nalgorithms. Experimental results show that APP achieves comparable clustering\nperformance while enforcing scalability at the same time.\n", "date": "2024-01-25", "categories": []}
{"id": "2401.10972", "title": "Clustering Molecular Energy Landscapes by Adaptive Network Embedding", "abstract": "  In order to efficiently explore the chemical space of all possible small\nmolecules, a common approach is to compress the dimension of the system to\nfacilitate downstream machine learning tasks. Towards this end, we present a\ndata driven approach for clustering potential energy landscapes of molecular\nstructures by applying recently developed Network Embedding techniques, to\nobtain latent variables defined through the embedding function. To scale up the\nmethod, we also incorporate an entropy sensitive adaptive scheme for\nhierarchical sampling of the energy landscape, based on Metadynamics and\nTransition Path Theory. By taking into account the kinetic information implied\nby a system's energy landscape, we are able to interpret dynamical node-node\nrelationships in reduced dimensions. We demonstrate the framework through\nLennard-Jones (LJ) clusters and a human DNA sequence.\n", "date": "2024-01-19", "categories": []}
{"id": "2401.11402", "title": "Enabling clustering algorithms to detect clusters of varying densities\n  through scale-invariant data preprocessing", "abstract": "  In this paper, we show that preprocessing data using a variant of rank\ntransformation called 'Average Rank over an Ensemble of Sub-samples (ARES)'\nmakes clustering algorithms robust to data representation and enable them to\ndetect varying density clusters. Our empirical results, obtained using three\nmost widely used clustering algorithms-namely KMeans, DBSCAN, and DP (Density\nPeak)-across a wide range of real-world datasets, show that clustering after\nARES transformation produces better and more consistent results.\n", "date": "2024-01-21", "categories": []}
{"id": "2401.11740", "title": "Multi-level Cross-modal Alignment for Image Clustering", "abstract": "  Recently, the cross-modal pretraining model has been employed to produce\nmeaningful pseudo-labels to supervise the training of an image clustering\nmodel. However, numerous erroneous alignments in a cross-modal pre-training\nmodel could produce poor-quality pseudo-labels and degrade clustering\nperformance. To solve the aforementioned issue, we propose a novel\n\\textbf{Multi-level Cross-modal Alignment} method to improve the alignments in\na cross-modal pretraining model for downstream tasks, by building a smaller but\nbetter semantic space and aligning the images and texts in three levels, i.e.,\ninstance-level, prototype-level, and semantic-level. Theoretical results show\nthat our proposed method converges, and suggests effective means to reduce the\nexpected clustering risk of our method. Experimental results on five benchmark\ndatasets clearly show the superiority of our new method.\n", "date": "2024-01-22", "categories": []}
{"id": "2304.00429", "title": "Information Recovery-Driven Deep Incomplete Multiview Clustering Network", "abstract": "  Incomplete multi-view clustering is a hot and emerging topic. It is well\nknown that unavoidable data incompleteness greatly weakens the effective\ninformation of multi-view data. To date, existing incomplete multi-view\nclustering methods usually bypass unavailable views according to prior missing\ninformation, which is considered as a second-best scheme based on evasion.\nOther methods that attempt to recover missing information are mostly applicable\nto specific two-view datasets. To handle these problems, in this paper, we\npropose an information recovery-driven deep incomplete multi-view clustering\nnetwork, termed as RecFormer. Concretely, a two-stage autoencoder network with\nthe self-attention structure is built to synchronously extract high-level\nsemantic representations of multiple views and recover the missing data.\nBesides, we develop a recurrent graph reconstruction mechanism that cleverly\nleverages the restored views to promote the representation learning and the\nfurther data reconstruction. Visualization of recovery results are given and\nsufficient experimental results confirm that our RecFormer has obvious\nadvantages over other top methods.\n", "date": "2023-04-02", "categories": []}
{"id": "2308.11164", "title": "Decoupled Contrastive Multi-View Clustering with High-Order Random Walks", "abstract": "  In recent, some robust contrastive multi-view clustering (MvC) methods have\nbeen proposed, which construct data pairs from neighborhoods to alleviate the\nfalse negative issue, i.e., some intra-cluster samples are wrongly treated as\nnegative pairs. Although promising performance has been achieved by these\nmethods, the false negative issue is still far from addressed and the false\npositive issue emerges because all in- and out-of-neighborhood samples are\nsimply treated as positive and negative, respectively. To address the issues,\nwe propose a novel robust method, dubbed decoupled contrastive multi-view\nclustering with high-order random walks (DIVIDE). In brief, DIVIDE leverages\nrandom walks to progressively identify data pairs in a global instead of local\nmanner. As a result, DIVIDE could identify in-neighborhood negatives and\nout-of-neighborhood positives. Moreover, DIVIDE embraces a novel MvC\narchitecture to perform inter- and intra-view contrastive learning in different\nembedding spaces, thus boosting clustering performance and embracing the\nrobustness against missing views. To verify the efficacy of DIVIDE, we carry\nout extensive experiments on four benchmark datasets comparing with nine\nstate-of-the-art MvC methods in both complete and incomplete MvC settings.\n", "date": "2023-08-22", "categories": []}
{"id": "2401.09266", "title": "P$^2$OT: Progressive Partial Optimal Transport for Deep Imbalanced\n  Clustering", "abstract": "  Deep clustering, which learns representation and semantic clustering without\nlabels information, poses a great challenge for deep learning-based approaches.\nDespite significant progress in recent years, most existing methods focus on\nuniformly distributed datasets, significantly limiting the practical\napplicability of their methods. In this paper, we first introduce a more\npractical problem setting named deep imbalanced clustering, where the\nunderlying classes exhibit an imbalance distribution. To tackle this problem,\nwe propose a novel pseudo-labeling-based learning framework. Our framework\nformulates pseudo-label generation as a progressive partial optimal transport\nproblem, which progressively transports each sample to imbalanced clusters\nunder prior distribution constraints, thus generating imbalance-aware\npseudo-labels and learning from high-confident samples. In addition, we\ntransform the initial formulation into an unbalanced optimal transport problem\nwith augmented constraints, which can be solved efficiently by a fast matrix\nscaling algorithm. Experiments on various datasets, including a human-curated\nlong-tailed CIFAR100, challenging ImageNet-R, and large-scale subsets of\nfine-grained iNaturalist2018 datasets, demonstrate the superiority of our\nmethod.\n", "date": "2024-01-17", "categories": []}
{"id": "2310.12600", "title": "FUSC: Fetal Ultrasound Semantic Clustering of Second Trimester Scans\n  Using Deep Self-supervised Learning", "abstract": "  Ultrasound is the primary imaging modality in clinical practice during\npregnancy. More than 140M fetuses are born yearly, resulting in numerous scans.\nThe availability of a large volume of fetal ultrasound scans presents the\nopportunity to train robust machine learning models. However, the abundance of\nscans also has its challenges, as manual labeling of each image is needed for\nsupervised methods. Labeling is typically labor-intensive and requires\nexpertise to annotate the images accurately. This study presents an\nunsupervised approach for automatically clustering ultrasound images into a\nlarge range of fetal views, reducing or eliminating the need for manual\nlabeling. Our Fetal Ultrasound Semantic Clustering (FUSC) method is developed\nusing a large dataset of 88,063 images and further evaluated on an additional\nunseen dataset of 8,187 images achieving over 92% clustering purity. The result\nof our investigation hold the potential to significantly impact the field of\nfetal ultrasound imaging and pave the way for more advanced automated labeling\nsolutions. Finally, we make the code and the experimental setup publicly\navailable to help advance the field.\n", "date": "2023-10-19", "categories": []}
{"id": "2312.13845", "title": "Image Clustering using Restricted Boltzman Machine", "abstract": "  In various verification systems, Restricted Boltzmann Machines (RBMs) have\ndemonstrated their efficacy in both front-end and back-end processes. In this\nwork, we propose the use of RBMs to the image clustering tasks. RBMs are\ntrained to convert images into image embeddings. We employ the conventional\nbottom-up Agglomerative Hierarchical Clustering (AHC) technique. To address the\nchallenge of limited test face image data, we introduce Agglomerative\nHierarchical Clustering based Method for Image Clustering using Restricted\nBoltzmann Machine (AHC-RBM) with two major steps. Initially, a universal RBM\nmodel is trained using all available training dataset. Subsequently, we train\nan adapted RBM model using the data from each test image. Finally, RBM vectors\nwhich is the embedding vector is generated by concatenating the\nvisible-to-hidden weight matrices of these adapted models, and the bias\nvectors. These vectors effectively preserve class-specific information and are\nutilized in image clustering tasks. Our experimental results, conducted on two\nbenchmark image datasets (MS-Celeb-1M and DeepFashion), demonstrate that our\nproposed approach surpasses well-known clustering algorithms such as k-means,\nspectral clustering, and approximate Rank-order.\n", "date": "2023-12-21", "categories": []}
{"id": "2401.07091", "title": "Optimization of Inter-group Criteria for Clustering with Minimum Size\n  Constraints", "abstract": "  Internal measures that are used to assess the quality of a clustering usually\ntake into account intra-group and/or inter-group criteria. There are many\npapers in the literature that propose algorithms with provable approximation\nguarantees for optimizing the former. However, the optimization of inter-group\ncriteria is much less understood.\n  Here, we contribute to the state-of-the-art of this literature by devising\nalgorithms with provable guarantees for the maximization of two natural\ninter-group criteria, namely the minimum spacing and the minimum spanning tree\nspacing. The former is the minimum distance between points in different groups\nwhile the latter captures separability through the cost of the minimum spanning\ntree that connects all groups. We obtain results for both the unrestricted\ncase, in which no constraint on the clusters is imposed, and for the\nconstrained case where each group is required to have a minimum number of\npoints. Our constraint is motivated by the fact that the popular Single\nLinkage, which optimizes both criteria in the unrestricted case, produces\nclusterings with many tiny groups.\n  To complement our work, we present an empirical study with 10 real datasets,\nproviding evidence that our methods work very well in practical settings.\n", "date": "2024-01-13", "categories": []}
{"id": "2401.07389", "title": "A Rapid Review of Clustering Algorithms", "abstract": "  Clustering algorithms aim to organize data into groups or clusters based on\nthe inherent patterns and similarities within the data. They play an important\nrole in today's life, such as in marketing and e-commerce, healthcare, data\norganization and analysis, and social media. Numerous clustering algorithms\nexist, with ongoing developments introducing new ones. Each algorithm possesses\nits own set of strengths and weaknesses, and as of now, there is no universally\napplicable algorithm for all tasks. In this work, we analyzed existing\nclustering algorithms and classify mainstream algorithms across five different\ndimensions: underlying principles and characteristics, data point assignment to\nclusters, dataset capacity, predefined cluster numbers and application area.\nThis classification facilitates researchers in understanding clustering\nalgorithms from various perspectives and helps them identify algorithms\nsuitable for solving specific tasks. Finally, we discussed the current trends\nand potential future directions in clustering algorithms. We also identified\nand discussed open challenges and unresolved issues in the field.\n", "date": "2024-01-14", "categories": []}
{"id": "2401.06595", "title": "Every Node is Different: Dynamically Fusing Self-Supervised Tasks for\n  Attributed Graph Clustering", "abstract": "  Attributed graph clustering is an unsupervised task that partitions nodes\ninto different groups. Self-supervised learning (SSL) shows great potential in\nhandling this task, and some recent studies simultaneously learn multiple SSL\ntasks to further boost performance. Currently, different SSL tasks are assigned\nthe same set of weights for all graph nodes. However, we observe that some\ngraph nodes whose neighbors are in different groups require significantly\ndifferent emphases on SSL tasks. In this paper, we propose to dynamically learn\nthe weights of SSL tasks for different nodes and fuse the embeddings learned\nfrom different SSL tasks to boost performance. We design an innovative graph\nclustering approach, namely Dynamically Fusing Self-Supervised Learning\n(DyFSS). Specifically, DyFSS fuses features extracted from diverse SSL tasks\nusing distinct weights derived from a gating network. To effectively learn the\ngating network, we design a dual-level self-supervised strategy that\nincorporates pseudo labels and the graph structure. Extensive experiments on\nfive datasets show that DyFSS outperforms the state-of-the-art multi-task SSL\nmethods by up to 8.66% on the accuracy metric. The code of DyFSS is available\nat: https://github.com/q086/DyFSS.\n", "date": "2024-01-12", "categories": []}
{"id": "2401.05479", "title": "The recursive scheme of clustering", "abstract": "  The problem of data clustering is one of the most important in data analysis.\nIt can be problematic when dealing with experimental data characterized by\nmeasurement uncertainties and errors. Our paper proposes a recursive scheme for\nclustering data obtained in geographical (climatological) experiments. The\ndiscussion of results obtained by k-means and SOM methods with the developed\nrecursive procedure is presented. We show that the clustering using the new\napproach gives more acceptable results when compared to experts assessments.\n", "date": "2024-01-10", "categories": []}
{"id": "2312.17286", "title": "Comparative study of clustering models for multivariate time series from\n  connected medical devices", "abstract": "  In healthcare, patient data is often collected as multivariate time series,\nproviding a comprehensive view of a patient's health status over time. While\nthis data can be sparse, connected devices may enhance its frequency. The goal\nis to create patient profiles from these time series. In the absence of labels,\na predictive model can be used to predict future values while forming a latent\ncluster space, evaluated based on predictive performance. We compare two models\non Withing's datasets, M AGMAC LUST which clusters entire time series and\nDGM${}^2$ which allows the group affiliation of an individual to change over\ntime (dynamic clustering).\n", "date": "2023-12-28", "categories": []}
{"id": "2401.04741", "title": "Masked AutoEncoder for Graph Clustering without Pre-defined Cluster\n  Number k", "abstract": "  Graph clustering algorithms with autoencoder structures have recently gained\npopularity due to their efficient performance and low training cost. However,\nfor existing graph autoencoder clustering algorithms based on GCN or GAT, not\nonly do they lack good generalization ability, but also the number of clusters\nclustered by such autoencoder models is difficult to determine automatically.\nTo solve this problem, we propose a new framework called Graph Clustering with\nMasked Autoencoders (GCMA). It employs our designed fusion autoencoder based on\nthe graph masking method for the fusion coding of graph. It introduces our\nimproved density-based clustering algorithm as a second decoder while decoding\nwith multi-target reconstruction. By decoding the mask embedding, our model can\ncapture more generalized and comprehensive knowledge. The number of clusters\nand clustering results can be output end-to-end while improving the\ngeneralization ability. As a nonparametric class method, extensive experiments\ndemonstrate the superiority of \\textit{GCMA} over state-of-the-art baselines.\n", "date": "2024-01-09", "categories": []}
{"id": "2401.04682", "title": "Mixture of multilayer stochastic block models for multiview clustering", "abstract": "  In this work, we propose an original method for aggregating multiple\nclustering coming from different sources of information. Each partition is\nencoded by a co-membership matrix between observations. Our approach uses a\nmixture of multilayer Stochastic Block Models (SBM) to group co-membership\nmatrices with similar information into components and to partition observations\ninto different clusters, taking into account their specificities within the\ncomponents. The identifiability of the model parameters is established and a\nvariational Bayesian EM algorithm is proposed for the estimation of these\nparameters. The Bayesian framework allows for selecting an optimal number of\nclusters and components. The proposed approach is compared using synthetic data\nwith consensus clustering and tensor-based algorithms for community detection\nin large-scale complex networks. Finally, the method is utilized to analyze\nglobal food trading networks, leading to structures of interest.\n", "date": "2024-01-09", "categories": []}
{"id": "2401.03198", "title": "Learning-Augmented K-Means Clustering Using Dimensional Reduction", "abstract": "  Learning augmented is a machine learning concept built to improve the\nperformance of a method or model, such as enhancing its ability to predict and\ngeneralize data or features, or testing the reliability of the method by\nintroducing noise and other factors. On the other hand, clustering is a\nfundamental aspect of data analysis and has long been used to understand the\nstructure of large datasets. Despite its long history, the k-means algorithm\nstill faces challenges. One approach, as suggested by Ergun et al,is to use a\npredictor to minimize the sum of squared distances between each data point and\na specified centroid. However, it is known that the computational cost of this\nalgorithm increases with the value of k, and it often gets stuck in local\nminima. In response to these challenges, we propose a solution to reduce the\ndimensionality of the dataset using Principal Component Analysis (PCA). It is\nworth noting that when using k values of 10 and 25, the proposed algorithm\nyields lower cost results compared to running it without PCA. \"Principal\ncomponent analysis (PCA) is the problem of fitting a low-dimensional affine\nsubspace to a set of data points in a high-dimensional space. PCA is\nwell-established in the literature and has become one of the most useful tools\nfor data modeling, compression, and visualization.\"\n", "date": "2024-01-06", "categories": []}
{"id": "2212.04443", "title": "A Distributed Block Chebyshev-Davidson Algorithm for Parallel Spectral\n  Clustering", "abstract": "  We develop a distributed Block Chebyshev-Davidson algorithm to solve\nlarge-scale leading eigenvalue problems for spectral analysis in spectral\nclustering. First, the efficiency of the Chebyshev-Davidson algorithm relies on\nthe prior knowledge of the eigenvalue spectrum, which could be expensive to\nestimate. This issue can be lessened by the analytic spectrum estimation of the\nLaplacian or normalized Laplacian matrices in spectral clustering, making the\nproposed algorithm very efficient for spectral clustering. Second, to make the\nproposed algorithm capable of analyzing big data, a distributed and parallel\nversion has been developed with attractive scalability. The speedup by parallel\ncomputing is approximately equivalent to $\\sqrt{p}$, where $p$ denotes the\nnumber of processes. {Numerical results will be provided to demonstrate its\nefficiency in spectral clustering and scalability advantage over existing\neigensolvers used for spectral clustering in parallel computing environments.}\n", "date": "2022-12-08", "categories": []}
{"id": "2401.02682", "title": "Homophily-Related: Adaptive Hybrid Graph Filter for Multi-View Graph\n  Clustering", "abstract": "  Recently there is a growing focus on graph data, and multi-view graph\nclustering has become a popular area of research interest. Most of the existing\nmethods are only applicable to homophilous graphs, yet the extensive real-world\ngraph data can hardly fulfill the homophily assumption, where the connected\nnodes tend to belong to the same class. Several studies have pointed out that\nthe poor performance on heterophilous graphs is actually due to the fact that\nconventional graph neural networks (GNNs), which are essentially low-pass\nfilters, discard information other than the low-frequency information on the\ngraph. Nevertheless, on certain graphs, particularly heterophilous ones,\nneglecting high-frequency information and focusing solely on low-frequency\ninformation impedes the learning of node representations. To break this\nlimitation, our motivation is to perform graph filtering that is closely\nrelated to the homophily degree of the given graph, with the aim of fully\nleveraging both low-frequency and high-frequency signals to learn\ndistinguishable node embedding. In this work, we propose Adaptive Hybrid Graph\nFilter for Multi-View Graph Clustering (AHGFC). Specifically, a graph joint\nprocess and graph joint aggregation matrix are first designed by using the\nintrinsic node features and adjacency relationship, which makes the low and\nhigh-frequency signals on the graph more distinguishable. Then we design an\nadaptive hybrid graph filter that is related to the homophily degree, which\nlearns the node embedding based on the graph joint aggregation matrix. After\nthat, the node embedding of each view is weighted and fused into a consensus\nembedding for the downstream task. Experimental results show that our proposed\nmodel performs well on six datasets containing homophilous and heterophilous\ngraphs.\n", "date": "2024-01-05", "categories": []}
{"id": "2401.02709", "title": "German Text Embedding Clustering Benchmark", "abstract": "  This work introduces a benchmark assessing the performance of clustering\nGerman text embeddings in different domains. This benchmark is driven by the\nincreasing use of clustering neural text embeddings in tasks that require the\ngrouping of texts (such as topic modeling) and the need for German resources in\nexisting benchmarks. We provide an initial analysis for a range of pre-trained\nmono- and multilingual models evaluated on the outcome of different clustering\nalgorithms. Results include strong performing mono- and multilingual models.\nReducing the dimensions of embeddings can further improve clustering.\nAdditionally, we conduct experiments with continued pre-training for German\nBERT models to estimate the benefits of this additional training. Our\nexperiments suggest that significant performance improvements are possible for\nshort text. All code and datasets are publicly available.\n", "date": "2024-01-05", "categories": []}
{"id": "2310.17878", "title": "A Sublinear-Time Spectral Clustering Oracle with Improved Preprocessing\n  Time", "abstract": "  We address the problem of designing a sublinear-time spectral clustering\noracle for graphs that exhibit strong clusterability. Such graphs contain $k$\nlatent clusters, each characterized by a large inner conductance (at least\n$\\varphi$) and a small outer conductance (at most $\\varepsilon$). Our aim is to\npreprocess the graph to enable clustering membership queries, with the key\nrequirement that both preprocessing and query answering should be performed in\nsublinear time, and the resulting partition should be consistent with a\n$k$-partition that is close to the ground-truth clustering. Previous oracles\nhave relied on either a $\\textrm{poly}(k)\\log n$ gap between inner and outer\nconductances or exponential (in $k/\\varepsilon$) preprocessing time. Our\nalgorithm relaxes these assumptions, albeit at the cost of a slightly higher\nmisclassification ratio. We also show that our clustering oracle is robust\nagainst a few random edge deletions. To validate our theoretical bounds, we\nconducted experiments on synthetic networks.\n", "date": "2023-10-27", "categories": []}
{"id": "2312.16830", "title": "A Contrastive Variational Graph Auto-Encoder for Node Clustering", "abstract": "  Variational Graph Auto-Encoders (VGAEs) have been widely used to solve the\nnode clustering task. However, the state-of-the-art methods have numerous\nchallenges. First, existing VGAEs do not account for the discrepancy between\nthe inference and generative models after incorporating the clustering\ninductive bias. Second, current models are prone to degenerate solutions that\nmake the latent codes match the prior independently of the input signal (i.e.,\nPosterior Collapse). Third, existing VGAEs overlook the effect of the noisy\nclustering assignments (i.e., Feature Randomness) and the impact of the strong\ntrade-off between clustering and reconstruction (i.e., Feature Drift). To\naddress these problems, we formulate a variational lower bound in a contrastive\nsetting. Our lower bound is a tighter approximation of the log-likelihood\nfunction than the corresponding Evidence Lower BOund (ELBO). Thanks to a newly\nidentified term, our lower bound can escape Posterior Collapse and has more\nflexibility to account for the difference between the inference and generative\nmodels. Additionally, our solution has two mechanisms to control the trade-off\nbetween Feature Randomness and Feature Drift. Extensive experiments show that\nthe proposed method achieves state-of-the-art clustering results on several\ndatasets. We provide strong evidence that this improvement is attributed to\nfour aspects: integrating contrastive learning and alleviating Feature\nRandomness, Feature Drift, and Posterior Collapse.\n", "date": "2023-12-28", "categories": []}
{"id": "2312.16926", "title": "Efficient High-Quality Clustering for Large Bipartite Graphs", "abstract": "  A bipartite graph contains inter-set edges between two disjoint vertex sets,\nand is widely used to model real-world data, such as user-item purchase\nrecords, author-article publications, and biological interactions between drugs\nand proteins. k-Bipartite Graph Clustering (k-BGC) is to partition the target\nvertex set in a bipartite graph into k disjoint clusters. The clustering\nquality is important to the utility of k-BGC in various applications like\nsocial network analysis, recommendation systems, text mining, and\nbioinformatics, to name a few. Existing approaches to k-BGC either output\nclustering results with compromised quality due to inadequate exploitation of\nhigh-order information between vertices, or fail to handle sizable bipartite\ngraphs with billions of edges.\n  Motivated by this, this paper presents two efficient k-BGC solutions, HOPE\nand HOPE+, which achieve state-of-the-art performance on large-scale bipartite\ngraphs. HOPE obtains high scalability and effectiveness through a new k-BGC\nproblem formulation based on the novel notion of high-order perspective (HOP)\nvectors and an efficient technique for low-rank approximation of HOP vectors.\nHOPE+ further elevates the k-BGC performance to another level with a judicious\nproblem transformation and a highly efficient two-stage optimization framework.\nTwo variants, HOPE+ (FNEM) and HOPE+ (SNEM) are designed when either the\nFrobenius norm or spectral norm is applied in the transformation. Extensive\nexperiments, comparing HOPE and HOPE+ against 13 competitors on 10 real-world\ndatasets, exhibit that our solutions, especially HOPE+, are superior to\nexisting methods in terms of result quality, while being up to orders of\nmagnitude faster. On the largest dataset MAG with 1.1 billion edges, HOPE+ is\nable to produce clusters with the highest clustering accuracy within 31\nminutes, which is unmatched by any existing solution for k-BGC.\n", "date": "2023-12-28", "categories": []}
{"id": "2312.15447", "title": "Superpixel-based and Spatially-regularized Diffusion Learning for\n  Unsupervised Hyperspectral Image Clustering", "abstract": "  Hyperspectral images (HSIs) provide exceptional spatial and spectral\nresolution of a scene, crucial for various remote sensing applications.\nHowever, the high dimensionality, presence of noise and outliers, and the need\nfor precise labels of HSIs present significant challenges to HSIs analysis,\nmotivating the development of performant HSI clustering algorithms. This paper\nintroduces a novel unsupervised HSI clustering algorithm, Superpixel-based and\nSpatially-regularized Diffusion Learning (S2DL), which addresses these\nchallenges by incorporating rich spatial information encoded in HSIs into\ndiffusion geometry-based clustering. S2DL employs the Entropy Rate Superpixel\n(ERS) segmentation technique to partition an image into superpixels, then\nconstructs a spatially-regularized diffusion graph using the most\nrepresentative high-density pixels. This approach reduces computational burden\nwhile preserving accuracy. Cluster modes, serving as exemplars for underlying\ncluster structure, are identified as the highest-density pixels farthest in\ndiffusion distance from other highest-density pixels. These modes guide the\nlabeling of the remaining representative pixels from ERS superpixels. Finally,\nmajority voting is applied to the labels assigned within each superpixel to\npropagate labels to the rest of the image. This spatial-spectral approach\nsimultaneously simplifies graph construction, reduces computational cost, and\nimproves clustering performance. S2DL's performance is illustrated with\nextensive experiments on three publicly available, real-world HSIs: Indian\nPines, Salinas, and Salinas A. Additionally, we apply S2DL to landscape-scale,\nunsupervised mangrove species mapping in the Mai Po Nature Reserve, Hong Kong,\nusing a Gaofen-5 HSI. The success of S2DL in these diverse numerical\nexperiments indicates its efficacy on a wide range of important unsupervised\nremote sensing analysis tasks.\n", "date": "2023-12-24", "categories": []}
{"id": "2312.15577", "title": "Deep Structure and Attention Aware Subspace Clustering", "abstract": "  Clustering is a fundamental unsupervised representation learning task with\nwide application in computer vision and pattern recognition. Deep clustering\nutilizes deep neural networks to learn latent representation, which is suitable\nfor clustering. However, previous deep clustering methods, especially image\nclustering, focus on the features of the data itself and ignore the\nrelationship between the data, which is crucial for clustering. In this paper,\nwe propose a novel Deep Structure and Attention aware Subspace Clustering\n(DSASC), which simultaneously considers data content and structure information.\nWe use a vision transformer to extract features, and the extracted features are\ndivided into two parts, structure features, and content features. The two\nfeatures are used to learn a more efficient subspace structure for spectral\nclustering. Extensive experimental results demonstrate that our method\nsignificantly outperforms state-of-the-art methods. Our code will be available\nat https://github.com/cs-whh/DSASC\n", "date": "2023-12-25", "categories": []}
{"id": "2312.15684", "title": "Stochastic mean-shift clustering", "abstract": "  In this paper we presented a stochastic version mean-shift clustering\nalgorithm. In the stochastic version the data points \"climb\" to the modes of\nthe distribution collectively, while in the deterministic mean-shift, each\ndatum \"climbs\" individually, while all other data points remains in their\noriginal coordinates. Stochastic version of the mean-shift clustering is\ncomparison with a standard (deterministic) mean-shift clustering on synthesized\n2- and 3-dimensional data distributed between several Gaussian component. The\ncomparison performed in terms of cluster purity and class data purity. It was\nfound the the stochastic mean-shift clustering outperformed in most of the\ncases the deterministic mean-shift.\n", "date": "2023-12-25", "categories": []}
{"id": "2211.01877", "title": "Convex Clustering through MM: An Efficient Algorithm to Perform\n  Hierarchical Clustering", "abstract": "  Convex clustering is a modern method with both hierarchical and $k$-means\nclustering characteristics. Although convex clustering can capture complex\nclustering structures hidden in data, the existing convex clustering algorithms\nare not scalable to large data sets with sample sizes greater than several\nthousands. Moreover, it is known that convex clustering sometimes fails to\nproduce a complete hierarchical clustering structure. This issue arises if\nclusters split up or the minimum number of possible clusters is larger than the\ndesired number of clusters. In this paper, we propose convex clustering through\nmajorization-minimization (CCMM) -- an iterative algorithm that uses cluster\nfusions and a highly efficient updating scheme derived using diagonal\nmajorization. Additionally, we explore different strategies to ensure that the\nhierarchical clustering structure terminates in a single cluster. With a\ncurrent desktop computer, CCMM efficiently solves convex clustering problems\nfeaturing over one million objects in seven-dimensional space, achieving a\nsolution time of 51 seconds on average.\n", "date": "2022-11-03", "categories": []}
{"id": "2305.12743", "title": "Semantic Invariant Multi-view Clustering with Fully Incomplete\n  Information", "abstract": "  Robust multi-view learning with incomplete information has received\nsignificant attention due to issues such as incomplete correspondences and\nincomplete instances that commonly affect real-world multi-view applications.\nExisting approaches heavily rely on paired samples to realign or impute\ndefective ones, but such preconditions cannot always be satisfied in practice\ndue to the complexity of data collection and transmission. To address this\nproblem, we present a novel framework called SeMantic Invariance LEarning\n(SMILE) for multi-view clustering with incomplete information that does not\nrequire any paired samples. To be specific, we discover the existence of\ninvariant semantic distribution across different views, which enables SMILE to\nalleviate the cross-view discrepancy to learn consensus semantics without\nrequiring any paired samples. The resulting consensus semantics remain\nunaffected by cross-view distribution shifts, making them useful for\nrealigning/imputing defective instances and forming clusters. We demonstrate\nthe effectiveness of SMILE through extensive comparison experiments with 13\nstate-of-the-art baselines on five benchmarks. Our approach improves the\nclustering accuracy of NoisyMNIST from 19.3\\%/23.2\\% to 82.7\\%/69.0\\% when the\ncorrespondences/instances are fully incomplete. The code could be accessed from\nhttps://pengxi.me.\n", "date": "2023-05-22", "categories": []}
{"id": "2312.14066", "title": "Upper Bounding Barlow Twins: A Novel Filter for Multi-Relational\n  Clustering", "abstract": "  Multi-relational clustering is a challenging task due to the fact that\ndiverse semantic information conveyed in multi-layer graphs is difficult to\nextract and fuse. Recent methods integrate topology structure and node\nattribute information through graph filtering. However, they often use a\nlow-pass filter without fully considering the correlation among multiple\ngraphs. To overcome this drawback, we propose to learn a graph filter motivated\nby the theoretical analysis of Barlow Twins. We find that input with a negative\nsemi-definite inner product provides a lower bound for Barlow Twins loss, which\nprevents it from reaching a better solution. We thus learn a filter that yields\nan upper bound for Barlow Twins. Afterward, we design a simple clustering\narchitecture and demonstrate its state-of-the-art performance on four benchmark\ndatasets.\n", "date": "2023-12-21", "categories": []}
{"id": "2312.12697", "title": "DGCLUSTER: A Neural Framework for Attributed Graph Clustering via\n  Modularity Maximization", "abstract": "  Graph clustering is a fundamental and challenging task in the field of graph\nmining where the objective is to group the nodes into clusters taking into\nconsideration the topology of the graph. It has several applications in diverse\ndomains spanning social network analysis, recommender systems, computer vision,\nand bioinformatics. In this work, we propose a novel method, DGCluster, which\nprimarily optimizes the modularity objective using graph neural networks and\nscales linearly with the graph size. Our method does not require the number of\nclusters to be specified as a part of the input and can also leverage the\navailability of auxiliary node level information. We extensively test DGCluster\non several real-world datasets of varying sizes, across multiple popular\ncluster quality metrics. Our approach consistently outperforms the\nstate-of-the-art methods, demonstrating significant performance gains in almost\nall settings.\n", "date": "2023-12-20", "categories": []}
{"id": "2312.11475", "title": "A Hybrid SOM and K-means Model for Time Series Energy Consumption\n  Clustering", "abstract": "  Energy consumption analysis plays a pivotal role in addressing the challenges\nof sustainability and resource management. This paper introduces a novel\napproach to effectively cluster monthly energy consumption patterns by\nintegrating two powerful techniques: Self-organizing maps and K-means\nclustering. The proposed method aims to exploit the benefits of both of these\nalgorithms to enhance the accuracy and interpretability of clustering results\nfor a dataset in which finding patterns is difficult. The main focus of this\nstudy is on a selection of time series energy consumption data from the Smart\nmeters in London dataset. The data was preprocessed and reduced in\ndimensionality to capture essential temporal patterns while retaining their\nunderlying structures. The SOM algorithm was utilized to extract the central\nrepresentatives of the consumption patterns for each one of the houses over the\ncourse of each month, effectively reducing the dimensionality of the dataset\nand making it easier for analysis. Subsequently, the obtained SOM centroids\nwere clustered using K-means, a popular centroid-based clustering technique.\nThe experimental results demonstrated a significant silhouette score of 66%,\nindicating strong intra-cluster cohesion and inter-cluster separation which\nconfirms the effectiveness of the proposed approach in the clustering task.\n", "date": "2023-11-25", "categories": []}
{"id": "2312.11769", "title": "Clustering Mixtures of Bounded Covariance Distributions Under Optimal\n  Separation", "abstract": "  We study the clustering problem for mixtures of bounded covariance\ndistributions, under a fine-grained separation assumption. Specifically, given\nsamples from a $k$-component mixture distribution $D = \\sum_{i =1}^k w_i P_i$,\nwhere each $w_i \\ge \\alpha$ for some known parameter $\\alpha$, and each $P_i$\nhas unknown covariance $\\Sigma_i \\preceq \\sigma^2_i \\cdot I_d$ for some unknown\n$\\sigma_i$, the goal is to cluster the samples assuming a pairwise mean\nseparation in the order of $(\\sigma_i+\\sigma_j)/\\sqrt{\\alpha}$ between every\npair of components $P_i$ and $P_j$. Our contributions are as follows:\n  For the special case of nearly uniform mixtures, we give the first poly-time\nalgorithm for this clustering task. Prior work either required separation\nscaling with the maximum cluster standard deviation (i.e. $\\max_i \\sigma_i$)\n[DKK+22b] or required both additional structural assumptions and mean\nseparation scaling as a large degree polynomial in $1/\\alpha$ [BKK22].\n  For general-weight mixtures, we point out that accurate clustering is\ninformation-theoretically impossible under our fine-grained mean separation\nassumptions. We introduce the notion of a clustering refinement -- a list of\nnot-too-small subsets satisfying a similar separation, and which can be merged\ninto a clustering approximating the ground truth -- and show that it is\npossible to efficiently compute an accurate clustering refinement of the\nsamples. Furthermore, under a variant of the \"no large sub-cluster'' condition\nfrom in prior work [BKK22], we show that our algorithm outputs an accurate\nclustering, not just a refinement, even for general-weight mixtures. As a\ncorollary, we obtain efficient clustering algorithms for mixtures of\nwell-conditioned high-dimensional log-concave distributions.\n  Moreover, our algorithm is robust to $\\Omega(\\alpha)$-fraction of adversarial\noutliers.\n", "date": "2023-12-19", "categories": []}
{"id": "2310.18890", "title": "Towards Generalized Multi-stage Clustering: Multi-view Self-distillation", "abstract": "  Existing multi-stage clustering methods independently learn the salient\nfeatures from multiple views and then perform the clustering task.\nParticularly, multi-view clustering (MVC) has attracted a lot of attention in\nmulti-view or multi-modal scenarios. MVC aims at exploring common semantics and\npseudo-labels from multiple views and clustering in a self-supervised manner.\nHowever, limited by noisy data and inadequate feature learning, such a\nclustering paradigm generates overconfident pseudo-labels that mis-guide the\nmodel to produce inaccurate predictions. Therefore, it is desirable to have a\nmethod that can correct this pseudo-label mistraction in multi-stage clustering\nto avoid the bias accumulation. To alleviate the effect of overconfident\npseudo-labels and improve the generalization ability of the model, this paper\nproposes a novel multi-stage deep MVC framework where multi-view\nself-distillation (DistilMVC) is introduced to distill dark knowledge of label\ndistribution. Specifically, in the feature subspace at different hierarchies,\nwe explore the common semantics of multiple views through contrastive learning\nand obtain pseudo-labels by maximizing the mutual information between views.\nAdditionally, a teacher network is responsible for distilling pseudo-labels\ninto dark knowledge, supervising the student network and improving its\npredictive capabilities to enhance the robustness. Extensive experiments on\nreal-world multi-view datasets show that our method has better clustering\nperformance than state-of-the-art methods.\n", "date": "2023-10-29", "categories": []}
{"id": "2312.10047", "title": "Clustering Students According to their Academic Achievement Using Fuzzy\n  Logic", "abstract": "  The software for clustering students according to their educational\nachievements using fuzzy logic was developed in Python using the Google Colab\ncloud service. In the process of analyzing educational data, the problems of\nData Mining are solved, since only some characteristics of the educational\nprocess are obtained from a large sample of data. Data clustering was performed\nusing the classic K-Means method, which is characterized by simplicity and high\nspeed. Cluster analysis was performed in the space of two features using the\nmachine learning library scikit-learn (Python). The obtained clusters are\ndescribed by fuzzy triangular membership functions, which allowed to correctly\ndetermine the membership of each student to a certain cluster. Creation of\nfuzzy membership functions is done using the scikit-fuzzy library. The\ndevelopment of fuzzy functions of objects belonging to clusters is also useful\nfor educational purposes, as it allows a better understanding of the principles\nof using fuzzy logic. As a result of processing test educational data using the\ndeveloped software, correct results were obtained. It is shown that the use of\nfuzzy membership functions makes it possible to correctly determine the\nbelonging of students to certain clusters, even if such clusters are not\nclearly separated. Due to this, it is possible to more accurately determine the\nrecommended level of difficulty of tasks for each student, depending on his\nprevious evaluations.\n", "date": "2023-12-01", "categories": []}
{"id": "2312.10917", "title": "Semi-Supervised Clustering via Structural Entropy with Different\n  Constraints", "abstract": "  Semi-supervised clustering techniques have emerged as valuable tools for\nleveraging prior information in the form of constraints to improve the quality\nof clustering outcomes. Despite the proliferation of such methods, the ability\nto seamlessly integrate various types of constraints remains limited. While\nstructural entropy has proven to be a powerful clustering approach with\nwide-ranging applications, it has lacked a variant capable of accommodating\nthese constraints. In this work, we present Semi-supervised clustering via\nStructural Entropy (SSE), a novel method that can incorporate different types\nof constraints from diverse sources to perform both partitioning and\nhierarchical clustering. Specifically, we formulate a uniform view for the\ncommonly used pairwise and label constraints for both types of clustering.\nThen, we design objectives that incorporate these constraints into structural\nentropy and develop tailored algorithms for their optimization. We evaluate SSE\non nine clustering datasets and compare it with eleven semi-supervised\npartitioning and hierarchical clustering methods. Experimental results\ndemonstrate the superiority of SSE on clustering accuracy with different types\nof constraints. Additionally, the functionality of SSE for biological data\nanalysis is demonstrated by cell clustering experiments conducted on four\nsingle-cell RNAseq datasets.\n", "date": "2023-12-18", "categories": []}
{"id": "2312.11169", "title": "Distributed Collapsed Gibbs Sampler for Dirichlet Process Mixture Models\n  in Federated Learning", "abstract": "  Dirichlet Process Mixture Models (DPMMs) are widely used to address\nclustering problems. Their main advantage lies in their ability to\nautomatically estimate the number of clusters during the inference process\nthrough the Bayesian non-parametric framework. However, the inference becomes\nconsiderably slow as the dataset size increases. This paper proposes a new\ndistributed Markov Chain Monte Carlo (MCMC) inference method for DPMMs (DisCGS)\nusing sufficient statistics. Our approach uses the collapsed Gibbs sampler and\nis specifically designed to work on distributed data across independent and\nheterogeneous machines, which habilitates its use in horizontal federated\nlearning. Our method achieves highly promising results and notable scalability.\nFor instance, with a dataset of 100K data points, the centralized algorithm\nrequires approximately 12 hours to complete 100 iterations while our approach\nachieves the same number of iterations in just 3 minutes, reducing the\nexecution time by a factor of 200 without compromising clustering performance.\nThe code source is publicly available at\nhttps://github.com/redakhoufache/DisCGS.\n", "date": "2023-12-18", "categories": []}
{"id": "2312.11323", "title": "UniForCE: The Unimodality Forest Method for Clustering and Estimation of\n  the Number of Clusters", "abstract": "  Estimating the number of clusters k while clustering the data is a\nchallenging task. An incorrect cluster assumption indicates that the number of\nclusters k gets wrongly estimated. Consequently, the model fitting becomes less\nimportant. In this work, we focus on the concept of unimodality and propose a\nflexible cluster definition called locally unimodal cluster. A locally unimodal\ncluster extends for as long as unimodality is locally preserved across pairs of\nsubclusters of the data. Then, we propose the UniForCE method for locally\nunimodal clustering. The method starts with an initial overclustering of the\ndata and relies on the unimodality graph that connects subclusters forming\nunimodal pairs. Such pairs are identified using an appropriate statistical\ntest. UniForCE identifies maximal locally unimodal clusters by computing a\nspanning forest in the unimodality graph. Experimental results on both real and\nsynthetic datasets illustrate that the proposed methodology is particularly\nflexible and robust in discovering regular and highly complex cluster shapes.\nMost importantly, it automatically provides an adequate estimation of the\nnumber of clusters.\n", "date": "2023-12-18", "categories": []}
{"id": "2312.09630", "title": "Pixel-Superpixel Contrastive Learning and Pseudo-Label Correction for\n  Hyperspectral Image Clustering", "abstract": "  Hyperspectral image (HSI) clustering is gaining considerable attention owing\nto recent methods that overcome the inefficiency and misleading results from\nthe absence of supervised information. Contrastive learning methods excel at\nexisting pixel level and super pixel level HSI clustering tasks. The\npixel-level contrastive learning method can effectively improve the ability of\nthe model to capture fine features of HSI but requires a large time overhead.\nThe super pixel-level contrastive learning method utilizes the homogeneity of\nHSI and reduces computing resources; however, it yields rough classification\nresults. To exploit the strengths of both methods, we present a pixel super\npixel contrastive learning and pseudo-label correction (PSCPC) method for the\nHSI clustering. PSCPC can reasonably capture domain-specific and fine-grained\nfeatures through super pixels and the comparative learning of a small number of\npixels within the super pixels. To improve the clustering performance of super\npixels, this paper proposes a pseudo-label correction module that aligns the\nclustering pseudo-labels of pixels and super-pixels. In addition, pixel-level\nclustering results are used to supervise super pixel-level clustering,\nimproving the generalization ability of the model. Extensive experiments\ndemonstrate the effectiveness and efficiency of PSCPC.\n", "date": "2023-12-15", "categories": []}
{"id": "2312.08697", "title": "Incomplete Contrastive Multi-View Clustering with High-Confidence\n  Guiding", "abstract": "  Incomplete multi-view clustering becomes an important research problem, since\nmulti-view data with missing values are ubiquitous in real-world applications.\nAlthough great efforts have been made for incomplete multi-view clustering,\nthere are still some challenges: 1) most existing methods didn't make full use\nof multi-view information to deal with missing values; 2) most methods just\nemploy the consistent information within multi-view data but ignore the\ncomplementary information; 3) For the existing incomplete multi-view clustering\nmethods, incomplete multi-view representation learning and clustering are\ntreated as independent processes, which leads to performance gap. In this work,\nwe proposed a novel Incomplete Contrastive Multi-View Clustering method with\nhigh-confidence guiding (ICMVC). Firstly, we proposed a multi-view consistency\nrelation transfer plus graph convolutional network to tackle missing values\nproblem. Secondly, instance-level attention fusion and high-confidence guiding\nare proposed to exploit the complementary information while instance-level\ncontrastive learning for latent representation is designed to employ the\nconsistent information. Thirdly, an end-to-end framework is proposed to\nintegrate multi-view missing values handling, multi-view representation\nlearning and clustering assignment for joint optimization. Experiments compared\nwith state-of-the-art approaches demonstrated the effectiveness and superiority\nof our method. Our code is publicly available at\nhttps://github.com/liunian-Jay/ICMVC.\n", "date": "2023-12-14", "categories": []}
{"id": "2312.09061", "title": "Fair Clustering: A Causal Perspective", "abstract": "  Clustering algorithms may unintentionally propagate or intensify existing\ndisparities, leading to unfair representations or biased decision-making.\nCurrent fair clustering methods rely on notions of fairness that do not capture\nany information on the underlying causal mechanisms. We show that optimising\nfor non-causal fairness notions can paradoxically induce direct discriminatory\neffects from a causal standpoint. We present a clustering approach that\nincorporates causal fairness metrics to provide a more nuanced approach to\nfairness in unsupervised learning. Our approach enables the specification of\nthe causal fairness metrics that should be minimised. We demonstrate the\nefficacy of our methodology using datasets known to harbour unfair biases.\n", "date": "2023-12-14", "categories": []}
{"id": "2312.07556", "title": "Federated Learning for Short Text Clustering", "abstract": "  Short text clustering has been popularly studied for its significance in\nmining valuable insights from many short texts. In this paper, we focus on the\nfederated short text clustering (FSTC) problem, i.e., clustering short texts\nthat are distributed in different clients, which is a realistic problem under\nprivacy requirements. Compared with the centralized short text clustering\nproblem that short texts are stored on a central server, the FSTC problem has\nnot been explored yet. To fill this gap, we propose a Federated Robust Short\nText Clustering (FSTC) framework. FSTC includes two main modules, i.e., robust\nshort text clustering module and federated cluster center aggregation module.\nThe robust short text clustering module aims to train an effective short text\nclustering model with local data in each client. We innovatively combine\noptimal transport to generate pseudo-labels with Gaussian-uniform mixture model\nto ensure the reliability of the pseudo-supervised data. The federated cluster\ncenter aggregation module aims to exchange knowledge across clients without\nsharing local raw data in an efficient way. The server aggregates the local\ncluster centers from different clients and then sends the global centers back\nto all clients in each communication round. Our empirical studies on three\nshort text clustering datasets demonstrate that FSTC significantly outperforms\nthe federated short text clustering baselines.\n", "date": "2023-11-23", "categories": []}
{"id": "2312.07769", "title": "Incremental hierarchical text clustering methods: a review", "abstract": "  The growth in Internet usage has contributed to a large volume of\ncontinuously available data, and has created the need for automatic and\nefficient organization of the data. In this context, text clustering techniques\nare significant because they aim to organize documents according to their\ncharacteristics. More specifically, hierarchical and incremental clustering\ntechniques can organize dynamic data in a hierarchical form, thus guaranteeing\nthat this organization is updated and its exploration is facilitated. Based on\nthe relevance and contemporary nature of the field, this study aims to analyze\nvarious hierarchical and incremental clustering techniques; the main\ncontribution of this research is the organization and comparison of the\ntechniques used by studies published between 2010 and 2018 that aimed to texts\ndocuments clustering. We describe the principal concepts related to the\nchallenge and the different characteristics of these published works in order\nto provide a better understanding of the research in this field.\n", "date": "2023-12-12", "categories": []}
{"id": "2312.08029", "title": "ClusterDDPM: An EM clustering framework with Denoising Diffusion\n  Probabilistic Models", "abstract": "  Variational autoencoder (VAE) and generative adversarial networks (GAN) have\nfound widespread applications in clustering and have achieved significant\nsuccess. However, the potential of these approaches may be limited due to VAE's\nmediocre generation capability or GAN's well-known instability during\nadversarial training. In contrast, denoising diffusion probabilistic models\n(DDPMs) represent a new and promising class of generative models that may\nunlock fresh dimensions in clustering. In this study, we introduce an\ninnovative expectation-maximization (EM) framework for clustering using DDPMs.\nIn the E-step, we aim to derive a mixture of Gaussian priors for the subsequent\nM-step. In the M-step, our focus lies in learning clustering-friendly latent\nrepresentations for the data by employing the conditional DDPM and matching the\ndistribution of latent representations to the mixture of Gaussian priors. We\npresent a rigorous theoretical analysis of the optimization process in the\nM-step, proving that the optimizations are equivalent to maximizing the lower\nbound of the Q function within the vanilla EM framework under certain\nconstraints. Comprehensive experiments validate the advantages of the proposed\nframework, showcasing superior performance in clustering, unsupervised\nconditional generation and latent representation learning.\n", "date": "2023-12-13", "categories": []}
{"id": "2301.10403", "title": "Exact and rapid linear clustering of networks with dynamic programming", "abstract": "  We study the problem of clustering networks whose nodes have imputed or\nphysical positions in a single dimension, for example prestige hierarchies or\nthe similarity dimension of hyperbolic embeddings. Existing algorithms, such as\nthe critical gap method and other greedy strategies, only offer approximate\nsolutions to this problem. Here, we introduce a dynamic programming approach\nthat returns provably optimal solutions in polynomial time -- O(n^2) steps --\nfor a broad class of clustering objectives. We demonstrate the algorithm\nthrough applications to synthetic and empirical networks and show that it\noutperforms existing heuristics by a significant margin, with a similar\nexecution time.\n", "date": "2023-01-25", "categories": []}
{"id": "2312.06068", "title": "Contrastive Multi-view Subspace Clustering of Hyperspectral Images based\n  on Graph Convolutional Networks", "abstract": "  High-dimensional and complex spectral structures make the clustering of\nhyperspectral images (HSI) a challenging task. Subspace clustering is an\neffective approach for addressing this problem. However, current subspace\nclustering algorithms are primarily designed for a single view and do not fully\nexploit the spatial or textural feature information in HSI. In this study,\ncontrastive multi-view subspace clustering of HSI was proposed based on graph\nconvolutional networks. Pixel neighbor textural and spatial-spectral\ninformation were sent to construct two graph convolutional subspaces to learn\ntheir affinity matrices. To maximize the interaction between different views, a\ncontrastive learning algorithm was introduced to promote the consistency of\npositive samples and assist the model in extracting robust features. An\nattention-based fusion module was used to adaptively integrate these affinity\nmatrices, constructing a more discriminative affinity matrix. The model was\nevaluated using four popular HSI datasets: Indian Pines, Pavia University,\nHouston, and Xu Zhou. It achieved overall accuracies of 97.61%, 96.69%, 87.21%,\nand 97.65%, respectively, and significantly outperformed state-of-the-art\nclustering methods. In conclusion, the proposed model effectively improves the\nclustering accuracy of HSI.\n", "date": "2023-12-11", "categories": []}
{"id": "2312.06546", "title": "Unsupervised KPIs-Based Clustering of Jobs in HPC Data Centers", "abstract": "  Performance analysis is an essential task in High-Performance Computing (HPC)\nsystems and it is applied for different purposes such as anomaly detection,\noptimal resource allocation, and budget planning. HPC monitoring tasks generate\na huge number of Key Performance Indicators (KPIs) to supervise the status of\nthe jobs running in these systems. KPIs give data about CPU usage, memory\nusage, network (interface) traffic, or other sensors that monitor the hardware.\nAnalyzing this data, it is possible to obtain insightful information about\nrunning jobs, such as their characteristics, performance, and failures. The\nmain contribution in this paper is to identify which metric/s (KPIs) is/are the\nmost appropriate to identify/classify different types of jobs according to\ntheir behavior in the HPC system. With this aim, we have applied different\nclustering techniques (partition and hierarchical clustering algorithms) using\na real dataset from the Galician Computation Center (CESGA). We have concluded\nthat (i) those metrics (KPIs) related to the Network (interface) traffic\nmonitoring provide the best cohesion and separation to cluster HPC jobs, and\n(ii) hierarchical clustering algorithms are the most suitable for this task.\nOur approach was validated using a different real dataset from the same HPC\ncenter.\n", "date": "2023-12-11", "categories": []}
{"id": "2312.05028", "title": "Cluster images with AntClust: a clustering algorithm based on the\n  chemical recognition system of ants", "abstract": "  We implement AntClust, a clustering algorithm based on the chemical\nrecognition system of ants and use it to cluster images of cars. We will give a\nshort recap summary of the main working principles of the algorithm as devised\nby the original paper [1]. Further, we will describe how to define a similarity\nfunction for images and how the implementation is used to cluster images of\ncars from the vehicle re-identification data set. We then test the clustering\nperformance of AntClust against DBSCAN, HDBSCAN and OPTICS. Finally one of the\ncore parts in AntClust, the rule set can be easily redefined with our\nimplementation, enabling a way for other bio-inspired algorithms to find rules\nin an automated process. The implementation can be found on GitLab [9].\n", "date": "2023-12-08", "categories": []}
{"id": "2312.04067", "title": "MeanCut: A Greedy-Optimized Graph Clustering via Path-based Similarity\n  and Degree Descent Criterion", "abstract": "  As the most typical graph clustering method, spectral clustering is popular\nand attractive due to the remarkable performance, easy implementation, and\nstrong adaptability. Classical spectral clustering measures the edge weights of\ngraph using pairwise Euclidean-based metric, and solves the optimal graph\npartition by relaxing the constraints of indicator matrix and performing\nLaplacian decomposition. However, Euclidean-based similarity might cause skew\ngraph cuts when handling non-spherical data distributions, and the relaxation\nstrategy introduces information loss. Meanwhile, spectral clustering requires\nspecifying the number of clusters, which is hard to determine without enough\nprior knowledge. In this work, we leverage the path-based similarity to enhance\nintra-cluster associations, and propose MeanCut as the objective function and\ngreedily optimize it in degree descending order for a nondestructive graph\npartition. This algorithm enables the identification of arbitrary shaped\nclusters and is robust to noise. To reduce the computational complexity of\nsimilarity calculation, we transform optimal path search into generating the\nmaximum spanning tree (MST), and develop a fast MST (FastMST) algorithm to\nfurther improve its time-efficiency. Moreover, we define a density gradient\nfactor (DGF) for separating the weakly connected clusters. The validity of our\nalgorithm is demonstrated by testifying on real-world benchmarks and\napplication of face recognition. The source code of MeanCut is available at\nhttps://github.com/ZPGuiGroupWhu/MeanCut-Clustering.\n", "date": "2023-12-07", "categories": []}
{"id": "2312.04209", "title": "Constrained Hierarchical Clustering via Graph Coarsening and Optimal\n  Cuts", "abstract": "  Motivated by extracting and summarizing relevant information in short\nsentence settings, such as satisfaction questionnaires, hotel reviews, and\nX/Twitter, we study the problem of clustering words in a hierarchical fashion.\nIn particular, we focus on the problem of clustering with horizontal and\nvertical structural constraints. Horizontal constraints are typically\ncannot-link and must-link among words, while vertical constraints are\nprecedence constraints among cluster levels. We overcome state-of-the-art\nbottlenecks by formulating the problem in two steps: first, as a\nsoft-constrained regularized least-squares which guides the result of a\nsequential graph coarsening algorithm towards the horizontal feasible set.\nThen, flat clusters are extracted from the resulting hierarchical tree by\ncomputing optimal cut heights based on the available constraints. We show that\nthe resulting approach compares very well with respect to existing algorithms\nand is computationally light.\n", "date": "2023-12-07", "categories": []}
{"id": "2312.04275", "title": "Estimating Countries with Similar Maternal Mortality Rate using Cluster\n  Analysis and Pairing Countries with Identical MMR", "abstract": "  In the evolving world, we require more additionally the young era to flourish\nand evolve into developed land. Most of the population all around the world are\nunaware of the complications involved in the routine they follow while they are\npregnant and how hospital facilities affect maternal health. Maternal Mortality\nis the death of a pregnant woman due to intricacies correlated to pregnancy,\nunderlying circumstances exacerbated by the pregnancy or management of these\nsituations. It is crucial to consider the Maternal Mortality Rate (MMR) in\ndiverse locations and determine which human routines and hospital facilities\ndiminish the Maternal Mortality Rate (MMR). This research aims to examine and\ndiscover the countries which are keeping more lavish threats of MMR and\ncountries alike in MMR encountered. Data is examined and collected for various\ncountries, data consists of the earlier years' observation. From the\nperspective of Machine Learning, Unsupervised Machine Learning is implemented\nto perform Cluster Analysis. Therefore the pairs of countries with similar MMR\nas well as the extreme opposite pair concerning the MMR are found.\n", "date": "2023-12-07", "categories": []}
{"id": "2310.09718", "title": "Efficient and Effective Deep Multi-view Subspace Clustering", "abstract": "  Recent multi-view subspace clustering achieves impressive results utilizing\ndeep networks, where the self-expressive correlation is typically modeled by a\nfully connected (FC) layer. However, they still suffer from two limitations. i)\nThe parameter scale of the FC layer is quadratic to sample numbers, resulting\nin high time and memory costs that significantly degrade their feasibility in\nlarge-scale datasets. ii) It is under-explored to extract a unified\nrepresentation that simultaneously satisfies minimal sufficiency and\ndiscriminability. To this end, we propose a novel deep framework, termed\nEfficient and Effective deep Multi-View Subspace Clustering (E$^2$MVSC).\nInstead of a parameterized FC layer, we design a Relation-Metric Net that\ndecouples network parameter scale from sample numbers for greater computational\nefficiency. Most importantly, the proposed method devises a multi-type\nauto-encoder to explicitly decouple consistent, complementary, and superfluous\ninformation from every view, which is supervised by a soft clustering\nassignment similarity constraint. Following information bottleneck theory and\nthe maximal coding rate reduction principle, a sufficient yet minimal unified\nrepresentation can be obtained, as well as pursuing intra-cluster aggregation\nand inter-cluster separability within it. Extensive experiments show that\nE$^2$MVSC yields comparable results to existing methods and achieves\nstate-of-the-art performance in various types of multi-view datasets.\n", "date": "2023-10-15", "categories": []}
{"id": "2312.01137", "title": "Fast and Robust Sparsity-Aware Block Diagonal Representation", "abstract": "  The block diagonal structure of an affinity matrix is a commonly desired\nproperty in cluster analysis because it represents clusters of feature vectors\nby non-zero coefficients that are concentrated in blocks. However, recovering a\nblock diagonal affinity matrix is challenging in real-world applications, in\nwhich the data may be subject to outliers and heavy-tailed noise that obscure\nthe hidden cluster structure. To address this issue, we first analyze the\neffect of different fundamental outlier types in graph-based cluster analysis.\nA key idea that simplifies the analysis is to introduce a vector that\nrepresents a block diagonal matrix as a piece-wise linear function of the\nsimilarity coefficients that form the affinity matrix. We reformulate the\nproblem as a robust piece-wise linear fitting problem and propose a Fast and\nRobust Sparsity-Aware Block Diagonal Representation (FRS-BDR) method, which\njointly estimates cluster memberships and the number of blocks. Comprehensive\nexperiments on a variety of real-world applications demonstrate the\neffectiveness of FRS-BDR in terms of clustering accuracy, robustness against\ncorrupted features, computation time and cluster enumeration performance.\n", "date": "2023-12-02", "categories": []}
{"id": "2303.07321", "title": "Collision Cross-entropy for Soft Class Labels and Deep Clustering", "abstract": "  We propose \"collision cross-entropy\" as a robust alternative to Shannon's\ncross-entropy (CE) loss when class labels are represented by soft categorical\ndistributions y. In general, soft labels can naturally represent ambiguous\ntargets in classification. They are particularly relevant for self-labeled\nclustering methods, where latent pseudo-labels are jointly estimated with the\nmodel parameters and uncertainty is prevalent. In case of soft labels,\nShannon's CE teaches the model predictions to reproduce the uncertainty in each\ntraining example, which inhibits the model's ability to learn and generalize\nfrom these examples. As an alternative loss, we propose the negative log of\n\"collision probability\" that maximizes the chance of equality between two\nrandom variables, predicted class and unknown true class. We show that it has\nthe properties of a generalized CE. The proposed collision CE agrees with\nShannon's CE for one-hot labels, but the training from soft labels differs. For\nexample, unlike Shannon's CE, data points where y is a uniform distribution\nhave zero contribution to the training. Collision CE significantly improves\nclassification supervised by soft uncertain targets. Unlike Shannon's,\ncollision CE is symmetric for y and network predictions, which is particularly\nrelevant when both distributions are estimated in the context of self-labeled\nclustering. Focusing on discriminative deep clustering where self-labeling and\nentropy-based losses are dominant, we show that the use of collision CE\nimproves the state-of-the-art. We also derive an efficient EM algorithm that\nsignificantly speeds up the pseudo-label estimation with collision CE.\n", "date": "2023-03-13", "categories": []}
{"id": "2311.17103", "title": "Single-cell Multi-view Clustering via Community Detection with Unknown\n  Number of Clusters", "abstract": "  Single-cell multi-view clustering enables the exploration of cellular\nheterogeneity within the same cell from different views. Despite the\ndevelopment of several multi-view clustering methods, two primary challenges\npersist. Firstly, most existing methods treat the information from both\nsingle-cell RNA (scRNA) and single-cell Assay of Transposase Accessible\nChromatin (scATAC) views as equally significant, overlooking the substantial\ndisparity in data richness between the two views. This oversight frequently\nleads to a degradation in overall performance. Additionally, the majority of\nclustering methods necessitate manual specification of the number of clusters\nby users. However, for biologists dealing with cell data, precisely determining\nthe number of distinct cell types poses a formidable challenge. To this end, we\nintroduce scUNC, an innovative multi-view clustering approach tailored for\nsingle-cell data, which seamlessly integrates information from different views\nwithout the need for a predefined number of clusters. The scUNC method\ncomprises several steps: initially, it employs a cross-view fusion network to\ncreate an effective embedding, which is then utilized to generate initial\nclusters via community detection. Subsequently, the clusters are automatically\nmerged and optimized until no further clusters can be merged. We conducted a\ncomprehensive evaluation of scUNC using three distinct single-cell datasets.\nThe results underscored that scUNC outperforms the other baseline methods.\n", "date": "2023-11-28", "categories": []}
{"id": "2311.16621", "title": "Beyond Labels: Advancing Cluster Analysis with the Entropy of Distance\n  Distribution (EDD)", "abstract": "  In the evolving landscape of data science, the accurate quantification of\nclustering in high-dimensional data sets remains a significant challenge,\nespecially in the absence of predefined labels. This paper introduces a novel\napproach, the Entropy of Distance Distribution (EDD), which represents a\nparadigm shift in label-free clustering analysis. Traditional methods, reliant\non discrete labels, often struggle to discern intricate cluster patterns in\nunlabeled data. EDD, however, leverages the characteristic differences in\npairwise point-to-point distances to discern clustering tendencies, independent\nof data labeling.\n  Our method employs the Shannon information entropy to quantify the\n'peakedness' or 'flatness' of distance distributions in a data set. This\nentropy measure, normalized against its maximum value, effectively\ndistinguishes between strongly clustered data (indicated by pronounced peaks in\ndistance distribution) and more homogeneous, non-clustered data sets. This\nlabel-free quantification is resilient against global translations and\npermutations of data points, and with an additional dimension-wise z-scoring,\nit becomes invariant to data set scaling.\n  We demonstrate the efficacy of EDD through a series of experiments involving\ntwo-dimensional data spaces with Gaussian cluster centers. Our findings reveal\na monotonic increase in the EDD value with the widening of cluster widths,\nmoving from well-separated to overlapping clusters. This behavior underscores\nthe method's sensitivity and accuracy in detecting varying degrees of\nclustering. EDD's potential extends beyond conventional clustering analysis,\noffering a robust, scalable tool for unraveling complex data structures without\nreliance on pre-assigned labels.\n", "date": "2023-11-28", "categories": []}
{"id": "2305.14067", "title": "DIVA: A Dirichlet Process Mixtures Based Incremental Deep Clustering\n  Algorithm via Variational Auto-Encoder", "abstract": "  Generative model-based deep clustering frameworks excel in classifying\ncomplex data, but are limited in handling dynamic and complex features because\nthey require prior knowledge of the number of clusters. In this paper, we\npropose a nonparametric deep clustering framework that employs an infinite\nmixture of Gaussians as a prior. Our framework utilizes a memoized online\nvariational inference method that enables the \"birth\" and \"merge\" moves of\nclusters, allowing our framework to cluster data in a \"dynamic-adaptive\"\nmanner, without requiring prior knowledge of the number of features. We name\nthe framework as DIVA, a Dirichlet Process-based Incremental deep clustering\nframework via Variational Auto-Encoder. Our framework, which outperforms\nstate-of-the-art baselines, exhibits superior performance in classifying\ncomplex data with dynamically changing features, particularly in the case of\nincremental features. We released our source code implementation at:\nhttps://github.com/Ghiara/diva\n", "date": "2023-05-23", "categories": []}
{"id": "2311.15214", "title": "A Novel Normalized-Cut Solver with Nearest Neighbor Hierarchical\n  Initialization", "abstract": "  Normalized-Cut (N-Cut) is a famous model of spectral clustering. The\ntraditional N-Cut solvers are two-stage: 1) calculating the continuous spectral\nembedding of normalized Laplacian matrix; 2) discretization via $K$-means or\nspectral rotation. However, this paradigm brings two vital problems: 1)\ntwo-stage methods solve a relaxed version of the original problem, so they\ncannot obtain good solutions for the original N-Cut problem; 2) solving the\nrelaxed problem requires eigenvalue decomposition, which has $\\mathcal{O}(n^3)$\ntime complexity ($n$ is the number of nodes). To address the problems, we\npropose a novel N-Cut solver designed based on the famous coordinate descent\nmethod. Since the vanilla coordinate descent method also has $\\mathcal{O}(n^3)$\ntime complexity, we design various accelerating strategies to reduce the time\ncomplexity to $\\mathcal{O}(|E|)$ ($|E|$ is the number of edges). To avoid\nreliance on random initialization which brings uncertainties to clustering, we\npropose an efficient initialization method that gives deterministic outputs.\nExtensive experiments on several benchmark datasets demonstrate that the\nproposed solver can obtain larger objective values of N-Cut, meanwhile\nachieving better clustering performance compared to traditional solvers.\n", "date": "2023-11-26", "categories": []}
{"id": "2311.15395", "title": "ConstraintMatch for Semi-constrained Clustering", "abstract": "  Constrained clustering allows the training of classification models using\npairwise constraints only, which are weak and relatively easy to mine, while\nstill yielding full-supervision-level model performance. While they perform\nwell even in the absence of the true underlying class labels, constrained\nclustering models still require large amounts of binary constraint annotations\nfor training. In this paper, we propose a semi-supervised context whereby a\nlarge amount of \\textit{unconstrained} data is available alongside a smaller\nset of constraints, and propose \\textit{ConstraintMatch} to leverage such\nunconstrained data. While a great deal of progress has been made in\nsemi-supervised learning using full labels, there are a number of challenges\nthat prevent a naive application of the resulting methods in the\nconstraint-based label setting. Therefore, we reason about and analyze these\nchallenges, specifically 1) proposing a \\textit{pseudo-constraining} mechanism\nto overcome the confirmation bias, a major weakness of pseudo-labeling, 2)\ndeveloping new methods for pseudo-labeling towards the selection of\n\\textit{informative} unconstrained samples, 3) showing that this also allows\nthe use of pairwise loss functions for the initial and auxiliary losses which\nfacilitates semi-constrained model training. In extensive experiments, we\ndemonstrate the effectiveness of ConstraintMatch over relevant baselines in\nboth the regular clustering and overclustering scenarios on five challenging\nbenchmarks and provide analyses of its several components.\n", "date": "2023-11-26", "categories": []}
{"id": "2311.15598", "title": "Optimal Clustering of Discrete Mixtures: Binomial, Poisson, Block\n  Models, and Multi-layer Networks", "abstract": "  In this paper, we first study the fundamental limit of clustering networks\nwhen a multi-layer network is present. Under the mixture multi-layer stochastic\nblock model (MMSBM), we show that the minimax optimal network clustering error\nrate, which takes an exponential form and is characterized by the Renyi\ndivergence between the edge probability distributions of the component\nnetworks. We propose a novel two-stage network clustering method including a\ntensor-based initialization algorithm involving both node and sample splitting\nand a refinement procedure by likelihood-based Lloyd algorithm. Network\nclustering must be accompanied by node community detection. Our proposed\nalgorithm achieves the minimax optimal network clustering error rate and allows\nextreme network sparsity under MMSBM. Numerical simulations and real data\nexperiments both validate that our method outperforms existing methods.\nOftentimes, the edges of networks carry count-type weights. We then extend our\nmethodology and analysis framework to study the minimax optimal clustering\nerror rate for mixture of discrete distributions including Binomial, Poisson,\nand multi-layer Poisson networks. The minimax optimal clustering error rates in\nthese discrete mixtures all take the same exponential form characterized by the\nRenyi divergences. These optimal clustering error rates in discrete mixtures\ncan also be achieved by our proposed two-stage clustering algorithm.\n", "date": "2023-11-27", "categories": []}
{"id": "2311.13766", "title": "A Unified Framework for Fair Spectral Clustering With Effective Graph\n  Learning", "abstract": "  We consider the problem of spectral clustering under group fairness\nconstraints, where samples from each sensitive group are approximately\nproportionally represented in each cluster. Traditional fair spectral\nclustering (FSC) methods consist of two consecutive stages, i.e., performing\nfair spectral embedding on a given graph and conducting $k$means to obtain\ndiscrete cluster labels. However, in practice, the graph is usually unknown,\nand we need to construct the underlying graph from potentially noisy data, the\nquality of which inevitably affects subsequent fair clustering performance.\nFurthermore, performing FSC through separate steps breaks the connections among\nthese steps, leading to suboptimal results. To this end, we first theoretically\nanalyze the effect of the constructed graph on FSC. Motivated by the analysis,\nwe propose a novel graph construction method with a node-adaptive graph filter\nto learn graphs from noisy data. Then, all independent stages of conventional\nFSC are integrated into a single objective function, forming an end-to-end\nframework that inputs raw data and outputs discrete cluster labels. An\nalgorithm is developed to jointly and alternately update the variables in each\nstage. Finally, we conduct extensive experiments on synthetic, benchmark, and\nreal data, which show that our model is superior to state-of-the-art fair\nclustering methods.\n", "date": "2023-11-23", "categories": []}
{"id": "2311.13953", "title": "Learning Uniform Clusters on Hypersphere for Deep Graph-level Clustering", "abstract": "  Graph clustering has been popularly studied in recent years. However, most\nexisting graph clustering methods focus on node-level clustering, i.e.,\ngrouping nodes in a single graph into clusters. In contrast, graph-level\nclustering, i.e., grouping multiple graphs into clusters, remains largely\nunexplored. Graph-level clustering is critical in a variety of real-world\napplications, such as, properties prediction of molecules and community\nanalysis in social networks. However, graph-level clustering is challenging due\nto the insufficient discriminability of graph-level representations, and the\ninsufficient discriminability makes deep clustering be more likely to obtain\ndegenerate solutions (cluster collapse). To address the issue, we propose a\nnovel deep graph-level clustering method called Uniform Deep Graph Clustering\n(UDGC). UDGC assigns instances evenly to different clusters and then scatters\nthose clusters on unit hypersphere, leading to a more uniform cluster-level\ndistribution and a slighter cluster collapse. Specifically, we first propose\nAugmentation-Consensus Optimal Transport (ACOT) for generating uniformly\ndistributed and reliable pseudo labels for partitioning clusters. Then we adopt\ncontrastive learning to scatter those clusters. Besides, we propose Center\nAlignment Optimal Transport (CAOT) for guiding the model to learn better\nparameters, which further promotes the cluster performance. Our empirical study\non eight well-known datasets demonstrates that UDGC significantly outperforms\nthe state-of-the-art models.\n", "date": "2023-11-23", "categories": []}
{"id": "2311.14310", "title": "Stable Cluster Discrimination for Deep Clustering", "abstract": "  Deep clustering can optimize representations of instances (i.e.,\nrepresentation learning) and explore the inherent data distribution (i.e.,\nclustering) simultaneously, which demonstrates a superior performance over\nconventional clustering methods with given features. However, the coupled\nobjective implies a trivial solution that all instances collapse to the uniform\nfeatures. To tackle the challenge, a two-stage training strategy is developed\nfor decoupling, where it introduces an additional pre-training stage for\nrepresentation learning and then fine-tunes the obtained model for clustering.\nMeanwhile, one-stage methods are developed mainly for representation learning\nrather than clustering, where various constraints for cluster assignments are\ndesigned to avoid collapsing explicitly. Despite the success of these methods,\nan appropriate learning objective tailored for deep clustering has not been\ninvestigated sufficiently. In this work, we first show that the prevalent\ndiscrimination task in supervised learning is unstable for one-stage clustering\ndue to the lack of ground-truth labels and positive instances for certain\nclusters in each mini-batch. To mitigate the issue, a novel stable cluster\ndiscrimination (SeCu) task is proposed and a new hardness-aware clustering\ncriterion can be obtained accordingly. Moreover, a global entropy constraint\nfor cluster assignments is studied with efficient optimization. Extensive\nexperiments are conducted on benchmark data sets and ImageNet. SeCu achieves\nstate-of-the-art performance on all of them, which demonstrates the\neffectiveness of one-stage deep clustering. Code is available at\n\\url{https://github.com/idstcv/SeCu}.\n", "date": "2023-11-24", "categories": []}
{"id": "2311.12859", "title": "Joint Multi-View Collaborative Clustering", "abstract": "  Data is increasingly being collected from multiple sources and described by\nmultiple views. These multi-view data provide richer information than\ntraditional single-view data. Fusing the former for specific tasks is an\nessential component of multi-view clustering. Since the goal of multi-view\nclustering algorithms is to discover the common latent structure shared by\nmultiple views, the majority of proposed solutions overlook the advantages of\nincorporating knowledge derived from horizontal collaboration between\nmulti-view data and the final consensus. To fill this gap, we propose the Joint\nMulti-View Collaborative Clustering (JMVCC) solution, which involves the\ngeneration of basic partitions using Non-negative Matrix Factorization (NMF)\nand the horizontal collaboration principle, followed by the fusion of these\nlocal partitions using ensemble clustering. Furthermore, we propose a weighting\nmethod to reduce the risk of negative collaboration (i.e., views with low\nquality) during the generation and fusion of local partitions. The experimental\nresults, which were obtained using a variety of data sets, demonstrate that\nJMVCC outperforms other multi-view clustering algorithms and is robust to noisy\nviews.\n", "date": "2023-10-25", "categories": []}
{"id": "2311.12501", "title": "Fair Polylog-Approximate Low-Cost Hierarchical Clustering", "abstract": "  Research in fair machine learning, and particularly clustering, has been\ncrucial in recent years given the many ethical controversies that modern\nintelligent systems have posed. Ahmadian et al. [2020] established the study of\nfairness in \\textit{hierarchical} clustering, a stronger, more structured\nvariant of its well-known flat counterpart, though their proposed algorithm\nthat optimizes for Dasgupta's [2016] famous cost function was highly\ntheoretical. Knittel et al. [2023] then proposed the first practical fair\napproximation for cost, however they were unable to break the\npolynomial-approximate barrier they posed as a hurdle of interest. We break\nthis barrier, proposing the first truly polylogarithmic-approximate low-cost\nfair hierarchical clustering, thus greatly bridging the gap between the best\nfair and vanilla hierarchical clustering approximations.\n", "date": "2023-11-21", "categories": []}
{"id": "2302.06335", "title": "Online Arbitrary Shaped Clustering through Correlated Gaussian Functions", "abstract": "  There is no convincing evidence that backpropagation is a biologically\nplausible mechanism, and further studies of alternative learning methods are\nneeded. A novel online clustering algorithm is presented that can produce\narbitrary shaped clusters from inputs in an unsupervised manner, and requires\nno prior knowledge of the number of clusters in the input data. This is\nachieved by finding correlated outputs from functions that capture commonly\noccurring input patterns. The algorithm can be deemed more biologically\nplausible than model optimization through backpropagation, although practical\napplicability may require additional research. However, the method yields\nsatisfactory results on several toy datasets on a noteworthy range of\nhyperparameters.\n", "date": "2023-02-13", "categories": []}
{"id": "2310.14858", "title": "Dynamically Weighted Federated k-Means", "abstract": "  Federated clustering, an integral aspect of federated machine learning,\nenables multiple data sources to collaboratively cluster their data,\nmaintaining decentralization and preserving privacy. In this paper, we\nintroduce a novel federated clustering algorithm named Dynamically Weighted\nFederated k-means (DWF k-means) based on Lloyd's method for k-means clustering,\nto address the challenges associated with distributed data sources and\nheterogeneous data. Our proposed algorithm combines the benefits of traditional\nclustering techniques with the privacy and scalability benefits offered by\nfederated learning. The algorithm facilitates collaborative clustering among\nmultiple data owners, allowing them to cluster their local data collectively\nwhile exchanging minimal information with the central coordinator. The\nalgorithm optimizes the clustering process by adaptively aggregating cluster\nassignments and centroids from each data source, thereby learning a global\nclustering solution that reflects the collective knowledge of the entire\nfederated network. We address the issue of empty clusters, which commonly\narises in the context of federated clustering. We conduct experiments on\nmultiple datasets and data distribution settings to evaluate the performance of\nour algorithm in terms of clustering score, accuracy, and v-measure. The\nresults demonstrate that our approach can match the performance of the\ncentralized classical k-means baseline, and outperform existing federated\nclustering methods like k-FED in realistic scenarios.\n", "date": "2023-10-23", "categories": []}
{"id": "2311.09272", "title": "Linear time Evidence Accumulation Clustering with KMeans", "abstract": "  Among ensemble clustering methods, Evidence Accumulation Clustering is one of\nthe simplest technics. In this approach, a co-association (CA) matrix\nrepresenting the co-clustering frequency is built and then clustered to extract\nconsensus clusters. Compared to other approaches, this one is simple as there\nis no need to find matches between clusters obtained from two different\npartitionings. Nevertheless, this method suffers from computational issues, as\nit requires to compute and store a matrix of size n x n, where n is the number\nof items. Due to the quadratic cost, this approach is reserved for small\ndatasets. This work describes a trick which mimic the behavior of average\nlinkage clustering. We found a way of computing efficiently the density of a\npartitioning, reducing the cost from a quadratic to linear complexity.\nAdditionally, we proved that the k-means maximizes naturally the density. We\nperformed experiments on several benchmark datasets where we compared the\nk-means and the bisecting version to other state-of-the-art consensus\nalgorithms. The k-means results are comparable to the best state of the art in\nterms of NMI while keeping the computational cost low. Additionally, the\nk-means led to the best results in terms of density. These results provide\nevidence that consensus clustering can be solved with simple algorithms.\n", "date": "2023-11-15", "categories": []}
{"id": "2304.03292", "title": "SE-shapelets: Semi-supervised Clustering of Time Series Using\n  Representative Shapelets", "abstract": "  Shapelets that discriminate time series using local features (subsequences)\nare promising for time series clustering. Existing time series clustering\nmethods may fail to capture representative shapelets because they discover\nshapelets from a large pool of uninformative subsequences, and thus result in\nlow clustering accuracy. This paper proposes a Semi-supervised Clustering of\nTime Series Using Representative Shapelets (SE-Shapelets) method, which\nutilizes a small number of labeled and propagated pseudo-labeled time series to\nhelp discover representative shapelets, thereby improving the clustering\naccuracy. In SE-Shapelets, we propose two techniques to discover representative\nshapelets for the effective clustering of time series. 1) A \\textit{salient\nsubsequence chain} ($SSC$) that can extract salient subsequences (as candidate\nshapelets) of a labeled/pseudo-labeled time series, which helps remove massive\nuninformative subsequences from the pool. 2) A \\textit{linear discriminant\nselection} ($LDS$) algorithm to identify shapelets that can capture\nrepresentative local features of time series in different classes, for\nconvenient clustering. Experiments on UCR time series datasets demonstrate that\nSE-shapelets discovers representative shapelets and achieves higher clustering\naccuracy than counterpart semi-supervised time series clustering methods.\n", "date": "2023-04-06", "categories": []}
{"id": "2211.10627", "title": "EGRC-Net: Embedding-induced Graph Refinement Clustering Network", "abstract": "  Existing graph clustering networks heavily rely on a predefined yet fixed\ngraph, which can lead to failures when the initial graph fails to accurately\ncapture the data topology structure of the embedding space. In order to address\nthis issue, we propose a novel clustering network called Embedding-Induced\nGraph Refinement Clustering Network (EGRC-Net), which effectively utilizes the\nlearned embedding to adaptively refine the initial graph and enhance the\nclustering performance. To begin, we leverage both semantic and topological\ninformation by employing a vanilla auto-encoder and a graph convolution\nnetwork, respectively, to learn a latent feature representation. Subsequently,\nwe utilize the local geometric structure within the feature embedding space to\nconstruct an adjacency matrix for the graph. This adjacency matrix is\ndynamically fused with the initial one using our proposed fusion architecture.\nTo train the network in an unsupervised manner, we minimize the Jeffreys\ndivergence between multiple derived distributions. Additionally, we introduce\nan improved approximate personalized propagation of neural predictions to\nreplace the standard graph convolution network, enabling EGRC-Net to scale\neffectively. Through extensive experiments conducted on nine widely-used\nbenchmark datasets, we demonstrate that our proposed methods consistently\noutperform several state-of-the-art approaches. Notably, EGRC-Net achieves an\nimprovement of more than 11.99\\% in Adjusted Rand Index (ARI) over the best\nbaseline on the DBLP dataset. Furthermore, our scalable approach exhibits a\n10.73% gain in ARI while reducing memory usage by 33.73% and decreasing running\ntime by 19.71%. The code for EGRC-Net will be made publicly available at\n\\url{https://github.com/ZhihaoPENG-CityU/EGRC-Net}.\n", "date": "2022-11-19", "categories": []}
{"id": "2301.05525", "title": "Understanding Concept Identification as Consistent Data Clustering\n  Across Multiple Feature Spaces", "abstract": "  Identifying meaningful concepts in large data sets can provide valuable\ninsights into engineering design problems. Concept identification aims at\nidentifying non-overlapping groups of design instances that are similar in a\njoint space of all features, but which are also similar when considering only\nsubsets of features. These subsets usually comprise features that characterize\na design with respect to one specific context, for example, constructive design\nparameters, performance values, or operation modes. It is desirable to evaluate\nthe quality of design concepts by considering several of these feature subsets\nin isolation. In particular, meaningful concepts should not only identify\ndense, well separated groups of data instances, but also provide\nnon-overlapping groups of data that persist when considering pre-defined\nfeature subsets separately. In this work, we propose to view concept\nidentification as a special form of clustering algorithm with a broad range of\npotential applications beyond engineering design. To illustrate the differences\nbetween concept identification and classical clustering algorithms, we apply a\nrecently proposed concept identification algorithm to two synthetic data sets\nand show the differences in identified solutions. In addition, we introduce the\nmutual information measure as a metric to evaluate whether solutions return\nconsistent clusters across relevant subsets. To support the novel understanding\nof concept identification, we consider a simulated data set from a\ndecision-making problem in the energy management domain and show that the\nidentified clusters are more interpretable with respect to relevant feature\nsubsets than clusters found by common clustering algorithms and are thus more\nsuitable to support a decision maker.\n", "date": "2023-01-13", "categories": []}
{"id": "2311.07833", "title": "Toward Efficient and Incremental Spectral Clustering via Parametric\n  Spectral Clustering", "abstract": "  Spectral clustering is a popular method for effectively clustering\nnonlinearly separable data. However, computational limitations, memory\nrequirements, and the inability to perform incremental learning challenge its\nwidespread application. To overcome these limitations, this paper introduces a\nnovel approach called parametric spectral clustering (PSC). By extending the\ncapabilities of spectral clustering, PSC addresses the challenges associated\nwith big data and real-time scenarios and enables efficient incremental\nclustering with new data points. Experimental evaluations conducted on various\nopen datasets demonstrate the superiority of PSC in terms of computational\nefficiency while achieving clustering quality mostly comparable to standard\nspectral clustering. The proposed approach has significant potential for\nincremental and real-time data analysis applications, facilitating timely and\naccurate clustering in dynamic and evolving datasets. The findings of this\nresearch contribute to the advancement of clustering techniques and open new\navenues for efficient and effective data analysis. We publish the experimental\ncode at https://github.com/109502518/PSC_BigData.\n", "date": "2023-11-14", "categories": []}
{"id": "2305.13749", "title": "Goal-Driven Explainable Clustering via Language Descriptions", "abstract": "  Unsupervised clustering is widely used to explore large corpora, but existing\nformulations neither consider the users' goals nor explain clusters' meanings.\nWe propose a new task formulation, \"Goal-Driven Clustering with Explanations\"\n(GoalEx), which represents both the goal and the explanations as free-form\nlanguage descriptions. For example, to categorize the errors made by a\nsummarization system, the input to GoalEx is a corpus of annotator-written\ncomments for system-generated summaries and a goal description \"cluster the\ncomments based on why the annotators think the summary is imperfect.''; the\noutputs are text clusters each with an explanation (\"this cluster mentions that\nthe summary misses important context information.\"), which relates to the goal\nand precisely explain which comments should (not) belong to a cluster. To\ntackle GoalEx, we prompt a language model with \"[corpus subset] + [goal] +\nBrainstorm a list of explanations each representing a cluster.\"; then we\nclassify whether each sample belongs to a cluster based on its explanation;\nfinally, we use integer linear programming to select a subset of candidate\nclusters to cover most samples while minimizing overlaps. Under both automatic\nand human evaluation on corpora with or without labels, our method produces\nmore accurate and goal-related explanations than prior methods. We release our\ndata and implementation at https://github.com/ZihanWangKi/GoalEx.\n", "date": "2023-05-23", "categories": []}
{"id": "2303.17896", "title": "Exploring the Limits of Deep Image Clustering using Pretrained Models", "abstract": "  We present a general methodology that learns to classify images without\nlabels by leveraging pretrained feature extractors. Our approach involves\nself-distillation training of clustering heads based on the fact that nearest\nneighbours in the pretrained feature space are likely to share the same label.\nWe propose a novel objective that learns associations between image features by\nintroducing a variant of pointwise mutual information together with instance\nweighting. We demonstrate that the proposed objective is able to attenuate the\neffect of false positive pairs while efficiently exploiting the structure in\nthe pretrained feature space. As a result, we improve the clustering accuracy\nover $k$-means on $17$ different pretrained models by $6.1$\\% and $12.2$\\% on\nImageNet and CIFAR100, respectively. Finally, using self-supervised vision\ntransformers, we achieve a clustering accuracy of $61.6$\\% on ImageNet. The\ncode is available at https://github.com/HHU-MMBS/TEMI-official-BMVC2023.\n", "date": "2023-03-31", "categories": []}
{"id": "2311.00322", "title": "Robust Graph Clustering via Meta Weighting for Noisy Graphs", "abstract": "  How can we find meaningful clusters in a graph robustly against noise edges?\nGraph clustering (i.e., dividing nodes into groups of similar ones) is a\nfundamental problem in graph analysis with applications in various fields.\nRecent studies have demonstrated that graph neural network (GNN) based\napproaches yield promising results for graph clustering. However, we observe\nthat their performance degenerates significantly on graphs with noise edges,\nwhich are prevalent in practice. In this work, we propose MetaGC for robust\nGNN-based graph clustering. MetaGC employs a decomposable clustering loss\nfunction, which can be rephrased as a sum of losses over node pairs. We add a\nlearnable weight to each node pair, and MetaGC adaptively adjusts the weights\nof node pairs using meta-weighting so that the weights of meaningful node pairs\nincrease and the weights of less-meaningful ones (e.g., noise edges) decrease.\nWe show empirically that MetaGC learns weights as intended and consequently\noutperforms the state-of-the-art GNN-based competitors, even when they are\nequipped with separate denoising schemes, on five real-world graphs under\nvarying levels of noise. Our code and datasets are available at\nhttps://github.com/HyeonsooJo/MetaGC.\n", "date": "2023-11-01", "categories": []}
{"id": "2308.09000", "title": "DealMVC: Dual Contrastive Calibration for Multi-view Clustering", "abstract": "  Benefiting from the strong view-consistent information mining capacity,\nmulti-view contrastive clustering has attracted plenty of attention in recent\nyears. However, we observe the following drawback, which limits the clustering\nperformance from further improvement. The existing multi-view models mainly\nfocus on the consistency of the same samples in different views while ignoring\nthe circumstance of similar but different samples in cross-view scenarios. To\nsolve this problem, we propose a novel Dual contrastive calibration network for\nMulti-View Clustering (DealMVC). Specifically, we first design a fusion\nmechanism to obtain a global cross-view feature. Then, a global contrastive\ncalibration loss is proposed by aligning the view feature similarity graph and\nthe high-confidence pseudo-label graph. Moreover, to utilize the diversity of\nmulti-view information, we propose a local contrastive calibration loss to\nconstrain the consistency of pair-wise view features. The feature structure is\nregularized by reliable class information, thus guaranteeing similar samples\nhave similar features in different views. During the training procedure, the\ninteracted cross-view feature is jointly optimized at both local and global\nlevels. In comparison with other state-of-the-art approaches, the comprehensive\nexperimental results obtained from eight benchmark datasets provide substantial\nvalidation of the effectiveness and superiority of our algorithm. We release\nthe code of DealMVC at https://github.com/xihongyang1999/DealMVC on GitHub.\n", "date": "2023-08-17", "categories": []}
{"id": "2305.14871", "title": "ClusterLLM: Large Language Models as a Guide for Text Clustering", "abstract": "  We introduce ClusterLLM, a novel text clustering framework that leverages\nfeedback from an instruction-tuned large language model, such as ChatGPT.\nCompared with traditional unsupervised methods that builds upon \"small\"\nembedders, ClusterLLM exhibits two intriguing advantages: (1) it enjoys the\nemergent capability of LLM even if its embeddings are inaccessible; and (2) it\nunderstands the user's preference on clustering through textual instruction\nand/or a few annotated data. First, we prompt ChatGPT for insights on\nclustering perspective by constructing hard triplet questions <does A better\ncorrespond to B than C>, where A, B and C are similar data points that belong\nto different clusters according to small embedder. We empirically show that\nthis strategy is both effective for fine-tuning small embedder and\ncost-efficient to query ChatGPT. Second, we prompt ChatGPT for helps on\nclustering granularity by carefully designed pairwise questions <do A and B\nbelong to the same category>, and tune the granularity from cluster hierarchies\nthat is the most consistent with the ChatGPT answers. Extensive experiments on\n14 datasets show that ClusterLLM consistently improves clustering quality, at\nan average cost of ~$0.6 per dataset. The code will be available at\nhttps://github.com/zhang-yu-wei/ClusterLLM.\n", "date": "2023-05-24", "categories": []}
{"id": "2305.16358", "title": "Differentiable Clustering with Perturbed Spanning Forests", "abstract": "  We introduce a differentiable clustering method based on stochastic\nperturbations of minimum-weight spanning forests. This allows us to include\nclustering in end-to-end trainable pipelines, with efficient gradients. We show\nthat our method performs well even in difficult settings, such as data sets\nwith high noise and challenging geometries. We also formulate an ad hoc loss to\nefficiently learn from partial clustering data using this operation. We\ndemonstrate its performance on several data sets for supervised and\nsemi-supervised tasks.\n", "date": "2023-05-25", "categories": []}
{"id": "2311.02306", "title": "Heteroskedastic Tensor Clustering", "abstract": "  Tensor clustering, which seeks to extract underlying cluster structures from\nnoisy tensor observations, has gained increasing attention. One extensively\nstudied model for tensor clustering is the tensor block model, which postulates\nthe existence of clustering structures along each mode and has found broad\napplications in areas like multi-tissue gene expression analysis and multilayer\nnetwork analysis. However, currently available computationally feasible methods\nfor tensor clustering either are limited to handling i.i.d. sub-Gaussian noise\nor suffer from suboptimal statistical performance, which restrains their\nutility in applications that have to deal with heteroskedastic data and/or low\nsignal-to-noise-ratio (SNR).\n  To overcome these challenges, we propose a two-stage method, named\n$\\mathsf{High\\text{-}order~HeteroClustering}$ ($\\mathsf{HHC}$), which starts by\nperforming tensor subspace estimation via a novel spectral algorithm called\n$\\mathsf{Thresholded~Deflated\\text{-}HeteroPCA}$, followed by approximate\n$k$-means to obtain cluster nodes. Encouragingly, our algorithm provably\nachieves exact clustering as long as the SNR exceeds the computational limit\n(ignoring logarithmic factors); here, the SNR refers to the ratio of the\npairwise disparity between nodes to the noise level, and the computational\nlimit indicates the lowest SNR that enables exact clustering with polynomial\nruntime. Comprehensive simulation and real-data experiments suggest that our\nalgorithm outperforms existing algorithms across various settings, delivering\nmore reliable clustering performance.\n", "date": "2023-11-04", "categories": []}
{"id": "2311.01840", "title": "Spectral Clustering of Attributed Multi-relational Graphs", "abstract": "  Graph clustering aims at discovering a natural grouping of the nodes such\nthat similar nodes are assigned to a common cluster. Many different algorithms\nhave been proposed in the literature: for simple graphs, for graphs with\nattributes associated to nodes, and for graphs where edges represent different\ntypes of relations among nodes. However, complex data in many domains can be\nrepresented as both attributed and multi-relational networks.\n  In this paper, we propose SpectralMix, a joint dimensionality reduction\ntechnique for multi-relational graphs with categorical node attributes.\nSpectralMix integrates all information available from the attributes, the\ndifferent types of relations, and the graph structure to enable a sound\ninterpretation of the clustering results. Moreover, it generalizes existing\ntechniques: it reduces to spectral embedding and clustering when only applied\nto a single graph and to homogeneity analysis when applied to categorical data.\nExperiments conducted on several real-world datasets enable us to detect\ndependencies between graph structure and categorical attributes, moreover, they\nexhibit the superiority of SpectralMix over existing methods.\n", "date": "2023-11-03", "categories": []}
{"id": "2311.00731", "title": "Enhancing Clustering Representations with Positive Proximity and Cluster\n  Dispersion Learning", "abstract": "  Contemporary deep clustering approaches often rely on either contrastive or\nnon-contrastive techniques to acquire effective representations for clustering\ntasks. Contrastive methods leverage negative pairs to achieve homogenous\nrepresentations but can introduce class collision issues, potentially\ncompromising clustering performance. On the contrary, non-contrastive\ntechniques prevent class collisions but may produce non-uniform representations\nthat lead to clustering collapse. In this work, we propose a novel end-to-end\ndeep clustering approach named PIPCDR, designed to harness the strengths of\nboth approaches while mitigating their limitations. PIPCDR incorporates a\npositive instance proximity loss and a cluster dispersion regularizer. The\npositive instance proximity loss ensures alignment between augmented views of\ninstances and their sampled neighbors, enhancing within-cluster compactness by\nselecting genuinely positive pairs within the embedding space. Meanwhile, the\ncluster dispersion regularizer maximizes inter-cluster distances while\nminimizing within-cluster compactness, promoting uniformity in the learned\nrepresentations. PIPCDR excels in producing well-separated clusters, generating\nuniform representations, avoiding class collision issues, and enhancing\nwithin-cluster compactness. We extensively validate the effectiveness of PIPCDR\nwithin an end-to-end Majorize-Minimization framework, demonstrating its\ncompetitive performance on moderate-scale clustering benchmark datasets and\nestablishing new state-of-the-art results on large-scale datasets.\n", "date": "2023-11-01", "categories": []}
{"id": "2311.01252", "title": "Sanitized Clustering against Confounding Bias", "abstract": "  Real-world datasets inevitably contain biases that arise from different\nsources or conditions during data collection. Consequently, such inconsistency\nitself acts as a confounding factor that disturbs the cluster analysis.\nExisting methods eliminate the biases by projecting data onto the orthogonal\ncomplement of the subspace expanded by the confounding factor before\nclustering. Therein, the interested clustering factor and the confounding\nfactor are coarsely considered in the raw feature space, where the correlation\nbetween the data and the confounding factor is ideally assumed to be linear for\nconvenient solutions. These approaches are thus limited in scope as the data in\nreal applications is usually complex and non-linearly correlated with the\nconfounding factor. This paper presents a new clustering framework named\nSanitized Clustering Against confounding Bias (SCAB), which removes the\nconfounding factor in the semantic latent space of complex data through a\nnon-linear dependence measure. To be specific, we eliminate the bias\ninformation in the latent space by minimizing the mutual information between\nthe confounding factor and the latent representation delivered by Variational\nAuto-Encoder (VAE). Meanwhile, a clustering module is introduced to cluster\nover the purified latent representations. Extensive experiments on complex\ndatasets demonstrate that our SCAB achieves a significant gain in clustering\nperformance by removing the confounding bias. The code is available at\n\\url{https://github.com/EvaFlower/SCAB}.\n", "date": "2023-11-02", "categories": []}
{"id": "2305.12114", "title": "GFDC: A Granule Fusion Density-Based Clustering with Evidential\n  Reasoning", "abstract": "  Currently, density-based clustering algorithms are widely applied because\nthey can detect clusters with arbitrary shapes. However, they perform poorly in\nmeasuring global density, determining reasonable cluster centers or structures,\nassigning samples accurately and handling data with large density differences\namong clusters. To overcome their drawbacks, this paper proposes a granule\nfusion density-based clustering with evidential reasoning (GFDC). Both local\nand global densities of samples are measured by a sparse degree metric first.\nThen information granules are generated in high-density and low-density\nregions, assisting in processing clusters with significant density differences.\nFurther, three novel granule fusion strategies are utilized to combine granules\ninto stable cluster structures, helping to detect clusters with arbitrary\nshapes. Finally, by an assignment method developed from Dempster-Shafer theory,\nunstable samples are assigned. After using GFDC, a reasonable clustering result\nand some identified outliers can be obtained. The experimental results on\nextensive datasets demonstrate the effectiveness of GFDC.\n", "date": "2023-05-20", "categories": []}
{"id": "2310.20224", "title": "Choose A Table: Tensor Dirichlet Process Multinomial Mixture Model with\n  Graphs for Passenger Trajectory Clustering", "abstract": "  Passenger clustering based on trajectory records is essential for\ntransportation operators. However, existing methods cannot easily cluster the\npassengers due to the hierarchical structure of the passenger trip information,\nincluding multiple trips within each passenger and multi-dimensional\ninformation about each trip. Furthermore, existing approaches rely on an\naccurate specification of the clustering number to start. Finally, existing\nmethods do not consider spatial semantic graphs such as geographical proximity\nand functional similarity between the locations. In this paper, we propose a\nnovel tensor Dirichlet Process Multinomial Mixture model with graphs, which can\npreserve the hierarchical structure of the multi-dimensional trip information\nand cluster them in a unified one-step manner with the ability to determine the\nnumber of clusters automatically. The spatial graphs are utilized in community\ndetection to link the semantic neighbors. We further propose a tensor version\nof Collapsed Gibbs Sampling method with a minimum cluster size requirement. A\ncase study based on Hong Kong metro passenger data is conducted to demonstrate\nthe automatic process of cluster amount evolution and better cluster quality\nmeasured by within-cluster compactness and cross-cluster separateness. The code\nis available at https://github.com/bonaldli/TensorDPMM-G.\n", "date": "2023-10-31", "categories": []}
{"id": "2310.20367", "title": "A Machine Learning-Based Framework for Clustering Residential\n  Electricity Load Profiles to Enhance Demand Response Programs", "abstract": "  Load shapes derived from smart meter data are frequently employed to analyze\ndaily energy consumption patterns, particularly in the context of applications\nlike Demand Response (DR). Nevertheless, one of the most important challenges\nto this endeavor lies in identifying the most suitable consumer clusters with\nsimilar consumption behaviors. In this paper, we present a novel machine\nlearning based framework in order to achieve optimal load profiling through a\nreal case study, utilizing data from almost 5000 households in London. Four\nwidely used clustering algorithms are applied specifically K-means, K-medoids,\nHierarchical Agglomerative Clustering and Density-based Spatial Clustering. An\nempirical analysis as well as multiple evaluation metrics are leveraged to\nassess those algorithms. Following that, we redefine the problem as a\nprobabilistic classification one, with the classifier emulating the behavior of\na clustering algorithm,leveraging Explainable AI (xAI) to enhance the\ninterpretability of our solution. According to the clustering algorithm\nanalysis the optimal number of clusters for this case is seven. Despite that,\nour methodology shows that two of the clusters, almost 10\\% of the dataset,\nexhibit significant internal dissimilarity and thus it splits them even further\nto create nine clusters in total. The scalability and versatility of our\nsolution makes it an ideal choice for power utility companies aiming to segment\ntheir users for creating more targeted Demand Response programs.\n", "date": "2023-10-31", "categories": []}
{"id": "2308.05309", "title": "Homophily-enhanced Structure Learning for Graph Clustering", "abstract": "  Graph clustering is a fundamental task in graph analysis, and recent advances\nin utilizing graph neural networks (GNNs) have shown impressive results.\nDespite the success of existing GNN-based graph clustering methods, they often\noverlook the quality of graph structure, which is inherent in real-world graphs\ndue to their sparse and multifarious nature, leading to subpar performance.\nGraph structure learning allows refining the input graph by adding missing\nlinks and removing spurious connections. However, previous endeavors in graph\nstructure learning have predominantly centered around supervised settings, and\ncannot be directly applied to our specific clustering tasks due to the absence\nof ground-truth labels. To bridge the gap, we propose a novel method called\n\\textbf{ho}mophily-enhanced structure \\textbf{le}arning for graph clustering\n(HoLe). Our motivation stems from the observation that subtly enhancing the\ndegree of homophily within the graph structure can significantly improve GNNs\nand clustering outcomes. To realize this objective, we develop two\nclustering-oriented structure learning modules, i.e., hierarchical correlation\nestimation and cluster-aware sparsification. The former module enables a more\naccurate estimation of pairwise node relationships by leveraging guidance from\nlatent and clustering spaces, while the latter one generates a sparsified\nstructure based on the similarity matrix and clustering assignments.\nAdditionally, we devise a joint optimization approach alternating between\ntraining the homophily-enhanced structure learning and GNN-based clustering,\nthereby enforcing their reciprocal effects. Extensive experiments on seven\nbenchmark datasets of various types and scales, across a range of clustering\nmetrics, demonstrate the superiority of HoLe against state-of-the-art\nbaselines.\n", "date": "2023-08-10", "categories": []}
{"id": "2309.02623", "title": "Superclustering by finding statistically significant separable groups of\n  optimal gaussian clusters", "abstract": "  The paper presents the algorithm for clustering a dataset by grouping the\noptimal, from the point of view of the BIC criterion, number of Gaussian\nclusters into the optimal, from the point of view of their statistical\nseparability, superclusters.\n  The algorithm consists of three stages: representation of the dataset as a\nmixture of Gaussian distributions - clusters, which number is determined based\non the minimum of the BIC criterion; using the Mahalanobis distance, to\nestimate the distances between the clusters and cluster sizes; combining the\nresulting clusters into superclusters using the DBSCAN method by finding its\nhyperparameter (maximum distance) providing maximum value of introduced matrix\nquality criterion at maximum number of superclusters. The matrix quality\ncriterion corresponds to the proportion of statistically significant separated\nsuperclusters among all found superclusters.\n  The algorithm has only one hyperparameter - statistical significance level,\nand automatically detects optimal number and shape of superclusters based of\nstatistical hypothesis testing approach. The algorithm demonstrates a good\nresults on test datasets in noise and noiseless situations. An essential\nadvantage of the algorithm is its ability to predict correct supercluster for\nnew data based on already trained clusterer and perform soft (fuzzy)\nclustering. The disadvantages of the algorithm are: its low speed and\nstochastic nature of the final clustering. It requires a sufficiently large\ndataset for clustering, which is typical for many statistical methods.\n", "date": "2023-09-05", "categories": []}
{"id": "2310.18614", "title": "Hierarchical Mutual Information Analysis: Towards Multi-view Clustering\n  in The Wild", "abstract": "  Multi-view clustering (MVC) can explore common semantics from unsupervised\nviews generated by different sources, and thus has been extensively used in\napplications of practical computer vision. Due to the spatio-temporal\nasynchronism, multi-view data often suffer from view missing and are unaligned\nin real-world applications, which makes it difficult to learn consistent\nrepresentations. To address the above issues, this work proposes a deep MVC\nframework where data recovery and alignment are fused in a hierarchically\nconsistent way to maximize the mutual information among different views and\nensure the consistency of their latent spaces. More specifically, we first\nleverage dual prediction to fill in missing views while achieving the\ninstance-level alignment, and then take the contrastive reconstruction to\nachieve the class-level alignment. To the best of our knowledge, this could be\nthe first successful attempt to handle the missing and unaligned data problem\nseparately with different learning paradigms. Extensive experiments on public\ndatasets demonstrate that our method significantly outperforms state-of-the-art\nmethods on multi-view clustering even in the cases of view missing and\nunalignment.\n", "date": "2023-10-28", "categories": []}
{"id": "2310.18727", "title": "Latent class analysis by regularized spectral clustering", "abstract": "  The latent class model is a powerful tool for identifying latent classes\nwithin populations that share common characteristics for categorical data in\nsocial, psychological, and behavioral sciences. In this article, we propose two\nnew algorithms to estimate a latent class model for categorical data. Our\nalgorithms are developed by using a newly defined regularized Laplacian matrix\ncalculated from the response matrix. We provide theoretical convergence rates\nof our algorithms by considering a sparsity parameter and show that our\nalgorithms stably yield consistent latent class analysis under mild conditions.\nAdditionally, we propose a metric to capture the strength of latent class\nanalysis and several procedures designed based on this metric to infer how many\nlatent classes one should use for real-world categorical data. The efficiency\nand accuracy of our algorithms are verified by extensive simulated experiments,\nand we further apply our algorithms to real-world categorical data with\npromising results.\n", "date": "2023-10-28", "categories": []}
{"id": "2310.18844", "title": "BanditPAM++: Faster $k$-medoids Clustering", "abstract": "  Clustering is a fundamental task in data science with wide-ranging\napplications. In $k$-medoids clustering, cluster centers must be actual\ndatapoints and arbitrary distance metrics may be used; these features allow for\ngreater interpretability of the cluster centers and the clustering of exotic\nobjects in $k$-medoids clustering, respectively. $k$-medoids clustering has\nrecently grown in popularity due to the discovery of more efficient $k$-medoids\nalgorithms. In particular, recent research has proposed BanditPAM, a randomized\n$k$-medoids algorithm with state-of-the-art complexity and clustering accuracy.\nIn this paper, we present BanditPAM++, which accelerates BanditPAM via two\nalgorithmic improvements, and is $O(k)$ faster than BanditPAM in complexity and\nsubstantially faster than BanditPAM in wall-clock runtime. First, we\ndemonstrate that BanditPAM has a special structure that allows the reuse of\nclustering information $\\textit{within}$ each iteration. Second, we demonstrate\nthat BanditPAM has additional structure that permits the reuse of information\n$\\textit{across}$ different iterations. These observations inspire our proposed\nalgorithm, BanditPAM++, which returns the same clustering solutions as\nBanditPAM but often several times faster. For example, on the CIFAR10 dataset,\nBanditPAM++ returns the same results as BanditPAM but runs over 10$\\times$\nfaster. Finally, we provide a high-performance C++ implementation of\nBanditPAM++, callable from Python and R, that may be of interest to\npractitioners at https://github.com/motiwari/BanditPAM. Auxiliary code to\nreproduce all of our experiments via a one-line script is available at\nhttps://github.com/ThrunGroup/BanditPAM_plusplus_experiments.\n", "date": "2023-10-28", "categories": []}
{"id": "2310.19210", "title": "Generalized Category Discovery with Clustering Assignment Consistency", "abstract": "  Generalized category discovery (GCD) is a recently proposed open-world task.\nGiven a set of images consisting of labeled and unlabeled instances, the goal\nof GCD is to automatically cluster the unlabeled samples using information\ntransferred from the labeled dataset. The unlabeled dataset comprises both\nknown and novel classes. The main challenge is that unlabeled novel class\nsamples and unlabeled known class samples are mixed together in the unlabeled\ndataset. To address the GCD without knowing the class number of unlabeled\ndataset, we propose a co-training-based framework that encourages clustering\nconsistency. Specifically, we first introduce weak and strong augmentation\ntransformations to generate two sufficiently different views for the same\nsample. Then, based on the co-training assumption, we propose a consistency\nrepresentation learning strategy, which encourages consistency between\nfeature-prototype similarity and clustering assignment. Finally, we use the\ndiscriminative embeddings learned from the semi-supervised representation\nlearning process to construct an original sparse network and use a community\ndetection method to obtain the clustering results and the number of categories\nsimultaneously. Extensive experiments show that our method achieves\nstate-of-the-art performance on three generic benchmarks and three fine-grained\nvisual recognition datasets. Especially in the ImageNet-100 data set, our\nmethod significantly exceeds the best baseline by 15.5\\% and 7.0\\% on the\n\\texttt{Novel} and \\texttt{All} classes, respectively.\n", "date": "2023-10-30", "categories": []}
{"id": "2209.09493", "title": "A framework for benchmarking clustering algorithms", "abstract": "  The evaluation of clustering algorithms can involve running them on a variety\nof benchmark problems, and comparing their outputs to the reference,\nground-truth groupings provided by experts. Unfortunately, many research papers\nand graduate theses consider only a small number of datasets. Also, the fact\nthat there can be many equally valid ways to cluster a given problem set is\nrarely taken into account. In order to overcome these limitations, we have\ndeveloped a framework whose aim is to introduce a consistent methodology for\ntesting clustering algorithms. Furthermore, we have aggregated, polished, and\nstandardised many clustering benchmark dataset collections referred to across\nthe machine learning and data mining literature, and included new datasets of\ndifferent dimensionalities, sizes, and cluster types. An interactive datasets\nexplorer, the documentation of the Python API, a description of the ways to\ninteract with the framework from other programming languages such as R or\nMATLAB, and other details are all provided at\n<https://clustering-benchmarks.gagolewski.com>.\n", "date": "2022-09-20", "categories": []}
{"id": "2303.05683", "title": "Hierarchical clustering with OWA-based linkages, the Lance-Williams\n  formula, and dendrogram inversions", "abstract": "  Agglomerative hierarchical clustering based on Ordered Weighted Averaging\n(OWA) operators not only generalises the single, complete, and average\nlinkages, but also includes intercluster distances based on a few nearest or\nfarthest neighbours, trimmed and winsorised means of pairwise point\nsimilarities, amongst many others. We explore the relationships between the\nfamous Lance-Williams update formula and the extended OWA-based linkages with\nweights generated via infinite coefficient sequences. Furthermore, we provide\nsome conditions for the weight generators to guarantee the resulting\ndendrograms to be free from unaesthetic inversions.\n", "date": "2023-03-10", "categories": []}
{"id": "2310.16552", "title": "DECWA : Density-Based Clustering using Wasserstein Distance", "abstract": "  Clustering is a data analysis method for extracting knowledge by discovering\ngroups of data called clusters. Among these methods, state-of-the-art\ndensity-based clustering methods have proven to be effective for\narbitrary-shaped clusters. Despite their encouraging results, they suffer to\nfind low-density clusters, near clusters with similar densities, and\nhigh-dimensional data. Our proposals are a new characterization of clusters and\na new clustering algorithm based on spatial density and probabilistic approach.\nFirst of all, sub-clusters are built using spatial density represented as\nprobability density function ($p.d.f$) of pairwise distances between points. A\nmethod is then proposed to agglomerate similar sub-clusters by using both their\ndensity ($p.d.f$) and their spatial distance. The key idea we propose is to use\nthe Wasserstein metric, a powerful tool to measure the distance between $p.d.f$\nof sub-clusters. We show that our approach outperforms other state-of-the-art\ndensity-based clustering methods on a wide variety of datasets.\n", "date": "2023-10-25", "categories": []}
{"id": "2310.16752", "title": "Simple, Scalable and Effective Clustering via One-Dimensional\n  Projections", "abstract": "  Clustering is a fundamental problem in unsupervised machine learning with\nmany applications in data analysis. Popular clustering algorithms such as\nLloyd's algorithm and $k$-means++ can take $\\Omega(ndk)$ time when clustering\n$n$ points in a $d$-dimensional space (represented by an $n\\times d$ matrix\n$X$) into $k$ clusters. In applications with moderate to large $k$, the\nmultiplicative $k$ factor can become very expensive. We introduce a simple\nrandomized clustering algorithm that provably runs in expected time\n$O(\\mathrm{nnz}(X) + n\\log n)$ for arbitrary $k$. Here $\\mathrm{nnz}(X)$ is the\ntotal number of non-zero entries in the input dataset $X$, which is upper\nbounded by $nd$ and can be significantly smaller for sparse datasets. We prove\nthat our algorithm achieves approximation ratio $\\smash{\\widetilde{O}(k^4)}$ on\nany input dataset for the $k$-means objective. We also believe that our\ntheoretical analysis is of independent interest, as we show that the\napproximation ratio of a $k$-means algorithm is approximately preserved under a\nclass of projections and that $k$-means++ seeding can be implemented in\nexpected $O(n \\log n)$ time in one dimension. Finally, we show experimentally\nthat our clustering algorithm gives a new tradeoff between running time and\ncluster quality compared to previous state-of-the-art methods for these tasks.\n", "date": "2023-10-25", "categories": []}
{"id": "2210.16524", "title": "Federated clustering with GAN-based data synthesis", "abstract": "  Federated clustering (FC) is an extension of centralized clustering in\nfederated settings. The key here is how to construct a global similarity\nmeasure without sharing private data, since the local similarity may be\ninsufficient to group local data correctly and the similarity of samples across\nclients cannot be directly measured due to privacy constraints. Obviously, the\nmost straightforward way to analyze FC is to employ the methods extended from\ncentralized ones, such as K-means (KM) and fuzzy c-means (FCM). However, they\nare vulnerable to non independent-and-identically-distributed (non-IID) data\namong clients. To handle this, we propose a new federated clustering framework,\nnamed synthetic data aided federated clustering (SDA-FC). It trains generative\nadversarial network locally in each client and uploads the generated synthetic\ndata to the server, where KM or FCM is performed on the synthetic data. The\nsynthetic data can make the model immune to the non-IID problem and enable us\nto capture the global similarity characteristics more effectively without\nsharing private data. Comprehensive experiments reveals the advantages of\nSDA-FC, including superior performance in addressing the non-IID problem and\nthe device failures.\n", "date": "2022-10-29", "categories": []}
{"id": "2310.13870", "title": "Fast Approximation of Similarity Graphs with Kernel Density Estimation", "abstract": "  Constructing a similarity graph from a set $X$ of data points in\n$\\mathbb{R}^d$ is the first step of many modern clustering algorithms. However,\ntypical constructions of a similarity graph have high time complexity, and a\nquadratic space dependency with respect to $|X|$. We address this limitation\nand present a new algorithmic framework that constructs a sparse approximation\nof the fully connected similarity graph while preserving its cluster structure.\nOur presented algorithm is based on the kernel density estimation problem, and\nis applicable for arbitrary kernel functions. We compare our designed algorithm\nwith the well-known implementations from the scikit-learn library and the FAISS\nlibrary, and find that our method significantly outperforms the implementation\nfrom both libraries on a variety of datasets.\n", "date": "2023-10-21", "categories": []}
{"id": "2310.14430", "title": "Clustering Students Based on Gamification User Types and Learning Styles", "abstract": "  The aim of this study is clustering students according to their gamification\nuser types and learning styles with the purpose of providing instructors with a\nnew perspective of grouping students in case of clustering which cannot be done\nby hand when there are multiple scales in data. The data used consists of 251\nstudents who were enrolled at a Turkish state university. When grouping\nstudents, K-means algorithm has been utilized as clustering algorithm. As for\ndetermining the gamification user types and learning styles of students,\nGamification User Type Hexad Scale and Grasha-Riechmann Student Learning Style\nScale have been used respectively. Silhouette coefficient is utilized as\nclustering quality measure. After fitting the algorithm in several ways,\nhighest Silhouette coefficient obtained was 0.12 meaning that results are\nneutral but not satisfactory. All the statistical operations and data\nvisualizations were made using Python programming language.\n", "date": "2023-10-22", "categories": []}
{"id": "2309.15420", "title": "The Triad of Failure Modes and a Possible Way Out", "abstract": "  We present a novel objective function for cluster-based self-supervised\nlearning (SSL) that is designed to circumvent the triad of failure modes,\nnamely representation collapse, cluster collapse, and the problem of invariance\nto permutations of cluster assignments. This objective consists of three key\ncomponents: (i) A generative term that penalizes representation collapse, (ii)\na term that promotes invariance to data augmentations, thereby addressing the\nissue of label permutations and (ii) a uniformity term that penalizes cluster\ncollapse. Additionally, our proposed objective possesses two notable\nadvantages. Firstly, it can be interpreted from a Bayesian perspective as a\nlower bound on the data log-likelihood. Secondly, it enables the training of a\nstandard backbone architecture without the need for asymmetric elements like\nstop gradients, momentum encoders, or specialized clustering layers. Due to its\nsimplicity and theoretical foundation, our proposed objective is well-suited\nfor optimization. Experiments on both toy and real world data demonstrate its\neffectiveness\n", "date": "2023-09-27", "categories": []}
{"id": "2310.13311", "title": "Non-Negative Spherical Relaxations for Universe-Free Multi-Matching and\n  Clustering", "abstract": "  We propose a novel non-negative spherical relaxation for optimization\nproblems over binary matrices with injectivity constraints, which in particular\nhas applications in multi-matching and clustering. We relax respective binary\nmatrix constraints to the (high-dimensional) non-negative sphere. To optimize\nour relaxed problem, we use a conditional power iteration method to iteratively\nimprove the objective function, while at same time sweeping over a continuous\nscalar parameter that is (indirectly) related to the universe size (or number\nof clusters). Opposed to existing procedures that require to fix the integer\nuniverse size before optimization, our method automatically adjusts the\nanalogous continuous parameter. Furthermore, while our approach shares\nsimilarities with spectral multi-matching and spectral clustering, our\nformulation has the strong advantage that we do not rely on additional\npost-processing procedures to obtain binary results. Our method shows\ncompelling results in various multi-matching and clustering settings, even when\ncompared to methods that use the ground truth universe size (or number of\nclusters).\n", "date": "2023-10-20", "categories": []}
{"id": "2310.13381", "title": "Accelerated sparse Kernel Spectral Clustering for large scale data\n  clustering problems", "abstract": "  An improved version of the sparse multiway kernel spectral clustering (KSC)\nis presented in this brief. The original algorithm is derived from weighted\nkernel principal component (KPCA) analysis formulated within the primal-dual\nleast-squares support vector machine (LS-SVM) framework. Sparsity is achieved\nthen by the combination of the incomplete Cholesky decomposition (ICD) based\nlow rank approximation of the kernel matrix with the so called reduced set\nmethod. The original ICD based sparse KSC algorithm was reported to be\ncomputationally far too demanding, especially when applied on large scale data\nclustering problems that actually it was designed for, which has prevented to\ngain more than simply theoretical relevance so far. This is altered by the\nmodifications reported in this brief that drastically improve the computational\ncharacteristics. Solving the alternative, symmetrized version of the\ncomputationally most demanding core eigenvalue problem eliminates the necessity\nof forming and SVD of large matrices during the model construction. This\nresults in solving clustering problems now within seconds that were reported to\nrequire hours without altering the results. Furthermore, sparsity is also\nimproved significantly, leading to more compact model representation,\nincreasing further not only the computational efficiency but also the\ndescriptive power. These transform the original, only theoretically relevant\nICD based sparse KSC algorithm applicable for large scale practical clustering\nproblems. Theoretical results and improvements are demonstrated by\ncomputational experiments on carefully selected synthetic data as well as on\nreal life problems such as image segmentation.\n", "date": "2023-10-20", "categories": []}
{"id": "2310.13474", "title": "An Analysis of $D^\\alpha$ seeding for $k$-means", "abstract": "  One of the most popular clustering algorithms is the celebrated $D^\\alpha$\nseeding algorithm (also know as $k$-means++ when $\\alpha=2$) by Arthur and\nVassilvitskii (2007), who showed that it guarantees in expectation an\n$O(2^{2\\alpha}\\cdot \\log k)$-approximate solution to the ($k$,$\\alpha$)-means\ncost (where euclidean distances are raised to the power $\\alpha$) for any\n$\\alpha\\ge 1$. More recently, Balcan, Dick, and White (2018) observed\nexperimentally that using $D^\\alpha$ seeding with $\\alpha>2$ can lead to a\nbetter solution with respect to the standard $k$-means objective (i.e. the\n$(k,2)$-means cost).\n  In this paper, we provide a rigorous understanding of this phenomenon. For\nany $\\alpha>2$, we show that $D^\\alpha$ seeding guarantees in expectation an\napproximation factor of $$ O_\\alpha \\left((g_\\alpha)^{2/\\alpha}\\cdot\n\\left(\\frac{\\sigma_{\\mathrm{max}}}{\\sigma_{\\mathrm{min}}}\\right)^{2-4/\\alpha}\\cdot\n(\\min\\{\\ell,\\log k\\})^{2/\\alpha}\\right)$$ with respect to the standard\n$k$-means cost of any underlying clustering; where $g_\\alpha$ is a parameter\ncapturing the concentration of the points in each cluster,\n$\\sigma_{\\mathrm{max}}$ and $\\sigma_{\\mathrm{min}}$ are the maximum and minimum\nstandard deviation of the clusters around their means, and $\\ell$ is the number\nof distinct mixing weights in the underlying clustering (after rounding them to\nthe nearest power of $2$). We complement these results by some lower bounds\nshowing that the dependency on $g_\\alpha$ and\n$\\sigma_{\\mathrm{max}}/\\sigma_{\\mathrm{min}}$ is tight.\n  Finally, we provide an experimental confirmation of the effects of the\naforementioned parameters when using $D^\\alpha$ seeding. Further, we\ncorroborate the observation that $\\alpha>2$ can indeed improve the $k$-means\ncost compared to $D^2$ seeding, and that this advantage remains even if we run\nLloyd's algorithm after the seeding.\n", "date": "2023-10-20", "categories": []}
{"id": "2207.06949", "title": "Seeking the Truth Beyond the Data. An Unsupervised Machine Learning\n  Approach", "abstract": "  Clustering is an unsupervised machine learning methodology where unlabeled\nelements/objects are grouped together aiming to the construction of\nwell-established clusters that their elements are classified according to their\nsimilarity. The goal of this process is to provide a useful aid to the\nresearcher that will help her/him to identify patterns among the data. Dealing\nwith large databases, such patterns may not be easily detectable without the\ncontribution of a clustering algorithm. This article provides a deep\ndescription of the most widely used clustering methodologies accompanied by\nuseful presentations concerning suitable parameter selection and\ninitializations. Simultaneously, this article not only represents a review\nhighlighting the major elements of examined clustering techniques but\nemphasizes the comparison of these algorithms' clustering efficiency based on 3\ndatasets, revealing their existing weaknesses and capabilities through accuracy\nand complexity, during the confrontation of discrete and continuous\nobservations. The produced results help us extract valuable conclusions about\nthe appropriateness of the examined clustering techniques in accordance with\nthe dataset's size.\n", "date": "2022-07-14", "categories": []}
{"id": "2310.12752", "title": "Discretize Relaxed Solution of Spectral Clustering via a Non-Heuristic\n  Algorithm", "abstract": "  Spectral clustering and its extensions usually consist of two steps: (1)\nconstructing a graph and computing the relaxed solution; (2) discretizing\nrelaxed solutions. Although the former has been extensively investigated, the\ndiscretization techniques are mainly heuristic methods, e.g., k-means, spectral\nrotation. Unfortunately, the goal of the existing methods is not to find a\ndiscrete solution that minimizes the original objective. In other words, the\nprimary drawback is the neglect of the original objective when computing the\ndiscrete solution. Inspired by the first-order optimization algorithms, we\npropose to develop a first-order term to bridge the original problem and\ndiscretization algorithm, which is the first non-heuristic to the best of our\nknowledge. Since the non-heuristic method is aware of the original graph cut\nproblem, the final discrete solution is more reliable and achieves the\npreferable loss value. We also theoretically show that the continuous optimum\nis beneficial to discretization algorithms though simply finding its closest\ndiscrete solution is an existing heuristic algorithm which is also unreliable.\nSufficient experiments significantly show the superiority of our method.\n", "date": "2023-10-19", "categories": []}
{"id": "2310.11940", "title": "Interpretable Spectral Variational AutoEncoder (ISVAE) for time series\n  clustering", "abstract": "  The best encoding is the one that is interpretable in nature. In this work,\nwe introduce a novel model that incorporates an interpretable bottleneck-termed\nthe Filter Bank (FB)-at the outset of a Variational Autoencoder (VAE). This\narrangement compels the VAE to attend on the most informative segments of the\ninput signal, fostering the learning of a novel encoding ${f_0}$ which boasts\nenhanced interpretability and clusterability over traditional latent spaces. By\ndeliberately constraining the VAE with this FB, we intentionally constrict its\ncapacity to access broad input domain information, promoting the development of\nan encoding that is discernible, separable, and of reduced dimensionality. The\nevolutionary learning trajectory of ${f_0}$ further manifests as a dynamic\nhierarchical tree, offering profound insights into cluster similarities.\nAdditionally, for handling intricate data configurations, we propose a tailored\ndecoder structure that is symmetrically aligned with FB's architecture.\nEmpirical evaluations highlight the superior efficacy of ISVAE, which compares\nfavorably to state-of-the-art results in clustering metrics across real-world\ndatasets.\n", "date": "2023-10-18", "categories": []}
{"id": "2207.07173", "title": "Deep Image Clustering with Contrastive Learning and Multi-scale Graph\n  Convolutional Networks", "abstract": "  Deep clustering has shown its promising capability in joint representation\nlearning and clustering via deep neural networks. Despite the significant\nprogress, the existing deep clustering works mostly utilize some\ndistribution-based clustering loss, lacking the ability to unify representation\nlearning and multi-scale structure learning. To address this, this paper\npresents a new deep clustering approach termed image clustering with\ncontrastive learning and multi-scale graph convolutional networks (IcicleGCN),\nwhich bridges the gap between convolutional neural network (CNN) and graph\nconvolutional network (GCN) as well as the gap between contrastive learning and\nmulti-scale structure learning for the deep clustering task. Our framework\nconsists of four main modules, namely, the CNN-based backbone, the Instance\nSimilarity Module (ISM), the Joint Cluster Structure Learning and Instance\nreconstruction Module (JC-SLIM), and the Multi-scale GCN module (M-GCN).\nSpecifically, the backbone network with two weight-sharing views is utilized to\nlearn the representations for the two augmented samples (from each image). The\nlearned representations are then fed to ISM and JC-SLIM for joint\ninstance-level and cluster-level contrastive learning, respectively, during\nwhich an auto-encoder in JC-SLIM is also pretrained to serve as a bridge to the\nM-GCN module. Further, to enforce multi-scale neighborhood structure learning,\ntwo streams of GCNs and the auto-encoder are simultaneously trained via (i) the\nlayer-wise interaction with representation fusion and (ii) the joint\nself-adaptive learning. Experiments on multiple image datasets demonstrate the\nsuperior clustering performance of IcicleGCN over the state-of-the-art. The\ncode is available at https://github.com/xuyuankun631/IcicleGCN.\n", "date": "2022-07-14", "categories": []}
{"id": "2310.10939", "title": "Fast and Simple Spectral Clustering in Theory and Practice", "abstract": "  Spectral clustering is a popular and effective algorithm designed to find $k$\nclusters in a graph $G$. In the classical spectral clustering algorithm, the\nvertices of $G$ are embedded into $\\mathbb{R}^k$ using $k$ eigenvectors of the\ngraph Laplacian matrix. However, computing this embedding is computationally\nexpensive and dominates the running time of the algorithm. In this paper, we\npresent a simple spectral clustering algorithm based on a vertex embedding with\n$O(\\log(k))$ vectors computed by the power method. The vertex embedding is\ncomputed in nearly-linear time with respect to the size of the graph, and the\nalgorithm provably recovers the ground truth clusters under natural assumptions\non the input graph. We evaluate the new algorithm on several synthetic and\nreal-world datasets, finding that it is significantly faster than alternative\nclustering algorithms, while producing results with approximately the same\nclustering accuracy.\n", "date": "2023-10-17", "categories": []}
{"id": "2309.03751", "title": "Medoid Silhouette clustering with automatic cluster number selection", "abstract": "  The evaluation of clustering results is difficult, highly dependent on the\nevaluated data set and the perspective of the beholder. There are many\ndifferent clustering quality measures, which try to provide a general measure\nto validate clustering results. A very popular measure is the Silhouette. We\ndiscuss the efficient medoid-based variant of the Silhouette, perform a\ntheoretical analysis of its properties, provide two fast versions for the\ndirect optimization, and discuss the use to choose the optimal number of\nclusters. We combine ideas from the original Silhouette with the well-known PAM\nalgorithm and its latest improvements FasterPAM. One of the versions guarantees\nequal results to the original variant and provides a run speedup of $O(k^2)$.\nIn experiments on real data with 30000 samples and $k$=100, we observed a\n10464$\\times$ speedup compared to the original PAMMEDSIL algorithm.\nAdditionally, we provide a variant to choose the optimal number of clusters\ndirectly.\n", "date": "2023-09-07", "categories": []}
{"id": "2310.09127", "title": "On Generalization Bounds for Projective Clustering", "abstract": "  Given a set of points, clustering consists of finding a partition of a point\nset into $k$ clusters such that the center to which a point is assigned is as\nclose as possible. Most commonly, centers are points themselves, which leads to\nthe famous $k$-median and $k$-means objectives. One may also choose centers to\nbe $j$ dimensional subspaces, which gives rise to subspace clustering. In this\npaper, we consider learning bounds for these problems. That is, given a set of\n$n$ samples $P$ drawn independently from some unknown, but fixed distribution\n$\\mathcal{D}$, how quickly does a solution computed on $P$ converge to the\noptimal clustering of $\\mathcal{D}$? We give several near optimal results. In\nparticular,\n  For center-based objectives, we show a convergence rate of\n$\\tilde{O}\\left(\\sqrt{{k}/{n}}\\right)$. This matches the known optimal bounds\nof [Fefferman, Mitter, and Narayanan, Journal of the Mathematical Society 2016]\nand [Bartlett, Linder, and Lugosi, IEEE Trans. Inf. Theory 1998] for $k$-means\nand extends it to other important objectives such as $k$-median.\n  For subspace clustering with $j$-dimensional subspaces, we show a convergence\nrate of $\\tilde{O}\\left(\\sqrt{\\frac{kj^2}{n}}\\right)$. These are the first\nprovable bounds for most of these problems. For the specific case of projective\nclustering, which generalizes $k$-means, we show a convergence rate of\n$\\Omega\\left(\\sqrt{\\frac{kj}{n}}\\right)$ is necessary, thereby proving that the\nbounds from [Fefferman, Mitter, and Narayanan, Journal of the Mathematical\nSociety 2016] are essentially optimal.\n", "date": "2023-10-13", "categories": []}
{"id": "2310.07491", "title": "Model-based Clustering of Individuals' Ecological Momentary Assessment\n  Time-series Data for Improving Forecasting Performance", "abstract": "  Through Ecological Momentary Assessment (EMA) studies, a number of\ntime-series data is collected across multiple individuals, continuously\nmonitoring various items of emotional behavior. Such complex data is commonly\nanalyzed in an individual level, using personalized models. However, it is\nbelieved that additional information of similar individuals is likely to\nenhance these models leading to better individuals' description. Thus,\nclustering is investigated with an aim to group together the most similar\nindividuals, and subsequently use this information in group-based models in\norder to improve individuals' predictive performance. More specifically, two\nmodel-based clustering approaches are examined, where the first is using\nmodel-extracted parameters of personalized models, whereas the second is\noptimized on the model-based forecasting performance. Both methods are then\nanalyzed using intrinsic clustering evaluation measures (e.g. Silhouette\ncoefficients) as well as the performance of a downstream forecasting scheme,\nwhere each forecasting group-model is devoted to describe all individuals\nbelonging to one cluster. Among these, clustering based on performance shows\nthe best results, in terms of all examined evaluation measures. As another\nlevel of evaluation, those group-models' performance is compared to three\nbaseline scenarios, the personalized, the all-in-one group and the random\ngroup-based concept. According to this comparison, the superiority of\nclustering-based methods is again confirmed, indicating that the utilization of\ngroup-based information could be effectively enhance the overall performance of\nall individuals' data.\n", "date": "2023-10-11", "categories": []}
{"id": "2310.02717", "title": "Online Clustering of Bandits with Misspecified User Models", "abstract": "  The contextual linear bandit is an important online learning problem where\ngiven arm features, a learning agent selects an arm at each round to maximize\nthe cumulative rewards in the long run. A line of works, called the clustering\nof bandits (CB), utilize the collaborative effect over user preferences and\nhave shown significant improvements over classic linear bandit algorithms.\nHowever, existing CB algorithms require well-specified linear user models and\ncan fail when this critical assumption does not hold. Whether robust CB\nalgorithms can be designed for more practical scenarios with misspecified user\nmodels remains an open problem. In this paper, we are the first to present the\nimportant problem of clustering of bandits with misspecified user models\n(CBMUM), where the expected rewards in user models can be perturbed away from\nperfect linear models. We devise two robust CB algorithms, RCLUMB and RSCLUMB\n(representing the learned clustering structure with dynamic graph and sets,\nrespectively), that can accommodate the inaccurate user preference estimations\nand erroneous clustering caused by model misspecifications. We prove regret\nupper bounds of $O(\\epsilon_*T\\sqrt{md\\log T} + d\\sqrt{mT}\\log T)$ for our\nalgorithms under milder assumptions than previous CB works (notably, we move\npast a restrictive technical assumption on the distribution of the arms), which\nmatch the lower bound asymptotically in $T$ up to logarithmic factors, and also\nmatch the state-of-the-art results in several degenerate cases. The techniques\nin proving the regret caused by misclustering users are quite general and may\nbe of independent interest. Experiments on both synthetic and real-world data\nshow our outperformance over previous algorithms.\n", "date": "2023-10-04", "categories": []}
{"id": "2210.08162", "title": "AMD-DBSCAN: An Adaptive Multi-density DBSCAN for datasets of extremely\n  variable density", "abstract": "  DBSCAN has been widely used in density-based clustering algorithms. However,\nwith the increasing demand for Multi-density clustering, previous traditional\nDSBCAN can not have good clustering results on Multi-density datasets. In order\nto address this problem, an adaptive Multi-density DBSCAN algorithm\n(AMD-DBSCAN) is proposed in this paper. An improved parameter adaptation method\nis proposed in AMD-DBSCAN to search for multiple parameter pairs (i.e., Eps and\nMinPts), which are the key parameters to determine the clustering results and\nperformance, therefore allowing the model to be applied to Multi-density\ndatasets. Moreover, only one hyperparameter is required for AMD-DBSCAN to avoid\nthe complicated repetitive initialization operations. Furthermore, the variance\nof the number of neighbors (VNN) is proposed to measure the difference in\ndensity between each cluster. The experimental results show that our AMD-DBSCAN\nreduces execution time by an average of 75% due to lower algorithm complexity\ncompared with the traditional adaptive algorithm. In addition, AMD-DBSCAN\nimproves accuracy by 24.7% on average over the state-of-the-art design on\nMulti-density datasets of extremely variable density, while having no\nperformance loss in Single-density scenarios. Our code and datasets are\navailable at https://github.com/AlexandreWANG915/AMD-DBSCAN.\n", "date": "2022-10-15", "categories": []}
{"id": "2210.09640", "title": "Clustering Categorical Data: Soft Rounding k-modes", "abstract": "  Over the last three decades, researchers have intensively explored various\nclustering tools for categorical data analysis. Despite the proposal of various\nclustering algorithms, the classical k-modes algorithm remains a popular choice\nfor unsupervised learning of categorical data. Surprisingly, our first insight\nis that in a natural generative block model, the k-modes algorithm performs\npoorly for a large range of parameters. We remedy this issue by proposing a\nsoft rounding variant of the k-modes algorithm (SoftModes) and theoretically\nprove that our variant addresses the drawbacks of the k-modes algorithm in the\ngenerative model. Finally, we empirically verify that SoftModes performs well\non both synthetic and real-world datasets.\n", "date": "2022-10-18", "categories": []}
{"id": "2307.12065", "title": "Spectral Normalized-Cut Graph Partitioning with Fairness Constraints", "abstract": "  Normalized-cut graph partitioning aims to divide the set of nodes in a graph\ninto $k$ disjoint clusters to minimize the fraction of the total edges between\nany cluster and all other clusters. In this paper, we consider a fair variant\nof the partitioning problem wherein nodes are characterized by a categorical\nsensitive attribute (e.g., gender or race) indicating membership to different\ndemographic groups. Our goal is to ensure that each group is approximately\nproportionally represented in each cluster while minimizing the normalized cut\nvalue. To resolve this problem, we propose a two-phase spectral algorithm\ncalled FNM. In the first phase, we add an augmented Lagrangian term based on\nour fairness criteria to the objective function for obtaining a fairer spectral\nnode embedding. Then, in the second phase, we design a rounding scheme to\nproduce $k$ clusters from the fair embedding that effectively trades off\nfairness and partition quality. Through comprehensive experiments on nine\nbenchmark datasets, we demonstrate the superior performance of FNM compared\nwith three baseline methods.\n", "date": "2023-07-22", "categories": []}
{"id": "2310.04946", "title": "Transferable Deep Clustering Model", "abstract": "  Deep learning has shown remarkable success in the field of clustering\nrecently. However, how to transfer a trained clustering model on a source\ndomain to a target domain by leveraging the acquired knowledge to guide the\nclustering process remains challenging. Existing deep clustering methods often\nlack generalizability to new domains because they typically learn a group of\nfixed cluster centroids, which may not be optimal for the new domain\ndistributions. In this paper, we propose a novel transferable deep clustering\nmodel that can automatically adapt the cluster centroids according to the\ndistribution of data samples. Rather than learning a fixed set of centroids,\nour approach introduces a novel attention-based module that can adapt the\ncentroids by measuring their relationship with samples. In addition, we\ntheoretically show that our model is strictly more powerful than some classical\nclustering algorithms such as k-means or Gaussian Mixture Model (GMM).\nExperimental results on both synthetic and real-world datasets demonstrate the\neffectiveness and efficiency of our proposed transfer learning framework, which\nsignificantly improves the performance on target domain and reduces the\ncomputational cost.\n", "date": "2023-10-07", "categories": []}
{"id": "2310.04038", "title": "Joint Projection Learning and Tensor Decomposition Based Incomplete\n  Multi-view Clustering", "abstract": "  Incomplete multi-view clustering (IMVC) has received increasing attention\nsince it is often that some views of samples are incomplete in reality. Most\nexisting methods learn similarity subgraphs from original incomplete multi-view\ndata and seek complete graphs by exploring the incomplete subgraphs of each\nview for spectral clustering. However, the graphs constructed on the original\nhigh-dimensional data may be suboptimal due to feature redundancy and noise.\nBesides, previous methods generally ignored the graph noise caused by the\ninter-class and intra-class structure variation during the transformation of\nincomplete graphs and complete graphs. To address these problems, we propose a\nnovel Joint Projection Learning and Tensor Decomposition Based method (JPLTD)\nfor IMVC. Specifically, to alleviate the influence of redundant features and\nnoise in high-dimensional data, JPLTD introduces an orthogonal projection\nmatrix to project the high-dimensional features into a lower-dimensional space\nfor compact feature learning.Meanwhile, based on the lower-dimensional space,\nthe similarity graphs corresponding to instances of different views are\nlearned, and JPLTD stacks these graphs into a third-order low-rank tensor to\nexplore the high-order correlations across different views. We further consider\nthe graph noise of projected data caused by missing samples and use a\ntensor-decomposition based graph filter for robust clustering.JPLTD decomposes\nthe original tensor into an intrinsic tensor and a sparse tensor. The intrinsic\ntensor models the true data similarities. An effective optimization algorithm\nis adopted to solve the JPLTD model. Comprehensive experiments on several\nbenchmark datasets demonstrate that JPLTD outperforms the state-of-the-art\nmethods. The code of JPLTD is available at https://github.com/weilvNJU/JPLTD.\n", "date": "2023-10-06", "categories": []}
{"id": "2310.00820", "title": "Determining the Optimal Number of Clusters for Time Series Datasets with\n  Symbolic Pattern Forest", "abstract": "  Clustering algorithms are among the most widely used data mining methods due\nto their exploratory power and being an initial preprocessing step that paves\nthe way for other techniques. But the problem of calculating the optimal number\nof clusters (say k) is one of the significant challenges for such methods. The\nmost widely used clustering algorithms like k-means and k-shape in time series\ndata mining also need the ground truth for the number of clusters that need to\nbe generated. In this work, we extended the Symbolic Pattern Forest algorithm,\nanother time series clustering algorithm, to determine the optimal number of\nclusters for the time series datasets. We used SPF to generate the clusters\nfrom the datasets and chose the optimal number of clusters based on the\nSilhouette Coefficient, a metric used to calculate the goodness of a clustering\ntechnique. Silhouette was calculated on both the bag of word vectors and the\ntf-idf vectors generated from the SAX words of each time series. We tested our\napproach on the UCR archive datasets, and our experimental results so far\nshowed significant improvement over the baseline.\n", "date": "2023-10-01", "categories": []}
{"id": "2309.16840", "title": "Constant Approximation for Individual Preference Stable Clustering", "abstract": "  Individual preference (IP) stability, introduced by Ahmadi et al. (ICML\n2022), is a natural clustering objective inspired by stability and fairness\nconstraints. A clustering is $\\alpha$-IP stable if the average distance of\nevery data point to its own cluster is at most $\\alpha$ times the average\ndistance to any other cluster. Unfortunately, determining if a dataset admits a\n$1$-IP stable clustering is NP-Hard. Moreover, before this work, it was unknown\nif an $o(n)$-IP stable clustering always \\emph{exists}, as the prior state of\nthe art only guaranteed an $O(n)$-IP stable clustering. We close this gap in\nunderstanding and show that an $O(1)$-IP stable clustering always exists for\ngeneral metrics, and we give an efficient algorithm which outputs such a\nclustering. We also introduce generalizations of IP stability beyond average\ndistance and give efficient, near-optimal algorithms in the cases where we\nconsider the maximum and minimum distances within and between clusters.\n", "date": "2023-09-28", "categories": []}
{"id": "2309.17383", "title": "Parallel Computation of Multi-Slice Clustering of Third-Order Tensors", "abstract": "  Machine Learning approaches like clustering methods deal with massive\ndatasets that present an increasing challenge. We devise parallel algorithms to\ncompute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method\nis based on spectral analysis of the tensor slices and works independently on\neach tensor mode. Such features fit well in the parallel paradigm via a\ndistributed memory system. We show that our parallel scheme outperforms\nsequential computing and allows for the scalability of the MSC method.\n", "date": "2023-09-29", "categories": []}
{"id": "2309.15322", "title": "On the Power of SVD in the Stochastic Block Model", "abstract": "  A popular heuristic method for improving clustering results is to apply\ndimensionality reduction before running clustering algorithms. It has been\nobserved that spectral-based dimensionality reduction tools, such as PCA or\nSVD, improve the performance of clustering algorithms in many applications.\nThis phenomenon indicates that spectral method not only serves as a\ndimensionality reduction tool, but also contributes to the clustering procedure\nin some sense. It is an interesting question to understand the behavior of\nspectral steps in clustering problems.\n  As an initial step in this direction, this paper studies the power of\nvanilla-SVD algorithm in the stochastic block model (SBM). We show that, in the\nsymmetric setting, vanilla-SVD algorithm recovers all clusters correctly. This\nresult answers an open question posed by Van Vu (Combinatorics Probability and\nComputing, 2018) in the symmetric setting.\n", "date": "2023-09-27", "categories": []}
{"id": "2309.13420", "title": "DenMune: Density peak based clustering using mutual nearest neighbors", "abstract": "  Many clustering algorithms fail when clusters are of arbitrary shapes, of\nvarying densities, or the data classes are unbalanced and close to each other,\neven in two dimensions. A novel clustering algorithm, DenMune is presented to\nmeet this challenge. It is based on identifying dense regions using mutual\nnearest neighborhoods of size K, where K is the only parameter required from\nthe user, besides obeying the mutual nearest neighbor consistency principle.\nThe algorithm is stable for a wide range of values of K. Moreover, it is able\nto automatically detect and remove noise from the clustering process as well as\ndetecting the target clusters. It produces robust results on various low and\nhigh-dimensional datasets relative to several known state-of-the-art clustering\nalgorithms.\n", "date": "2023-09-23", "categories": []}
{"id": "2309.13697", "title": "Federated Deep Multi-View Clustering with Global Self-Supervision", "abstract": "  Federated multi-view clustering has the potential to learn a global\nclustering model from data distributed across multiple devices. In this\nsetting, label information is unknown and data privacy must be preserved,\nleading to two major challenges. First, views on different clients often have\nfeature heterogeneity, and mining their complementary cluster information is\nnot trivial. Second, the storage and usage of data from multiple clients in a\ndistributed environment can lead to incompleteness of multi-view data. To\naddress these challenges, we propose a novel federated deep multi-view\nclustering method that can mine complementary cluster structures from multiple\nclients, while dealing with data incompleteness and privacy concerns.\nSpecifically, in the server environment, we propose sample alignment and data\nextension techniques to explore the complementary cluster structures of\nmultiple views. The server then distributes global prototypes and global\npseudo-labels to each client as global self-supervised information. In the\nclient environment, multiple clients use the global self-supervised information\nand deep autoencoders to learn view-specific cluster assignments and embedded\nfeatures, which are then uploaded to the server for refining the global\nself-supervised information. Finally, the results of our extensive experiments\ndemonstrate that our proposed method exhibits superior performance in\naddressing the challenges of incomplete multi-view data in distributed\nenvironments.\n", "date": "2023-09-24", "categories": []}
{"id": "2309.13949", "title": "Characterising User Transfer Amid Industrial Resource Variation: A\n  Bayesian Nonparametric Approach", "abstract": "  In a multitude of industrial fields, a key objective entails optimising\nresource management whilst satisfying user requirements. Resource management by\nindustrial practitioners can result in a passive transfer of user loads across\nresource providers, a phenomenon whose accurate characterisation is both\nchallenging and crucial. This research reveals the existence of user clusters,\nwhich capture macro-level user transfer patterns amid resource variation. We\nthen propose CLUSTER, an interpretable hierarchical Bayesian nonparametric\nmodel capable of automating cluster identification, and thereby predicting user\ntransfer in response to resource variation. Furthermore, CLUSTER facilitates\nuncertainty quantification for further reliable decision-making. Our method\nenables privacy protection by functioning independently of personally\nidentifiable information. Experiments with simulated and real-world data from\nthe communications industry reveal a pronounced alignment between prediction\nresults and empirical observations across a spectrum of resource management\nscenarios. This research establishes a solid groundwork for advancing resource\nmanagement strategy development.\n", "date": "2023-09-25", "categories": []}
{"id": "2309.13989", "title": "A Novel Approach for Effective Multi-View Clustering with\n  Information-Theoretic Perspective", "abstract": "  Multi-view clustering (MVC) is a popular technique for improving clustering\nperformance using various data sources. However, existing methods primarily\nfocus on acquiring consistent information while often neglecting the issue of\nredundancy across multiple views. This study presents a new approach called\nSufficient Multi-View Clustering (SUMVC) that examines the multi-view\nclustering framework from an information-theoretic standpoint. Our proposed\nmethod consists of two parts. Firstly, we develop a simple and reliable\nmulti-view clustering method SCMVC (simple consistent multi-view clustering)\nthat employs variational analysis to generate consistent information. Secondly,\nwe propose a sufficient representation lower bound to enhance consistent\ninformation and minimise unnecessary information among views. The proposed\nSUMVC method offers a promising solution to the problem of multi-view\nclustering and provides a new perspective for analyzing multi-view data.\n  To verify the effectiveness of our model, we conducted a theoretical analysis\nbased on the Bayes Error Rate, and experiments on multiple multi-view datasets\ndemonstrate the superior performance of SUMVC.\n", "date": "2023-09-25", "categories": []}
{"id": "2304.09512", "title": "Community Detection Using Revised Medoid-Shift Based on KNN", "abstract": "  Community detection becomes an important problem with the booming of social\nnetworks. The Medoid-Shift algorithm preserves the benefits of Mean-Shift and\ncan be applied to problems based on distance matrix, such as community\ndetection. One drawback of the Medoid-Shift algorithm is that there may be no\ndata points within the neighborhood region defined by a distance parameter. To\ndeal with the community detection problem better, a new algorithm called\nRevised Medoid-Shift (RMS) in this work is thus proposed. During the process of\nfinding the next medoid, the RMS algorithm is based on a neighborhood defined\nby KNN, while the original Medoid-Shift is based on a neighborhood defined by a\ndistance parameter. Since the neighborhood defined by KNN is more stable than\nthe one defined by the distance parameter in terms of the number of data points\nwithin the neighborhood, the RMS algorithm may converge more smoothly. In the\nRMS method, each of the data points is shifted towards a medoid within the\nneighborhood defined by KNN. After the iterative process of shifting, each of\nthe data point converges into a cluster center, and the data points converging\ninto the same center are grouped into the same cluster. The RMS algorithm is\ntested on two kinds of datasets including community datasets with known ground\ntruth partition and community datasets without ground truth partition\nrespectively. The experiment results show sthat the proposed RMS algorithm\ngenerally produces betster results than Medoid-Shift and some state-of-the-art\ntogether with most classic community detection algorithms on different kinds of\ncommunity detection datasets.\n", "date": "2023-04-19", "categories": []}
{"id": "2309.10047", "title": "A Modular Spatial Clustering Algorithm with Noise Specification", "abstract": "  Clustering techniques have been the key drivers of data mining, machine\nlearning and pattern recognition for decades. One of the most popular\nclustering algorithms is DBSCAN due to its high accuracy and noise tolerance.\nMany superior algorithms such as DBSCAN have input parameters that are hard to\nestimate. Therefore, finding those parameters is a time consuming process. In\nthis paper, we propose a novel clustering algorithm Bacteria-Farm, which\nbalances the performance and ease of finding the optimal parameters for\nclustering. Bacteria- Farm algorithm is inspired by the growth of bacteria in\nclosed experimental farms - their ability to consume food and grow - which\nclosely represents the ideal cluster growth desired in clustering algorithms.\nIn addition, the algorithm features a modular design to allow the creation of\nversions of the algorithm for specific tasks / distributions of data. In\ncontrast with other clustering algorithms, our algorithm also has a provision\nto specify the amount of noise to be excluded during clustering.\n", "date": "2023-09-18", "categories": []}
{"id": "2309.10408", "title": "Unsupervised Learning via Network-Aware Embeddings", "abstract": "  Data clustering, the task of grouping observations according to their\nsimilarity, is a key component of unsupervised learning -- with real world\napplications in diverse fields such as biology, medicine, and social science.\nOften in these fields the data comes with complex interdependencies between the\ndimensions of analysis, for instance the various characteristics and opinions\npeople can have live on a complex social network. Current clustering methods\nare ill-suited to tackle this complexity: deep learning can approximate these\ndependencies, but not take their explicit map as the input of the analysis. In\nthis paper, we aim at fixing this blind spot in the unsupervised learning\nliterature. We can create network-aware embeddings by estimating the network\ndistance between numeric node attributes via the generalized Euclidean\ndistance. Differently from all methods in the literature that we know of, we do\nnot cluster the nodes of the network, but rather its node attributes. In our\nexperiments we show that having these network embeddings is always beneficial\nfor the learning task; that our method scales to large networks; and that we\ncan actually provide actionable insights in applications in a variety of fields\nsuch as marketing, economics, and political science. Our method is fully open\nsource and data and code are available to reproduce all results in the paper.\n", "date": "2023-09-19", "categories": []}
{"id": "2206.00359", "title": "DeepCluE: Enhanced Image Clustering via Multi-layer Ensembles in Deep\n  Neural Networks", "abstract": "  Deep clustering has recently emerged as a promising technique for complex\ndata clustering. Despite the considerable progress, previous deep clustering\nworks mostly build or learn the final clustering by only utilizing a single\nlayer of representation, e.g., by performing the K-means clustering on the last\nfully-connected layer or by associating some clustering loss to a specific\nlayer, which neglect the possibilities of jointly leveraging multi-layer\nrepresentations for enhancing the deep clustering performance. In view of this,\nthis paper presents a Deep Clustering via Ensembles (DeepCluE) approach, which\nbridges the gap between deep clustering and ensemble clustering by harnessing\nthe power of multiple layers in deep neural networks. In particular, we utilize\na weight-sharing convolutional neural network as the backbone, which is trained\nwith both the instance-level contrastive learning (via an instance projector)\nand the cluster-level contrastive learning (via a cluster projector) in an\nunsupervised manner. Thereafter, multiple layers of feature representations are\nextracted from the trained network, upon which the ensemble clustering process\nis further conducted. Specifically, a set of diversified base clusterings are\ngenerated from the multi-layer representations via a highly efficient\nclusterer. Then the reliability of clusters in multiple base clusterings is\nautomatically estimated by exploiting an entropy-based criterion, based on\nwhich the set of base clusterings are re-formulated into a weighted-cluster\nbipartite graph. By partitioning this bipartite graph via transfer cut, the\nfinal consensus clustering can be obtained. Experimental results on six image\ndatasets confirm the advantages of DeepCluE over the state-of-the-art deep\nclustering approaches.\n", "date": "2022-06-01", "categories": []}
{"id": "2309.08757", "title": "Circular Clustering with Polar Coordinate Reconstruction", "abstract": "  There is a growing interest in characterizing circular data found in\nbiological systems. Such data are wide ranging and varied, from signal phase in\nneural recordings to nucleotide sequences in round genomes. Traditional\nclustering algorithms are often inadequate due to their limited ability to\ndistinguish differences in the periodic component. Current clustering schemes\nthat work in a polar coordinate system have limitations, such as being only\nangle-focused or lacking generality. To overcome these limitations, we propose\na new analysis framework that utilizes projections onto a cylindrical\ncoordinate system to better represent objects in a polar coordinate system.\nUsing the mathematical properties of circular data, we show our approach always\nfinds the correct clustering result within the reconstructed dataset, given\nsufficient periodic repetitions of the data. Our approach is generally\napplicable and adaptable and can be incorporated into most state-of-the-art\nclustering algorithms. We demonstrate on synthetic and real data that our\nmethod generates more appropriate and consistent clustering results compared to\nstandard methods. In summary, our proposed analysis framework overcomes the\nlimitations of existing polar coordinate-based clustering methods and provides\na more accurate and efficient way to cluster circular data.\n", "date": "2023-09-15", "categories": []}
{"id": "2309.09473", "title": "Self-supervised Multi-view Clustering in Computer Vision: A Survey", "abstract": "  Multi-view clustering (MVC) has had significant implications in cross-modal\nrepresentation learning and data-driven decision-making in recent years. It\naccomplishes this by leveraging the consistency and complementary information\namong multiple views to cluster samples into distinct groups. However, as\ncontrastive learning continues to evolve within the field of computer vision,\nself-supervised learning has also made substantial research progress and is\nprogressively becoming dominant in MVC methods. It guides the clustering\nprocess by designing proxy tasks to mine the representation of image and video\ndata itself as supervisory information. Despite the rapid development of\nself-supervised MVC, there has yet to be a comprehensive survey to analyze and\nsummarize the current state of research progress. Therefore, this paper\nexplores the reasons and advantages of the emergence of self-supervised MVC and\ndiscusses the internal connections and classifications of common datasets, data\nissues, representation learning methods, and self-supervised learning methods.\nThis paper does not only introduce the mechanisms for each category of methods\nbut also gives a few examples of how these techniques are used. In the end,\nsome open problems are pointed out for further investigation and development.\n", "date": "2023-09-18", "categories": []}
{"id": "2309.09830", "title": "Clustering of Urban Traffic Patterns by K-Means and Dynamic Time\n  Warping: Case Study", "abstract": "  Clustering of urban traffic patterns is an essential task in many different\nareas of traffic management and planning. In this paper, two significant\napplications in the clustering of urban traffic patterns are described. The\nfirst application estimates the missing speed values using the speed of road\nsegments with similar traffic patterns to colorify map tiles. The second one is\nthe estimation of essential road segments for generating addresses for a local\npoint on the map, using the similarity patterns of different road segments. The\nspeed time series extracts the traffic pattern in different road segments. In\nthis paper, we proposed the time series clustering algorithm based on K-Means\nand Dynamic Time Warping. The case study of our proposed algorithm is based on\nthe Snapp application's driver speed time series data. The results of the two\napplications illustrate that the proposed method can extract similar urban\ntraffic patterns.\n", "date": "2023-09-18", "categories": []}
{"id": "2309.08533", "title": "Automated dermatoscopic pattern discovery by clustering neural network\n  output for human-computer interaction", "abstract": "  Background: As available medical image datasets increase in size, it becomes\ninfeasible for clinicians to review content manually for knowledge extraction.\nThe objective of this study was to create an automated clustering resulting in\nhuman-interpretable pattern discovery.\n  Methods: Images from the public HAM10000 dataset, including 7 common\npigmented skin lesion diagnoses, were tiled into 29420 tiles and clustered via\nk-means using neural network-extracted image features. The final number of\nclusters per diagnosis was chosen by either the elbow method or a compactness\nmetric balancing intra-lesion variance and cluster numbers. The amount of\nresulting non-informative clusters, defined as those containing less than six\nimage tiles, was compared between the two methods.\n  Results: Applying k-means, the optimal elbow cutoff resulted in a mean of\n24.7 (95%-CI: 16.4-33) clusters for every included diagnosis, including 14.9%\n(95% CI: 0.8-29.0) non-informative clusters. The optimal cutoff, as estimated\nby the compactness metric, resulted in significantly fewer clusters (13.4;\n95%-CI 11.8-15.1; p=0.03) and less non-informative ones (7.5%; 95% CI: 0-19.5;\np=0.017). The majority of clusters (93.6%) from the compactness metric could be\nmanually mapped to previously described dermatoscopic diagnostic patterns.\n  Conclusions: Automatically constraining unsupervised clustering can produce\nan automated extraction of diagnostically relevant and human-interpretable\nclusters of visual patterns from a large image dataset.\n", "date": "2023-09-15", "categories": []}
{"id": "2304.14541", "title": "Deep Spatiotemporal Clustering: A Temporal Clustering Approach for\n  Multi-dimensional Climate Data", "abstract": "  Clustering high-dimensional spatiotemporal data using an unsupervised\napproach is a challenging problem for many data-driven applications. Existing\nstate-of-the-art methods for unsupervised clustering use different similarity\nand distance functions but focus on either spatial or temporal features of the\ndata. Concentrating on joint deep representation learning of spatial and\ntemporal features, we propose Deep Spatiotemporal Clustering (DSC), a novel\nalgorithm for the temporal clustering of high-dimensional spatiotemporal data\nusing an unsupervised deep learning method. Inspired by the U-net architecture,\nDSC utilizes an autoencoder integrating CNN-RNN layers to learn latent\nrepresentations of the spatiotemporal data. DSC also includes a unique layer\nfor cluster assignment on latent representations that uses the Student's\nt-distribution. By optimizing the clustering loss and data reconstruction loss\nsimultaneously, the algorithm gradually improves clustering assignments and the\nnonlinear mapping between low-dimensional latent feature space and\nhigh-dimensional original data space. A multivariate spatiotemporal climate\ndataset is used to evaluate the efficacy of the proposed method. Our extensive\nexperiments show our approach outperforms both conventional and deep\nlearning-based unsupervised clustering algorithms. Additionally, we compared\nthe proposed model with its various variants (CNN encoder, CNN autoencoder,\nCNN-RNN encoder, CNN-RNN autoencoder, etc.) to get insight into using both the\nCNN and RNN layers in the autoencoder, and our proposed technique outperforms\nthese variants in terms of clustering results.\n", "date": "2023-04-27", "categories": []}
{"id": "2211.12875", "title": "A Survey of Deep Graph Clustering: Taxonomy, Challenge, Application, and\n  Open Resource", "abstract": "  Graph clustering, which aims to divide nodes in the graph into several\ndistinct clusters, is a fundamental yet challenging task. Benefiting from the\npowerful representation capability of deep learning, deep graph clustering\nmethods have achieved great success in recent years. However, the corresponding\nsurvey paper is relatively scarce, and it is imminent to make a summary of this\nfield. From this motivation, we conduct a comprehensive survey of deep graph\nclustering. Firstly, we introduce formulaic definition, evaluation, and\ndevelopment in this field. Secondly, the taxonomy of deep graph clustering\nmethods is presented based on four different criteria, including graph type,\nnetwork architecture, learning paradigm, and clustering method. Thirdly, we\ncarefully analyze the existing methods via extensive experiments and summarize\nthe challenges and opportunities from five perspectives, including graph data\nquality, stability, scalability, discriminative capability, and unknown cluster\nnumber. Besides, the applications of deep graph clustering methods in six\ndomains, including computer vision, natural language processing, recommendation\nsystems, social network analyses, bioinformatics, and medical science, are\npresented. Last but not least, this paper provides open resource supports,\nincluding 1) a collection\n(\\url{https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering}) of\nstate-of-the-art deep graph clustering methods (papers, codes, and datasets)\nand 2) a unified framework\n(\\url{https://github.com/Marigoldwu/A-Unified-Framework-for-Deep-Attribute-Graph-Clustering})\nof deep graph clustering. We hope this work can serve as a quick guide and help\nresearchers overcome challenges in this vibrant field.\n", "date": "2022-11-23", "categories": []}
{"id": "2309.04694", "title": "Redundancy-Free Self-Supervised Relational Learning for Graph Clustering", "abstract": "  Graph clustering, which learns the node representations for effective cluster\nassignments, is a fundamental yet challenging task in data analysis and has\nreceived considerable attention accompanied by graph neural networks in recent\nyears. However, most existing methods overlook the inherent relational\ninformation among the non-independent and non-identically distributed nodes in\na graph. Due to the lack of exploration of relational attributes, the semantic\ninformation of the graph-structured data fails to be fully exploited which\nleads to poor clustering performance. In this paper, we propose a novel\nself-supervised deep graph clustering method named Relational Redundancy-Free\nGraph Clustering (R$^2$FGC) to tackle the problem. It extracts the attribute-\nand structure-level relational information from both global and local views\nbased on an autoencoder and a graph autoencoder. To obtain effective\nrepresentations of the semantic information, we preserve the consistent\nrelation among augmented nodes, whereas the redundant relation is further\nreduced for learning discriminative embeddings. In addition, a simple yet valid\nstrategy is utilized to alleviate the over-smoothing issue. Extensive\nexperiments are performed on widely used benchmark datasets to validate the\nsuperiority of our R$^2$FGC over state-of-the-art baselines. Our codes are\navailable at https://github.com/yisiyu95/R2FGC.\n", "date": "2023-09-09", "categories": []}
{"id": "2309.02552", "title": "Data Aggregation for Hierarchical Clustering", "abstract": "  Hierarchical Agglomerative Clustering (HAC) is likely the earliest and most\nflexible clustering method, because it can be used with many distances,\nsimilarities, and various linkage strategies. It is often used when the number\nof clusters the data set forms is unknown and some sort of hierarchy in the\ndata is plausible. Most algorithms for HAC operate on a full distance matrix,\nand therefore require quadratic memory. The standard algorithm also has cubic\nruntime to produce a full hierarchy. Both memory and runtime are especially\nproblematic in the context of embedded or otherwise very resource-constrained\nsystems. In this section, we present how data aggregation with BETULA, a\nnumerically stable version of the well known BIRCH data aggregation algorithm,\ncan be used to make HAC viable on systems with constrained resources with only\nsmall losses on clustering quality, and hence allow exploratory data analysis\nof very large data sets.\n", "date": "2023-09-05", "categories": []}
{"id": "2309.02557", "title": "Sparse Partitioning Around Medoids", "abstract": "  Partitioning Around Medoids (PAM, k-Medoids) is a popular clustering\ntechnique to use with arbitrary distance functions or similarities, where each\ncluster is represented by its most central object, called the medoid or the\ndiscrete median. In operations research, this family of problems is also known\nas facility location problem (FLP). FastPAM recently introduced a speedup for\nlarge k to make it applicable for larger problems, but the method still has a\nruntime quadratic in N. In this chapter, we discuss a sparse and asymmetric\nvariant of this problem, to be used for example on graph data such as road\nnetworks. By exploiting sparsity, we can avoid the quadratic runtime and memory\nrequirements, and make this method scalable to even larger problems, as long as\nwe are able to build a small enough graph of sufficient connectivity to perform\nlocal optimization. Furthermore, we consider asymmetric cases, where the set of\nmedoids is not identical to the set of points to be covered (or in the\ninterpretation of facility location, where the possible facility locations are\nnot identical to the consumer locations). Because of sparsity, it may be\nimpossible to cover all points with just k medoids for too small k, which would\nrender the problem unsolvable, and this breaks common heuristics for finding a\ngood starting condition. We, hence, consider determining k as a part of the\noptimization problem and propose to first construct a greedy initial solution\nwith a larger k, then to optimize the problem by alternating between PAM-style\n\"swap\" operations where the result is improved by replacing medoids with better\nalternatives and \"remove\" operations to reduce the number of k until neither\nallows further improving the result quality. We demonstrate the usefulness of\nthis method on a problem from electrical engineering, with the input graph\nderived from cartographic data.\n", "date": "2023-09-05", "categories": []}
{"id": "2309.02710", "title": "Improved Outlier Robust Seeding for k-means", "abstract": "  The $k$-means is a popular clustering objective, although it is inherently\nnon-robust and sensitive to outliers. Its popular seeding or initialization\ncalled $k$-means++ uses $D^{2}$ sampling and comes with a provable $O(\\log k)$\napproximation guarantee \\cite{AV2007}. However, in the presence of adversarial\nnoise or outliers, $D^{2}$ sampling is more likely to pick centers from distant\noutliers instead of inlier clusters, and therefore its approximation guarantees\n\\textit{w.r.t.} $k$-means solution on inliers, does not hold.\n  Assuming that the outliers constitute a constant fraction of the given data,\nwe propose a simple variant in the $D^2$ sampling distribution, which makes it\nrobust to the outliers. Our algorithm runs in $O(ndk)$ time, outputs $O(k)$\nclusters, discards marginally more points than the optimal number of outliers,\nand comes with a provable $O(1)$ approximation guarantee.\n  Our algorithm can also be modified to output exactly $k$ clusters instead of\n$O(k)$ clusters, while keeping its running time linear in $n$ and $d$. This is\nan improvement over previous results for robust $k$-means based on LP\nrelaxation and rounding \\cite{Charikar}, \\cite{KrishnaswamyLS18} and\n\\textit{robust $k$-means++} \\cite{DeshpandeKP20}. Our empirical results show\nthe advantage of our algorithm over $k$-means++~\\cite{AV2007}, uniform random\nseeding, greedy sampling for $k$ means~\\cite{tkmeanspp}, and robust\n$k$-means++~\\cite{DeshpandeKP20}, on standard real-world and synthetic data\nsets used in previous work. Our proposal is easily amenable to scalable,\nfaster, parallel implementations of $k$-means++ \\cite{Bahmani,BachemL017} and\nis of independent interest for coreset constructions in the presence of\noutliers \\cite{feldman2007ptas,langberg2010universal,feldman2011unified}.\n", "date": "2023-09-06", "categories": []}
{"id": "2309.02858", "title": "Generalised Mutual Information: a Framework for Discriminative\n  Clustering", "abstract": "  In the last decade, recent successes in deep clustering majorly involved the\nMutual Information (MI) as an unsupervised objective for training neural\nnetworks with increasing regularisations. While the quality of the\nregularisations have been largely discussed for improvements, little attention\nhas been dedicated to the relevance of MI as a clustering objective. In this\npaper, we first highlight how the maximisation of MI does not lead to\nsatisfying clusters. We identified the Kullback-Leibler divergence as the main\nreason of this behaviour. Hence, we generalise the mutual information by\nchanging its core distance, introducing the Generalised Mutual Information\n(GEMINI): a set of metrics for unsupervised neural network training. Unlike MI,\nsome GEMINIs do not require regularisations when training as they are\ngeometry-aware thanks to distances or kernels in the data space. Finally, we\nhighlight that GEMINIs can automatically select a relevant number of clusters,\na property that has been little studied in deep discriminative clustering\ncontext where the number of clusters is a priori unknown.\n", "date": "2023-09-06", "categories": []}
{"id": "2309.00866", "title": "Tutorial: a priori estimation of sample size, effect size, and\n  statistical power for cluster analysis, latent class analysis, and\n  multivariate mixture models", "abstract": "  Before embarking on data collection, researchers typically compute how many\nindividual observations they should do. This is vital for doing studies with\nsufficient statistical power, and often a cornerstone in study\npre-registrations and grant applications. For traditional statistical tests,\none would typically determine an acceptable level of statistical power,\n(gu)estimate effect size, and then use both values to compute the required\nsample size. However, for analyses that identify subgroups, statistical power\nis harder to establish. Once sample size reaches a sufficient threshold, effect\nsize is primarily determined by the number of measured features and the\nunderlying subgroup separation. As a consequence, a priory computations of\nstatistical power are notoriously complex. In this tutorial, I will provide a\nroadmap to determining sample size and effect size for analyses that identify\nsubgroups. First, I introduce a procedure that allows researchers to formalise\ntheir expectations about effect sizes in their domain of choice, and use this\nto compute the minimally required number of measured variables. Next, I outline\nhow to establish the minimum sample size in subgroup analyses. Finally, I use\nsimulations to provide a reference table for the most popular subgroup\nanalyses: k-means, Ward agglomerative hierarchical clustering, c-means fuzzy\nclustering, latent class analysis, latent profile analysis, and Gaussian\nmixture modelling. The table shows the minimum numbers of observations per\nexpected subgroup (sample size) and features (measured variables) to achieve\nacceptable statistical power, and can be readily used in study design.\n", "date": "2023-09-02", "categories": []}
{"id": "2309.01140", "title": "Interpretable Sequence Clustering", "abstract": "  Categorical sequence clustering plays a crucial role in various fields, but\nthe lack of interpretability in cluster assignments poses significant\nchallenges. Sequences inherently lack explicit features, and existing sequence\nclustering algorithms heavily rely on complex representations, making it\ndifficult to explain their results. To address this issue, we propose a method\ncalled Interpretable Sequence Clustering Tree (ISCT), which combines sequential\npatterns with a concise and interpretable tree structure. ISCT leverages k-1\npatterns to generate k leaf nodes, corresponding to k clusters, which provides\nan intuitive explanation on how each cluster is formed. More precisely, ISCT\nfirst projects sequences into random subspaces and then utilizes the k-means\nalgorithm to obtain high-quality initial cluster assignments. Subsequently, it\nconstructs a pattern-based decision tree using a boosting-based construction\nstrategy in which sequences are re-projected and re-clustered at each node\nbefore mining the top-1 discriminative splitting pattern. Experimental results\non 14 real-world data sets demonstrate that our proposed method provides an\ninterpretable tree structure while delivering fast and accurate cluster\nassignments.\n", "date": "2023-09-03", "categories": []}
{"id": "2211.07136", "title": "C3: Cross-instance guided Contrastive Clustering", "abstract": "  Clustering is the task of gathering similar data samples into clusters\nwithout using any predefined labels. It has been widely studied in machine\nlearning literature, and recent advancements in deep learning have revived\ninterest in this field. Contrastive clustering (CC) models are a staple of deep\nclustering in which positive and negative pairs of each data instance are\ngenerated through data augmentation. CC models aim to learn a feature space\nwhere instance-level and cluster-level representations of positive pairs are\ngrouped together. Despite improving the SOTA, these algorithms ignore the\ncross-instance patterns, which carry essential information for improving\nclustering performance. This increases the false-negative-pair rate of the\nmodel while decreasing its true-positive-pair rate. In this paper, we propose a\nnovel contrastive clustering method, Cross-instance guided Contrastive\nClustering (C3), that considers the cross-sample relationships to increase the\nnumber of positive pairs and mitigate the impact of false negative, noise, and\nanomaly sample on the learned representation of data. In particular, we define\na new loss function that identifies similar instances using the instance-level\nrepresentation and encourages them to aggregate together. Moreover, we propose\na novel weighting method to select negative samples in a more efficient way.\nExtensive experimental evaluations show that our proposed method can outperform\nstate-of-the-art algorithms on benchmark computer vision datasets: we improve\nthe clustering accuracy by 6.6%, 3.3%, 5.0%, 1.3% and 0.3% on CIFAR-10,\nCIFAR-100, ImageNet-10, ImageNet-Dogs, and Tiny-ImageNet.\n", "date": "2022-11-14", "categories": []}
{"id": "2309.00024", "title": "Efficient Multi-View Graph Clustering with Local and Global Structure\n  Preservation", "abstract": "  Anchor-based multi-view graph clustering (AMVGC) has received abundant\nattention owing to its high efficiency and the capability to capture\ncomplementary structural information across multiple views. Intuitively, a\nhigh-quality anchor graph plays an essential role in the success of AMVGC.\nHowever, the existing AMVGC methods only consider single-structure information,\ni.e., local or global structure, which provides insufficient information for\nthe learning task. To be specific, the over-scattered global structure leads to\nlearned anchors failing to depict the cluster partition well. In contrast, the\nlocal structure with an improper similarity measure results in potentially\ninaccurate anchor assignment, ultimately leading to sub-optimal clustering\nperformance. To tackle the issue, we propose a novel anchor-based multi-view\ngraph clustering framework termed Efficient Multi-View Graph Clustering with\nLocal and Global Structure Preservation (EMVGC-LG). Specifically, a unified\nframework with a theoretical guarantee is designed to capture local and global\ninformation. Besides, EMVGC-LG jointly optimizes anchor construction and graph\nlearning to enhance the clustering quality. In addition, EMVGC-LG inherits the\nlinear complexity of existing AMVGC methods respecting the sample number, which\nis time-economical and scales well with the data size. Extensive experiments\ndemonstrate the effectiveness and efficiency of our proposed method.\n", "date": "2023-08-31", "categories": []}
{"id": "2309.00474", "title": "Asymmetric double-winged multi-view clustering network for exploring\n  Diverse and Consistent Information", "abstract": "  In unsupervised scenarios, deep contrastive multi-view clustering (DCMVC) is\nbecoming a hot research spot, which aims to mine the potential relationships\nbetween different views. Most existing DCMVC algorithms focus on exploring the\nconsistency information for the deep semantic features, while ignoring the\ndiverse information on shallow features. To fill this gap, we propose a novel\nmulti-view clustering network termed CodingNet to explore the diverse and\nconsistent information simultaneously in this paper. Specifically, instead of\nutilizing the conventional auto-encoder, we design an asymmetric structure\nnetwork to extract shallow and deep features separately. Then, by aligning the\nsimilarity matrix on the shallow feature to the zero matrix, we ensure the\ndiversity for the shallow features, thus offering a better description of\nmulti-view data. Moreover, we propose a dual contrastive mechanism that\nmaintains consistency for deep features at both view-feature and pseudo-label\nlevels. Our framework's efficacy is validated through extensive experiments on\nsix widely used benchmark datasets, outperforming most state-of-the-art\nmulti-view clustering algorithms.\n", "date": "2023-09-01", "categories": []}
{"id": "2308.16541", "title": "Scalable Incomplete Multi-View Clustering with Structure Alignment", "abstract": "  The success of existing multi-view clustering (MVC) relies on the assumption\nthat all views are complete. However, samples are usually partially available\ndue to data corruption or sensor malfunction, which raises the research of\nincomplete multi-view clustering (IMVC). Although several anchor-based IMVC\nmethods have been proposed to process the large-scale incomplete data, they\nstill suffer from the following drawbacks: i) Most existing approaches neglect\nthe inter-view discrepancy and enforce cross-view representation to be\nconsistent, which would corrupt the representation capability of the model; ii)\nDue to the samples disparity between different views, the learned anchor might\nbe misaligned, which we referred as the Anchor-Unaligned Problem for Incomplete\ndata (AUP-ID). Such the AUP-ID would cause inaccurate graph fusion and degrades\nclustering performance. To tackle these issues, we propose a novel incomplete\nanchor graph learning framework termed Scalable Incomplete Multi-View\nClustering with Structure Alignment (SIMVC-SA). Specially, we construct the\nview-specific anchor graph to capture the complementary information from\ndifferent views. In order to solve the AUP-ID, we propose a novel structure\nalignment module to refine the cross-view anchor correspondence. Meanwhile, the\nanchor graph construction and alignment are jointly optimized in our unified\nframework to enhance clustering quality. Through anchor graph construction\ninstead of full graphs, the time and space complexity of the proposed SIMVC-SA\nis proven to be linearly correlated with the number of samples. Extensive\nexperiments on seven incomplete benchmark datasets demonstrate the\neffectiveness and efficiency of our proposed method. Our code is publicly\navailable at https://github.com/wy1019/SIMVC-SA.\n", "date": "2023-08-31", "categories": []}
{"id": "2308.15553", "title": "Dimensionality Reduction Using pseudo-Boolean polynomials For Cluster\n  Analysis", "abstract": "  We introduce usage of a reduction property of penalty-based formulation of\npseudo-Boolean polynomials as a mechanism for invariant dimensionality\nreduction in cluster analysis processes. In our experiments, we show that\nmultidimensional data, like 4-dimensional Iris Flower dataset can be reduced to\n2-dimensional space while the 30-dimensional Wisconsin Diagnostic Breast Cancer\n(WDBC) dataset can be reduced to 3-dimensional space, and by searching lines or\nplanes that lie between reduced samples we can extract clusters in a linear and\nunbiased manner with competitive accuracies, reproducibility and clear\ninterpretation.\n", "date": "2023-08-29", "categories": []}
{"id": "2308.15667", "title": "Bridging Distribution Learning and Image Clustering in High-dimensional\n  Space", "abstract": "  Distribution learning focuses on learning the probability density function\nfrom a set of data samples. In contrast, clustering aims to group similar\nobjects together in an unsupervised manner. Usually, these two tasks are\nconsidered unrelated. However, the relationship between the two may be\nindirectly correlated, with Gaussian Mixture Models (GMM) acting as a bridge.\nIn this paper, we focus on exploring the correlation between distribution\nlearning and clustering, with the motivation to fill the gap between these two\nfields, utilizing an autoencoder (AE) to encode images into a high-dimensional\nlatent space. Then, Monte-Carlo Marginalization (MCMarg) and Kullback-Leibler\n(KL) divergence loss are used to fit the Gaussian components of the GMM and\nlearn the data distribution. Finally, image clustering is achieved through each\nGaussian component of GMM. Yet, the \"curse of dimensionality\" poses severe\nchallenges for most clustering algorithms. Compared with the classic\nExpectation-Maximization (EM) Algorithm, experimental results show that MCMarg\nand KL divergence can greatly alleviate the difficulty. Based on the\nexperimental results, we believe distribution learning can exploit the\npotential of GMM in image clustering within high-dimensional space.\n", "date": "2023-08-29", "categories": []}
{"id": "2308.14478", "title": "Some issues in robust clustering", "abstract": "  Some key issues in robust clustering are discussed with focus on Gaussian\nmixture model based clustering, namely the formal definition of outliers,\nambiguity between groups of outliers and clusters, the interaction between\nrobust clustering and the estimation of the number of clusters, the essential\ndependence of (not only) robust clustering on tuning decisions, and\nshortcomings of existing measurements of cluster stability when it comes to\noutliers.\n", "date": "2023-08-28", "categories": []}
{"id": "2207.08162", "title": "Natural language processing for clusterization of genes according to\n  their functions", "abstract": "  There are hundreds of methods for analysis of data obtained in\nmRNA-sequencing. The most of them are focused on small number of genes. In this\nstudy, we propose an approach that reduces the analysis of several thousand\ngenes to analysis of several clusters. The list of genes is enriched with\ninformation from open databases. Then, the descriptions are encoded as vectors\nusing the pretrained language model (BERT) and some text processing approaches.\nThe encoded gene function pass through the dimensionality reduction and\nclusterization. Aiming to find the most efficient pipeline, 180 cases of\npipeline with different methods in the major pipeline steps were analyzed. The\nperformance was evaluated with clusterization indexes and expert review of the\nresults.\n", "date": "2022-07-17", "categories": []}
{"id": "2301.01805", "title": "Unsupervised Manifold Linearizing and Clustering", "abstract": "  We consider the problem of simultaneously clustering and learning a linear\nrepresentation of data lying close to a union of low-dimensional manifolds, a\nfundamental task in machine learning and computer vision. When the manifolds\nare assumed to be linear subspaces, this reduces to the classical problem of\nsubspace clustering, which has been studied extensively over the past two\ndecades. Unfortunately, many real-world datasets such as natural images can not\nbe well approximated by linear subspaces. On the other hand, numerous works\nhave attempted to learn an appropriate transformation of the data, such that\ndata is mapped from a union of general non-linear manifolds to a union of\nlinear subspaces (with points from the same manifold being mapped to the same\nsubspace). However, many existing works have limitations such as assuming\nknowledge of the membership of samples to clusters, requiring high sampling\ndensity, or being shown theoretically to learn trivial representations. In this\npaper, we propose to optimize the Maximal Coding Rate Reduction metric with\nrespect to both the data representation and a novel doubly stochastic cluster\nmembership, inspired by state-of-the-art subspace clustering results. We give a\nparameterization of such a representation and membership, allowing efficient\nmini-batching and one-shot initialization. Experiments on CIFAR-10, -20, -100,\nand TinyImageNet-200 datasets show that the proposed method is much more\naccurate and scalable than state-of-the-art deep clustering methods, and\nfurther learns a latent linear representation of the data.\n", "date": "2023-01-04", "categories": []}
{"id": "2308.10999", "title": "Eigenvalue-based Incremental Spectral Clustering", "abstract": "  Our previous experiments demonstrated that subsets collections of (short)\ndocuments (with several hundred entries) share a common normalized in some way\neigenvalue spectrum of combinatorial Laplacian. Based on this insight, we\npropose a method of incremental spectral clustering. The method consists of the\nfollowing steps: (1) split the data into manageable subsets, (2) cluster each\nof the subsets, (3) merge clusters from different subsets based on the\neigenvalue spectrum similarity to form clusters of the entire set. This method\ncan be especially useful for clustering methods of complexity strongly\nincreasing with the size of the data sample,like in case of typical spectral\nclustering. Experiments were performed showing that in fact the clustering and\nmerging the subsets yields clusters close to clustering the entire dataset.\n", "date": "2023-08-18", "categories": []}
{"id": "2307.03206", "title": "Optimal Bandwidth Selection for DENCLUE Algorithm", "abstract": "  In modern day industry, clustering algorithms are daily routines of algorithm\nengineers. Although clustering algorithms experienced rapid growth before 2010.\nInnovation related to the research topic has stagnated after deep learning\nbecame the de facto industrial standard for machine learning applications. In\n2007, a density-based clustering algorithm named DENCLUE was invented to solve\nclustering problem for nonlinear data structures. However, its parameter\nselection problem was largely neglected until 2011. In this paper, we propose a\nnew approach to compute the optimal parameters for the DENCLUE algorithm, and\ndiscuss its performance in the experiment section.\n", "date": "2023-07-06", "categories": []}
{"id": "2308.07705", "title": "Parametric entropy based Cluster Centriod Initialization for k-means\n  clustering of various Image datasets", "abstract": "  One of the most employed yet simple algorithm for cluster analysis is the\nk-means algorithm. k-means has successfully witnessed its use in artificial\nintelligence, market segmentation, fraud detection, data mining, psychology,\netc., only to name a few. The k-means algorithm, however, does not always yield\nthe best quality results. Its performance heavily depends upon the number of\nclusters supplied and the proper initialization of the cluster centroids or\nseeds. In this paper, we conduct an analysis of the performance of k-means on\nimage data by employing parametric entropies in an entropy based centroid\ninitialization method and propose the best fitting entropy measures for general\nimage datasets. We use several entropies like Taneja entropy, Kapur entropy,\nAczel Daroczy entropy, Sharma Mittal entropy. We observe that for different\ndatasets, different entropies provide better results than the conventional\nmethods. We have applied our proposed algorithm on these datasets: Satellite,\nToys, Fruits, Cars, Brain MRI, Covid X-Ray.\n", "date": "2023-08-15", "categories": []}
{"id": "2308.06448", "title": "Latent Random Steps as Relaxations of Max-Cut, Min-Cut, and More", "abstract": "  Algorithms for node clustering typically focus on finding homophilous\nstructure in graphs. That is, they find sets of similar nodes with many edges\nwithin, rather than across, the clusters. However, graphs often also exhibit\nheterophilous structure, as exemplified by (nearly) bipartite and tripartite\ngraphs, where most edges occur across the clusters. Grappling with such\nstructure is typically left to the task of graph simplification. We present a\nprobabilistic model based on non-negative matrix factorization which unifies\nclustering and simplification, and provides a framework for modeling arbitrary\ngraph structure. Our model is based on factorizing the process of taking a\nrandom walk on the graph. It permits an unconstrained parametrization, allowing\nfor optimization via simple gradient descent. By relaxing the hard clustering\nto a soft clustering, our algorithm relaxes potentially hard clustering\nproblems to a tractable ones. We illustrate our algorithm's capabilities on a\nsynthetic graph, as well as simple unsupervised learning tasks involving\nbipartite and tripartite clustering of orthographic and phonological data.\n", "date": "2023-08-12", "categories": []}
{"id": "2308.06827", "title": "Reinforcement Graph Clustering with Unknown Cluster Number", "abstract": "  Deep graph clustering, which aims to group nodes into disjoint clusters by\nneural networks in an unsupervised manner, has attracted great attention in\nrecent years. Although the performance has been largely improved, the excellent\nperformance of the existing methods heavily relies on an accurately predefined\ncluster number, which is not always available in the real-world scenario. To\nenable the deep graph clustering algorithms to work without the guidance of the\npredefined cluster number, we propose a new deep graph clustering method termed\nReinforcement Graph Clustering (RGC). In our proposed method, cluster number\ndetermination and unsupervised representation learning are unified into a\nuniform framework by the reinforcement learning mechanism. Concretely, the\ndiscriminative node representations are first learned with the contrastive\npretext task. Then, to capture the clustering state accurately with both local\nand global information in the graph, both node and cluster states are\nconsidered. Subsequently, at each state, the qualities of different cluster\nnumbers are evaluated by the quality network, and the greedy action is executed\nto determine the cluster number. In order to conduct feedback actions, the\nclustering-oriented reward function is proposed to enhance the cohesion of the\nsame clusters and separate the different clusters. Extensive experiments\ndemonstrate the effectiveness and efficiency of our proposed method. The source\ncode of RGC is shared at https://github.com/yueliu1999/RGC and a collection\n(papers, codes and, datasets) of deep graph clustering is shared at\nhttps://github.com/yueliu1999/Awesome-Deep-Graph-Clustering on Github.\n", "date": "2023-08-13", "categories": []}
{"id": "2308.04697", "title": "An Analytical Study of Covid-19 Dataset using Graph-Based Clustering\n  Algorithms", "abstract": "  Corona VIrus Disease abbreviated as COVID-19 is a novel virus which is\ninitially identified in Wuhan of China in December of 2019 and now this deadly\ndisease has spread all over the world. According to World Health Organization\n(WHO), a total of 3,124,905 people died from 2019 to 2021, April. In this case,\nmany methods, AI base techniques, and machine learning algorithms have been\nresearched and are being used to save people from this pandemic. The SARS-CoV\nand the 2019-nCoV, SARS-CoV-2 virus invade our bodies, causing some differences\nin the structure of cell proteins. Protein-protein interaction (PPI) is an\nessential process in our cells and plays a very important role in the\ndevelopment of medicines and gives ideas about the disease. In this study, we\nperformed clustering on PPI networks generated from 92 genes of the Covi-19\ndataset. We have used three graph-based clustering algorithms to give intuition\nto the analysis of clusters.\n", "date": "2023-08-09", "categories": []}
{"id": "2308.04778", "title": "Multi-modal Multi-view Clustering based on Non-negative Matrix\n  Factorization", "abstract": "  By combining related objects, unsupervised machine learning techniques aim to\nreveal the underlying patterns in a data set. Non-negative Matrix Factorization\n(NMF) is a data mining technique that splits data matrices by imposing\nrestrictions on the elements' non-negativity into two matrices: one\nrepresenting the data partitions and the other to represent the cluster\nprototypes of the data set. This method has attracted a lot of attention and is\nused in a wide range of applications, including text mining, clustering,\nlanguage modeling, music transcription, and neuroscience (gene separation). The\ninterpretation of the generated matrices is made simpler by the absence of\nnegative values. In this article, we propose a study on multi-modal clustering\nalgorithms and present a novel method called multi-modal multi-view\nnon-negative matrix factorization, in which we analyze the collaboration of\nseveral local NMF models. The experimental results show the value of the\nproposed approach, which was evaluated using a variety of data sets, and the\nobtained results are very promising compared to state of art methods.\n", "date": "2023-08-09", "categories": []}
{"id": "2308.03894", "title": "A new approach for evaluating internal cluster validation indices", "abstract": "  A vast number of different methods are available for unsupervised\nclassification. Since no algorithm and parameter setting performs best in all\ntypes of data, there is a need for cluster validation to select the actually\nbest-performing algorithm. Several indices were proposed for this purpose\nwithout using any additional (external) information. These internal validation\nindices can be evaluated by applying them to classifications of datasets with a\nknown cluster structure. Evaluation approaches differ in how they use the\ninformation on the ground-truth classification. This paper reviews these\napproaches, considering their advantages and disadvantages, and then suggests a\nnew approach.\n", "date": "2023-08-02", "categories": []}
{"id": "2308.03464", "title": "Wide Gaps and Clustering Axioms", "abstract": "  The widely applied k-means algorithm produces clusterings that violate our\nexpectations with respect to high/low similarity/density and is in conflict\nwith Kleinberg's axiomatic system for distance based clustering algorithms that\nformalizes those expectations in a natural way. k-means violates in particular\nthe consistency axiom. We hypothesise that this clash is due to the not\nexplicated expectation that the data themselves should have the property of\nbeing clusterable in order to expect the algorithm clustering hem to fit a\nclustering axiomatic system. To demonstrate this, we introduce two new\nclusterability properties, variational k-separability and residual\nk-separability and show that then the Kleinberg's consistency axiom holds for\nk-means operating in the Euclidean or non-Euclidean space. Furthermore, we\npropose extensions of k-means algorithm that fit approximately the Kleinberg's\nrichness axiom that does not hold for k-means. In this way, we reconcile\nk-means with Kleinberg's axiomatic framework in Euclidean and non-Euclidean\nsettings. Besides contribution to the theory of axiomatic frameworks of\nclustering and for clusterability theory, practical contribution is the\npossibility to construct {datasets for testing purposes of algorithms\noptimizing k-means cost function. This includes a method of construction of\n{clusterable data with known in advance global optimum.\n", "date": "2023-08-07", "categories": []}
{"id": "2308.01926", "title": "Are Easy Data Easy (for K-Means)", "abstract": "  This paper investigates the capability of correctly recovering well-separated\nclusters by various brands of the $k$-means algorithm. The concept of\nwell-separatedness used here is derived directly from the common definition of\nclusters, which imposes an interplay between the requirements of\nwithin-cluster-homogenicity and between-clusters-diversity. Conditions are\nderived for a special case of well-separated clusters such that the global\nminimum of $k$-means cost function coincides with the well-separatedness. An\nexperimental investigation is performed to find out whether or no various\nbrands of $k$-means are actually capable of discovering well separated\nclusters. It turns out that they are not. A new algorithm is proposed that is a\nvariation of $k$-means++ via repeated {sub}sampling when choosing a seed. The\nnew algorithm outperforms four other algorithms from $k$-means family on the\ntask.\n", "date": "2023-08-02", "categories": []}
{"id": "2304.11435", "title": "Hyper-Laplacian Regularized Concept Factorization in Low-rank Tensor\n  Space for Multi-view Clustering", "abstract": "  Tensor-oriented multi-view subspace clustering has achieved significant\nstrides in assessing high-order correlations and improving clustering analysis\nof multi-view data. Nevertheless, most of existing investigations are typically\nhampered by the two flaws. First, self-representation based tensor subspace\nlearning usually induces high time and space complexity, and is limited in\nperceiving nonlinear local structure in the embedding space. Second, the tensor\nsingular value decomposition (t-SVD) model redistributes each singular value\nequally without considering the diverse importance among them. To well cope\nwith the issues, we propose a hyper-Laplacian regularized concept factorization\n(HLRCF) in low-rank tensor space for multi-view clustering. Specifically, we\nadopt the concept factorization to explore the latent cluster-wise\nrepresentation of each view. Further, the hypergraph Laplacian regularization\nendows the model with the capability of extracting the nonlinear local\nstructures in the latent space. Considering that different tensor singular\nvalues associate structural information with unequal importance, we develop a\nself-weighted tensor Schatten p-norm to constrain the tensor comprised of all\ncluster-wise representations. Notably, the tensor with smaller size greatly\ndecreases the time and space complexity in the low-rank optimization. Finally,\nexperimental results on eight benchmark datasets exhibit that HLRCF outperforms\nother multi-view methods, showingcasing its superior performance.\n", "date": "2023-04-22", "categories": []}
{"id": "2308.00504", "title": "Explainable Graph Spectral Clustering of Text Documents", "abstract": "  Spectral clustering methods are known for their ability to represent clusters\nof diverse shapes, densities etc. However, results of such algorithms, when\napplied e.g. to text documents, are hard to explain to the user, especially due\nto embedding in the spectral space which has no obvious relation to document\ncontents. Therefore there is an urgent need to elaborate methods for explaining\nthe outcome of the clustering. This paper presents a contribution towards this\ngoal. We present a proposal of explanation of results of combinatorial\nLaplacian based graph spectral clustering. It is based on showing (approximate)\nequivalence of combinatorial Laplacian embedding, $K$-embedding (proposed in\nthis paper) and term vector space embedding. Hence a bridge is constructed\nbetween the textual contents and the clustering results. We provide theoretical\nbackground for this approach. We performed experimental study showing that\n$K$-embedding approximates well Laplacian embedding under favourable block\nmatrix conditions and show that approximation is good enough under other\nconditions.\n", "date": "2023-08-01", "categories": []}
{"id": "2308.00588", "title": "Relation-Aware Distribution Representation Network for Person Clustering\n  with Multiple Modalities", "abstract": "  Person clustering with multi-modal clues, including faces, bodies, and\nvoices, is critical for various tasks, such as movie parsing and identity-based\nmovie editing. Related methods such as multi-view clustering mainly project\nmulti-modal features into a joint feature space. However, multi-modal clue\nfeatures are usually rather weakly correlated due to the semantic gap from the\nmodality-specific uniqueness. As a result, these methods are not suitable for\nperson clustering. In this paper, we propose a Relation-Aware Distribution\nrepresentation Network (RAD-Net) to generate a distribution representation for\nmulti-modal clues. The distribution representation of a clue is a vector\nconsisting of the relation between this clue and all other clues from all\nmodalities, thus being modality agnostic and good for person clustering.\nAccordingly, we introduce a graph-based method to construct distribution\nrepresentation and employ a cyclic update policy to refine distribution\nrepresentation progressively. Our method achieves substantial improvements of\n+6% and +8.2% in F-score on the Video Person-Clustering Dataset (VPCD) and\nVoxCeleb2 multi-view clustering dataset, respectively. Codes will be released\npublicly upon acceptance.\n", "date": "2023-08-01", "categories": []}
{"id": "2305.03022", "title": "FastAMI -- a Monte Carlo Approach to the Adjustment for Chance in\n  Clustering Comparison Metrics", "abstract": "  Clustering is at the very core of machine learning, and its applications\nproliferate with the increasing availability of data. However, as datasets\ngrow, comparing clusterings with an adjustment for chance becomes\ncomputationally difficult, preventing unbiased ground-truth comparisons and\nsolution selection. We propose FastAMI, a Monte Carlo-based method to\nefficiently approximate the Adjusted Mutual Information (AMI) and extend it to\nthe Standardized Mutual Information (SMI). The approach is compared with the\nexact calculation and a recently developed variant of the AMI based on pairwise\npermutations, using both synthetic and real data. In contrast to the exact\ncalculation our method is fast enough to enable these adjusted\ninformation-theoretic comparisons for large datasets while maintaining\nconsiderably more accurate results than the pairwise approach.\n", "date": "2023-05-03", "categories": []}
{"id": "2307.06060", "title": "Interpreting deep embeddings for disease progression clustering", "abstract": "  We propose a novel approach for interpreting deep embeddings in the context\nof patient clustering. We evaluate our approach on a dataset of participants\nwith type 2 diabetes from the UK Biobank, and demonstrate clinically meaningful\ninsights into disease progression patterns.\n", "date": "2023-07-12", "categories": []}
{"id": "2307.15099", "title": "Clustering of illustrations by atmosphere using a combination of\n  supervised and unsupervised learning", "abstract": "  The distribution of illustrations on social media, such as Twitter and Pixiv\nhas increased with the growing popularity of animation, games, and animated\nmovies. The \"atmosphere\" of illustrations plays an important role in user\npreferences. Classifying illustrations by atmosphere can be helpful for\nrecommendations and searches. However, assigning clear labels to the elusive\n\"atmosphere\" and conventional supervised classification is not always\npractical. Furthermore, even images with similar colors, edges, and low-level\nfeatures may not have similar atmospheres, making classification based on\nlow-level features challenging. In this paper, this problem is solved using\nboth supervised and unsupervised learning with pseudo-labels. The feature\nvectors are obtained using the supervised method with pseudo-labels that\ncontribute to an ambiguous atmosphere. Further, clustering is performed based\non these feature vectors. Experimental analyses show that our method\noutperforms conventional methods in human-like clustering on datasets manually\nclassified by humans.\n", "date": "2023-07-27", "categories": []}
{"id": "2307.03430", "title": "Differential Privacy for Clustering Under Continual Observation", "abstract": "  We consider the problem of clustering privately a dataset in $\\mathbb{R}^d$\nthat undergoes both insertion and deletion of points. Specifically, we give an\n$\\varepsilon$-differentially private clustering mechanism for the $k$-means\nobjective under continual observation. This is the first approximation\nalgorithm for that problem with an additive error that depends only\nlogarithmically in the number $T$ of updates. The multiplicative error is\nalmost the same as non privately. To do so we show how to perform dimension\nreduction under continual observation and combine it with a differentially\nprivate greedy approximation algorithm for $k$-means. We also partially extend\nour results to the $k$-median problem.\n", "date": "2023-07-07", "categories": []}
{"id": "2307.14375", "title": "DBGSA: A Novel Data Adaptive Bregman Clustering Algorithm", "abstract": "  With the development of Big data technology, data analysis has become\nincreasingly important. Traditional clustering algorithms such as K-means are\nhighly sensitive to the initial centroid selection and perform poorly on\nnon-convex datasets. In this paper, we address these problems by proposing a\ndata-driven Bregman divergence parameter optimization clustering algorithm\n(DBGSA), which combines the Universal Gravitational Algorithm to bring similar\npoints closer in the dataset. We construct a gravitational coefficient equation\nwith a special property that gradually reduces the influence factor as the\niteration progresses. Furthermore, we introduce the Bregman divergence\ngeneralized power mean information loss minimization to identify cluster\ncenters and build a hyperparameter identification optimization model, which\neffectively solves the problems of manual adjustment and uncertainty in the\nimproved dataset. Extensive experiments are conducted on four simulated\ndatasets and six real datasets. The results demonstrate that DBGSA\nsignificantly improves the accuracy of various clustering algorithms by an\naverage of 63.8\\% compared to other similar approaches like enhanced clustering\nalgorithms and improved datasets. Additionally, a three-dimensional grid search\nwas established to compare the effects of different parameter values within\nthreshold conditions, and it was discovered the parameter set provided by our\nmodel is optimal. This finding provides strong evidence of the high accuracy\nand robustness of the algorithm.\n", "date": "2023-07-25", "categories": []}
{"id": "2212.01771", "title": "Can Evolutionary Clustering Have Theoretical Guarantees?", "abstract": "  Clustering is a fundamental problem in many areas, which aims to partition a\ngiven data set into groups based on some distance measure, such that the data\npoints in the same group are similar while that in different groups are\ndissimilar. Due to its importance and NP-hardness, a lot of methods have been\nproposed, among which evolutionary algorithms are a class of popular ones.\nEvolutionary clustering has found many successful applications, but all the\nresults are empirical, lacking theoretical support. This paper fills this gap\nby proving that the approximation performance of the GSEMO (a simple\nmulti-objective evolutionary algorithm) for solving four formulations of\nclustering, i.e., $k$-tMM, $k$-center, discrete $k$-median and $k$-means, can\nbe theoretically guaranteed. Furthermore, we consider clustering under\nfairness, which tries to avoid algorithmic bias, and has recently been an\nimportant research topic in machine learning. We prove that for discrete\n$k$-median clustering under individual fairness, the approximation performance\nof the GSEMO can be theoretically guaranteed with respect to both the objective\nfunction and the fairness constraint.\n", "date": "2022-12-04", "categories": []}
{"id": "2306.09256", "title": "A Survey of Some Density Based Clustering Techniques", "abstract": "  Density Based Clustering are a type of Clustering methods using in data\nmining for extracting previously unknown patterns from data sets. There are a\nnumber of density based clustering methods such as DBSCAN, OPTICS, DENCLUE,\nVDBSCAN, DVBSCAN, DBCLASD and ST-DBSCAN. In this paper, a study of these\nmethods is done along with their characteristics, advantages and disadvantages\nand most importantly, their applicability to different types of data sets to\nmine useful and appropriate patterns.\n", "date": "2023-06-15", "categories": []}
{"id": "2306.08617", "title": "Multi-class Graph Clustering via Approximated Effective $p$-Resistance", "abstract": "  This paper develops an approximation to the (effective) $p$-resistance and\napplies it to multi-class clustering. Spectral methods based on the graph\nLaplacian and its generalization to the graph $p$-Laplacian have been a\nbackbone of non-euclidean clustering techniques. The advantage of the\n$p$-Laplacian is that the parameter $p$ induces a controllable bias on cluster\nstructure. The drawback of $p$-Laplacian eigenvector based methods is that the\nthird and higher eigenvectors are difficult to compute. Thus, instead, we are\nmotivated to use the $p$-resistance induced by the $p$-Laplacian for\nclustering. For $p$-resistance, small $p$ biases towards clusters with high\ninternal connectivity while large $p$ biases towards clusters of small\n\"extent,\" that is a preference for smaller shortest-path distances between\nvertices in the cluster. However, the $p$-resistance is expensive to compute.\nWe overcome this by developing an approximation to the $p$-resistance. We prove\nupper and lower bounds on this approximation and observe that it is exact when\nthe graph is a tree. We also provide theoretical justification for the use of\n$p$-resistance for clustering. Finally, we provide experiments comparing our\napproximated $p$-resistance clustering to other $p$-Laplacian based methods.\n", "date": "2023-06-14", "categories": []}
{"id": "2306.05439", "title": "Contrastive Representation Disentanglement for Clustering", "abstract": "  Clustering continues to be a significant and challenging task. Recent studies\nhave demonstrated impressive results by applying clustering to feature\nrepresentations acquired through self-supervised learning, particularly on\nsmall datasets. However, when dealing with datasets containing a large number\nof clusters, such as ImageNet, current methods struggle to achieve satisfactory\nclustering performance. In this paper, we introduce a novel method called\nContrastive representation Disentanglement for Clustering (CDC) that leverages\ncontrastive learning to directly disentangle the feature representation for\nclustering. In CDC, we decompose the representation into two distinct\ncomponents: one component encodes categorical information under an\nequipartition constraint, and the other component captures instance-specific\nfactors. To train our model, we propose a contrastive loss that effectively\nutilizes both components of the representation. We conduct a theoretical\nanalysis of the proposed loss and highlight how it assigns different weights to\nnegative samples during the process of disentangling the feature\nrepresentation. Further analysis of the gradients reveals that larger weights\nemphasize a stronger focus on hard negative samples. As a result, the proposed\nloss exhibits strong expressiveness, enabling efficient disentanglement of\ncategorical information. Through experimental evaluation on various benchmark\ndatasets, our method demonstrates either state-of-the-art or highly competitive\nclustering performance. Notably, on the complete ImageNet dataset, we achieve\nan accuracy of 53.4%, surpassing existing methods by a substantial margin of\n+10.2%.\n", "date": "2023-06-08", "categories": []}
{"id": "2212.12189", "title": "Stop using the elbow criterion for k-means and how to choose the number\n  of clusters instead", "abstract": "  A major challenge when using k-means clustering often is how to choose the\nparameter k, the number of clusters. In this letter, we want to point out that\nit is very easy to draw poor conclusions from a common heuristic, the \"elbow\nmethod\". Better alternatives have been known in literature for a long time, and\nwe want to draw attention to some of these easy to use options, that often\nperform better. This letter is a call to stop using the elbow method\naltogether, because it severely lacks theoretic support, and we want to\nencourage educators to discuss the problems of the method -- if introducing it\nin class at all -- and teach alternatives instead, while researchers and\nreviewers should reject conclusions drawn from the elbow method.\n", "date": "2022-12-23", "categories": []}
{"id": "2307.08104", "title": "Using Decision Trees for Interpretable Supervised Clustering", "abstract": "  In this paper, we address an issue of finding explainable clusters of\nclass-uniform data in labelled datasets. The issue falls into the domain of\ninterpretable supervised clustering. Unlike traditional clustering, supervised\nclustering aims at forming clusters of labelled data with high probability\ndensities. We are particularly interested in finding clusters of data of a\ngiven class and describing the clusters with the set of comprehensive rules. We\npropose an iterative method to extract high-density clusters with the help of\ndecisiontree-based classifiers as the most intuitive learning method, and\ndiscuss the method of node selection to maximize quality of identified groups.\n", "date": "2023-07-16", "categories": []}
{"id": "2307.08591", "title": "Snapshot Spectral Clustering -- a costless approach to deep clustering\n  ensembles generation", "abstract": "  Despite tremendous advancements in Artificial Intelligence, learning from\nlarge sets of data in an unsupervised manner remains a significant challenge.\nClassical clustering algorithms often fail to discover complex dependencies in\nlarge datasets, especially considering sparse, high-dimensional spaces.\nHowever, deep learning techniques proved to be successful when dealing with\nlarge quantities of data, efficiently reducing their dimensionality without\nlosing track of underlying information. Several interesting advancements have\nalready been made to combine deep learning and clustering. Still, the idea of\nenhancing the clustering results by combining multiple views of the data\ngenerated by deep neural networks appears to be insufficiently explored yet.\nThis paper aims to investigate this direction and bridge the gap between deep\nneural networks, clustering techniques and ensemble learning methods. To\nachieve this goal, we propose a novel deep clustering ensemble method -\nSnapshot Spectral Clustering, designed to maximize the gain from combining\nmultiple data views while minimizing the computational costs of creating the\nensemble. Comparative analysis and experiments described in this paper prove\nthe proposed concept, while the conducted hyperparameter study provides a\nvaluable intuition to follow when selecting proper values.\n", "date": "2023-07-17", "categories": []}
{"id": "2211.12271", "title": "Global $k$-means$++$: an effective relaxation of the global $k$-means\n  clustering algorithm", "abstract": "  The $k$-means algorithm is a prevalent clustering method due to its\nsimplicity, effectiveness, and speed. However, its main disadvantage is its\nhigh sensitivity to the initial positions of the cluster centers. The global\n$k$-means is a deterministic algorithm proposed to tackle the random\ninitialization problem of k-means but its well-known that requires high\ncomputational cost. It partitions the data to $K$ clusters by solving all\n$k$-means sub-problems incrementally for all $k=1,\\ldots, K$. For each $k$\ncluster problem, the method executes the $k$-means algorithm $N$ times, where\n$N$ is the number of datapoints. In this paper, we propose the \\emph{global\n$k$-means\\texttt{++}} clustering algorithm, which is an effective way of\nacquiring quality clustering solutions akin to those of global $k$-means with a\nreduced computational load. This is achieved by exploiting the center selection\nprobability that is effectively used in the $k$-means\\texttt{++} algorithm. The\nproposed method has been tested and compared in various benchmark datasets\nyielding very satisfactory results in terms of clustering quality and execution\nspeed.\n", "date": "2022-11-22", "categories": []}
{"id": "2305.18405", "title": "Dink-Net: Neural Clustering on Large Graphs", "abstract": "  Deep graph clustering, which aims to group the nodes of a graph into disjoint\nclusters with deep neural networks, has achieved promising progress in recent\nyears. However, the existing methods fail to scale to the large graph with\nmillion nodes. To solve this problem, a scalable deep graph clustering method\n(Dink-Net) is proposed with the idea of dilation and shrink. Firstly, by\ndiscriminating nodes, whether being corrupted by augmentations, representations\nare learned in a self-supervised manner. Meanwhile, the cluster centres are\ninitialized as learnable neural parameters. Subsequently, the clustering\ndistribution is optimized by minimizing the proposed cluster dilation loss and\ncluster shrink loss in an adversarial manner. By these settings, we unify the\ntwo-step clustering, i.e., representation learning and clustering optimization,\ninto an end-to-end framework, guiding the network to learn clustering-friendly\nfeatures. Besides, Dink-Net scales well to large graphs since the designed loss\nfunctions adopt the mini-batch data to optimize the clustering distribution\neven without performance drops. Both experimental results and theoretical\nanalyses demonstrate the superiority of our method. Compared to the runner-up,\nDink-Net achieves 9.62% NMI improvement on the ogbn-papers100M dataset with 111\nmillion nodes and 1.6 billion edges. The source code is released at\nhttps://github.com/yueliu1999/Dink-Net. Besides, a collection (papers, codes,\nand datasets) of deep graph clustering is shared at\nhttps://github.com/yueliu1999/Awesome-Deep-Graph-Clustering.\n", "date": "2023-05-28", "categories": []}
{"id": "2307.05750", "title": "Fermat Distances: Metric Approximation, Spectral Convergence, and\n  Clustering Algorithms", "abstract": "  We analyze the convergence properties of Fermat distances, a family of\ndensity-driven metrics defined on Riemannian manifolds with an associated\nprobability measure. Fermat distances may be defined either on discrete samples\nfrom the underlying measure, in which case they are random, or in the continuum\nsetting, in which they are induced by geodesics under a density-distorted\nRiemannian metric. We prove that discrete, sample-based Fermat distances\nconverge to their continuum analogues in small neighborhoods with a precise\nrate that depends on the intrinsic dimensionality of the data and the parameter\ngoverning the extent of density weighting in Fermat distances. This is done by\nleveraging novel geometric and statistical arguments in percolation theory that\nallow for non-uniform densities and curved domains. Our results are then used\nto prove that discrete graph Laplacians based on discrete, sample-driven Fermat\ndistances converge to corresponding continuum operators. In particular, we show\nthe discrete eigenvalues and eigenvectors converge to their continuum analogues\nat a dimension-dependent rate, which allows us to interpret the efficacy of\ndiscrete spectral clustering using Fermat distances in terms of the resulting\ncontinuum limit. The perspective afforded by our discrete-to-continuum Fermat\ndistance analysis leads to new clustering algorithms for data and related\ninsights into efficient computations associated to density-driven spectral\nclustering. Our theoretical analysis is supported with numerical simulations\nand experiments on synthetic and real image data.\n", "date": "2023-07-07", "categories": []}
{"id": "2302.01851", "title": "Unsupervised hierarchical clustering using the learning dynamics of RBMs", "abstract": "  Datasets in the real world are often complex and to some degree hierarchical,\nwith groups and sub-groups of data sharing common characteristics at different\nlevels of abstraction. Understanding and uncovering the hidden structure of\nthese datasets is an important task that has many practical applications. To\naddress this challenge, we present a new and general method for building\nrelational data trees by exploiting the learning dynamics of the Restricted\nBoltzmann Machine (RBM). Our method is based on the mean-field approach,\nderived from the Plefka expansion, and developed in the context of disordered\nsystems. It is designed to be easily interpretable. We tested our method in an\nartificially created hierarchical dataset and on three different real-world\ndatasets (images of digits, mutations in the human genome, and a homologous\nfamily of proteins). The method is able to automatically identify the\nhierarchical structure of the data. This could be useful in the study of\nhomologous protein sequences, where the relationships between proteins are\ncritical for understanding their function and evolution.\n", "date": "2023-02-03", "categories": []}
{"id": "2306.15437", "title": "COMPASS: Unsupervised and Online Clustering of Complex Human Activities\n  from Smartphone Sensors", "abstract": "  Modern mobile devices are able to provide context-aware and personalized\nservices to the users, by leveraging on their sensing capabilities to infer the\nactivity and situation in which a person is currently involved. Current\nsolutions for context-recognition rely on annotated data and experts’ knowledge\nto predict the user context. In addition, their prediction ability is strongly\nlimited to the set of situations considered during the model training or\ndefinition. However, in a mobile environment, the user context continuously\nevolves, and it cannot be merely restricted to a set of predefined classes. To\novercome these limitations, we propose COMPASS, a novel unsupervised and online\nclustering algorithm aimed at identifying the user context in mobile\nenvironments based on the stream of high-dimensional data generated by\nsmartphone sensors. COMPASScan distinguish an arbitrary number of user’s\ncontexts from the sensors’ data, without defining a priori the collection of\nexpected situations. This key feature makes it a general-purpose solution to\nprovide context-aware features to mobile devices, supporting a broad set of\napplications. Experimental results on 18 synthetic and 2 real-world datasets\nshow that COMPASS correctly identifies the user context from the sensors’ data\nstream, and outperforms the state-of-the-art solutions in terms of both\nclusters configuration and purity. Eventually, we evaluate its performances in\nterms of execution time and the results show that COMPASS can process 1000\nhigh-dimensional samples in less than 20 seconds, while the reference solutions\nrequire about 60 minutes to evaluate the entire dataset. Keywords:\nContext-awareness, Unsupervised Machine Learning, Online Clustering, Mobile\nComputing\n", "date": "2023-06-27", "categories": []}
{"id": "2307.03476", "title": "Unpaired Multi-View Graph Clustering with Cross-View Structure Matching", "abstract": "  Multi-view clustering (MVC), which effectively fuses information from\nmultiple views for better performance, has received increasing attention. Most\nexisting MVC methods assume that multi-view data are fully paired, which means\nthat the mappings of all corresponding samples between views are pre-defined or\ngiven in advance. However, the data correspondence is often incomplete in\nreal-world applications due to data corruption or sensor differences, referred\nas the data-unpaired problem (DUP) in multi-view literature. Although several\nattempts have been made to address the DUP issue, they suffer from the\nfollowing drawbacks: 1) Most methods focus on the feature representation while\nignoring the structural information of multi-view data, which is essential for\nclustering tasks; 2) Existing methods for partially unpaired problems rely on\npre-given cross-view alignment information, resulting in their inability to\nhandle fully unpaired problems; 3) Their inevitable parameters degrade the\nefficiency and applicability of the models. To tackle these issues, we propose\na novel parameter-free graph clustering framework termed Unpaired Multi-view\nGraph Clustering framework with Cross-View Structure Matching (UPMGC-SM).\nSpecifically, unlike the existing methods, UPMGC-SM effectively utilizes the\nstructural information from each view to refine cross-view correspondences.\nBesides, our UPMGC-SM is a unified framework for both the fully and partially\nunpaired multi-view graph clustering. Moreover, existing graph clustering\nmethods can adopt our UPMGC-SM to enhance their ability for unpaired scenarios.\nExtensive experiments demonstrate the effectiveness and generalization of our\nproposed framework for both paired and unpaired datasets.\n", "date": "2023-07-07", "categories": []}
{"id": "2305.10457", "title": "Time Series Clustering With Random Convolutional Kernels", "abstract": "  Time series data, spanning applications ranging from climatology to finance\nto healthcare, presents significant challenges in data mining due to its size\nand complexity. One open issue lies in time series clustering, which is crucial\nfor processing large volumes of unlabeled time series data and unlocking\nvaluable insights. Traditional and modern analysis methods, however, often\nstruggle with these complexities. To address these limitations, we introduce\nR-Clustering, a novel method that utilizes convolutional architectures with\nrandomly selected parameters. Through extensive evaluations, R-Clustering\ndemonstrates superior performance over existing methods in terms of clustering\naccuracy, computational efficiency and scalability. Empirical results obtained\nusing the UCR archive demonstrate the effectiveness of our approach across\ndiverse time series datasets. The findings highlight the significance of\nR-Clustering in various domains and applications, contributing to the\nadvancement of time series data mining.\n", "date": "2023-05-17", "categories": []}
{"id": "2307.01400", "title": "Spatio-Temporal Surrogates for Interaction of a Jet with High\n  Explosives: Part II -- Clustering Extremely High-Dimensional Grid-Based Data", "abstract": "  Building an accurate surrogate model for the spatio-temporal outputs of a\ncomputer simulation is a challenging task. A simple approach to improve the\naccuracy of the surrogate is to cluster the outputs based on similarity and\nbuild a separate surrogate model for each cluster. This clustering is\nrelatively straightforward when the output at each time step is of moderate\nsize. However, when the spatial domain is represented by a large number of grid\npoints, numbering in the millions, the clustering of the data becomes more\nchallenging. In this report, we consider output data from simulations of a jet\ninteracting with high explosives. These data are available on spatial domains\nof different sizes, at grid points that vary in their spatial coordinates, and\nin a format that distributes the output across multiple files at each time step\nof the simulation. We first describe how we bring these data into a consistent\nformat prior to clustering. Borrowing the idea of random projections from data\nmining, we reduce the dimension of our data by a factor of thousand, making it\npossible to use the iterative k-means method for clustering. We show how we can\nuse the randomness of both the random projections, and the choice of initial\ncentroids in k-means clustering, to determine the number of clusters in our\ndata set. Our approach makes clustering of extremely high dimensional data\ntractable, generating meaningful cluster assignments for our problem, despite\nthe approximation introduced in the random projections.\n", "date": "2023-07-03", "categories": []}
{"id": "2307.01955", "title": "Algorithme EM r\\'egularis\\'e", "abstract": "  Expectation-Maximization (EM) algorithm is a widely used iterative algorithm\nfor computing maximum likelihood estimate when dealing with Gaussian Mixture\nModel (GMM). When the sample size is smaller than the data dimension, this\ncould lead to a singular or poorly conditioned covariance matrix and, thus, to\nperformance reduction. This paper presents a regularized version of the EM\nalgorithm that efficiently uses prior knowledge to cope with a small sample\nsize. This method aims to maximize a penalized GMM likelihood where regularized\nestimation may ensure positive definiteness of covariance matrix updates by\nshrinking the estimators towards some structured target covariance matrices.\nFinally, experiments on real data highlight the good performance of the\nproposed algorithm for clustering purposes\n", "date": "2023-07-04", "categories": []}
{"id": "2210.16424", "title": "Machine Unlearning of Federated Clusters", "abstract": "  Federated clustering (FC) is an unsupervised learning problem that arises in\na number of practical applications, including personalized recommender and\nhealthcare systems. With the adoption of recent laws ensuring the \"right to be\nforgotten\", the problem of machine unlearning for FC methods has become of\nsignificant importance. We introduce, for the first time, the problem of\nmachine unlearning for FC, and propose an efficient unlearning mechanism for a\ncustomized secure FC framework. Our FC framework utilizes special\ninitialization procedures that we show are well-suited for unlearning. To\nprotect client data privacy, we develop the secure compressed multiset\naggregation (SCMA) framework that addresses sparse secure federated learning\n(FL) problems encountered during clustering as well as more general problems.\nTo simultaneously facilitate low communication complexity and secret sharing\nprotocols, we integrate Reed-Solomon encoding with special evaluation points\ninto our SCMA pipeline, and prove that the client communication cost is\nlogarithmic in the vector dimension. Additionally, to demonstrate the benefits\nof our unlearning mechanism over complete retraining, we provide a theoretical\nanalysis for the unlearning performance of our approach. Simulation results\nshow that the new FC framework exhibits superior clustering performance\ncompared to previously reported FC baselines when the cluster sizes are highly\nimbalanced. Compared to completely retraining K-means++ locally and globally\nfor each removal request, our unlearning procedure offers an average speed-up\nof roughly 84x across seven datasets. Our implementation for the proposed\nmethod is available at https://github.com/thupchnsky/mufc.\n", "date": "2022-10-28", "categories": []}
{"id": "2307.00524", "title": "Large Language Models Enable Few-Shot Clustering", "abstract": "  Unlike traditional unsupervised clustering, semi-supervised clustering allows\nusers to provide meaningful structure to the data, which helps the clustering\nalgorithm to match the user's intent. Existing approaches to semi-supervised\nclustering require a significant amount of feedback from an expert to improve\nthe clusters. In this paper, we ask whether a large language model can amplify\nan expert's guidance to enable query-efficient, few-shot semi-supervised text\nclustering. We show that LLMs are surprisingly effective at improving\nclustering. We explore three stages where LLMs can be incorporated into\nclustering: before clustering (improving input features), during clustering (by\nproviding constraints to the clusterer), and after clustering (using LLMs\npost-correction). We find incorporating LLMs in the first two stages can\nroutinely provide significant improvements in cluster quality, and that LLMs\nenable a user to make trade-offs between cost and accuracy to produce desired\nclusters. We release our code and LLM prompts for the public to use.\n", "date": "2023-07-02", "categories": []}
{"id": "2307.00924", "title": "Semi-supervised multi-view concept decomposition", "abstract": "  Concept Factorization (CF), as a novel paradigm of representation learning,\nhas demonstrated superior performance in multi-view clustering tasks. It\novercomes limitations such as the non-negativity constraint imposed by\ntraditional matrix factorization methods and leverages kernel methods to learn\nlatent representations that capture the underlying structure of the data,\nthereby improving data representation. However, existing multi-view concept\nfactorization methods fail to consider the limited labeled information inherent\nin real-world multi-view data. This often leads to significant performance\nloss. To overcome these limitations, we propose a novel semi-supervised\nmulti-view concept factorization model, named SMVCF. In the SMVCF model, we\nfirst extend the conventional single-view CF to a multi-view version, enabling\nmore effective exploration of complementary information across multiple views.\nWe then integrate multi-view CF, label propagation, and manifold learning into\na unified framework to leverage and incorporate valuable information present in\nthe data. Additionally, an adaptive weight vector is introduced to balance the\nimportance of different views in the clustering process. We further develop\ntargeted optimization methods specifically tailored for the SMVCF model.\nFinally, we conduct extensive experiments on four diverse datasets with varying\nlabel ratios to evaluate the performance of SMVCF. The experimental results\ndemonstrate the effectiveness and superiority of our proposed approach in\nmulti-view clustering tasks.\n", "date": "2023-07-03", "categories": []}
{"id": "2306.15138", "title": "A Restarted Large-Scale Spectral Clustering with Self-Guiding and Block\n  Diagonal Representation", "abstract": "  Spectral clustering is one of the most popular unsupervised machine learning\nmethods. Constructing similarity matrix is crucial to this type of method. In\nmost existing works, the similarity matrix is computed once for all or is\nupdated alternatively. However, the former is difficult to reflect\ncomprehensive relationships among data points, and the latter is time-consuming\nand is even infeasible for large-scale problems. In this work, we propose a\nrestarted clustering framework with self-guiding and block diagonal\nrepresentation. An advantage of the strategy is that some useful clustering\ninformation obtained from previous cycles could be preserved as much as\npossible. To the best of our knowledge, this is the first work that applies\nrestarting strategy to spectral clustering. The key difference is that we\nreclassify the samples in each cycle of our method, while they are classified\nonly once in existing methods. To further release the overhead, we introduce a\nblock diagonal representation with Nystr\\\"{o}m approximation for constructing\nthe similarity matrix. Theoretical results are established to show the\nrationality of inexact computations in spectral clustering. Comprehensive\nexperiments are performed on some benchmark databases, which show the\nsuperiority of our proposed algorithms over many state-of-the-art algorithms\nfor large-scale problems. Specifically, our framework has a potential boost for\nclustering algorithms and works well even using an initial guess chosen\nrandomly.\n", "date": "2023-06-27", "categories": []}
{"id": "2306.16354", "title": "cuSLINK: Single-linkage Agglomerative Clustering on the GPU", "abstract": "  In this paper, we propose cuSLINK, a novel and state-of-the-art reformulation\nof the SLINK algorithm on the GPU which requires only $O(Nk)$ space and uses a\nparameter $k$ to trade off space and time. We also propose a set of novel and\nreusable building blocks that compose cuSLINK. These building blocks include\nhighly optimized computational patterns for $k$-NN graph construction, spanning\ntrees, and dendrogram cluster extraction. We show how we used our primitives to\nimplement cuSLINK end-to-end on the GPU, further enabling a wide range of\nreal-world data mining and machine learning applications that were once\nintractable. In addition to being a primary computational bottleneck in the\npopular HDBSCAN algorithm, the impact of our end-to-end cuSLINK algorithm spans\na large range of important applications, including cluster analysis in social\nand computer networks, natural language processing, and computer vision. Users\ncan obtain cuSLINK at\nhttps://docs.rapids.ai/api/cuml/latest/api/#agglomerative-clustering\n", "date": "2023-06-28", "categories": []}
{"id": "2306.05437", "title": "One-step Multi-view Clustering with Diverse Representation", "abstract": "  Multi-view clustering has attracted broad attention due to its capacity to\nutilize consistent and complementary information among views. Although\ntremendous progress has been made recently, most existing methods undergo high\ncomplexity, preventing them from being applied to large-scale tasks. Multi-view\nclustering via matrix factorization is a representative to address this issue.\nHowever, most of them map the data matrices into a fixed dimension, limiting\nthe model's expressiveness. Moreover, a range of methods suffers from a\ntwo-step process, i.e., multimodal learning and the subsequent $k$-means,\ninevitably causing a sub-optimal clustering result. In light of this, we\npropose a one-step multi-view clustering with diverse representation method,\nwhich incorporates multi-view learning and $k$-means into a unified framework.\nSpecifically, we first project original data matrices into various latent\nspaces to attain comprehensive information and auto-weight them in a\nself-supervised manner. Then we directly use the information matrices under\ndiverse dimensions to obtain consensus discrete clustering labels. The unified\nwork of representation learning and clustering boosts the quality of the final\nresults. Furthermore, we develop an efficient optimization algorithm with\nproven convergence to solve the resultant problem. Comprehensive experiments on\nvarious datasets demonstrate the promising clustering performance of our\nproposed method.\n", "date": "2023-06-08", "categories": []}
{"id": "2306.13794", "title": "Tensor Dirichlet Process Multinomial Mixture Model for Passenger\n  Trajectory Clustering", "abstract": "  Passenger clustering based on travel records is essential for transportation\noperators. However, existing methods cannot easily cluster the passengers due\nto the hierarchical structure of the passenger trip information, namely: each\npassenger has multiple trips, and each trip contains multi-dimensional\nmulti-mode information. Furthermore, existing approaches rely on an accurate\nspecification of the clustering number to start, which is difficult when\nmillions of commuters are using the transport systems on a daily basis. In this\npaper, we propose a novel Tensor Dirichlet Process Multinomial Mixture model\n(Tensor-DPMM), which is designed to preserve the multi-mode and hierarchical\nstructure of the multi-dimensional trip information via tensor, and cluster\nthem in a unified one-step manner. The model also has the ability to determine\nthe number of clusters automatically by using the Dirichlet Process to decide\nthe probabilities for a passenger to be either assigned in an existing cluster\nor to create a new cluster: This allows our model to grow the clusters as\nneeded in a dynamic manner. Finally, existing methods do not consider spatial\nsemantic graphs such as geographical proximity and functional similarity\nbetween the locations, which may cause inaccurate clustering. To this end, we\nfurther propose a variant of our model, namely the Tensor-DPMM with Graph. For\nthe algorithm, we propose a tensor Collapsed Gibbs Sampling method, with an\ninnovative step of \"disband and relocating\", which disbands clusters with too\nsmall amount of members and relocates them to the remaining clustering. This\navoids uncontrollable growing amounts of clusters. A case study based on Hong\nKong metro passenger data is conducted to demonstrate the automatic process of\nlearning the number of clusters, and the learned clusters are better in\nwithin-cluster compactness and cross-cluster separateness.\n", "date": "2023-06-23", "categories": []}
{"id": "2306.14346", "title": "Evolution of $K$-means solution landscapes with the addition of dataset\n  outliers and a robust clustering comparison measure for their analysis", "abstract": "  The $K$-means algorithm remains one of the most widely-used clustering\nmethods due to its simplicity and general utility. The performance of $K$-means\ndepends upon location of minima low in cost function, amongst a potentially\nvast number of solutions. Here, we use the energy landscape approach to map the\nchange in $K$-means solution space as a result of increasing dataset outliers\nand show that the cost function surface becomes more funnelled. Kinetic\nanalysis reveals that in all cases the overall funnel is composed of shallow\nlocally-funnelled regions, each of which are separated by areas that do not\nsupport any clustering solutions. These shallow regions correspond to different\ntypes of clustering solution and their increasing number with outliers leads to\nlonger pathways within the funnel and a reduced correlation between accuracy\nand cost function. Finally, we propose that the rates obtained from kinetic\nanalysis provide a novel measure of clustering similarity that incorporates\ninformation about the paths between them. This measure is robust to outliers\nand we illustrate the application to datasets containing multiple outliers.\n", "date": "2023-06-25", "categories": []}
{"id": "2306.06778", "title": "Approximation Algorithms for Fair Range Clustering", "abstract": "  This paper studies the fair range clustering problem in which the data points\nare from different demographic groups and the goal is to pick $k$ centers with\nthe minimum clustering cost such that each group is at least minimally\nrepresented in the centers set and no group dominates the centers set. More\nprecisely, given a set of $n$ points in a metric space $(P,d)$ where each point\nbelongs to one of the $\\ell$ different demographics (i.e., $P = P_1 \\uplus P_2\n\\uplus \\cdots \\uplus P_\\ell$) and a set of $\\ell$ intervals $[\\alpha_1,\n\\beta_1], \\cdots, [\\alpha_\\ell, \\beta_\\ell]$ on desired number of centers from\neach group, the goal is to pick a set of $k$ centers $C$ with minimum\n$\\ell_p$-clustering cost (i.e., $(\\sum_{v\\in P} d(v,C)^p)^{1/p}$) such that for\neach group $i\\in \\ell$, $|C\\cap P_i| \\in [\\alpha_i, \\beta_i]$. In particular,\nthe fair range $\\ell_p$-clustering captures fair range $k$-center, $k$-median\nand $k$-means as its special cases. In this work, we provide efficient constant\nfactor approximation algorithms for fair range $\\ell_p$-clustering for all\nvalues of $p\\in [1,\\infty)$.\n", "date": "2023-06-11", "categories": []}
{"id": "2306.13023", "title": "AugDMC: Data Augmentation Guided Deep Multiple Clustering", "abstract": "  Clustering aims to group similar objects together while separating dissimilar\nones apart. Thereafter, structures hidden in data can be identified to help\nunderstand data in an unsupervised manner. Traditional clustering methods such\nas k-means provide only a single clustering for one data set. Deep clustering\nmethods such as auto-encoder based clustering methods have shown a better\nperformance, but still provide a single clustering. However, a given dataset\nmight have multiple clustering structures and each represents a unique\nperspective of the data. Therefore, some multiple clustering methods have been\ndeveloped to discover multiple independent structures hidden in data. Although\ndeep multiple clustering methods provide better performance, how to efficiently\ncapture the alternative perspectives in data is still a problem. In this paper,\nwe propose AugDMC, a novel data Augmentation guided Deep Multiple Clustering\nmethod, to tackle the challenge. Specifically, AugDMC leverages data\naugmentations to automatically extract features related to a certain aspect of\nthe data using a self-supervised prototype-based representation learning, where\ndifferent aspects of the data can be preserved under different data\naugmentations. Moreover, a stable optimization strategy is proposed to\nalleviate the unstable problem from different augmentations. Thereafter,\nmultiple clusterings based on different aspects of the data can be obtained.\nExperimental results on three real-world datasets compared with\nstate-of-the-art methods validate the effectiveness of the proposed method.\n", "date": "2023-06-22", "categories": []}
{"id": "2303.03389", "title": "Contrastive Hierarchical Clustering", "abstract": "  Deep clustering has been dominated by flat models, which split a dataset into\na predefined number of groups. Although recent methods achieve an extremely\nhigh similarity with the ground truth on popular benchmarks, the information\ncontained in the flat partition is limited. In this paper, we introduce\nCoHiClust, a Contrastive Hierarchical Clustering model based on deep neural\nnetworks, which can be applied to typical image data. By employing a\nself-supervised learning approach, CoHiClust distills the base network into a\nbinary tree without access to any labeled data. The hierarchical clustering\nstructure can be used to analyze the relationship between clusters, as well as\nto measure the similarity between data points. Experiments demonstrate that\nCoHiClust generates a reasonable structure of clusters, which is consistent\nwith our intuition and image semantics. Moreover, it obtains superior\nclustering accuracy on most of the image datasets compared to the\nstate-of-the-art flat clustering models.\n", "date": "2023-03-03", "categories": []}
{"id": "2302.10383", "title": "On Interpretable Approaches to Cluster, Classify and Represent\n  Multi-Subspace Data via Minimum Lossy Coding Length based on Rate-Distortion\n  Theory", "abstract": "  To cluster, classify and represent are three fundamental objectives of\nlearning from high-dimensional data with intrinsic structure. To this end, this\npaper introduces three interpretable approaches, i.e., segmentation\n(clustering) via the Minimum Lossy Coding Length criterion, classification via\nthe Minimum Incremental Coding Length criterion and representation via the\nMaximal Coding Rate Reduction criterion. These are derived based on the lossy\ndata coding and compression framework from the principle of rate distortion in\ninformation theory. These algorithms are particularly suitable for dealing with\nfinite-sample data (allowed to be sparse or almost degenerate) of mixed\nGaussian distributions or subspaces. The theoretical value and attractive\nfeatures of these methods are summarized by comparison with other learning\nmethods or evaluation criteria. This summary note aims to provide a theoretical\nguide to researchers (also engineers) interested in understanding 'white-box'\nmachine (deep) learning methods.\n", "date": "2023-02-21", "categories": []}
{"id": "2304.14531", "title": "High-dimensional Clustering onto Hamiltonian Cycle", "abstract": "  Clustering aims to group unlabelled samples based on their similarities. It\nhas become a significant tool for the analysis of high-dimensional data.\nHowever, most of the clustering methods merely generate pseudo labels and thus\nare unable to simultaneously present the similarities between different\nclusters and outliers. This paper proposes a new framework called\nHigh-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above\nproblems. First, HCHC combines global structure with local structure in one\nobjective function for deep clustering, improving the labels as relative\nprobabilities, to mine the similarities between different clusters while\nkeeping the local structure in each cluster. Then, the anchors of different\nclusters are sorted on the optimal Hamiltonian cycle generated by the cluster\nsimilarities and mapped on the circumference of a circle. Finally, a sample\nwith a higher probability of a cluster will be mapped closer to the\ncorresponding anchor. In this way, our framework allows us to appreciate three\naspects visually and simultaneously - clusters (formed by samples with high\nprobabilities), cluster similarities (represented as circular distances), and\noutliers (recognized as dots far away from all clusters). The experiments\nillustrate the superiority of HCHC.\n", "date": "2023-04-27", "categories": []}
{"id": "2306.09906", "title": "Correlation Clustering of Bird Sounds", "abstract": "  Bird sound classification is the task of relating any sound recording to\nthose species of bird that can be heard in the recording. Here, we study bird\nsound clustering, the task of deciding for any pair of sound recordings whether\nthe same species of bird can be heard in both. We address this problem by first\nlearning, from a training set, probabilities of pairs of recordings being\nrelated in this way, and then inferring a maximally probable partition of a\ntest set by correlation clustering. We address the following questions: How\naccurate is this clustering, compared to a classification of the test set? How\ndo the clusters thus inferred relate to the clusters obtained by\nclassification? How accurate is this clustering when applied to recordings of\nbird species not heard during training? How effective is this clustering in\nseparating, from bird sounds, environmental noise not heard during training?\n", "date": "2023-06-16", "categories": []}
{"id": "2306.11592", "title": "Deep Double Self-Expressive Subspace Clustering", "abstract": "  Deep subspace clustering based on auto-encoder has received wide attention.\nHowever, most subspace clustering based on auto-encoder does not utilize the\nstructural information in the self-expressive coefficient matrix, which limits\nthe clustering performance. In this paper, we propose a double self-expressive\nsubspace clustering algorithm. The key idea of our solution is to view the\nself-expressive coefficient as a feature representation of the example to get\nanother coefficient matrix. Then, we use the two coefficient matrices to\nconstruct the affinity matrix for spectral clustering. We find that it can\nreduce the subspace-preserving representation error and improve connectivity.\nTo further enhance the clustering performance, we proposed a self-supervised\nmodule based on contrastive learning, which can further improve the performance\nof the trained network. Experiments on several benchmark datasets demonstrate\nthat the proposed algorithm can achieve better clustering than state-of-the-art\nmethods.\n", "date": "2023-06-20", "categories": []}
{"id": "2306.09950", "title": "Nearly-Optimal Hierarchical Clustering for Well-Clustered Graphs", "abstract": "  This paper presents two efficient hierarchical clustering (HC) algorithms\nwith respect to Dasgupta's cost function. For any input graph $G$ with a clear\ncluster-structure, our designed algorithms run in nearly-linear time in the\ninput size of $G$, and return an $O(1)$-approximate HC tree with respect to\nDasgupta's cost function. We compare the performance of our algorithm against\nthe previous state-of-the-art on synthetic and real-world datasets and show\nthat our designed algorithm produces comparable or better HC trees with much\nlower running time.\n", "date": "2023-06-16", "categories": []}
{"id": "2306.08003", "title": "DTW k-means clustering for fault detection in photovoltaic modules", "abstract": "  The increase in the use of photovoltaic (PV) energy in the world has shown\nthat the useful life and maintenance of a PV plant directly depend on\ntheability to quickly detect severe faults on a PV plant. To solve this problem\nof detection, data based approaches have been proposed in the\nliterature.However, these previous solutions consider only specific behavior of\none or few faults. Most of these approaches can be qualified as supervised,\nrequiring an enormous labelling effort (fault types clearly identified in each\ntechnology). In addition, most of them are validated in PV cells or one PV\nmodule. That is hardly applicable in large-scale PV plants considering their\ncomplexity. Alternatively, some unsupervised well-known approaches based on\ndata try to detect anomalies but are not able to identify precisely the type of\nfault. The most performant of these methods do manage to efficiently group\nhealthy panels and separate them from faulty panels. In that way, this article\npresents an unsupervised approach called DTW K-means. This approach takes\nadvantages of both the dynamic time warping (DWT) metric and the Kmeans\nclustering algorithm as a data-driven approach. The results of this mixed\nmethod in a PV string are compared to diagnostic labels established by visual\ninspection of the panels.\n", "date": "2023-06-13", "categories": []}
{"id": "2306.07503", "title": "PaVa: a novel Path-based Valley-seeking clustering algorithm", "abstract": "  Clustering methods are being applied to a wider range of scenarios involving\nmore complex datasets, where the shapes of clusters tend to be arbitrary. In\nthis paper, we propose a novel Path-based Valley-seeking clustering algorithm\nfor arbitrarily shaped clusters. This work aims to seek the valleys among\nclusters and then individually extract clusters. Three vital techniques are\nused in this algorithm. First, path distance (minmax distance) is employed to\ntransform the irregular boundaries among clusters, that is density valleys,\ninto perfect spherical shells. Second, a suitable density measurement,\n$k$-distance, is employed to make adjustment on Minimum Spanning Tree, by which\na robust minmax distance is calculated. Third, we seek the transformed density\nvalleys by determining their centers and radius. First, the clusters are\nwrapped in spherical shells after the distance transformation, making the\nextraction process efficient even with clusters of arbitrary shape. Second,\nadjusted Minimum Spanning Tree enhances the robustness of minmax distance under\ndifferent kinds of noise. Last, the number of clusters does not need to be\ninputted or decided manually due to the individual extraction process. After\napplying the proposed algorithm to several commonly used synthetic datasets,\nthe results indicate that the Path-based Valley-seeking algorithm is accurate\nand efficient. The algorithm is based on the dissimilarity of objects, so it\ncan be applied to a wide range of fields. Its performance on real-world\ndatasets illustrates its versatility.\n", "date": "2023-06-13", "categories": []}
{"id": "2306.06061", "title": "clustering an african hairstyle dataset using pca and k-means", "abstract": "  The adoption of digital transformation was not expressed in building an\nAfrican face shape classifier. In this paper, an approach is presented that\nuses k-means to classify African women images. African women rely on beauty\nstandards recommendations, personal preference, or the newest trends in\nhairstyles to decide on the appropriate hairstyle for them. In this paper, an\napproach is presented that uses K-means clustering to classify African women's\nimages. In order to identify potential facial clusters, Haarcascade is used for\nfeature-based training, and K-means clustering is applied for image\nclassification.\n", "date": "2023-05-25", "categories": []}
{"id": "2306.04884", "title": "Faster Approximation Algorithms for Parameterized Graph Clustering and\n  Edge Labeling", "abstract": "  Graph clustering is a fundamental task in network analysis where the goal is\nto detect sets of nodes that are well-connected to each other but sparsely\nconnected to the rest of the graph. We present faster approximation algorithms\nfor an NP-hard parameterized clustering framework called LambdaCC, which is\ngoverned by a tunable resolution parameter and generalizes many other\nclustering objectives such as modularity, sparsest cut, and cluster deletion.\nPrevious LambdaCC algorithms are either heuristics with no approximation\nguarantees, or computationally expensive approximation algorithms. We provide\nfast new approximation algorithms that can be made purely combinatorial. These\nrely on a new parameterized edge labeling problem we introduce that generalizes\nprevious edge labeling problems that are based on the principle of strong\ntriadic closure and are of independent interest in social network analysis. Our\nmethods are orders of magnitude more scalable than previous approximation\nalgorithms and our lower bounds allow us to obtain a posteriori approximation\nguarantees for previous heuristics that have no approximation guarantees of\ntheir own.\n", "date": "2023-06-08", "categories": []}
{"id": "2306.04962", "title": "arXiv4TGC: Large-Scale Datasets for Temporal Graph Clustering", "abstract": "  Temporal graph clustering (TGC) is a crucial task in temporal graph learning.\nIts focus is on node clustering on temporal graphs, and it offers greater\nflexibility for large-scale graph structures due to the mechanism of temporal\ngraph methods. However, the development of TGC is currently constrained by a\nsignificant problem: the lack of suitable and reliable large-scale temporal\ngraph datasets to evaluate clustering performance. In other words, most\nexisting temporal graph datasets are in small sizes, and even large-scale\ndatasets contain only a limited number of available node labels. It makes\nevaluating models for large-scale temporal graph clustering challenging. To\naddress this challenge, we build arXiv4TGC, a set of novel academic datasets\n(including arXivAI, arXivCS, arXivMath, arXivPhy, and arXivLarge) for\nlarge-scale temporal graph clustering. In particular, the largest dataset,\narXivLarge, contains 1.3 million labeled available nodes and 10 million\ntemporal edges. We further compare the clustering performance with typical\ntemporal graph learning models on both previous classic temporal graph datasets\nand the new datasets proposed in this paper. The clustering performance on\narXiv4TGC can be more apparent for evaluating different models, resulting in\nhigher clustering confidence and more suitable for large-scale temporal graph\nclustering. The arXiv4TGC datasets are publicly available at:\nhttps://github.com/MGitHubL/arXiv4TGC.\n", "date": "2023-06-08", "categories": []}
{"id": "2306.05363", "title": "Subject clustering by IF-PCA and several recent methods", "abstract": "  Subject clustering (i.e., the use of measured features to cluster subjects,\nsuch as patients or cells, into multiple groups) is a problem of great\ninterest. In recent years, many approaches were proposed, among which\nunsupervised deep learning (UDL) has received a great deal of attention. Two\ninteresting questions are (a) how to combine the strengths of UDL and other\napproaches, and (b) how these approaches compare to one other.\n  We combine Variational Auto-Encoder (VAE), a popular UDL approach, with the\nrecent idea of Influential Feature PCA (IF-PCA), and propose IF-VAE as a new\nmethod for subject clustering. We study IF-VAE and compare it with several\nother methods (including IF-PCA, VAE, Seurat, and SC3) on $10$ gene microarray\ndata sets and $8$ single-cell RNA-seq data sets. We find that IF-VAE\nsignificantly improves over VAE, but still underperforms IF-PCA. We also find\nthat IF-PCA is quite competitive, which slightly outperforms Seurat and SC3\nover the $8$ single-cell data sets. IF-PCA is conceptually simple and permits\ndelicate analysis. We demonstrate that IF-PCA is capable of achieving the phase\ntransition in a Rare/Weak model. Comparatively, Seurat and SC3 are more complex\nand theoretically difficult to analyze (for these reasons, their optimality\nremains unclear).\n", "date": "2023-06-08", "categories": []}
{"id": "2207.04600", "title": "Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Model", "abstract": "  This paper investigates the computational and statistical limits in\nclustering matrix-valued observations. We propose a low-rank mixture model\n(LrMM), adapted from the classical Gaussian mixture model (GMM) to treat\nmatrix-valued observations, which assumes low-rankness for population center\nmatrices. A computationally efficient clustering method is designed by\nintegrating Lloyd's algorithm and low-rank approximation. Once\nwell-initialized, the algorithm converges fast and achieves an exponential-type\nclustering error rate that is minimax optimal. Meanwhile, we show that a\ntensor-based spectral method delivers a good initial clustering. Comparable to\nGMM, the minimax optimal clustering error rate is decided by the separation\nstrength, i.e., the minimal distance between population center matrices. By\nexploiting low-rankness, the proposed algorithm is blessed with a weaker\nrequirement on the separation strength. Unlike GMM, however, the computational\ndifficulty of LrMM is characterized by the signal strength, i.e., the smallest\nnon-zero singular values of population center matrices. Evidence is provided\nshowing that no polynomial-time algorithm is consistent if the signal strength\nis not strong enough, even though the separation strength is strong. Intriguing\ndifferences between estimation and clustering under LrMM are discussed. The\nmerits of low-rank Lloyd's algorithm are confirmed by comprehensive simulation\nexperiments. Finally, our method outperforms others in the literature on\nreal-world datasets.\n", "date": "2022-07-11", "categories": []}
{"id": "2306.04425", "title": "Towards High-Performance Exploratory Data Analysis (EDA) Via Stable\n  Equilibrium Point", "abstract": "  Exploratory data analysis (EDA) is a vital procedure for data science\nprojects. In this work, we introduce a stable equilibrium point (SEP) - based\nframework for improving the efficiency and solution quality of EDA. By\nexploiting the SEPs to be the representative points, our approach aims to\ngenerate high-quality clustering and data visualization for large-scale data\nsets. A very unique property of the proposed method is that the SEPs will\ndirectly encode the clustering properties of data sets. Compared with prior\nstate-of-the-art clustering and data visualization methods, the proposed\nmethods allow substantially improving computing efficiency and solution quality\nfor large-scale data analysis tasks.\n", "date": "2023-06-07", "categories": []}
{"id": "2306.03209", "title": "End-to-end Differentiable Clustering with Associative Memories", "abstract": "  Clustering is a widely used unsupervised learning technique involving an\nintensive discrete optimization problem. Associative Memory models or AMs are\ndifferentiable neural networks defining a recursive dynamical system, which\nhave been integrated with various deep learning architectures. We uncover a\nnovel connection between the AM dynamics and the inherent discrete assignment\nnecessary in clustering to propose a novel unconstrained continuous relaxation\nof the discrete clustering problem, enabling end-to-end differentiable\nclustering with AM, dubbed ClAM. Leveraging the pattern completion ability of\nAMs, we further develop a novel self-supervised clustering loss. Our\nevaluations on varied datasets demonstrate that ClAM benefits from the\nself-supervision, and significantly improves upon both the traditional Lloyd's\nk-means algorithm, and more recent continuous clustering relaxations (by upto\n60% in terms of the Silhouette Coefficient).\n", "date": "2023-06-05", "categories": []}
{"id": "2301.12159", "title": "ClusterFuG: Clustering Fully connected Graphs by Multicut", "abstract": "  We propose a graph clustering formulation based on multicut (a.k.a. weighted\ncorrelation clustering) on the complete graph. Our formulation does not need\nspecification of the graph topology as in the original sparse formulation of\nmulticut, making our approach simpler and potentially better performing. In\ncontrast to unweighted correlation clustering we allow for a more expressive\nweighted cost structure. In dense multicut, the clustering objective is given\nin a factorized form as inner products of node feature vectors. This allows for\nan efficient formulation and inference in contrast to multicut/weighted\ncorrelation clustering, which has at least quadratic representation and\ncomputation complexity when working on the complete graph. We show how to\nrewrite classical greedy algorithms for multicut in our dense setting and how\nto modify them for greater efficiency and solution quality. In particular, our\nalgorithms scale to graphs with tens of thousands of nodes. Empirical evidence\non instance segmentation on Cityscapes and clustering of ImageNet datasets\nshows the merits of our approach.\n", "date": "2023-01-28", "categories": []}
{"id": "2306.02389", "title": "Fast Continual Multi-View Clustering with Incomplete Views", "abstract": "  Multi-view clustering (MVC) has gained broad attention owing to its capacity\nto exploit consistent and complementary information across views. This paper\nfocuses on a challenging issue in MVC called the incomplete continual data\nproblem (ICDP). In specific, most existing algorithms assume that views are\navailable in advance and overlook the scenarios where data observations of\nviews are accumulated over time. Due to privacy considerations or memory\nlimitations, previous views cannot be stored in these situations. Some works\nare proposed to handle it, but all fail to address incomplete views. Such an\nincomplete continual data problem (ICDP) in MVC is tough to solve since\nincomplete information with continual data increases the difficulty of\nextracting consistent and complementary knowledge among views. We propose Fast\nContinual Multi-View Clustering with Incomplete Views (FCMVC-IV) to address it.\nSpecifically, it maintains a consensus coefficient matrix and updates knowledge\nwith the incoming incomplete view rather than storing and recomputing all the\ndata matrices. Considering that the views are incomplete, the newly collected\nview might contain samples that have yet to appear; two indicator matrices and\na rotation matrix are developed to match matrices with different dimensions.\nBesides, we design a three-step iterative algorithm to solve the resultant\nproblem in linear complexity with proven convergence. Comprehensive experiments\non various datasets show the superiority of FCMVC-IV.\n", "date": "2023-06-04", "categories": []}
{"id": "2306.00152", "title": "Learning the Right Layers: a Data-Driven Layer-Aggregation Strategy for\n  Semi-Supervised Learning on Multilayer Graphs", "abstract": "  Clustering (or community detection) on multilayer graphs poses several\nadditional complications with respect to standard graphs as different layers\nmay be characterized by different structures and types of information. One of\nthe major challenges is to establish the extent to which each layer contributes\nto the cluster assignment in order to effectively take advantage of the\nmultilayer structure and improve upon the classification obtained using the\nindividual layers or their union. However, making an informed a-priori\nassessment about the clustering information content of the layers can be very\ncomplicated. In this work, we assume a semi-supervised learning setting, where\nthe class of a small percentage of nodes is initially provided, and we propose\na parameter-free Laplacian-regularized model that learns an optimal nonlinear\ncombination of the different layers from the available input labels. The\nlearning algorithm is based on a Frank-Wolfe optimization scheme with inexact\ngradient, combined with a modified Label Propagation iteration. We provide a\ndetailed convergence analysis of the algorithm and extensive experiments on\nsynthetic and real-world datasets, showing that the proposed method compares\nfavourably with a variety of baselines and outperforms each individual layer\nwhen used in isolation.\n", "date": "2023-05-31", "categories": []}
{"id": "2305.19391", "title": "Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric\n  Regularization Approach", "abstract": "  The recent integration of deep learning and pairwise similarity\nannotation-based constrained clustering -- i.e., $\\textit{deep constrained\nclustering}$ (DCC) -- has proven effective for incorporating weak supervision\ninto massive data clustering: Less than 1% of pair similarity annotations can\noften substantially enhance the clustering accuracy. However, beyond empirical\nsuccesses, there is a lack of understanding of DCC. In addition, many DCC\nparadigms are sensitive to annotation noise, but performance-guaranteed noisy\nDCC methods have been largely elusive. This work first takes a deep look into a\nrecently emerged logistic loss function of DCC, and characterizes its\ntheoretical properties. Our result shows that the logistic DCC loss ensures the\nidentifiability of data membership under reasonable conditions, which may shed\nlight on its effectiveness in practice. Building upon this understanding, a new\nloss function based on geometric factor analysis is proposed to fend against\nnoisy annotations. It is shown that even under $\\textit{unknown}$ annotation\nconfusions, the data membership can still be $\\textit{provably}$ identified\nunder our proposed learning criterion. The proposed approach is tested over\nmultiple datasets to validate our claims.\n", "date": "2023-05-30", "categories": []}
{"id": "2305.19475", "title": "Doubly Constrained Fair Clustering", "abstract": "  The remarkable attention which fair clustering has received in the last few\nyears has resulted in a significant number of different notions of fairness.\nDespite the fact that these notions are well-justified, they are often\nmotivated and studied in a disjoint manner where one fairness desideratum is\nconsidered exclusively in isolation from the others. This leaves the\nunderstanding of the relations between different fairness notions as an\nimportant open problem in fair clustering. In this paper, we take the first\nstep in this direction. Specifically, we consider the two most prominent\ndemographic representation fairness notions in clustering: (1) Group Fairness\n(GF), where the different demographic groups are supposed to have close to\npopulation-level representation in each cluster and (2) Diversity in Center\nSelection (DS), where the selected centers are supposed to have close to\npopulation-level representation of each group. We show that given a constant\napproximation algorithm for one constraint (GF or DS only) we can obtain a\nconstant approximation solution that satisfies both constraints simultaneously.\nInterestingly, we prove that any given solution that satisfies the GF\nconstraint can always be post-processed at a bounded degradation to the\nclustering cost to additionally satisfy the DS constraint while the reverse is\nnot true. Furthermore, we show that both GF and DS are incompatible (having an\nempty feasibility set in the worst case) with a collection of other\ndistance-based fairness notions. Finally, we carry experiments to validate our\ntheoretical findings.\n", "date": "2023-05-31", "categories": []}
{"id": "2305.19992", "title": "A Nested Matrix-Tensor Model for Noisy Multi-view Clustering", "abstract": "  In this paper, we propose a nested matrix-tensor model which extends the\nspiked rank-one tensor model of order three. This model is particularly\nmotivated by a multi-view clustering problem in which multiple noisy\nobservations of each data point are acquired, with potentially non-uniform\nvariances along the views. In this case, data can be naturally represented by\nan order-three tensor where the views are stacked. Given such a tensor, we\nconsider the estimation of the hidden clusters via performing a best rank-one\ntensor approximation. In order to study the theoretical performance of this\napproach, we characterize the behavior of this best rank-one approximation in\nterms of the alignments of the obtained component vectors with the hidden model\nparameter vectors, in the large-dimensional regime. In particular, we show that\nour theoretical results allow us to anticipate the exact accuracy of the\nproposed clustering approach. Furthermore, numerical experiments indicate that\nleveraging our tensor-based approach yields better accuracy compared to a naive\nunfolding-based algorithm which ignores the underlying low-rank tensor\nstructure. Our analysis unveils unexpected and non-trivial phase transition\nphenomena depending on the model parameters, ``interpolating'' between the\ntypical behavior observed for the spiked matrix and tensor models.\n", "date": "2023-05-31", "categories": []}
{"id": "2302.04421", "title": "Information Theoretical Importance Sampling Clustering", "abstract": "  A current assumption of most clustering methods is that the training data and\nfuture data are taken from the same distribution. However, this assumption may\nnot hold in most real-world scenarios. In this paper, we propose an information\ntheoretical importance sampling based approach for clustering problems (ITISC)\nwhich minimizes the worst case of expected distortions under the constraint of\ndistribution deviation. The distribution deviation constraint can be converted\nto the constraint over a set of weight distributions centered on the uniform\ndistribution derived from importance sampling. The objective of the proposed\napproach is to minimize the loss under maximum degradation hence the resulting\nproblem is a constrained minimax optimization problem which can be reformulated\nto an unconstrained problem using the Lagrange method. The optimization problem\ncan be solved by both an alternative optimization algorithm or a general\noptimization routine by commercially available software. Experiment results on\nsynthetic datasets and a real-world load forecasting problem validate the\neffectiveness of the proposed model. Furthermore, we show that fuzzy c-means is\na special case of ITISC with the logarithmic distortion, and this observation\nprovides an interesting physical interpretation for fuzzy exponent $m$.\n", "date": "2023-02-09", "categories": []}
{"id": "2302.08743", "title": "Multi-View Clustering from the Perspective of Mutual Information", "abstract": "  Exploring the complementary information of multi-view data to improve\nclustering effects is a crucial issue in multi-view clustering. In this paper,\nwe propose a novel model based on information theory termed Informative\nMulti-View Clustering (IMVC), which extracts the common and view-specific\ninformation hidden in multi-view data and constructs a clustering-oriented\ncomprehensive representation. More specifically, we concatenate multiple\nfeatures into a unified feature representation, then pass it through a encoder\nto retrieve the common representation across views. Simultaneously, the\nfeatures of each view are sent to a encoder to produce a compact view-specific\nrepresentation, respectively. Thus, we constrain the mutual information between\nthe common representation and view-specific representations to be minimal for\nobtaining multi-level information. Further, the common representation and\nview-specific representation are spliced to model the refined representation of\neach view, which is fed into a decoder to reconstruct the initial data with\nmaximizing their mutual information. In order to form a comprehensive\nrepresentation, the common representation and all view-specific representations\nare concatenated. Furthermore, to accommodate the comprehensive representation\nbetter for the clustering task, we maximize the mutual information between an\ninstance and its k-nearest neighbors to enhance the intra-cluster aggregation,\nthus inducing well separation of different clusters at the overall aspect.\nFinally, we conduct extensive experiments on six benchmark datasets, and the\nexperimental results indicate that the proposed IMVC outperforms other methods.\n", "date": "2023-02-17", "categories": []}
{"id": "2305.18492", "title": "DMS: Differentiable Mean Shift for Dataset Agnostic Task Specific\n  Clustering Using Side Information", "abstract": "  We present a novel approach, in which we learn to cluster data directly from\nside information, in the form of a small set of pairwise examples. Unlike\nprevious methods, with or without side information, we do not need to know the\nnumber of clusters, their centers or any kind of distance metric for\nsimilarity. Our method is able to divide the same data points in various ways\ndependant on the needs of a specific task, defined by the side information.\nContrastingly, other work generally finds only the intrinsic, most obvious,\nclusters. Inspired by the mean shift algorithm, we implement our new clustering\napproach using a custom iterative neural network to create Differentiable Mean\nShift (DMS), a state of the art, dataset agnostic, clustering method. We found\nthat it was possible to train a strong cluster definition without enforcing a\nconstraint that each cluster must be presented during training. DMS outperforms\ncurrent methods in both the intrinsic and non-intrinsic dataset tasks.\n", "date": "2023-05-29", "categories": []}
{"id": "2305.18880", "title": "Research on Multilingual News Clustering Based on Cross-Language Word\n  Embeddings", "abstract": "  Classifying the same event reported by different countries is of significant\nimportance for public opinion control and intelligence gathering. Due to the\ndiverse types of news, relying solely on transla-tors would be costly and\ninefficient, while depending solely on translation systems would incur\nconsiderable performance overheads in invoking translation interfaces and\nstoring translated texts. To address this issue, we mainly focus on the\nclustering problem of cross-lingual news. To be specific, we use a combination\nof sentence vector representations of news headlines in a mixed semantic space\nand the topic probability distributions of news content to represent a news\narticle. In the training of cross-lingual models, we employ knowledge\ndistillation techniques to fit two semantic spaces into a mixed semantic space.\nWe abandon traditional static clustering methods like K-Means and AGNES in\nfavor of the incremental clustering algorithm Single-Pass, which we further\nmodify to better suit cross-lingual news clustering scenarios. Our main\ncontributions are as follows: (1) We adopt the English standard BERT as the\nteacher model and XLM-Roberta as the student model, training a cross-lingual\nmodel through knowledge distillation that can represent sentence-level\nbilingual texts in both Chinese and English. (2) We use the LDA topic model to\nrepresent news as a combina-tion of cross-lingual vectors for headlines and\ntopic probability distributions for con-tent, introducing concepts such as\ntopic similarity to address the cross-lingual issue in news content\nrepresentation. (3) We adapt the Single-Pass clustering algorithm for the news\ncontext to make it more applicable. Our optimizations of Single-Pass include\nad-justing the distance algorithm between samples and clusters, adding cluster\nmerging operations, and incorporating a news time parameter.\n", "date": "2023-05-30", "categories": []}
{"id": "2209.15097", "title": "Likelihood Adjusted Semidefinite Programs for Clustering Heterogeneous\n  Data", "abstract": "  Clustering is a widely deployed unsupervised learning tool. Model-based\nclustering is a flexible framework to tackle data heterogeneity when the\nclusters have different shapes. Likelihood-based inference for mixture\ndistributions often involves non-convex and high-dimensional objective\nfunctions, imposing difficult computational and statistical challenges. The\nclassic expectation-maximization (EM) algorithm is a computationally thrifty\niterative method that maximizes a surrogate function minorizing the\nlog-likelihood of observed data in each iteration, which however suffers from\nbad local maxima even in the special case of the standard Gaussian mixture\nmodel with common isotropic covariance matrices. On the other hand, recent\nstudies reveal that the unique global solution of a semidefinite programming\n(SDP) relaxed $K$-means achieves the information-theoretically sharp threshold\nfor perfectly recovering the cluster labels under the standard Gaussian mixture\nmodel. In this paper, we extend the SDP approach to a general setting by\nintegrating cluster labels as model parameters and propose an iterative\nlikelihood adjusted SDP (iLA-SDP) method that directly maximizes the exact\nobserved likelihood in the presence of data heterogeneity. By lifting the\ncluster assignment to group-specific membership matrices, iLA-SDP avoids\ncentroids estimation -- a key feature that allows exact recovery under\nwell-separateness of centroids without being trapped by their adversarial\nconfigurations. Thus iLA-SDP is less sensitive than EM to initialization and\nmore stable on high-dimensional data. Our numeric experiments demonstrate that\niLA-SDP can achieve lower mis-clustering errors over several widely used\nclustering methods including $K$-means, SDP and EM algorithms.\n", "date": "2022-09-29", "categories": []}
{"id": "2302.13457", "title": "A Self-Supervised Learning-based Approach to Clustering Multivariate\n  Time-Series Data with Missing Values (SLAC-Time): An Application to TBI\n  Phenotyping", "abstract": "  Self-supervised learning approaches provide a promising direction for\nclustering multivariate time-series data. However, real-world time-series data\noften include missing values, and the existing approaches require imputing\nmissing values before clustering, which may cause extensive computations and\nnoise and result in invalid interpretations. To address these challenges, we\npresent a Self-supervised Learning-based Approach to Clustering multivariate\nTime-series data with missing values (SLAC-Time). SLAC-Time is a\nTransformer-based clustering method that uses time-series forecasting as a\nproxy task for leveraging unlabeled data and learning more robust time-series\nrepresentations. This method jointly learns the neural network parameters and\nthe cluster assignments of the learned representations. It iteratively clusters\nthe learned representations with the K-means method and then utilizes the\nsubsequent cluster assignments as pseudo-labels to update the model parameters.\nTo evaluate our proposed approach, we applied it to clustering and phenotyping\nTraumatic Brain Injury (TBI) patients in the Transforming Research and Clinical\nKnowledge in Traumatic Brain Injury (TRACK-TBI) study. Our experiments\ndemonstrate that SLAC-Time outperforms the baseline K-means clustering\nalgorithm in terms of silhouette coefficient, Calinski Harabasz index, Dunn\nindex, and Davies Bouldin index. We identified three TBI phenotypes that are\ndistinct from one another in terms of clinically significant variables as well\nas clinical outcomes, including the Extended Glasgow Outcome Scale (GOSE)\nscore, Intensive Care Unit (ICU) length of stay, and mortality rate. The\nexperiments show that the TBI phenotypes identified by SLAC-Time can be\npotentially used for developing targeted clinical trials and therapeutic\nstrategies.\n", "date": "2023-02-27", "categories": []}
{"id": "2305.17492", "title": "Dynamic User Segmentation and Usage Profiling", "abstract": "  Usage data of a group of users distributed across a number of categories,\nsuch as songs, movies, webpages, links, regular household products, mobile\napps, games, etc. can be ultra-high dimensional and massive in size. More often\nthis kind of data is categorical and sparse in nature making it even more\ndifficult to interpret any underlying hidden patterns such as clusters of\nusers. However, if this information can be estimated accurately, it will have\nhuge impacts in different business areas such as user recommendations for apps,\nsongs, movies, and other similar products, health analytics using electronic\nhealth record (EHR) data, and driver profiling for insurance premium estimation\nor fleet management.\n  In this work, we propose a clustering strategy of such categorical big data,\nutilizing the hidden sparsity of the dataset. Most traditional clustering\nmethods fail to give proper clusters for such data and end up giving one big\ncluster with small clusters around it irrespective of the true structure of the\ndata clusters. We propose a feature transformation, which maps the\nbinary-valued usage vector to a lower dimensional continuous feature space in\nterms of groups of usage categories, termed as covariate classes. The lower\ndimensional feature representations in terms of covariate classes can be used\nfor clustering. We implemented the proposed strategy and applied it to a large\nsized very high-dimensional song playlist dataset for the performance\nvalidation. The results are impressive as we achieved similar-sized user\nclusters with minimal between-cluster overlap in the feature space (8%) on\naverage). As the proposed strategy has a very generic framework, it can be\nutilized as the analytic engine of many of the above-mentioned business use\ncases allowing an intelligent and dynamic personal recommendation system or a\nsupport system for smart business decision-making.\n", "date": "2023-05-27", "categories": []}
{"id": "2305.17557", "title": "Fair Clustering via Hierarchical Fair-Dirichlet Process", "abstract": "  The advent of ML-driven decision-making and policy formation has led to an\nincreasing focus on algorithmic fairness. As clustering is one of the most\ncommonly used unsupervised machine learning approaches, there has naturally\nbeen a proliferation of literature on {\\em fair clustering}. A popular notion\nof fairness in clustering mandates the clusters to be {\\em balanced}, i.e.,\neach level of a protected attribute must be approximately equally represented\nin each cluster. Building upon the original framework, this literature has\nrapidly expanded in various aspects. In this article, we offer a novel\nmodel-based formulation of fair clustering, complementing the existing\nliterature which is almost exclusively based on optimizing appropriate\nobjective functions.\n", "date": "2023-05-27", "categories": []}
{"id": "2305.16335", "title": "Robust Representation Learning with Reliable Pseudo-labels Generation\n  via Self-Adaptive Optimal Transport for Short Text Clustering", "abstract": "  Short text clustering is challenging since it takes imbalanced and noisy data\nas inputs. Existing approaches cannot solve this problem well, since (1) they\nare prone to obtain degenerate solutions especially on heavy imbalanced\ndatasets, and (2) they are vulnerable to noises. To tackle the above issues, we\npropose a Robust Short Text Clustering (RSTC) model to improve robustness\nagainst imbalanced and noisy data. RSTC includes two modules, i.e.,\npseudo-label generation module and robust representation learning module. The\nformer generates pseudo-labels to provide supervision for the later, which\ncontributes to more robust representations and correctly separated clusters. To\nprovide robustness against the imbalance in data, we propose self-adaptive\noptimal transport in the pseudo-label generation module. To improve robustness\nagainst the noise in data, we further introduce both class-wise and\ninstance-wise contrastive learning in the robust representation learning\nmodule. Our empirical studies on eight short text clustering datasets\ndemonstrate that RSTC significantly outperforms the state-of-the-art models.\nThe code is available at: https://github.com/hmllmh/RSTC.\n", "date": "2023-05-23", "categories": []}
{"id": "2305.16372", "title": "Metrics for quantifying isotropy in high dimensional unsupervised\n  clustering tasks in a materials context", "abstract": "  Clustering is a common task in machine learning, but clusters of unlabelled\ndata can be hard to quantify. The application of clustering algorithms in\nchemistry is often dependant on material representation. Ascertaining the\neffects of different representations, clustering algorithms, or data\ntransformations on the resulting clusters is difficult due to the\ndimensionality of these data. We present a thorough analysis of measures for\nisotropy of a cluster, including a novel implantation based on an existing\nderivation. Using fractional anisotropy, a common method used in medical\nimaging for comparison, we then expand these measures to examine the average\nisotropy of a set of clusters. A use case for such measures is demonstrated by\nquantifying the effects of kernel approximation functions on different\nrepresentations of the Inorganic Crystal Structure Database. Broader\napplicability of these methods is demonstrated in analysing learnt embedding of\nthe MNIST dataset. Random clusters are explored to examine the differences\nbetween isotropy measures presented, and to see how each method scales with the\ndimensionality. Python implementations of these measures are provided for use\nby the community.\n", "date": "2023-05-25", "categories": []}
{"id": "2305.16890", "title": "Universal Weak Coreset", "abstract": "  Coresets for $k$-means and $k$-median problems yield a small summary of the\ndata, which preserve the clustering cost with respect to any set of $k$\ncenters. Recently coresets have also been constructed for constrained $k$-means\nand $k$-median problems. However, the notion of coresets has the drawback that\n(i) they can only be applied in settings where the input points are allowed to\nhave weights, and (ii) in general metric spaces, the size of the coresets can\ndepend logarithmically on the number of points. The notion of weak coresets,\nwhich have less stringent requirements than coresets, has been studied in the\ncontext of classical $k$-means and $k$-median problems. A weak coreset is a\npair $(J,S)$ of subsets of points, where $S$ acts as a summary of the point set\nand $J$ as a set of potential centers. This pair satisfies the properties that\n(i) $S$ is a good summary of the data as long as the $k$ centers are chosen\nfrom $J$ only, and (ii) there is a good choice of $k$ centers in $J$ with cost\nclose to the optimal cost. We develop this framework, which we call universal\nweak coresets, for constrained clustering settings. In conjunction with recent\ncoreset constructions for constrained settings, our designs give greater data\ncompression, are conceptually simpler, and apply to a wide range of constrained\n$k$-median and $k$-means problems.\n", "date": "2023-05-26", "categories": []}
{"id": "2305.15417", "title": "Entropy-Aware Similarity for Balanced Clustering: A Case Study with\n  Melanoma Detection", "abstract": "  Clustering data is an unsupervised learning approach that aims to divide a\nset of data points into multiple groups. It is a crucial yet demanding subject\nin machine learning and data mining. Its successful applications span various\nfields. However, conventional clustering techniques necessitate the\nconsideration of balance significance in specific applications. Therefore, this\npaper addresses the challenge of imbalanced clustering problems and presents a\nnew method for balanced clustering by utilizing entropy-aware similarity, which\ncan be defined as the degree of balances. We have coined the term,\nentropy-aware similarity for balanced clustering (EASB), which maximizes\nbalance during clustering by complementary clustering of unbalanced data and\nincorporating entropy in a novel similarity formula that accounts for both\nangular differences and distances. The effectiveness of the proposed approach\nis evaluated on actual melanoma medial data, specifically the International\nSkin Imaging Collaboration (ISIC) 2019 and 2020 challenge datasets, to\ndemonstrate how it can successfully cluster the data while preserving balance.\nLastly, we can confirm that the proposed method exhibited outstanding\nperformance in detecting melanoma, comparing to classical methods.\n", "date": "2023-05-11", "categories": []}
{"id": "2302.00037", "title": "Differentially-Private Hierarchical Clustering with Provable\n  Approximation Guarantees", "abstract": "  Hierarchical Clustering is a popular unsupervised machine learning method\nwith decades of history and numerous applications. We initiate the study of\ndifferentially private approximation algorithms for hierarchical clustering\nunder the rigorous framework introduced by (Dasgupta, 2016). We show strong\nlower bounds for the problem: that any $\\epsilon$-DP algorithm must exhibit\n$O(|V|^2/ \\epsilon)$-additive error for an input dataset $V$. Then, we exhibit\na polynomial-time approximation algorithm with $O(|V|^{2.5}/\n\\epsilon)$-additive error, and an exponential-time algorithm that meets the\nlower bound. To overcome the lower bound, we focus on the stochastic block\nmodel, a popular model of graphs, and, with a separation assumption on the\nblocks, propose a private $1+o(1)$ approximation algorithm which also recovers\nthe blocks exactly. Finally, we perform an empirical study of our algorithms\nand validate their performance.\n", "date": "2023-01-31", "categories": []}
{"id": "2305.01479", "title": "On the properties of Gaussian Copula Mixture Models", "abstract": "  This paper investigates Gaussian copula mixture models (GCMM), which are an\nextension of Gaussian mixture models (GMM) that incorporate copula concepts.\nThe paper presents the mathematical definition of GCMM and explores the\nproperties of its likelihood function. Additionally, the paper proposes\nextended Expectation Maximum algorithms to estimate parameters for the mixture\nof copulas. The marginal distributions corresponding to each component are\nestimated separately using nonparametric statistical methods. In the\nexperiment, GCMM demonstrates improved goodness-of-fitting compared to GMM when\nusing the same number of clusters. Furthermore, GCMM has the ability to\nleverage un-synchronized data across dimensions for more comprehensive data\nanalysis.\n", "date": "2023-05-02", "categories": []}
{"id": "2305.13560", "title": "Single-Pass Pivot Algorithm for Correlation Clustering. Keep it simple!", "abstract": "  We show that a simple single-pass semi-streaming variant of the Pivot\nalgorithm for Correlation Clustering gives a (3 + {\\epsilon})-approximation\nusing O(n/{\\epsilon}) words of memory. This is a slight improvement over the\nrecent results of Cambus, Kuhn, Lindy, Pai, and Uitto, who gave a (3 +\n{\\epsilon})-approximation using O(n log n) words of memory, and Behnezhad,\nCharikar, Ma, and Tan, who gave a 5-approximation using O(n) words of memory.\nOne of the main contributions of this paper is that both the algorithm and its\nanalysis are very simple, and also the algorithm is easy to implement.\n", "date": "2023-05-23", "categories": []}
{"id": "2301.03421", "title": "A review of clustering models in educational data science towards\n  fairness-aware learning", "abstract": "  Ensuring fairness is essential for every education system. Machine learning\nis increasingly supporting the education system and educational data science\n(EDS) domain, from decision support to educational activities and learning\nanalytics. However, the machine learning-based decisions can be biased because\nthe algorithms may generate the results based on students' protected attributes\nsuch as race or gender. Clustering is an important machine learning technique\nto explore student data in order to support the decision-maker, as well as\nsupport educational activities, such as group assignments. Therefore, ensuring\nhigh-quality clustering models along with satisfying fairness constraints are\nimportant requirements. This chapter comprehensively surveys clustering models\nand their fairness in EDS. We especially focus on investigating the fair\nclustering models applied in educational activities. These models are believed\nto be practical tools for analyzing students' data and ensuring fairness in\nEDS.\n", "date": "2023-01-09", "categories": []}
{"id": "2302.05134", "title": "Neural Capacitated Clustering", "abstract": "  Recent work on deep clustering has found new promising methods also for\nconstrained clustering problems. Their typically pairwise constraints often can\nbe used to guide the partitioning of the data. Many problems however, feature\ncluster-level constraints, e.g. the Capacitated Clustering Problem (CCP), where\neach point has a weight and the total weight sum of all points in each cluster\nis bounded by a prescribed capacity. In this paper we propose a new method for\nthe CCP, Neural Capacited Clustering, that learns a neural network to predict\nthe assignment probabilities of points to cluster centers from a data set of\noptimal or near optimal past solutions of other problem instances. During\ninference, the resulting scores are then used in an iterative k-means like\nprocedure to refine the assignment under capacity constraints. In our\nexperiments on artificial data and two real world datasets our approach\noutperforms several state-of-the-art mathematical and heuristic solvers from\nthe literature. Moreover, we apply our method in the context of a\ncluster-first-route-second approach to the Capacitated Vehicle Routing Problem\n(CVRP) and show competitive results on the well-known Uchoa benchmark.\n", "date": "2023-02-10", "categories": []}
{"id": "2305.11489", "title": "Incomplete Multi-view Clustering via Diffusion Completion", "abstract": "  Incomplete multi-view clustering is a challenging and non-trivial task to\nprovide effective data analysis for large amounts of unlabeled data in the real\nworld. All incomplete multi-view clustering methods need to address the problem\nof how to reduce the impact of missing views. To address this issue, we propose\ndiffusion completion to recover the missing views integrated into an incomplete\nmulti-view clustering framework. Based on the observable views information, the\ndiffusion model is used to recover the missing views, and then the consistency\ninformation of the multi-view data is learned by contrastive learning to\nimprove the performance of multi-view clustering. To the best of our knowledge,\nthis may be the first work to incorporate diffusion models into an incomplete\nmulti-view clustering framework. Experimental results show that the proposed\nmethod performs well in recovering the missing views while achieving superior\nclustering performance compared to state-of-the-art methods.\n", "date": "2023-05-19", "categories": []}
{"id": "2211.16553", "title": "Simple and Scalable Algorithms for Cluster-Aware Precision Medicine", "abstract": "  AI-enabled precision medicine promises a transformational improvement in\nhealthcare outcomes by enabling data-driven personalized diagnosis, prognosis,\nand treatment. However, the well-known \"curse of dimensionality\" and the\nclustered structure of biomedical data together interact to present a joint\nchallenge in the high dimensional, limited observation precision medicine\nregime. To overcome both issues simultaneously we propose a simple and scalable\napproach to joint clustering and embedding that combines standard embedding\nmethods with a convex clustering penalty in a modular way. This novel,\ncluster-aware embedding approach overcomes the complexity and limitations of\ncurrent joint embedding and clustering methods, which we show with\nstraightforward implementations of hierarchically clustered principal component\nanalysis (PCA), locally linear embedding (LLE), and canonical correlation\nanalysis (CCA). Through both numerical experiments and real-world examples, we\ndemonstrate that our approach outperforms traditional and contemporary\nclustering methods on highly underdetermined problems (e.g., with just tens of\nobservations) as well as on large sample datasets. Importantly, our approach\ndoes not require the user to choose the desired number of clusters, but instead\nyields interpretable dendrograms of hierarchically clustered embeddings. Thus\nour approach improves significantly on existing methods for identifying patient\nsubgroups in multiomics and neuroimaging data, enabling scalable and\ninterpretable biomarkers for precision medicine.\n", "date": "2022-11-29", "categories": []}
{"id": "2302.13339", "title": "MCoCo: Multi-level Consistency Collaborative Multi-view Clustering", "abstract": "  Multi-view clustering can explore consistent information from different views\nto guide clustering. Most existing works focus on pursuing shallow consistency\nin the feature space and integrating the information of multiple views into a\nunified representation for clustering. These methods did not fully consider and\nexplore the consistency in the semantic space. To address this issue, we\nproposed a novel Multi-level Consistency Collaborative learning framework\n(MCoCo) for multi-view clustering. Specifically, MCoCo jointly learns cluster\nassignments of multiple views in feature space and aligns semantic labels of\ndifferent views in semantic space by contrastive learning. Further, we designed\na multi-level consistency collaboration strategy, which utilizes the consistent\ninformation of semantic space as a self-supervised signal to collaborate with\nthe cluster assignments in feature space. Thus, different levels of spaces\ncollaborate with each other while achieving their own consistency goals, which\nmakes MCoCo fully mine the consistent information of different views without\nfusion. Compared with state-of-the-art methods, extensive experiments\ndemonstrate the effectiveness and superiority of our method.\n", "date": "2023-02-26", "categories": []}
{"id": "2301.12671", "title": "Optimal Decision Trees For Interpretable Clustering with Constraints\n  (Extended Version)", "abstract": "  Constrained clustering is a semi-supervised task that employs a limited\namount of labelled data, formulated as constraints, to incorporate\ndomain-specific knowledge and to significantly improve clustering accuracy.\nPrevious work has considered exact optimization formulations that can guarantee\noptimal clustering while satisfying all constraints, however these approaches\nlack interpretability. Recently, decision-trees have been used to produce\ninherently interpretable clustering solutions, however existing approaches do\nnot support clustering constraints and do not provide strong theoretical\nguarantees on solution quality. In this work, we present a novel SAT-based\nframework for interpretable clustering that supports clustering constraints and\nthat also provides strong theoretical guarantees on solution quality. We also\npresent new insight into the trade-off between interpretability and\nsatisfaction of such user-provided constraints. Our framework is the first\napproach for interpretable and constrained clustering. Experiments with a range\nof real-world and synthetic datasets demonstrate that our approach can produce\nhigh-quality and interpretable constrained clustering solutions.\n", "date": "2023-01-30", "categories": []}
{"id": "2305.09071", "title": "FiMReSt: Finite Mixture of Multivariate Regulated Skew-t Kernels -- A\n  Flexible Probabilistic Model for Multi-Clustered Data with\n  Asymmetrically-Scattered Non-Gaussian Kernels", "abstract": "  Recently skew-t mixture models have been introduced as a flexible\nprobabilistic modeling technique taking into account both skewness in data\nclusters and the statistical degree of freedom (S-DoF) to improve modeling\ngeneralizability, and robustness to heavy tails and skewness. In this paper, we\nshow that the state-of-the-art skew-t mixture models fundamentally suffer from\na hidden phenomenon named here as \"S-DoF explosion,\" which results in local\nminima in the shapes of normal kernels during the non-convex iterative process\nof expectation maximization. For the first time, this paper provides insights\ninto the instability of the S-DoF, which can result in the divergence of the\nkernels from the mixture of t-distribution, losing generalizability and power\nfor modeling the outliers. Thus, in this paper, we propose a regularized\niterative optimization process to train the mixture model, enhancing the\ngeneralizability and resiliency of the technique. The resulting mixture model\nis named Finite Mixture of Multivariate Regulated Skew-t (FiMReSt) Kernels,\nwhich stabilizes the S-DoF profile during optimization process of learning. To\nvalidate the performance, we have conducted a comprehensive experiment on\nseveral real-world datasets and a synthetic dataset. The results highlight (a)\nsuperior performance of the FiMReSt, (b) generalizability in the presence of\noutliers, and (c) convergence of S-DoF.\n", "date": "2023-05-15", "categories": []}
{"id": "2305.09095", "title": "Multi-view MERA Subspace Clustering", "abstract": "  Tensor-based multi-view subspace clustering (MSC) can capture high-order\ncorrelation in the self-representation tensor. Current tensor decompositions\nfor MSC suffer from highly unbalanced unfolding matrices or rotation\nsensitivity, failing to fully explore inter/intra-view information. Using the\nadvanced tensor network, namely, multi-scale entanglement renormalization\nansatz (MERA), we propose a low-rank MERA based MSC (MERA-MSC) algorithm, where\nMERA factorizes a tensor into contractions of one top core factor and the rest\northogonal/semi-orthogonal factors. Benefiting from multiple interactions among\northogonal/semi-orthogonal (low-rank) factors, the low-rank MERA has a strong\nrepresentation power to capture the complex inter/intra-view information in the\nself-representation tensor. The alternating direction method of multipliers is\nadopted to solve the optimization model. Experimental results on five\nmulti-view datasets demonstrate MERA-MSC has superiority against the compared\nalgorithms on six evaluation metrics. Furthermore, we extend MERA-MSC by\nincorporating anchor learning to develop a scalable low-rank MERA based\nmulti-view clustering method (sMREA-MVC). The effectiveness and efficiency of\nsMERA-MVC have been validated on three large-scale multi-view datasets. To our\nknowledge, this is the first work to introduce MERA to the multi-view\nclustering topic. The codes of MERA-MSC and sMERA-MVC are publicly available at\nhttps://github.com/longzhen520/MERA-MSC.\n", "date": "2023-05-16", "categories": []}
{"id": "2304.09868", "title": "Accelerate Support Vector Clustering via Spectrum-Preserving Data\n  Compression", "abstract": "  This paper proposes a novel framework for accelerating support vector\nclustering. The proposed method first computes much smaller compressed data\nsets while preserving the key cluster properties of the original data sets\nbased on a novel spectral data compression approach. Then, the resultant\nspectrally-compressed data sets are leveraged for the development of fast and\nhigh quality algorithm for support vector clustering. We conducted extensive\nexperiments using real-world data sets and obtained very promising results. The\nproposed method allows us to achieve 100X and 115X speedups over the state of\nthe art SVC method on the Pendigits and USPS data sets, respectively, while\nachieving even better clustering quality. To the best of our knowledge, this\nrepresents the first practical method for high-quality and fast SVC on\nlarge-scale real-world data sets\n", "date": "2023-04-19", "categories": []}
{"id": "2305.07213", "title": "Rethinking k-means from manifold learning perspective", "abstract": "  Although numerous clustering algorithms have been developed, many existing\nmethods still leverage k-means technique to detect clusters of data points.\nHowever, the performance of k-means heavily depends on the estimation of\ncenters of clusters, which is very difficult to achieve an optimal solution.\nAnother major drawback is that it is sensitive to noise and outlier data. In\nthis paper, from manifold learning perspective, we rethink k-means and present\na new clustering algorithm which directly detects clusters of data without mean\nestimation. Specifically, we construct distance matrix between data points by\nButterworth filter such that distance between any two data points in the same\nclusters equals to a small constant, while increasing the distance between\nother data pairs from different clusters. To well exploit the complementary\ninformation embedded in different views, we leverage the tensor Schatten p-norm\nregularization on the 3rd-order tensor which consists of indicator matrices of\ndifferent views. Finally, an efficient alternating algorithm is derived to\noptimize our model. The constructed sequence was proved to converge to the\nstationary KKT point. Extensive experimental results indicate the superiority\nof our proposed method.\n", "date": "2023-05-12", "categories": []}
{"id": "2305.07386", "title": "One-step Bipartite Graph Cut: A Normalized Formulation and Its\n  Application to Scalable Subspace Clustering", "abstract": "  The bipartite graph structure has shown its promising ability in facilitating\nthe subspace clustering and spectral clustering algorithms for large-scale\ndatasets. To avoid the post-processing via k-means during the bipartite graph\npartitioning, the constrained Laplacian rank (CLR) is often utilized for\nconstraining the number of connected components (i.e., clusters) in the\nbipartite graph, which, however, neglects the distribution (or normalization)\nof these connected components and may lead to imbalanced or even ill clusters.\nDespite the significant success of normalized cut (Ncut) in general graphs, it\nremains surprisingly an open problem how to enforce a one-step normalized cut\nfor bipartite graphs, especially with linear-time complexity. In this paper, we\nfirst characterize a novel one-step bipartite graph cut (OBCut) criterion with\nnormalized constraints, and theoretically prove its equivalence to a trace\nmaximization problem. Then we extend this cut criterion to a scalable subspace\nclustering approach, where adaptive anchor learning, bipartite graph learning,\nand one-step normalized bipartite graph partitioning are simultaneously modeled\nin a unified objective function, and an alternating optimization algorithm is\nfurther designed to solve it in linear time. Experiments on a variety of\ngeneral and large-scale datasets demonstrate the effectiveness and scalability\nof our approach.\n", "date": "2023-05-12", "categories": []}
{"id": "2305.06541", "title": "Spectral Clustering on Large Datasets: When Does it Work? Theory from\n  Continuous Clustering and Density Cheeger-Buser", "abstract": "  Spectral clustering is one of the most popular clustering algorithms that has\nstood the test of time. It is simple to describe, can be implemented using\nstandard linear algebra, and often finds better clusters than traditional\nclustering algorithms like $k$-means and $k$-centers. The foundational\nalgorithm for two-way spectral clustering, by Shi and Malik, creates a\ngeometric graph from data and finds a spectral cut of the graph.\n  In modern machine learning, many data sets are modeled as a large number of\npoints drawn from a probability density function. Little is known about when\nspectral clustering works in this setting -- and when it doesn't. Past\nresearchers justified spectral clustering by appealing to the graph Cheeger\ninequality (which states that the spectral cut of a graph approximates the\n``Normalized Cut''), but this justification is known to break down on large\ndata sets.\n  We provide theoretically-informed intuition about spectral clustering on\nlarge data sets drawn from probability densities, by proving when a continuous\nform of spectral clustering considered by past researchers (the unweighted\nspectral cut of a probability density) finds good clusters of the underlying\ndensity itself. Our work suggests that Shi-Malik spectral clustering works well\non data drawn from mixtures of Laplace distributions, and works poorly on data\ndrawn from certain other densities, such as a density we call the `square-root\ntrough'.\n  Our core theorem proves that weighted spectral cuts have low weighted\nisoperimetry for all probability densities. Our key tool is a new Cheeger-Buser\ninequality for all probability densities, including discontinuous ones.\n", "date": "2023-05-11", "categories": []}
{"id": "2305.06576", "title": "Clustering of Time-Varying Graphs Based on Temporal Label Smoothness", "abstract": "  We propose a node clustering method for time-varying graphs based on the\nassumption that the cluster labels are changed smoothly over time. Clustering\nis one of the fundamental tasks in many science and engineering fields\nincluding signal processing, machine learning, and data mining. Although most\nexisting studies focus on the clustering of nodes in static graphs, we often\nencounter time-varying graphs for time-series data, e.g., social networks,\nbrain functional connectivity, and point clouds. In this paper, we formulate a\nnode clustering of time-varying graphs as an optimization problem based on\nspectral clustering, with a smoothness constraint of the node labels. We solve\nthe problem with a primal-dual splitting algorithm. Experiments on synthetic\nand real-world time-varying graphs are performed to validate the effectiveness\nof the proposed approach.\n", "date": "2023-05-11", "categories": []}
{"id": "2305.06799", "title": "GCFAgg: Global and Cross-view Feature Aggregation for Multi-view\n  Clustering", "abstract": "  Multi-view clustering can partition data samples into their categories by\nlearning a consensus representation in unsupervised way and has received more\nand more attention in recent years. However, most existing deep clustering\nmethods learn consensus representation or view-specific representations from\nmultiple views via view-wise aggregation way, where they ignore structure\nrelationship of all samples. In this paper, we propose a novel multi-view\nclustering network to address these problems, called Global and Cross-view\nFeature Aggregation for Multi-View Clustering (GCFAggMVC). Specifically, the\nconsensus data presentation from multiple views is obtained via cross-sample\nand cross-view feature aggregation, which fully explores the complementary\nofsimilar samples. Moreover, we align the consensus representation and the\nview-specific representation by the structure-guided contrastive learning\nmodule, which makes the view-specific representations from different samples\nwith high structure relationship similar. The proposed module is a flexible\nmulti-view data representation module, which can be also embedded to the\nincomplete multi-view data clustering task via plugging our module into other\nframeworks. Extensive experiments show that the proposed method achieves\nexcellent performance in both complete multi-view data clustering tasks and\nincomplete multi-view data clustering tasks.\n", "date": "2023-05-11", "categories": []}
{"id": "2305.06939", "title": "Deep Multi-View Subspace Clustering with Anchor Graph", "abstract": "  Deep multi-view subspace clustering (DMVSC) has recently attracted increasing\nattention due to its promising performance. However, existing DMVSC methods\nstill have two issues: (1) they mainly focus on using autoencoders to\nnonlinearly embed the data, while the embedding may be suboptimal for\nclustering because the clustering objective is rarely considered in\nautoencoders, and (2) existing methods typically have a quadratic or even cubic\ncomplexity, which makes it challenging to deal with large-scale data. To\naddress these issues, in this paper we propose a novel deep multi-view subspace\nclustering method with anchor graph (DMCAG). To be specific, DMCAG firstly\nlearns the embedded features for each view independently, which are used to\nobtain the subspace representations. To significantly reduce the complexity, we\nconstruct an anchor graph with small size for each view. Then, spectral\nclustering is performed on an integrated anchor graph to obtain pseudo-labels.\nTo overcome the negative impact caused by suboptimal embedded features, we use\npseudo-labels to refine the embedding process to make it more suitable for the\nclustering task. Pseudo-labels and embedded features are updated alternately.\nFurthermore, we design a strategy to keep the consistency of the labels based\non contrastive learning to enhance the clustering performance. Empirical\nstudies on real-world datasets show that our method achieves superior\nclustering performance over other state-of-the-art methods.\n", "date": "2023-05-11", "categories": []}
{"id": "2305.02931", "title": "Beyond Homophily: Reconstructing Structure for Graph-agnostic Clustering", "abstract": "  Graph neural networks (GNNs) based methods have achieved impressive\nperformance on node clustering task. However, they are designed on the\nhomophilic assumption of graph and clustering on heterophilic graph is\noverlooked. Due to the lack of labels, it is impossible to first identify a\ngraph as homophilic or heterophilic before a suitable GNN model can be found.\nHence, clustering on real-world graph with various levels of homophily poses a\nnew challenge to the graph research community. To fill this gap, we propose a\nnovel graph clustering method, which contains three key components: graph\nreconstruction, a mixed filter, and dual graph clustering network. To be\ngraph-agnostic, we empirically construct two graphs which are high homophily\nand heterophily from each data. The mixed filter based on the new graphs\nextracts both low-frequency and high-frequency information. To reduce the\nadverse coupling between node attribute and topological structure, we\nseparately map them into two subspaces in dual graph clustering network.\nExtensive experiments on 11 benchmark graphs demonstrate our promising\nperformance. In particular, our method dominates others on heterophilic graphs.\n", "date": "2023-05-03", "categories": []}
{"id": "2305.04142", "title": "Transformer-Based Hierarchical Clustering for Brain Network Analysis", "abstract": "  Brain networks, graphical models such as those constructed from MRI, have\nbeen widely used in pathological prediction and analysis of brain functions.\nWithin the complex brain system, differences in neuronal connection strengths\nparcellate the brain into various functional modules (network communities),\nwhich are critical for brain analysis. However, identifying such communities\nwithin the brain has been a nontrivial issue due to the complexity of neuronal\ninteractions. In this work, we propose a novel interpretable transformer-based\nmodel for joint hierarchical cluster identification and brain network\nclassification. Extensive experimental results on real-world brain network\ndatasets show that with the help of hierarchical clustering, the model achieves\nincreased accuracy and reduced runtime complexity while providing plausible\ninsight into the functional organization of brain regions. The implementation\nis available at https://github.com/DDVD233/THC.\n", "date": "2023-05-06", "categories": []}
{"id": "2305.04217", "title": "Influence of Swarm Intelligence in Data Clustering Mechanisms", "abstract": "  Data mining focuses on discovering interesting, non-trivial and meaningful\ninformation from large datasets. Data clustering is one of the unsupervised and\ndescriptive data mining task which group data based on similarity features and\nphysically stored together. As a partitioning clustering method, K-means is\nwidely used due to its simplicity and easiness of implementation. But this\nmethod has limitations such as local optimal convergence and initial point\nsensibility. Due to these impediments, nature inspired Swarm based algorithms\nsuch as Artificial Bee Colony Algorithm, Ant Colony Optimization, Firefly\nAlgorithm, Bat Algorithm and etc. are used for data clustering to cope with\nlarger datasets with lack and inconsistency of data. In some cases, those\nalgorithms are used with traditional approaches such as K-means as hybrid\napproaches to produce better results. This paper reviews the performances of\nthese new approaches and compares which is best for certain problematic\nsituation.\n", "date": "2023-05-07", "categories": []}
{"id": "2305.04364", "title": "A Generalized Framework for Predictive Clustering and Optimization", "abstract": "  Clustering is a powerful and extensively used data science tool. While\nclustering is generally thought of as an unsupervised learning technique, there\nare also supervised variations such as Spath's clusterwise regression that\nattempt to find clusters of data that yield low regression error on a\nsupervised target. We believe that clusterwise regression is just a single\nvertex of a largely unexplored design space of supervised clustering models. In\nthis article, we define a generalized optimization framework for predictive\nclustering that admits different cluster definitions (arbitrary point\nassignment, closest center, and bounding box) and both regression and\nclassification objectives. We then present a joint optimization strategy that\nexploits mixed-integer linear programming (MILP) for global optimization in\nthis generalized framework. To alleviate scalability concerns for large\ndatasets, we also provide highly scalable greedy algorithms inspired by the\nMajorization-Minimization (MM) framework. Finally, we demonstrate the ability\nof our models to uncover different interpretable discrete cluster structures in\ndata by experimenting with four real-world datasets.\n", "date": "2023-05-07", "categories": []}
{"id": "2206.04949", "title": "Deep Multi-View Semi-Supervised Clustering with Sample Pairwise\n  Constraints", "abstract": "  Multi-view clustering has attracted much attention thanks to the capacity of\nmulti-source information integration. Although numerous advanced methods have\nbeen proposed in past decades, most of them generally overlook the significance\nof weakly-supervised information and fail to preserve the feature properties of\nmultiple views, thus resulting in unsatisfactory clustering performance. To\naddress these issues, in this paper, we propose a novel Deep Multi-view\nSemi-supervised Clustering (DMSC) method, which jointly optimizes three kinds\nof losses during networks finetuning, including multi-view clustering loss,\nsemi-supervised pairwise constraint loss and multiple autoencoders\nreconstruction loss. Specifically, a KL divergence based multi-view clustering\nloss is imposed on the common representation of multi-view data to perform\nheterogeneous feature optimization, multi-view weighting and clustering\nprediction simultaneously. Then, we innovatively propose to integrate pairwise\nconstraints into the process of multi-view clustering by enforcing the learned\nmulti-view representation of must-link samples (cannot-link samples) to be\nsimilar (dissimilar), such that the formed clustering architecture can be more\ncredible. Moreover, unlike existing rivals that only preserve the encoders for\neach heterogeneous branch during networks finetuning, we further propose to\ntune the intact autoencoders frame that contains both encoders and decoders. In\nthis way, the issue of serious corruption of view-specific and view-shared\nfeature space could be alleviated, making the whole training procedure more\nstable. Through comprehensive experiments on eight popular image datasets, we\ndemonstrate that our proposed approach performs better than the\nstate-of-the-art multi-view and single-view competitors.\n", "date": "2022-06-10", "categories": []}
{"id": "2305.03144", "title": "Influence of various text embeddings on clustering performance in NLP", "abstract": "  With the advent of e-commerce platforms, reviews are crucial for customers to\nassess the credibility of a product. The star ratings do not always match the\nreview text written by the customer. For example, a three star rating (out of\nfive) may be incongruous with the review text, which may be more suitable for a\nfive star review. A clustering approach can be used to relabel the correct star\nratings by grouping the text reviews into individual groups. In this work, we\nexplore the task of choosing different text embeddings to represent these\nreviews and also explore the impact the embedding choice has on the performance\nof various classes of clustering algorithms. We use contextual (BERT) and\nnon-contextual (Word2Vec) text embeddings to represent the text and measure\ntheir impact of three classes on clustering algorithms - partitioning based\n(KMeans), single linkage agglomerative hierarchical, and density based (DBSCAN\nand HDBSCAN), each with various experimental settings. We use the silhouette\nscore, adjusted rand index score, and cluster purity score metrics to evaluate\nthe performance of the algorithms and discuss the impact of different\nembeddings on the clustering performance. Our results indicate that the type of\nembedding chosen drastically affects the performance of the algorithm, the\nperformance varies greatly across different types of clustering algorithms, no\nembedding type is better than the other, and DBSCAN outperforms KMeans and\nsingle linkage agglomerative clustering but also labels more data points as\noutliers. We provide a thorough comparison of the performances of different\nalgorithms and provide numerous ideas to foster further research in the domain\nof text clustering.\n", "date": "2023-05-04", "categories": []}
{"id": "2305.03414", "title": "Adaptive Graph Convolutional Subspace Clustering", "abstract": "  Spectral-type subspace clustering algorithms have shown excellent performance\nin many subspace clustering applications. The existing spectral-type subspace\nclustering algorithms either focus on designing constraints for the\nreconstruction coefficient matrix or feature extraction methods for finding\nlatent features of original data samples. In this paper, inspired by graph\nconvolutional networks, we use the graph convolution technique to develop a\nfeature extraction method and a coefficient matrix constraint simultaneously.\nAnd the graph-convolutional operator is updated iteratively and adaptively in\nour proposed algorithm. Hence, we call the proposed method adaptive graph\nconvolutional subspace clustering (AGCSC). We claim that by using AGCSC, the\naggregated feature representation of original data samples is suitable for\nsubspace clustering, and the coefficient matrix could reveal the subspace\nstructure of the original data set more faithfully. Finally, plenty of subspace\nclustering experiments prove our conclusions and show that AGCSC outperforms\nsome related methods as well as some deep models.\n", "date": "2023-05-05", "categories": []}
{"id": "2305.03555", "title": "Contrastive Graph Clustering in Curvature Spaces", "abstract": "  Graph clustering is a longstanding research topic, and has achieved\nremarkable success with the deep learning methods in recent years.\nNevertheless, we observe that several important issues largely remain open. On\nthe one hand, graph clustering from the geometric perspective is appealing but\nhas rarely been touched before, as it lacks a promising space for geometric\nclustering. On the other hand, contrastive learning boosts the deep graph\nclustering but usually struggles in either graph augmentation or hard sample\nmining. To bridge this gap, we rethink the problem of graph clustering from\ngeometric perspective and, to the best of our knowledge, make the first attempt\nto introduce a heterogeneous curvature space to graph clustering problem.\nCorrespondingly, we present a novel end-to-end contrastive graph clustering\nmodel named CONGREGATE, addressing geometric graph clustering with Ricci\ncurvatures. To support geometric clustering, we construct a theoretically\ngrounded Heterogeneous Curvature Space where deep representations are generated\nvia the product of the proposed fully Riemannian graph convolutional nets.\nThereafter, we train the graph clusters by an augmentation-free reweighted\ncontrastive approach where we pay more attention to both hard negatives and\nhard positives in our curvature space. Empirical results on real-world graphs\nshow that our model outperforms the state-of-the-art competitors.\n", "date": "2023-05-05", "categories": []}
{"id": "2209.08680", "title": "HiPart: Hierarchical Divisive Clustering Toolbox", "abstract": "  This paper presents the HiPart package, an open-source native python library\nthat provides efficient and interpret-able implementations of divisive\nhierarchical clustering algorithms. HiPart supports interactive visualizations\nfor the manipulation of the execution steps allowing the direct intervention of\nthe clustering outcome. This package is highly suited for Big Data applications\nas the focus has been given to the computational efficiency of the implemented\nclustering methodologies. The dependencies used are either Python build-in\npackages or highly maintained stable external packages. The software is\nprovided under the MIT license. The package's source code and documentation can\nbe found at https://github.com/panagiotisanagnostou/HiPart.\n", "date": "2022-09-18", "categories": []}
{"id": "2304.09989", "title": "CKmeans and FCKmeans : Two deterministic initialization procedures for\n  Kmeans algorithm using a modified crowding distance", "abstract": "  This paper presents two novel deterministic initialization procedures for\nK-means clustering based on a modified crowding distance. The procedures, named\nCKmeans and FCKmeans, use more crowded points as initial centroids.\nExperimental studies on multiple datasets demonstrate that the proposed\napproach outperforms Kmeans and Kmeans++ in terms of clustering accuracy. The\neffectiveness of CKmeans and FCKmeans is attributed to their ability to select\nbetter initial centroids based on the modified crowding distance. Overall, the\nproposed approach provides a promising alternative for improving K-means\nclustering.\n", "date": "2023-04-19", "categories": []}
{"id": "2305.00001", "title": "Feature Embedding Clustering using POCS-based Clustering Algorithm", "abstract": "  An application of the POCS-based clustering algorithm (POCS stands for\nProjection Onto Convex Set), a novel clustering technique, for feature\nembedding clustering problems is proposed in this paper. The POCS-based\nclustering algorithm applies the POCS's convergence property to clustering\nproblems and has shown competitive performance when compared with that of other\nclassical clustering schemes in terms of clustering error and execution speed.\nSpecifically, the POCS-based clustering algorithm treats each data point as a\nconvex set and applies a parallel projection operation from every cluster\nprototype to corresponding data members in order to minimize the objective\nfunction and update the prototypes. The experimental results on the synthetic\nembedding datasets extracted from the 5 Celebrity Faces and MNIST datasets show\nthat the POCS-based clustering algorithm can perform with favorable results\nwhen compared with those of other classical clustering schemes such as the\nK-Means and Fuzzy C-Means algorithms in feature embedding clustering problems.\n", "date": "2023-03-25", "categories": []}
{"id": "2305.00473", "title": "Time series clustering based on prediction accuracy of global\n  forecasting models", "abstract": "  In this paper, a novel method to perform model-based clustering of time\nseries is proposed. The procedure relies on two iterative steps: (i) K global\nforecasting models are fitted via pooling by considering the series pertaining\nto each cluster and (ii) each series is assigned to the group associated with\nthe model producing the best forecasts according to a particular criterion.\nUnlike most techniques proposed in the literature, the method considers the\npredictive accuracy as the main element for constructing the clustering\npartition, which contains groups jointly minimizing the overall forecasting\nerror. Thus, the approach leads to a new clustering paradigm where the quality\nof the clustering solution is measured in terms of its predictive capability.\nIn addition, the procedure gives rise to an effective mechanism for selecting\nthe number of clusters in a time series database and can be used in combination\nwith any class of regression model. An extensive simulation study shows that\nour method outperforms several alternative techniques concerning both\nclustering effectiveness and predictive accuracy. The approach is also applied\nto perform clustering in several datasets used as standard benchmarks in the\ntime series literature, obtaining great results.\n", "date": "2023-04-30", "categories": []}
{"id": "2305.00716", "title": "Adaptively Topological Tensor Network for Multi-view Subspace Clustering", "abstract": "  Multi-view subspace clustering methods have employed learned\nself-representation tensors from different tensor decompositions to exploit low\nrank information. However, the data structures embedded with\nself-representation tensors may vary in different multi-view datasets.\nTherefore, a pre-defined tensor decomposition may not fully exploit low rank\ninformation for a certain dataset, resulting in sub-optimal multi-view\nclustering performance. To alleviate the aforementioned limitations, we propose\nthe adaptively topological tensor network (ATTN) by determining the edge ranks\nfrom the structural information of the self-representation tensor, and it can\ngive a better tensor representation with the data-driven strategy.\nSpecifically, in multi-view tensor clustering, we analyze the higher-order\ncorrelations among different modes of a self-representation tensor, and prune\nthe links of the weakly correlated ones from a fully connected tensor network.\nTherefore, the newly obtained tensor networks can efficiently explore the\nessential clustering information with self-representation with different tensor\nstructures for various datasets. A greedy adaptive rank-increasing strategy is\nfurther applied to improve the capture capacity of low rank structure. We apply\nATTN on multi-view subspace clustering and utilize the alternating direction\nmethod of multipliers to solve it. Experimental results show that multi-view\nsubspace clustering based on ATTN outperforms the counterparts on six\nmulti-view datasets.\n", "date": "2023-05-01", "categories": []}
{"id": "2206.07602", "title": "Sparse Subspace Clustering in Diverse Multiplex Network Model", "abstract": "  The paper considers the DIverse MultiPLEx (DIMPLE) network model, introduced\nin Pensky and Wang (2021), where all layers of the network have the same\ncollection of nodes and are equipped with the Stochastic Block Models. In\naddition, all layers can be partitioned into groups with the same community\nstructures, although the layers in the same group may have different matrices\nof block connection probabilities. The DIMPLE model generalizes a multitude of\npapers that study multilayer networks with the same community structures in all\nlayers, as well as the Mixture Multilayer Stochastic Block Model (MMLSBM),\nwhere the layers in the same group have identical matrices of block connection\nprobabilities. While Pensky and Wang (2021) applied spectral clustering to the\nproxy of the adjacency tensor, the present paper uses Sparse Subspace\nClustering (SSC) for identifying groups of layers with identical community\nstructures. Under mild conditions, the latter leads to the strongly consistent\nbetween-layer clustering. In addition, SSC allows to handle much larger\nnetworks than methodology of Pensky and Wang (2021), and is perfectly suitable\nfor application of parallel computing.\n", "date": "2022-06-15", "categories": []}
{"id": "2304.12249", "title": "Fuzzy clustering of ordinal time series based on two novel distances\n  with economic applications", "abstract": "  Time series clustering is a central machine learning task with applications\nin many fields. While the majority of the methods focus on real-valued time\nseries, very few works consider series with discrete response. In this paper,\nthe problem of clustering ordinal time series is addressed. To this aim, two\nnovel distances between ordinal time series are introduced and used to\nconstruct fuzzy clustering procedures. Both metrics are functions of the\nestimated cumulative probabilities, thus automatically taking advantage of the\nordering inherent to the series' range. The resulting clustering algorithms are\ncomputationally efficient and able to group series generated from similar\nstochastic processes, reaching accurate results even though the series come\nfrom a wide variety of models. Since the dynamic of the series may vary over\nthe time, we adopt a fuzzy approach, thus enabling the procedures to locate\neach series into several clusters with different membership degrees. An\nextensive simulation study shows that the proposed methods outperform several\nalternative procedures. Weighted versions of the clustering algorithms are also\npresented and their advantages with respect to the original methods are\ndiscussed. Two specific applications involving economic time series illustrate\nthe usefulness of the proposed approaches.\n", "date": "2023-04-24", "categories": []}
{"id": "2209.12396", "title": "Deep Fair Clustering via Maximizing and Minimizing Mutual Information:\n  Theory, Algorithm and Metric", "abstract": "  Fair clustering aims to divide data into distinct clusters while preventing\nsensitive attributes (\\textit{e.g.}, gender, race, RNA sequencing technique)\nfrom dominating the clustering. Although a number of works have been conducted\nand achieved huge success recently, most of them are heuristical, and there\nlacks a unified theory for algorithm design. In this work, we fill this blank\nby developing a mutual information theory for deep fair clustering and\naccordingly designing a novel algorithm, dubbed FCMI. In brief, through\nmaximizing and minimizing mutual information, FCMI is designed to achieve four\ncharacteristics highly expected by deep fair clustering, \\textit{i.e.},\ncompact, balanced, and fair clusters, as well as informative features. Besides\nthe contributions to theory and algorithm, another contribution of this work is\nproposing a novel fair clustering metric built upon information theory as well.\nUnlike existing evaluation metrics, our metric measures the clustering quality\nand fairness as a whole instead of separate manner. To verify the effectiveness\nof the proposed FCMI, we conduct experiments on six benchmarks including a\nsingle-cell RNA-seq atlas compared with 11 state-of-the-art methods in terms of\nfive metrics. The code could be accessed from \\url{ https://pengxi.me}.\n", "date": "2022-09-26", "categories": []}
{"id": "2304.10831", "title": "Learn to Cluster Faces with Better Subgraphs", "abstract": "  Face clustering can provide pseudo-labels to the massive unlabeled face data\nand improve the performance of different face recognition models. The existing\nclustering methods generally aggregate the features within subgraphs that are\noften implemented based on a uniform threshold or a learned cutoff position.\nThis may reduce the recall of subgraphs and hence degrade the clustering\nperformance. This work proposed an efficient neighborhood-aware subgraph\nadjustment method that can significantly reduce the noise and improve the\nrecall of the subgraphs, and hence can drive the distant nodes to converge\ntowards the same centers. More specifically, the proposed method consists of\ntwo components, i.e. face embeddings enhancement using the embeddings from\nneighbors, and enclosed subgraph construction of node pairs for structural\ninformation extraction. The embeddings are combined to predict the linkage\nprobabilities for all node pairs to replace the cosine similarities to produce\nnew subgraphs that can be further used for aggregation of GCNs or other\nclustering methods. The proposed method is validated through extensive\nexperiments against a range of clustering solutions using three benchmark\ndatasets and numerical results confirm that it outperforms the SOTA solutions\nin terms of generalization capability.\n", "date": "2023-04-21", "categories": []}
{"id": "2304.11061", "title": "CEIL: A General Classification-Enhanced Iterative Learning Framework for\n  Text Clustering", "abstract": "  Text clustering, as one of the most fundamental challenges in unsupervised\nlearning, aims at grouping semantically similar text segments without relying\non human annotations. With the rapid development of deep learning, deep\nclustering has achieved significant advantages over traditional clustering\nmethods. Despite the effectiveness, most existing deep text clustering methods\nrely heavily on representations pre-trained in general domains, which may not\nbe the most suitable solution for clustering in specific target domains. To\naddress this issue, we propose CEIL, a novel Classification-Enhanced Iterative\nLearning framework for short text clustering, which aims at generally promoting\nthe clustering performance by introducing a classification objective to\niteratively improve feature representations. In each iteration, we first adopt\na language model to retrieve the initial text representations, from which the\nclustering results are collected using our proposed Category Disentangled\nContrastive Clustering (CDCC) algorithm. After strict data filtering and\naggregation processes, samples with clean category labels are retrieved, which\nserve as supervision information to update the language model with the\nclassification objective via a prompt learning approach. Finally, the updated\nlanguage model with improved representation ability is used to enhance\nclustering in the next iteration. Extensive experiments demonstrate that the\nCEIL framework significantly improves the clustering performance over\niterations, and is generally effective on various clustering algorithms.\nMoreover, by incorporating CEIL on CDCC, we achieve the state-of-the-art\nclustering performance on a wide range of short text clustering benchmarks\noutperforming other strong baseline methods.\n", "date": "2023-04-20", "categories": []}
{"id": "2304.09082", "title": "Unsupervised clustering of file dialects according to monotonic\n  decompositions of mixtures", "abstract": "  This paper proposes an unsupervised classification method that partitions a\nset of files into non-overlapping dialects based upon their behaviors,\ndetermined by messages produced by a collection of programs that consume them.\nThe pattern of messages can be used as the signature of a particular kind of\nbehavior, with the understanding that some messages are likely to co-occur,\nwhile others are not. Patterns of messages can be used to classify files into\ndialects. A dialect is defined by a subset of messages, called the required\nmessages. Once files are conditioned upon dialect and its required messages,\nthe remaining messages are statistically independent.\n  With this definition of dialect in hand, we present a greedy algorithm that\ndeduces candidate dialects from a dataset consisting of a matrix of\nfile-message data, demonstrate its performance on several file formats, and\nprove conditions under which it is optimal. We show that an analyst needs to\nconsider fewer dialects than distinct message patterns, which reduces their\ncognitive load when studying a complex format.\n", "date": "2023-02-09", "categories": []}
{"id": "2210.16435", "title": "Scalable Spectral Clustering with Group Fairness Constraints", "abstract": "  There are synergies of research interests and industrial efforts in modeling\nfairness and correcting algorithmic bias in machine learning. In this paper, we\npresent a scalable algorithm for spectral clustering (SC) with group fairness\nconstraints. Group fairness is also known as statistical parity where in each\ncluster, each protected group is represented with the same proportion as in the\nentirety. While FairSC algorithm (Kleindessner et al., 2019) is able to find\nthe fairer clustering, it is compromised by high costs due to the kernels of\ncomputing nullspaces and the square roots of dense matrices explicitly. We\npresent a new formulation of underlying spectral computation by incorporating\nnullspace projection and Hotelling's deflation such that the resulting\nalgorithm, called s-FairSC, only involves the sparse matrix-vector products and\nis able to fully exploit the sparsity of the fair SC model. The experimental\nresults on the modified stochastic block model demonstrate that s-FairSC is\ncomparable with FairSC in recovering fair clustering. Meanwhile, it is sped up\nby a factor of 12 for moderate model sizes. s-FairSC is further demonstrated to\nbe scalable in the sense that the computational costs of s-FairSC only increase\nmarginally compared to the SC without fairness constraints.\n", "date": "2022-10-28", "categories": []}
{"id": "2208.09849", "title": "Semantic-Enhanced Image Clustering", "abstract": "  Image clustering is an important and open-challenging task in computer\nvision. Although many methods have been proposed to solve the image clustering\ntask, they only explore images and uncover clusters according to the image\nfeatures, thus being unable to distinguish visually similar but semantically\ndifferent images. In this paper, we propose to investigate the task of image\nclustering with the help of a visual-language pre-training model. Different\nfrom the zero-shot setting, in which the class names are known, we only know\nthe number of clusters in this setting. Therefore, how to map images to a\nproper semantic space and how to cluster images from both image and semantic\nspaces are two key problems. To solve the above problems, we propose a novel\nimage clustering method guided by the visual-language pre-training model CLIP,\nnamed \\textbf{Semantic-Enhanced Image Clustering (SIC)}. In this new method, we\npropose a method to map the given images to a proper semantic space first and\nefficient methods to generate pseudo-labels according to the relationships\nbetween images and semantics. Finally, we propose performing clustering with\nconsistency learning in both image space and semantic space, in a\nself-supervised learning fashion. The theoretical result of convergence\nanalysis shows that our proposed method can converge at a sublinear speed.\nTheoretical analysis of expectation risk also shows that we can reduce the\nexpected risk by improving neighborhood consistency, increasing prediction\nconfidence, or reducing neighborhood imbalance. Experimental results on five\nbenchmark datasets clearly show the superiority of our new method.\n", "date": "2022-08-21", "categories": []}
{"id": "2208.12933", "title": "Consistency between ordering and clustering methods for graphs", "abstract": "  A relational dataset is often analyzed by optimally assigning a label to each\nelement through clustering or ordering. While similar characterizations of a\ndataset would be achieved by both clustering and ordering methods, the former\nhas been studied much more actively than the latter, particularly for the data\nrepresented as graphs. This study fills this gap by investigating\nmethodological relationships between several clustering and ordering methods,\nfocusing on spectral techniques. Furthermore, we evaluate the resulting\nperformance of the clustering and ordering methods. To this end, we propose a\nmeasure called the label continuity error, which generically quantifies the\ndegree of consistency between a sequence and partition for a set of elements.\nBased on synthetic and real-world datasets, we evaluate the extents to which an\nordering method identifies a module structure and a clustering method\nidentifies a banded structure.\n", "date": "2022-08-27", "categories": []}
{"id": "2304.02841", "title": "Learning Neural Eigenfunctions for Unsupervised Semantic Segmentation", "abstract": "  Unsupervised semantic segmentation is a long-standing challenge in computer\nvision with great significance. Spectral clustering is a theoretically grounded\nsolution to it where the spectral embeddings for pixels are computed to\nconstruct distinct clusters. Despite recent progress in enhancing spectral\nclustering with powerful pre-trained models, current approaches still suffer\nfrom inefficiencies in spectral decomposition and inflexibility in applying\nthem to the test data. This work addresses these issues by casting spectral\nclustering as a parametric approach that employs neural network-based\neigenfunctions to produce spectral embeddings. The outputs of the neural\neigenfunctions are further restricted to discrete vectors that indicate\nclustering assignments directly. As a result, an end-to-end NN-based paradigm\nof spectral clustering emerges. In practice, the neural eigenfunctions are\nlightweight and take the features from pre-trained models as inputs, improving\ntraining efficiency and unleashing the potential of pre-trained models for\ndense prediction. We conduct extensive empirical studies to validate the\neffectiveness of our approach and observe significant performance gains over\ncompetitive baselines on Pascal Context, Cityscapes, and ADE20K benchmarks.\n", "date": "2023-04-06", "categories": []}
{"id": "2209.04213", "title": "Autoencoder Based Iterative Modeling and Multivariate Time-Series\n  Subsequence Clustering Algorithm", "abstract": "  This paper introduces an algorithm for the detection of change-points and the\nidentification of the corresponding subsequences in transient multivariate\ntime-series data (MTSD). The analysis of such data has become more and more\nimportant due to the increase of availability in many industrial fields.\nLabeling, sorting or filtering highly transient measurement data for training\ncondition based maintenance (CbM) models is cumbersome and error-prone. For\nsome applications it can be sufficient to filter measurements by simple\nthresholds or finding change-points based on changes in mean value and\nvariation. But a robust diagnosis of a component within a component group for\nexample, which has a complex non-linear correlation between multiple sensor\nvalues, a simple approach would not be feasible. No meaningful and coherent\nmeasurement data which could be used for training a CbM model would emerge.\nTherefore, we introduce an algorithm which uses a recurrent neural network\n(RNN) based Autoencoder (AE) which is iteratively trained on incoming data. The\nscoring function uses the reconstruction error and latent space information. A\nmodel of the identified subsequence is saved and used for recognition of\nrepeating subsequences as well as fast offline clustering. For evaluation, we\npropose a new similarity measure based on the curvature for a more intuitive\ntime-series subsequence clustering metric. A comparison with seven other\nstate-of-the-art algorithms and eight datasets shows the capability and the\nincreased performance of our algorithm to cluster MTSD online and offline in\nconjunction with mechatronic systems.\n", "date": "2022-09-09", "categories": []}
{"id": "2304.01450", "title": "Clustering Validation with The Area Under Precision-Recall Curves", "abstract": "  Confusion matrices and derived metrics provide a comprehensive framework for\nthe evaluation of model performance in machine learning. These are well-known\nand extensively employed in the supervised learning domain, particularly\nclassification. Surprisingly, such a framework has not been fully explored in\nthe context of clustering validation. Indeed, just recently such a gap has been\nbridged with the introduction of the Area Under the ROC Curve for Clustering\n(AUCC), an internal/relative Clustering Validation Index (CVI) that allows for\nclustering validation in real application scenarios. In this work we explore\nthe Area Under Precision-Recall Curve (and related metrics) in the context of\nclustering validation. We show that these are not only appropriate as CVIs, but\nshould also be preferred in the presence of cluster imbalance. We perform a\ncomprehensive evaluation of proposed and state-of-art CVIs on real and\nsimulated data sets. Our observations corroborate towards an unified validation\nframework for supervised and unsupervised learning, given that they are\nconsistent with existing guidelines established for the evaluation of\nsupervised learning models.\n", "date": "2023-04-04", "categories": []}
{"id": "2211.16459", "title": "A Revenue Function for Comparison-Based Hierarchical Clustering", "abstract": "  Comparison-based learning addresses the problem of learning when, instead of\nexplicit features or pairwise similarities, one only has access to comparisons\nof the form: \\emph{Object $A$ is more similar to $B$ than to $C$.} Recently, it\nhas been shown that, in Hierarchical Clustering, single and complete linkage\ncan be directly implemented using only such comparisons while several\nalgorithms have been proposed to emulate the behaviour of average linkage.\nHence, finding hierarchies (or dendrograms) using only comparisons is a well\nunderstood problem. However, evaluating their meaningfulness when no\nground-truth nor explicit similarities are available remains an open question.\n  In this paper, we bridge this gap by proposing a new revenue function that\nallows one to measure the goodness of dendrograms using only comparisons. We\nshow that this function is closely related to Dasgupta's cost for hierarchical\nclustering that uses pairwise similarities. On the theoretical side, we use the\nproposed revenue function to resolve the open problem of whether one can\napproximately recover a latent hierarchy using few triplet comparisons. On the\npractical side, we present principled algorithms for comparison-based\nhierarchical clustering based on the maximisation of the revenue and we\nempirically compare them with existing methods.\n", "date": "2022-11-29", "categories": []}
{"id": "2304.00419", "title": "Mini-batch $k$-means terminates within $O(d/\\epsilon)$ iterations", "abstract": "  We answer the question: \"Does local progress (on batches) imply global\nprogress (on the entire dataset) for mini-batch $k$-means?\". Specifically, we\nconsider mini-batch $k$-means which terminates only when the improvement in the\nquality of the clustering on the sampled batch is below some threshold.\n  Although at first glance it appears that this algorithm might execute\nforever, we answer the above question in the affirmative and show that if the\nbatch is of size $\\tilde{\\Omega}((d/\\epsilon)^2)$, it must terminate within\n$O(d/\\epsilon)$ iterations with high probability, where $d$ is the dimension of\nthe input, and $\\epsilon$ is a threshold parameter for termination. This is\ntrue regardless of how the centers are initialized. When the algorithm is\ninitialized with the $k$-means++ initialization scheme, it achieves an\napproximation ratio of $O(\\log k)$ (the same as the full-batch version).\n  Finally, we show the applicability of our results to the mini-batch $k$-means\nalgorithm implemented in the scikit-learn (sklearn) python library.\n", "date": "2023-04-02", "categories": []}
{"id": "2304.00653", "title": "Enhancing Cluster Quality of Numerical Datasets with Domain Ontology", "abstract": "  Ontology-based clustering has gained attention in recent years due to the\npotential benefits of ontology. Current ontology-based clustering approaches\nhave mainly been applied to reduce the dimensionality of attributes in text\ndocument clustering. Reduction in dimensionality of attributes using ontology\nhelps to produce high quality clusters for a dataset. However, ontology-based\napproaches in clustering numerical datasets have not been gained enough\nattention. Moreover, some literature mentions that ontology-based clustering\ncan produce either high quality or low-quality clusters from a dataset.\nTherefore, in this paper we present a clustering approach that is based on\ndomain ontology to reduce the dimensionality of attributes in a numerical\ndataset using domain ontology and to produce high quality clusters. For every\ndataset, we produce three datasets using domain ontology. We then cluster these\ndatasets using a genetic algorithm-based clustering technique called\nGenClust++. The clusters of each dataset are evaluated in terms of Sum of\nSquared-Error (SSE). We use six numerical datasets to evaluate the performance\nof our ontology-based approach. The experimental results of our approach\nindicate that cluster quality gradually improves from lower to the higher\nlevels of a domain ontology.\n", "date": "2023-04-02", "categories": []}
{"id": "2304.01042", "title": "DivClust: Controlling Diversity in Deep Clustering", "abstract": "  Clustering has been a major research topic in the field of machine learning,\none to which Deep Learning has recently been applied with significant success.\nHowever, an aspect of clustering that is not addressed by existing deep\nclustering methods, is that of efficiently producing multiple, diverse\npartitionings for a given dataset. This is particularly important, as a diverse\nset of base clusterings are necessary for consensus clustering, which has been\nfound to produce better and more robust results than relying on a single\nclustering. To address this gap, we propose DivClust, a diversity controlling\nloss that can be incorporated into existing deep clustering frameworks to\nproduce multiple clusterings with the desired degree of diversity. We conduct\nexperiments with multiple datasets and deep clustering frameworks and show\nthat: a) our method effectively controls diversity across frameworks and\ndatasets with very small additional computational cost, b) the sets of\nclusterings learned by DivClust include solutions that significantly outperform\nsingle-clustering baselines, and c) using an off-the-shelf consensus clustering\nalgorithm, DivClust produces consensus clustering solutions that consistently\noutperform single-clustering baselines, effectively improving the performance\nof the base deep clustering framework.\n", "date": "2023-04-03", "categories": []}
{"id": "2302.04694", "title": "Partial Optimality in Cubic Correlation Clustering", "abstract": "  The higher-order correlation clustering problem is an expressive model, and\nrecently, local search heuristics have been proposed for several applications.\nCertifying optimality, however, is NP-hard and practically hampered already by\nthe complexity of the problem statement. Here, we focus on establishing partial\noptimality conditions for the special case of complete graphs and cubic\nobjective functions. In addition, we define and implement algorithms for\ntesting these conditions and examine their effect numerically, on two datasets.\n", "date": "2023-02-09", "categories": []}
{"id": "2303.15689", "title": "Deep Incomplete Multi-view Clustering with Cross-view Partial Sample and\n  Prototype Alignment", "abstract": "  The success of existing multi-view clustering relies on the assumption of\nsample integrity across multiple views. However, in real-world scenarios,\nsamples of multi-view are partially available due to data corruption or sensor\nfailure, which leads to incomplete multi-view clustering study (IMVC). Although\nseveral attempts have been proposed to address IMVC, they suffer from the\nfollowing drawbacks: i) Existing methods mainly adopt cross-view contrastive\nlearning forcing the representations of each sample across views to be exactly\nthe same, which might ignore view discrepancy and flexibility in\nrepresentations; ii) Due to the absence of non-observed samples across multiple\nviews, the obtained prototypes of clusters might be unaligned and biased,\nleading to incorrect fusion. To address the above issues, we propose a\nCross-view Partial Sample and Prototype Alignment Network (CPSPAN) for Deep\nIncomplete Multi-view Clustering. Firstly, unlike existing contrastive-based\nmethods, we adopt pair-observed data alignment as 'proxy supervised signals' to\nguide instance-to-instance correspondence construction among views. Then,\nregarding of the shifted prototypes in IMVC, we further propose a prototype\nalignment module to achieve incomplete distribution calibration across views.\nExtensive experimental results showcase the effectiveness of our proposed\nmodules, attaining noteworthy performance improvements when compared to\nexisting IMVC competitors on benchmark datasets.\n", "date": "2023-03-28", "categories": []}
{"id": "2303.17393", "title": "Dynamic Conceptional Contrastive Learning for Generalized Category\n  Discovery", "abstract": "  Generalized category discovery (GCD) is a recently proposed open-world\nproblem, which aims to automatically cluster partially labeled data. The main\nchallenge is that the unlabeled data contain instances that are not only from\nknown categories of the labeled data but also from novel categories. This leads\ntraditional novel category discovery (NCD) methods to be incapacitated for GCD,\ndue to their assumption of unlabeled data are only from novel categories. One\neffective way for GCD is applying self-supervised learning to learn\ndiscriminate representation for unlabeled data. However, this manner largely\nignores underlying relationships between instances of the same concepts (e.g.,\nclass, super-class, and sub-class), which results in inferior representation\nlearning. In this paper, we propose a Dynamic Conceptional Contrastive Learning\n(DCCL) framework, which can effectively improve clustering accuracy by\nalternately estimating underlying visual conceptions and learning conceptional\nrepresentation. In addition, we design a dynamic conception generation and\nupdate mechanism, which is able to ensure consistent conception learning and\nthus further facilitate the optimization of DCCL. Extensive experiments show\nthat DCCL achieves new state-of-the-art performances on six generic and\nfine-grained visual recognition datasets, especially on fine-grained ones. For\nexample, our method significantly surpasses the best competitor by 16.2% on the\nnew classes for the CUB-200 dataset. Code is available at\nhttps://github.com/TPCD/DCCL.\n", "date": "2023-03-30", "categories": []}
{"id": "2303.01082", "title": "GBMST: An Efficient Minimum Spanning Tree Clustering Based on\n  Granular-Ball Computing", "abstract": "  Most of the existing clustering methods are based on a single granularity of\ninformation, such as the distance and density of each data. This most\nfine-grained based approach is usually inefficient and susceptible to noise.\nTherefore, we propose a clustering algorithm that combines multi-granularity\nGranular-Ball and minimum spanning tree (MST). We construct coarsegrained\ngranular-balls, and then use granular-balls and MST to implement the clustering\nmethod based on \"large-scale priority\", which can greatly avoid the influence\nof outliers and accelerate the construction process of MST. Experimental\nresults on several data sets demonstrate the power of the algorithm. All codes\nhave been released at https://github.com/xjnine/GBMST.\n", "date": "2023-03-02", "categories": []}
{"id": "2303.16748", "title": "Multi-View Clustering via Semi-non-negative Tensor Factorization", "abstract": "  Multi-view clustering (MVC) based on non-negative matrix factorization (NMF)\nand its variants have received a huge amount of attention in recent years due\nto their advantages in clustering interpretability. However, existing NMF-based\nmulti-view clustering methods perform NMF on each view data respectively and\nignore the impact of between-view. Thus, they can't well exploit the\nwithin-view spatial structure and between-view complementary information. To\nresolve this issue, we present semi-non-negative tensor factorization\n(Semi-NTF) and develop a novel multi-view clustering based on Semi-NTF with\none-side orthogonal constraint. Our model directly performs Semi-NTF on the\n3rd-order tensor which is composed of anchor graphs of views. Thus, our model\ndirectly considers the between-view relationship. Moreover, we use the tensor\nSchatten p-norm regularization as a rank approximation of the 3rd-order tensor\nwhich characterizes the cluster structure of multi-view data and exploits the\nbetween-view complementary information. In addition, we provide an optimization\nalgorithm for the proposed method and prove mathematically that the algorithm\nalways converges to the stationary KKT point. Extensive experiments on various\nbenchmark datasets indicate that our proposed method is able to achieve\nsatisfactory clustering performance.\n", "date": "2023-03-29", "categories": []}
{"id": "2303.16841", "title": "Randomly Projected Convex Clustering Model: Motivation, Realization, and\n  Cluster Recovery Guarantees", "abstract": "  In this paper, we propose a randomly projected convex clustering model for\nclustering a collection of $n$ high dimensional data points in $\\mathbb{R}^d$\nwith $K$ hidden clusters. Compared to the convex clustering model for\nclustering original data with dimension $d$, we prove that, under some mild\nconditions, the perfect recovery of the cluster membership assignments of the\nconvex clustering model, if exists, can be preserved by the randomly projected\nconvex clustering model with embedding dimension $m = O(\\epsilon^{-2}\\log(n))$,\nwhere $0 < \\epsilon < 1$ is some given parameter. We further prove that the\nembedding dimension can be improved to be $O(\\epsilon^{-2}\\log(K))$, which is\nindependent of the number of data points. Extensive numerical experiment\nresults will be presented in this paper to demonstrate the robustness and\nsuperior performance of the randomly projected convex clustering model. The\nnumerical results presented in this paper also demonstrate that the randomly\nprojected convex clustering model can outperform the randomly projected K-means\nmodel in practice.\n", "date": "2023-03-29", "categories": []}
{"id": "2303.14366", "title": "Hybrid Fuzzy-Crisp Clustering Algorithm: Theory and Experiments", "abstract": "  With the membership function being strictly positive, the conventional fuzzy\nc-means clustering method sometimes causes imbalanced influence when clusters\nof vastly different sizes exist. That is, an outstandingly large cluster drags\nto its center all the other clusters, however far they are separated. To solve\nthis problem, we propose a hybrid fuzzy-crisp clustering algorithm based on a\ntarget function combining linear and quadratic terms of the membership\nfunction. In this algorithm, the membership of a data point to a cluster is\nautomatically set to exactly zero if the data point is ``sufficiently'' far\nfrom the cluster center. In this paper, we present a new algorithm for hybrid\nfuzzy-crisp clustering along with its geometric interpretation. The algorithm\nis tested on twenty simulated data generated and five real-world datasets from\nthe UCI repository and compared with conventional fuzzy and crisp clustering\nmethods. The proposed algorithm is demonstrated to outperform the conventional\nmethods on imbalanced datasets and can be competitive on more balanced\ndatasets.\n", "date": "2023-03-25", "categories": []}
{"id": "2303.14989", "title": "Regularized EM algorithm", "abstract": "  Expectation-Maximization (EM) algorithm is a widely used iterative algorithm\nfor computing (local) maximum likelihood estimate (MLE). It can be used in an\nextensive range of problems, including the clustering of data based on the\nGaussian mixture model (GMM). Numerical instability and convergence problems\nmay arise in situations where the sample size is not much larger than the data\ndimensionality. In such low sample support (LSS) settings, the covariance\nmatrix update in the EM-GMM algorithm may become singular or poorly\nconditioned, causing the algorithm to crash. On the other hand, in many signal\nprocessing problems, a priori information can be available indicating certain\nstructures for different cluster covariance matrices. In this paper, we present\na regularized EM algorithm for GMM-s that can make efficient use of such prior\nknowledge as well as cope with LSS situations. The method aims to maximize a\npenalized GMM likelihood where regularized estimation may be used to ensure\npositive definiteness of covariance matrix updates and shrink the estimators\ntowards some structured target covariance matrices. We show that the\ntheoretical guarantees of convergence hold, leading to better performing EM\nalgorithm for structured covariance matrix models or with low sample settings.\n", "date": "2023-03-27", "categories": []}
{"id": "2303.07768", "title": "DBSCAN of Multi-Slice Clustering for Third-Order Tensors", "abstract": "  Several methods for triclustering three-dimensional data require the cluster\nsize or the number of clusters in each dimension to be specified. To address\nthis issue, the Multi-Slice Clustering (MSC) for 3-order tensor finds signal\nslices that lie in a low dimensional subspace for a rank-one tensor dataset in\norder to find a cluster based on the threshold similarity. We propose an\nextension algorithm called MSC-DBSCAN to extract the different clusters of\nslices that lie in the different subspaces from the data if the dataset is a\nsum of r rank-one tensor (r > 1). Our algorithm uses the same input as the MSC\nalgorithm and can find the same solution for rank-one tensor data as MSC.\n", "date": "2023-03-14", "categories": []}
{"id": "2303.13665", "title": "Clustering based on Mixtures of Sparse Gaussian Processes", "abstract": "  Creating low dimensional representations of a high dimensional data set is an\nimportant component in many machine learning applications. How to cluster data\nusing their low dimensional embedded space is still a challenging problem in\nmachine learning. In this article, we focus on proposing a joint formulation\nfor both clustering and dimensionality reduction. When a probabilistic model is\ndesired, one possible solution is to use the mixture models in which both\ncluster indicator and low dimensional space are learned. Our algorithm is based\non a mixture of sparse Gaussian processes, which is called Sparse Gaussian\nProcess Mixture Clustering (SGP-MIC). The main advantages to our approach over\nexisting methods are that the probabilistic nature of this model provides more\nadvantages over existing deterministic methods, it is straightforward to\nconstruct non-linear generalizations of the model, and applying a sparse model\nand an efficient variational EM approximation help to speed up the algorithm.\n", "date": "2023-03-23", "categories": []}
{"id": "2208.08888", "title": "POCS-based Clustering Algorithm", "abstract": "  A novel clustering technique based on the projection onto convex set (POCS)\nmethod, called POCS-based clustering algorithm, is proposed in this paper. The\nproposed POCS-based clustering algorithm exploits a parallel projection method\nof POCS to find appropriate cluster prototypes in the feature space. The\nalgorithm considers each data point as a convex set and projects the cluster\nprototypes parallelly to the member data points. The projections are convexly\ncombined to minimize the objective function for data clustering purpose. The\nperformance of the proposed POCS-based clustering algorithm is verified through\nexperiments on various synthetic datasets. The experimental results show that\nthe proposed POCS-based clustering algorithm is competitive and efficient in\nterms of clustering error and execution speed when compared with other\nconventional clustering methods including Fuzzy C-Means (FCM) and K-means\nclustering algorithms.\n", "date": "2022-08-15", "categories": []}
{"id": "2303.13245", "title": "CrOC: Cross-View Online Clustering for Dense Visual Representation\n  Learning", "abstract": "  Learning dense visual representations without labels is an arduous task and\nmore so from scene-centric data. We propose to tackle this challenging problem\nby proposing a Cross-view consistency objective with an Online Clustering\nmechanism (CrOC) to discover and segment the semantics of the views. In the\nabsence of hand-crafted priors, the resulting method is more generalizable and\ndoes not require a cumbersome pre-processing step. More importantly, the\nclustering algorithm conjointly operates on the features of both views, thereby\nelegantly bypassing the issue of content not represented in both views and the\nambiguous matching of objects from one crop to the other. We demonstrate\nexcellent performance on linear and unsupervised segmentation transfer tasks on\nvarious datasets and similarly for video object segmentation. Our code and\npre-trained models are publicly available at https://github.com/stegmuel/CrOC.\n", "date": "2023-03-23", "categories": []}
{"id": "2209.04187", "title": "Efficient Multi-view Clustering via Unified and Discrete Bipartite Graph\n  Learning", "abstract": "  Although previous graph-based multi-view clustering algorithms have gained\nsignificant progress, most of them are still faced with three limitations.\nFirst, they often suffer from high computational complexity, which restricts\ntheir applications in large-scale scenarios. Second, they usually perform graph\nlearning either at the single-view level or at the view-consensus level, but\noften neglect the possibility of the joint learning of single-view and\nconsensus graphs. Third, many of them rely on the k-means for discretization of\nthe spectral embeddings, which lack the ability to directly learn the graph\nwith discrete cluster structure. In light of this, this paper presents an\nefficient multi-view clustering approach via unified and discrete bipartite\ngraph learning (UDBGL). Specifically, the anchor-based subspace learning is\nincorporated to learn the view-specific bipartite graphs from multiple views,\nupon which the bipartite graph fusion is leveraged to learn a view-consensus\nbipartite graph with adaptive weight learning. Further, the Laplacian rank\nconstraint is imposed to ensure that the fused bipartite graph has discrete\ncluster structures (with a specific number of connected components). By\nsimultaneously formulating the view-specific bipartite graph learning, the\nview-consensus bipartite graph learning, and the discrete cluster structure\nlearning into a unified objective function, an efficient minimization algorithm\nis then designed to tackle this optimization problem and directly achieve a\ndiscrete clustering solution without requiring additional partitioning, which\nnotably has linear time complexity in data size. Experiments on a variety of\nmulti-view datasets demonstrate the robustness and efficiency of our UDBGL\napproach. The code is available at https://github.com/huangdonghere/UDBGL.\n", "date": "2022-09-09", "categories": []}
{"id": "2303.12241", "title": "Preventing Dimensional Collapse of Incomplete Multi-View Clustering via\n  Direct Contrastive Learning", "abstract": "  Incomplete multi-view clustering (IMVC) is an unsupervised approach, among\nwhich IMVC via contrastive learning has received attention due to its excellent\nperformance. The previous methods have the following problems: 1) Over-reliance\non additional projection heads when solving the dimensional collapse problem in\nwhich latent features are only valid in lower-dimensional subspaces during\nclustering. However, many parameters in the projection heads are unnecessary.\n2) The recovered view contain inconsistent private information and useless\nprivate information will mislead the learning of common semantics due to\nconsistent learning and reconstruction learning on the same feature. To address\nthe above issues, we propose a novel incomplete multi-view contrastive\nclustering framework. This framework directly optimizes the latent feature\nsubspace, utilizes the learned feature vectors and their sub-vectors for\nreconstruction learning and consistency learning, thereby effectively avoiding\ndimensional collapse without relying on projection heads. Since reconstruction\nloss and contrastive loss are performed on different features, the adverse\neffect of useless private information is reduced. For the incomplete data, the\nmissing information is recovered by the cross-view prediction mechanism and the\ninconsistent information from different views is discarded by the minimum\nconditional entropy to further avoid the influence of private information.\nExtensive experimental results of the method on 5 public datasets show that the\nmethod achieves state-of-the-art clustering results.\n", "date": "2023-03-22", "categories": []}
{"id": "2303.11936", "title": "Clustering US Counties to Find Patterns Related to the COVID-19 Pandemic", "abstract": "  When COVID-19 first started spreading and quarantine was implemented, the\nSociety for Industrial and Applied Mathematics (SIAM) Student Chapter at the\nUniversity of Minnesota-Twin Cities began a collaboration with Ecolab to use\nour skills as data scientists and mathematicians to extract useful insights\nfrom relevant data relating to the pandemic. This collaboration consisted of\nmultiple groups working on different projects. In this write-up we focus on\nusing clustering techniques to help us find groups of similar counties in the\nUS and use that to help us understand the pandemic. Our team for this project\nconsisted of University of Minnesota students Cora Brown, Sarah Milstein,\nTianyi Sun, and Cooper Zhao, with help from Ecolab Data Scientist Jimmy\nBroomfield and University of Minnesota student Skye Ke. In the sections below\nwe describe all of the work done for this project. In Section 2, we list the\ndata we gathered, as well as the feature engineering we performed. In Section\n3, we describe the metrics we used for evaluating our models. In Section 4, we\nexplain the methods we used for interpreting the results of our various\nclustering approaches. In Section 5, we describe the different clustering\nmethods we implemented. In Section 6, we present the results of our clustering\ntechniques and provide relevant interpretation. Finally, in Section 7, we\nprovide some concluding remarks comparing the different clustering methods.\n", "date": "2023-03-19", "categories": []}
{"id": "2303.09827", "title": "DORIC : Domain Robust Fine-Tuning for Open Intent Clustering through\n  Dependency Parsing", "abstract": "  We present our work on Track 2 in the Dialog System Technology Challenges 11\n(DSTC11). DSTC11-Track2 aims to provide a benchmark for zero-shot,\ncross-domain, intent-set induction. In the absence of in-domain training\ndataset, robust utterance representation that can be used across domains is\nnecessary to induce users' intentions. To achieve this, we leveraged a\nmulti-domain dialogue dataset to fine-tune the language model and proposed\nextracting Verb-Object pairs to remove the artifacts of unnecessary\ninformation. Furthermore, we devised the method that generates each cluster's\nname for the explainability of clustered results. Our approach achieved 3rd\nplace in the precision score and showed superior accuracy and normalized mutual\ninformation (NMI) score than the baseline model on various domain datasets.\n", "date": "2023-03-17", "categories": []}
{"id": "2303.09877", "title": "On the Effects of Self-supervision and Contrastive Alignment in Deep\n  Multi-view Clustering", "abstract": "  Self-supervised learning is a central component in recent approaches to deep\nmulti-view clustering (MVC). However, we find large variations in the\ndevelopment of self-supervision-based methods for deep MVC, potentially slowing\nthe progress of the field. To address this, we present DeepMVC, a unified\nframework for deep MVC that includes many recent methods as instances. We\nleverage our framework to make key observations about the effect of\nself-supervision, and in particular, drawbacks of aligning representations with\ncontrastive learning. Further, we prove that contrastive alignment can\nnegatively influence cluster separability, and that this effect becomes worse\nwhen the number of views increases. Motivated by our findings, we develop\nseveral new DeepMVC instances with new forms of self-supervision. We conduct\nextensive experiments and find that (i) in line with our theoretical findings,\ncontrastive alignments decreases performance on datasets with many views; (ii)\nall methods benefit from some form of self-supervision; and (iii) our new\ninstances outperform previous methods on several datasets. Based on our\nresults, we suggest several promising directions for future research. To\nenhance the openness of the field, we provide an open-source implementation of\nDeepMVC, including recent models and our new instances. Our implementation\nincludes a consistent evaluation protocol, facilitating fair and accurate\nevaluation of methods and components.\n", "date": "2023-03-17", "categories": []}
{"id": "2303.07646", "title": "Clustering with Simplicial Complexes", "abstract": "  In this work, we propose a new clustering algorithm to group nodes in\nnetworks based on second-order simplices (aka filled triangles) to leverage\nhigher-order network interactions. We define a simplicial conductance function,\nwhich on minimizing, yields an optimal partition with a higher density of\nfilled triangles within the set while the density of filled triangles is\nsmaller across the sets. To this end, we propose a simplicial adjacency\noperator that captures the relation between the nodes through second-order\nsimplices. This allows us to extend the well-known Cheeger inequality to\ncluster a simplicial complex. Then, leveraging the Cheeger inequality, we\npropose the simplicial spectral clustering algorithm. We report results from\nnumerical experiments on synthetic and real-world network data to demonstrate\nthe efficacy of the proposed approach.\n", "date": "2023-03-14", "categories": []}
{"id": "2303.07757", "title": "Multiway clustering of 3-order tensor via affinity matrix", "abstract": "  We propose a new method of multiway clustering for 3-order tensors via\naffinity matrix (MCAM). Based on a notion of similarity between the tensor\nslices and the spread of information of each slice, our model builds an\naffinity/similarity matrix on which we apply advanced clustering methods. The\ncombination of all clusters of the three modes delivers the desired multiway\nclustering. Finally, MCAM achieves competitive results compared with other\nknown algorithms on synthetics and real datasets.\n", "date": "2023-03-14", "categories": []}
{"id": "2208.02998", "title": "Localized Sparse Incomplete Multi-view Clustering", "abstract": "  Incomplete multi-view clustering, which aims to solve the clustering problem\non the incomplete multi-view data with partial view missing, has received more\nand more attention in recent years. Although numerous methods have been\ndeveloped, most of the methods either cannot flexibly handle the incomplete\nmulti-view data with arbitrary missing views or do not consider the negative\nfactor of information imbalance among views. Moreover, some methods do not\nfully explore the local structure of all incomplete views. To tackle these\nproblems, this paper proposes a simple but effective method, named localized\nsparse incomplete multi-view clustering (LSIMVC). Different from the existing\nmethods, LSIMVC intends to learn a sparse and structured consensus latent\nrepresentation from the incomplete multi-view data by optimizing a sparse\nregularized and novel graph embedded multi-view matrix factorization model.\nSpecifically, in such a novel model based on the matrix factorization, a l1\nnorm based sparse constraint is introduced to obtain the sparse low-dimensional\nindividual representations and the sparse consensus representation. Moreover, a\nnovel local graph embedding term is introduced to learn the structured\nconsensus representation. Different from the existing works, our local graph\nembedding term aggregates the graph embedding task and consensus representation\nlearning task into a concise term. Furthermore, to reduce the imbalance factor\nof incomplete multi-view learning, an adaptive weighted learning scheme is\nintroduced to LSIMVC. Finally, an efficient optimization strategy is given to\nsolve the optimization problem of our proposed model. Comprehensive\nexperimental results performed on six incomplete multi-view databases verify\nthat the performance of our LSIMVC is superior to the state-of-the-art IMC\napproaches. The code is available in https://github.com/justsmart/LSIMVC.\n", "date": "2022-08-05", "categories": []}
{"id": "2210.11879", "title": "GLCC: A General Framework for Graph-Level Clustering", "abstract": "  This paper studies the problem of graph-level clustering, which is a novel\nyet challenging task. This problem is critical in a variety of real-world\napplications such as protein clustering and genome analysis in bioinformatics.\nRecent years have witnessed the success of deep clustering coupled with graph\nneural networks (GNNs). However, existing methods focus on clustering among\nnodes given a single graph, while exploring clustering on multiple graphs is\nstill under-explored. In this paper, we propose a general graph-level\nclustering framework named Graph-Level Contrastive Clustering (GLCC) given\nmultiple graphs. Specifically, GLCC first constructs an adaptive affinity graph\nto explore instance- and cluster-level contrastive learning (CL).\nInstance-level CL leverages graph Laplacian based contrastive loss to learn\nclustering-friendly representations while cluster-level CL captures\ndiscriminative cluster representations incorporating neighbor information of\neach sample. Moreover, we utilize neighbor-aware pseudo-labels to reward the\noptimization of representation learning. The two steps can be alternatively\ntrained to collaborate and benefit each other. Experiments on a range of\nwell-known datasets demonstrate the superiority of our proposed GLCC over\ncompetitive baselines.\n", "date": "2022-10-21", "categories": []}
{"id": "2303.03590", "title": "Research on Efficient Fuzzy Clustering Method Based on Local Fuzzy\n  Granular balls", "abstract": "  In recent years, the problem of fuzzy clustering has been widely concerned.\nThe membership iteration of existing methods is mostly considered globally,\nwhich has considerable problems in noisy environments, and iterative\ncalculations for clusters with a large number of different sample sizes are not\naccurate and efficient. In this paper, starting from the strategy of\nlarge-scale priority, the data is fuzzy iterated using granular-balls, and the\nmembership degree of data only considers the two granular-balls where it is\nlocated, thus improving the efficiency of iteration. The formed fuzzy\ngranular-balls set can use more processing methods in the face of different\ndata scenarios, which enhances the practicability of fuzzy clustering\ncalculations.\n", "date": "2023-03-07", "categories": []}
{"id": "2303.04154", "title": "Adaptive Weighted Multiview Kernel Matrix Factorization with its\n  application in Alzheimer's Disease Analysis -- A clustering Perspective", "abstract": "  Recent technology and equipment advancements provide with us opportunities to\nbetter analyze Alzheimer's disease (AD), where we could collect and employ the\ndata from different image and genetic modalities that may potentially enhance\nthe predictive performance. To perform better clustering in AD analysis, in\nthis paper we propose a novel model to leverage data from all different\nmodalities/views, which can learn the weights of each view adaptively.\nDifferent from previous vanilla Non-negative Matrix Factorization which assumes\ndata is linearly separable, we propose a simple yet efficient method based on\nkernel matrix factorization, which is not only able to deal with non-linear\ndata structure but also can achieve better prediction accuracy. Experimental\nresults on ADNI dataset demonstrate the effectiveness of our proposed method,\nwhich indicate promising prospects of kernel application in AD analysis.\n", "date": "2023-03-07", "categories": []}
{"id": "2303.04188", "title": "Clustering large 3D volumes: A sampling-based approach", "abstract": "  In many applications of X-ray computed tomography, an unsupervised\nsegmentation of the reconstructed 3D volumes forms an important step in the\nimage processing chain for further investigation of the digitized object.\nTherefore, the goal is to train a clustering algorithm on the volume, which\nproduces a voxelwise classification by assigning a cluster index to each voxel.\nHowever, clustering methods, e.g., K-Means, typically have an asymptotic\npolynomial runtime with respect to the dataset size, and thus, these techniques\nare rarely applicable to large volumes. In this work, we introduce a novel\nclustering technique based on random sampling, which allows for the voxelwise\nclassification of arbitrarily large volumes. The presented method conducts\nefficient linear passes over the data to extract a representative random sample\nof a fixed size on which the classifier can be trained. Then, a final linear\npass performs the segmentation and assigns a cluster index to each individual\nvoxel. Quantitative and qualitative evaluations show that excellent results can\nbe achieved even with a very small sample size. Consequently, the unsupervised\nsegmentation by means of clustering becomes feasible for arbitrarily large\nvolumes.\n", "date": "2023-03-07", "categories": []}
{"id": "2303.01983", "title": "Auto-weighted Multi-view Clustering for Large-scale Data", "abstract": "  Multi-view clustering has gained broad attention owing to its capacity to\nexploit complementary information across multiple data views. Although existing\nmethods demonstrate delightful clustering performance, most of them are of high\ntime complexity and cannot handle large-scale data. Matrix factorization-based\nmodels are a representative of solving this problem. However, they assume that\nthe views share a dimension-fixed consensus coefficient matrix and\nview-specific base matrices, limiting their representability. Moreover, a\nseries of large-scale algorithms that bear one or more hyperparameters are\nimpractical in real-world applications. To address the two issues, we propose\nan auto-weighted multi-view clustering (AWMVC) algorithm. Specifically, AWMVC\nfirst learns coefficient matrices from corresponding base matrices of different\ndimensions, then fuses them to obtain an optimal consensus matrix. By mapping\noriginal features into distinctive low-dimensional spaces, we can attain more\ncomprehensive knowledge, thus obtaining better clustering results. Moreover, we\ndesign a six-step alternative optimization algorithm proven to be convergent\ntheoretically. Also, AWMVC shows excellent performance on various benchmark\ndatasets compared with existing ones. The code of AWMVC is publicly available\nat https://github.com/wanxinhang/AAAI-2023-AWMVC.\n", "date": "2023-01-21", "categories": []}
{"id": "2210.17028", "title": "Improved Learning-augmented Algorithms for k-means and k-medians\n  Clustering", "abstract": "  We consider the problem of clustering in the learning-augmented setting,\nwhere we are given a data set in $d$-dimensional Euclidean space, and a label\nfor each data point given by an oracle indicating what subsets of points should\nbe clustered together. This setting captures situations where we have access to\nsome auxiliary information about the data set relevant for our clustering\nobjective, for instance the labels output by a neural network. Following prior\nwork, we assume that there are at most an $\\alpha \\in (0,c)$ for some $c<1$\nfraction of false positives and false negatives in each predicted cluster, in\nthe absence of which the labels would attain the optimal clustering cost\n$\\mathrm{OPT}$.\n  For a dataset of size $m$, we propose a deterministic $k$-means algorithm\nthat produces centers with improved bound on clustering cost compared to the\nprevious randomized algorithm while preserving the $O( d m \\log m)$ runtime.\nFurthermore, our algorithm works even when the predictions are not very\naccurate, i.e. our bound holds for $\\alpha$ up to $1/2$, an improvement over\n$\\alpha$ being at most $1/7$ in the previous work. For the $k$-medians problem\nwe improve upon prior work by achieving a biquadratic improvement in the\ndependence of the approximation factor on the accuracy parameter $\\alpha$ to\nget a cost of $(1+O(\\alpha))\\mathrm{OPT}$, while requiring essentially just\n$O(md \\log^3 m/\\alpha)$ runtime.\n", "date": "2022-10-31", "categories": []}
{"id": "2303.00002", "title": "Multi-view Semantic Consistency based Information Bottleneck for\n  Clustering", "abstract": "  Multi-view clustering can make use of multi-source information for\nunsupervised clustering. Most existing methods focus on learning a fused\nrepresentation matrix, while ignoring the influence of private information and\nnoise. To address this limitation, we introduce a novel Multi-view Semantic\nConsistency based Information Bottleneck for clustering (MSCIB). Specifically,\nMSCIB pursues semantic consistency to improve the learning process of\ninformation bottleneck for different views. It conducts the alignment operation\nof multiple views in the semantic space and jointly achieves the valuable\nconsistent information of multi-view data. In this way, the learned semantic\nconsistency from multi-view data can improve the information bottleneck to more\nexactly distinguish the consistent information and learn a unified feature\nrepresentation with more discriminative consistent information for clustering.\nExperiments on various types of multi-view datasets show that MSCIB achieves\nstate-of-the-art performance.\n", "date": "2023-02-28", "categories": []}
{"id": "2303.00522", "title": "Semi-Supervised Constrained Clustering: An In-Depth Overview, Ranked\n  Taxonomy and Future Research Directions", "abstract": "  Clustering is a well-known unsupervised machine learning approach capable of\nautomatically grouping discrete sets of instances with similar characteristics.\nConstrained clustering is a semi-supervised extension to this process that can\nbe used when expert knowledge is available to indicate constraints that can be\nexploited. Well-known examples of such constraints are must-link (indicating\nthat two instances belong to the same group) and cannot-link (two instances\ndefinitely do not belong together). The research area of constrained clustering\nhas grown significantly over the years with a large variety of new algorithms\nand more advanced types of constraints being proposed. However, no unifying\noverview is available to easily understand the wide variety of available\nmethods, constraints and benchmarks. To remedy this, this study presents\nin-detail the background of constrained clustering and provides a novel ranked\ntaxonomy of the types of constraints that can be used in constrained\nclustering. In addition, it focuses on the instance-level pairwise constraints,\nand gives an overview of its applications and its historical context. Finally,\nit presents a statistical analysis covering 307 constrained clustering methods,\ncategorizes them according to their features, and provides a ranking score\nindicating which methods have the most potential based on their popularity and\nvalidation quality. Finally, based upon this analysis, potential pitfalls and\nfuture research directions are provided.\n", "date": "2023-02-28", "categories": []}
{"id": "2302.14060", "title": "Semi-supervised Clustering with Two Types of Background Knowledge:\n  Fusing Pairwise Constraints and Monotonicity Constraints", "abstract": "  This study addresses the problem of performing clustering in the presence of\ntwo types of background knowledge: pairwise constraints and monotonicity\nconstraints. To achieve this, the formal framework to perform clustering under\nmonotonicity constraints is, firstly, defined, resulting in a specific distance\nmeasure. Pairwise constraints are integrated afterwards by designing an\nobjective function which combines the proposed distance measure and a pairwise\nconstraint-based penalty term, in order to fuse both types of information. This\nobjective function can be optimized with an EM optimization scheme. The\nproposed method serves as the first approach to the problem it addresses, as it\nis the first method designed to work with the two types of background knowledge\nmentioned above. Our proposal is tested in a variety of benchmark datasets and\nin a real-world case of study.\n", "date": "2023-02-25", "categories": []}
{"id": "2302.13165", "title": "A parameter-free graph reduction for spectral clustering and SpectralNet", "abstract": "  Graph-based clustering methods like spectral clustering and SpectralNet are\nvery efficient in detecting clusters of non-convex shapes. Unlike the popular\n$k$-means, graph-based clustering methods do not assume that each cluster has a\nsingle mean. However, these methods need a graph where vertices in the same\ncluster are connected by edges of large weights. To achieve this goal, many\nstudies have proposed graph reduction methods with parameters. Unfortunately,\nthese parameters have to be tuned for every dataset. We introduce a graph\nreduction method that does not require any parameters. First, the distances\nfrom every point $p$ to its neighbors are filtered using an adaptive threshold\nto only keep neighbors with similar surrounding density. Second, the\nsimilarities with close neighbors are computed and only high similarities are\nkept. The edges that survive these two filtering steps form the constructed\ngraph that was passed to spectral clustering and SpectralNet. The experiments\nshowed that our method provides a stable alternative, where other methods\nperformance fluctuated according to the setting of their parameters.\n", "date": "2023-02-25", "categories": []}
{"id": "2302.13168", "title": "Random projection tree similarity metric for SpectralNet", "abstract": "  SpectralNet is a graph clustering method that uses neural network to find an\nembedding that separates the data. So far it was only used with $k$-nn graphs,\nwhich are usually constructed using a distance metric (e.g., Euclidean\ndistance). $k$-nn graphs restrict the points to have a fixed number of\nneighbors regardless of the local statistics around them. We proposed a new\nSpectralNet similarity metric based on random projection trees (rpTrees). Our\nexperiments revealed that SpectralNet produces better clustering accuracy using\nrpTree similarity metric compared to $k$-nn graph with a distance metric. Also,\nwe found out that rpTree parameters do not affect the clustering accuracy.\nThese parameters include the leaf size and the selection of projection\ndirection. It is computationally efficient to keep the leaf size in order of\n$\\log(n)$, and project the points onto a random direction instead of trying to\nfind the direction with the maximum dispersion.\n", "date": "2023-02-25", "categories": []}
{"id": "2302.12619", "title": "T-Phenotype: Discovering Phenotypes of Predictive Temporal Patterns in\n  Disease Progression", "abstract": "  Clustering time-series data in healthcare is crucial for clinical phenotyping\nto understand patients' disease progression patterns and to design treatment\nguidelines tailored to homogeneous patient subgroups. While rich temporal\ndynamics enable the discovery of potential clusters beyond static correlations,\ntwo major challenges remain outstanding: i) discovery of predictive patterns\nfrom many potential temporal correlations in the multi-variate time-series data\nand ii) association of individual temporal patterns to the target label\ndistribution that best characterizes the underlying clinical progression. To\naddress such challenges, we develop a novel temporal clustering method,\nT-Phenotype, to discover phenotypes of predictive temporal patterns from\nlabeled time-series data. We introduce an efficient representation learning\napproach in frequency domain that can encode variable-length,\nirregularly-sampled time-series into a unified representation space, which is\nthen applied to identify various temporal patterns that potentially contribute\nto the target label using a new notion of path-based similarity. Throughout the\nexperiments on synthetic and real-world datasets, we show that T-Phenotype\nachieves the best phenotype discovery performance over all the evaluated\nbaselines. We further demonstrate the utility of T-Phenotype by uncovering\nclinically meaningful patient subgroups characterized by unique temporal\npatterns.\n", "date": "2023-02-24", "categories": []}
{"id": "2208.11907", "title": "Time Series Clustering with an EM algorithm for Mixtures of Linear\n  Gaussian State Space Models", "abstract": "  In this paper, we consider the task of clustering a set of individual time\nseries while modeling each cluster, that is, model-based time series\nclustering. The task requires a parametric model with sufficient flexibility to\ndescribe the dynamics in various time series. To address this problem, we\npropose a novel model-based time series clustering method with mixtures of\nlinear Gaussian state space models, which have high flexibility. The proposed\nmethod uses a new expectation-maximization algorithm for the mixture model to\nestimate the model parameters, and determines the number of clusters using the\nBayesian information criterion. Experiments on a simulated dataset demonstrate\nthe effectiveness of the method in clustering, parameter estimation, and model\nselection. The method is applied to real datasets commonly used to evaluate\ntime series clustering methods. Results showed that the proposed method\nproduces clustering results that are as accurate or more accurate than those\nobtained using previous methods.\n", "date": "2022-08-25", "categories": []}
{"id": "2302.11296", "title": "Refining a $k$-nearest neighbor graph for a computationally efficient\n  spectral clustering", "abstract": "  Spectral clustering became a popular choice for data clustering for its\nability of uncovering clusters of different shapes. However, it is not always\npreferable over other clustering methods due to its computational demands. One\nof the effective ways to bypass these computational demands is to perform\nspectral clustering on a subset of points (data representatives) then\ngeneralize the clustering outcome, this is known as approximate spectral\nclustering (ASC). ASC uses sampling or quantization to select data\nrepresentatives. This makes it vulnerable to 1) performance inconsistency\n(since these methods have a random step either in initialization or training),\n2) local statistics loss (because the pairwise similarities are extracted from\ndata representatives instead of data points). We proposed a refined version of\n$k$-nearest neighbor graph, in which we keep data points and aggressively\nreduce number of edges for computational efficiency. Local statistics were\nexploited to keep the edges that do not violate the intra-cluster distances and\nnullify all other edges in the $k$-nearest neighbor graph. We also introduced\nan optional step to automatically select the number of clusters $C$. The\nproposed method was tested on synthetic and real datasets. Compared to ASC\nmethods, the proposed method delivered a consistent performance despite\nsignificant reduction of edges.\n", "date": "2023-02-22", "categories": []}
{"id": "2302.11297", "title": "Approximate spectral clustering with eigenvector selection and\n  self-tuned $k$", "abstract": "  The recently emerged spectral clustering surpasses conventional clustering\nmethods by detecting clusters of any shape without the convexity assumption.\nUnfortunately, with a computational complexity of $O(n^3)$, it was infeasible\nfor multiple real applications, where $n$ could be large. This stimulates\nresearchers to propose the approximate spectral clustering (ASC). However, most\nof ASC methods assumed that the number of clusters $k$ was known. In practice,\nmanual setting of $k$ could be subjective or time consuming. The proposed\nalgorithm has two relevance metrics for estimating $k$ in two vital steps of\nASC. One for selecting the eigenvectors spanning the embedding space, and the\nother to discover the number of clusters in that space. The algorithm used a\ngrowing neural gas (GNG) approximation, GNG is superior in preserving input\ndata topology. The experimental setup demonstrates the efficiency of the\nproposed algorithm and its ability to compete with similar methods where $k$\nwas set manually.\n", "date": "2023-02-22", "categories": []}
{"id": "2302.11298", "title": "Approximate spectral clustering density-based similarity for noisy\n  datasets", "abstract": "  Approximate spectral clustering (ASC) was developed to overcome heavy\ncomputational demands of spectral clustering (SC). It maintains SC ability in\npredicting non-convex clusters. Since it involves a preprocessing step, ASC\ndefines new similarity measures to assign weights on graph edges. Connectivity\nmatrix (CONN) is an efficient similarity measure to construct graphs for ASC.\nIt defines the weight between two vertices as the number of points assigned to\nthem during vector quantization training. However, this relationship is\nundirected, where it is not clear which of the vertices is contributing more to\nthat edge. Also, CONN could be tricked by noisy density between clusters. We\ndefined a directed version of CONN, named DCONN, to get insights on vertices\ncontributions to edges. Also, we provided filtering schemes to ensure CONN\nedges are highlighting potential clusters. Experiments reveal that the proposed\nfiltering was highly efficient when noise cannot be tolerated by CONN.\n", "date": "2023-02-22", "categories": []}
{"id": "2208.14450", "title": "Dual Representation Learning for One-Step Clustering of Multi-View Data", "abstract": "  Multi-view data are commonly encountered in data mining applications.\nEffective extraction of information from multi-view data requires specific\ndesign of clustering methods to cater for data with multiple views, which is\nnon-trivial and challenging. In this paper, we propose a novel one-step\nmulti-view clustering method by exploiting the dual representation of both the\ncommon and specific information of different views. The motivation originates\nfrom the rationale that multi-view data contain not only the consistent\nknowledge between views but also the unique knowledge of each view. Meanwhile,\nto make the representation learning more specific to the clustering task, a\none-step learning framework is proposed to integrate representation learning\nand clustering partition as a whole. With this framework, the representation\nlearning and clustering partition mutually benefit each other, which\neffectively improve the clustering performance. Results from extensive\nexperiments conducted on benchmark multi-view datasets clearly demonstrate the\nsuperiority of the proposed method.\n", "date": "2022-08-30", "categories": []}
{"id": "2210.01953", "title": "Robust Fair Clustering: A Novel Fairness Attack and Defense Framework", "abstract": "  Clustering algorithms are widely used in many societal resource allocation\napplications, such as loan approvals and candidate recruitment, among others,\nand hence, biased or unfair model outputs can adversely impact individuals that\nrely on these applications. To this end, many fair clustering approaches have\nbeen recently proposed to counteract this issue. Due to the potential for\nsignificant harm, it is essential to ensure that fair clustering algorithms\nprovide consistently fair outputs even under adversarial influence. However,\nfair clustering algorithms have not been studied from an adversarial attack\nperspective. In contrast to previous research, we seek to bridge this gap and\nconduct a robustness analysis against fair clustering by proposing a novel\nblack-box fairness attack. Through comprehensive experiments, we find that\nstate-of-the-art models are highly susceptible to our attack as it can reduce\ntheir fairness performance significantly. Finally, we propose Consensus Fair\nClustering (CFC), the first robust fair clustering approach that transforms\nconsensus clustering into a fair graph partitioning problem, and iteratively\nlearns to generate fair cluster outputs. Experimentally, we observe that CFC is\nhighly robust to the proposed attack and is thus a truly robust fair clustering\nalternative.\n", "date": "2022-10-04", "categories": []}
{"id": "2210.07063", "title": "Deep Clustering With Consensus Representations", "abstract": "  The field of deep clustering combines deep learning and clustering to learn\nrepresentations that improve both the learned representation and the\nperformance of the considered clustering method. Most existing deep clustering\nmethods are designed for a single clustering method, e.g., k-means, spectral\nclustering, or Gaussian mixture models, but it is well known that no clustering\nalgorithm works best in all circumstances. Consensus clustering tries to\nalleviate the individual weaknesses of clustering algorithms by building a\nconsensus between members of a clustering ensemble. Currently, there is no deep\nclustering method that can include multiple heterogeneous clustering algorithms\nin an ensemble to update representations and clusterings together. To close\nthis gap, we introduce the idea of a consensus representation that maximizes\nthe agreement between ensemble members. Further, we propose DECCS (Deep\nEmbedded Clustering with Consensus representationS), a deep consensus\nclustering method that learns a consensus representation by enhancing the\nembedded space to such a degree that all ensemble members agree on a common\nclustering result. Our contributions are the following: (1) We introduce the\nidea of learning consensus representations for heterogeneous clusterings, a\nnovel notion to approach consensus clustering. (2) We propose DECCS, the first\ndeep clustering method that jointly improves the representation and clustering\nresults of multiple heterogeneous clustering algorithms. (3) We show in\nexperiments that learning a consensus representation with DECCS is\noutperforming several relevant baselines from deep clustering and consensus\nclustering. Our code can be found at https://gitlab.cs.univie.ac.at/lukas/deccs\n", "date": "2022-10-13", "categories": []}
{"id": "2302.10765", "title": "Hybridization of K-means with improved firefly algorithm for automatic\n  clustering in high dimension", "abstract": "  K-means Clustering is the most well-known partitioning algorithm among all\nclustering, by which we can partition the data objects very easily in to more\nthan one clusters. However, for K-means to choose an appropriate number of\nclusters without any prior domain knowledge about the dataset is challenging,\nespecially in high-dimensional data objects. Hence, we have implemented the\nSilhouette and Elbow methods with PCA to find an optimal number of clusters.\nAlso, previously, so many meta-heuristic swarm intelligence algorithms inspired\nby nature have been employed to handle the automatic data clustering problem.\nFirefly is efficient and robust for automatic clustering. However, in the\nFirefly algorithm, the entire population is automatically subdivided into\nsub-populations that decrease the convergence rate speed and trapping to local\nminima in high-dimensional optimization problems. Thus, our study proposed an\nenhanced firefly, i.e., a hybridized K-means with an ODFA model for automatic\nclustering. The experimental part shows output and graphs of the Silhouette and\nElbow methods as well as the Firefly algorithm\n", "date": "2023-02-09", "categories": []}
{"id": "2302.07045", "title": "Multi-Prototypes Convex Merging Based K-Means Clustering Algorithm", "abstract": "  K-Means algorithm is a popular clustering method. However, it has two\nlimitations: 1) it gets stuck easily in spurious local minima, and 2) the\nnumber of clusters k has to be given a priori. To solve these two issues, a\nmulti-prototypes convex merging based K-Means clustering algorithm (MCKM) is\npresented. First, based on the structure of the spurious local minima of the\nK-Means problem, a multi-prototypes sampling (MPS) is designed to select the\nappropriate number of multi-prototypes for data with arbitrary shapes. A\ntheoretical proof is given to guarantee that the multi-prototypes selected by\nMPS can achieve a constant factor approximation to the optimal cost of the\nK-Means problem. Then, a merging technique, called convex merging (CM), merges\nthe multi-prototypes to get a better local minima without k being given a\npriori. Specifically, CM can obtain the optimal merging and estimate the\ncorrect k. By integrating these two techniques with K-Means algorithm, the\nproposed MCKM is an efficient and explainable clustering algorithm for escaping\nthe undesirable local minima of K-Means problem without given k first.\nExperimental results performed on synthetic and real-world data sets have\nverified the effectiveness of the proposed algorithm.\n", "date": "2023-02-14", "categories": []}
{"id": "2302.07060", "title": "Accelerated Fuzzy C-Means Clustering Based on New Affinity Filtering and\n  Membership Scaling", "abstract": "  Fuzzy C-Means (FCM) is a widely used clustering method. However, FCM and its\nmany accelerated variants have low efficiency in the mid-to-late stage of the\nclustering process. In this stage, all samples are involved in the update of\ntheir non-affinity centers, and the fuzzy membership grades of the most of\nsamples, whose assignment is unchanged, are still updated by calculating the\nsamples-centers distances. All those lead to the algorithms converging slowly.\nIn this paper, a new affinity filtering technique is developed to recognize a\ncomplete set of the non-affinity centers for each sample with low computations.\nThen, a new membership scaling technique is suggested to set the membership\ngrades between each sample and its non-affinity centers to 0 and maintain the\nfuzzy membership grades for others. By integrating those two techniques, FCM\nbased on new affinity filtering and membership scaling (AMFCM) is proposed to\naccelerate the whole convergence process of FCM. Many experimental results\nperformed on synthetic and real-world data sets have shown the feasibility and\nefficiency of the proposed algorithm. Compared with the state-of-the-art\nalgorithms, AMFCM is significantly faster and more effective. For example,\nAMFCM reduces the number of the iteration of FCM by 80% on average.\n", "date": "2023-02-14", "categories": []}
{"id": "2302.05788", "title": "Fairness-aware Multi-view Clustering", "abstract": "  In the era of big data, we are often facing the challenge of data\nheterogeneity and the lack of label information simultaneously. In the\nfinancial domain (e.g., fraud detection), the heterogeneous data may include\nnot only numerical data (e.g., total debt and yearly income), but also text and\nimages (e.g., financial statement and invoice images). At the same time, the\nlabel information (e.g., fraud transactions) may be missing for building\npredictive models. To address these challenges, many state-of-the-art\nmulti-view clustering methods have been proposed and achieved outstanding\nperformance. However, these methods typically do not take into consideration\nthe fairness aspect and are likely to generate biased results using sensitive\ninformation such as race and gender. Therefore, in this paper, we propose a\nfairness-aware multi-view clustering method named FairMVC. It incorporates the\ngroup fairness constraint into the soft membership assignment for each cluster\nto ensure that the fraction of different groups in each cluster is\napproximately identical to the entire data set. Meanwhile, we adopt the idea of\nboth contrastive learning and non-contrastive learning and propose novel\nregularizers to handle heterogeneous data in complex scenarios with missing\ndata or noisy features. Experimental results on real-world data sets\ndemonstrate the effectiveness and efficiency of the proposed framework. We also\nderive insights regarding the relative performance of the proposed regularizers\nin various scenarios.\n", "date": "2023-02-11", "categories": []}
{"id": "2302.03151", "title": "Fair Minimum Representation Clustering", "abstract": "  Clustering is an unsupervised learning task that aims to partition data into\na set of clusters. In many applications, these clusters correspond to\nreal-world constructs (e.g. electoral districts) whose benefit can only be\nattained by groups when they reach a minimum level of representation (e.g. 50\\%\nto elect their desired candidate). This paper considers the problem of\nperforming k-means clustering while ensuring groups (e.g. demographic groups)\nhave that minimum level of representation in a specified number of clusters. We\nshow that the popular $k$-means algorithm, Lloyd's algorithm, can result in\nunfair outcomes where certain groups lack sufficient representation past the\nminimum threshold in a proportional number of clusters. We formulate the\nproblem through a mixed-integer optimization framework and present a variant of\nLloyd's algorithm, called MiniReL, that directly incorporates the fairness\nconstraints. We show that incorporating the fairness criteria leads to a\nNP-Hard sub-problem within Lloyd's algorithm, but we provide computational\napproaches that make the problem tractable for even large datasets. Numerical\nresults show that the approach is able to create fairer clusters with\npractically no increase in the k-means clustering cost across standard\nbenchmark datasets.\n", "date": "2023-02-06", "categories": []}
{"id": "2302.03136", "title": "Learned Accelerator Framework for Angular-Distance-Based\n  High-Dimensional DBSCAN", "abstract": "  Density-based clustering is a commonly used tool in data science. Today many\ndata science works are utilizing high-dimensional neural embeddings. However,\ntraditional density-based clustering techniques like DBSCAN have a degraded\nperformance on high-dimensional data. In this paper, we propose LAF, a generic\nlearned accelerator framework to speed up the original DBSCAN and the\nsampling-based variants of DBSCAN on high-dimensional data with angular\ndistance metric. This framework consists of a learned cardinality estimator and\na post-processing module. The cardinality estimator can fast predict whether a\ndata point is core or not to skip unnecessary range queries, while the\npost-processing module detects the false negative predictions and merges the\nfalsely separated clusters. The evaluation shows our LAF-enhanced DBSCAN method\noutperforms the state-of-the-art efficient DBSCAN variants on both efficiency\nand quality.\n", "date": "2023-02-06", "categories": []}
{"id": "2302.02369", "title": "Deep Graph-Level Clustering Using Pseudo-Label-Guided Mutual Information\n  Maximization Network", "abstract": "  In this work, we study the problem of partitioning a set of graphs into\ndifferent groups such that the graphs in the same group are similar while the\ngraphs in different groups are dissimilar. This problem was rarely studied\npreviously, although there have been a lot of work on node clustering and graph\nclassification. The problem is challenging because it is difficult to measure\nthe similarity or distance between graphs. One feasible approach is using graph\nkernels to compute a similarity matrix for the graphs and then performing\nspectral clustering, but the effectiveness of existing graph kernels in\nmeasuring the similarity between graphs is very limited. To solve the problem,\nwe propose a novel method called Deep Graph-Level Clustering (DGLC). DGLC\nutilizes a graph isomorphism network to learn graph-level representations by\nmaximizing the mutual information between the representations of entire graphs\nand substructures, under the regularization of a clustering module that ensures\ndiscriminative representations via pseudo labels. DGLC achieves graph-level\nrepresentation learning and graph-level clustering in an end-to-end manner. The\nexperimental results on six benchmark datasets of graphs show that our DGLC has\nstate-of-the-art performance in comparison to many baselines.\n", "date": "2023-02-05", "categories": []}
{"id": "2302.01569", "title": "Uniform tensor clustering by jointly exploring sample affinities of\n  various orders", "abstract": "  Conventional clustering methods based on pairwise affinity usually suffer\nfrom the concentration effect while processing huge dimensional features yet\nlow sample sizes data, resulting in inaccuracy to encode the sample proximity\nand suboptimal performance in clustering. To address this issue, we propose a\nunified tensor clustering method (UTC) that characterizes sample proximity\nusing multiple samples' affinity, thereby supplementing rich spatial sample\ndistributions to boost clustering. Specifically, we find that the triadic\ntensor affinity can be constructed via the Khari-Rao product of two affinity\nmatrices. Furthermore, our early work shows that the fourth-order tensor\naffinity is defined by the Kronecker product. Therefore, we utilize\narithmetical products, Khatri-Rao and Kronecker products, to mathematically\nintegrate different orders of affinity into a unified tensor clustering\nframework. Thus, the UTC jointly learns a joint low-dimensional embedding to\ncombine various orders. Finally, a numerical scheme is designed to solve the\nproblem. Experiments on synthetic datasets and real-world datasets demonstrate\nthat 1) the usage of high-order tensor affinity could provide a supplementary\ncharacterization of sample proximity to the popular affinity matrix; 2) the\nproposed method of UTC is affirmed to enhance clustering by exploiting\ndifferent order affinities when processing high-dimensional data.\n", "date": "2023-02-03", "categories": []}
{"id": "2302.00192", "title": "Density peak clustering using tensor network", "abstract": "  Tensor networks, which have been traditionally used to simulate many-body\nphysics, have recently gained significant attention in the field of machine\nlearning due to their powerful representation capabilities. In this work, we\npropose a density-based clustering algorithm inspired by tensor networks. We\nencode classical data into tensor network states on an extended Hilbert space\nand train the tensor network states to capture the features of the clusters.\nHere, we define density and related concepts in terms of fidelity, rather than\nusing a classical distance measure. We evaluate the performance of our\nalgorithm on six synthetic data sets, four real world data sets, and three\ncommonly used computer vision data sets. The results demonstrate that our\nmethod provides state-of-the-art performance on several synthetic data sets and\nreal world data sets, even when the number of clusters is unknown.\nAdditionally, our algorithm performs competitively with state-of-the-art\nalgorithms on the MNIST, USPS, and Fashion-MNIST image data sets. These\nfindings reveal the great potential of tensor networks for machine learning\napplications.\n", "date": "2023-02-01", "categories": []}
{"id": "2212.08665", "title": "Hard Sample Aware Network for Contrastive Deep Graph Clustering", "abstract": "  Contrastive deep graph clustering, which aims to divide nodes into disjoint\ngroups via contrastive mechanisms, is a challenging research spot. Among the\nrecent works, hard sample mining-based algorithms have achieved great attention\nfor their promising performance. However, we find that the existing hard sample\nmining methods have two problems as follows. 1) In the hardness measurement,\nthe important structural information is overlooked for similarity calculation,\ndegrading the representativeness of the selected hard negative samples. 2)\nPrevious works merely focus on the hard negative sample pairs while neglecting\nthe hard positive sample pairs. Nevertheless, samples within the same cluster\nbut with low similarity should also be carefully learned. To solve the\nproblems, we propose a novel contrastive deep graph clustering method dubbed\nHard Sample Aware Network (HSAN) by introducing a comprehensive similarity\nmeasure criterion and a general dynamic sample weighing strategy. Concretely,\nin our algorithm, the similarities between samples are calculated by\nconsidering both the attribute embeddings and the structure embeddings, better\nrevealing sample relationships and assisting hardness measurement. Moreover,\nunder the guidance of the carefully collected high-confidence clustering\ninformation, our proposed weight modulating function will first recognize the\npositive and negative samples and then dynamically up-weight the hard sample\npairs while down-weighting the easy ones. In this way, our method can mine not\nonly the hard negative samples but also the hard positive sample, thus\nimproving the discriminative capability of the samples further. Extensive\nexperiments and analyses demonstrate the superiority and effectiveness of our\nproposed method.\n", "date": "2022-12-16", "categories": []}
{"id": "2301.11045", "title": "Incomplete Multi-view Clustering via Prototype-based Imputation", "abstract": "  In this paper, we study how to achieve two characteristics highly-expected by\nincomplete multi-view clustering (IMvC). Namely, i) instance commonality refers\nto that within-cluster instances should share a common pattern, and ii) view\nversatility refers to that cross-view samples should own view-specific\npatterns. To this end, we design a novel dual-stream model which employs a dual\nattention layer and a dual contrastive learning loss to learn view-specific\nprototypes and model the sample-prototype relationship. When the view is\nmissed, our model performs data recovery using the prototypes in the missing\nview and the sample-prototype relationship inherited from the observed view.\nThanks to our dual-stream model, both cluster- and view-specific information\ncould be captured, and thus the instance commonality and view versatility could\nbe preserved to facilitate IMvC. Extensive experiments demonstrate the\nsuperiority of our method on six challenging benchmarks compared with 11\napproaches. The code will be released.\n", "date": "2023-01-26", "categories": []}
{"id": "2301.10772", "title": "Gene-SGAN: a method for discovering disease subtypes with imaging and\n  genetic signatures via multi-view weakly-supervised deep clustering", "abstract": "  Disease heterogeneity has been a critical challenge for precision diagnosis\nand treatment, especially in neurologic and neuropsychiatric diseases. Many\ndiseases can display multiple distinct brain phenotypes across individuals,\npotentially reflecting disease subtypes that can be captured using MRI and\nmachine learning methods. However, biological interpretability and treatment\nrelevance are limited if the derived subtypes are not associated with genetic\ndrivers or susceptibility factors. Herein, we describe Gene-SGAN - a\nmulti-view, weakly-supervised deep clustering method - which dissects disease\nheterogeneity by jointly considering phenotypic and genetic data, thereby\nconferring genetic correlations to the disease subtypes and associated\nendophenotypic signatures. We first validate the generalizability,\ninterpretability, and robustness of Gene-SGAN in semi-synthetic experiments. We\nthen demonstrate its application to real multi-site datasets from 28,858\nindividuals, deriving subtypes of Alzheimer's disease and brain endophenotypes\nassociated with hypertension, from MRI and SNP data. Derived brain phenotypes\ndisplayed significant differences in neuroanatomical patterns, genetic\ndeterminants, biological and clinical biomarkers, indicating potentially\ndistinct underlying neuropathologic processes, genetic drivers, and\nsusceptibility factors. Overall, Gene-SGAN is broadly applicable to disease\nsubtyping and endophenotype discovery, and is herein tested on disease-related,\ngenetically-driven neuroimaging phenotypes.\n", "date": "2023-01-25", "categories": []}
{"id": "2301.10901", "title": "Re-embedding data to strengthen recovery guarantees of clustering", "abstract": "  We propose a clustering method that involves chaining four known techniques\ninto a pipeline yielding an algorithm with stronger recovery guarantees than\nany of the four components separately. Given $n$ points in $\\mathbb R^d$, the\nfirst component of our pipeline, which we call leapfrog distances, is\nreminiscent of density-based clustering, yielding an $n\\times n$ distance\nmatrix. The leapfrog distances are then translated to new embeddings using\nmultidimensional scaling and spectral methods, two other known techniques,\nyielding new embeddings of the $n$ points in $\\mathbb R^{d'}$, where $d'$\nsatisfies $d'\\ll d$ in general. Finally, sum-of-norms (SON) clustering is\napplied to the re-embedded points. Although the fourth step (SON clustering)\ncan in principle be replaced by any other clustering method, our focus is on\nprovable guarantees of recovery of underlying structure. Therefore, we\nestablish that the re-embedding improves recovery SON clustering, since SON\nclustering is a well-studied method that already has provable guarantees.\n", "date": "2023-01-26", "categories": []}
{"id": "2207.09728", "title": "Revisiting data augmentation for subspace clustering", "abstract": "  Subspace clustering is the classical problem of clustering a collection of\ndata samples that approximately lie around several low-dimensional subspaces.\nThe current state-of-the-art approaches for this problem are based on the\nself-expressive model which represents the samples as linear combination of\nother samples. However, these approaches require sufficiently well-spread\nsamples for accurate representation which might not be necessarily accessible\nin many applications. In this paper, we shed light on this commonly neglected\nissue and argue that data distribution within each subspace plays a critical\nrole in the success of self-expressive models. Our proposed solution to tackle\nthis issue is motivated by the central role of data augmentation in the\ngeneralization power of deep neural networks. We propose two subspace\nclustering frameworks for both unsupervised and semi-supervised settings that\nuse augmented samples as an enlarged dictionary to improve the quality of the\nself-expressive representation. We present an automatic augmentation strategy\nusing a few labeled samples for the semi-supervised problem relying on the fact\nthat the data samples lie in the union of multiple linear subspaces.\nExperimental results confirm the effectiveness of data augmentation, as it\nsignificantly improves the performance of general self-expressive models.\n", "date": "2022-07-20", "categories": []}
{"id": "2212.14111", "title": "Effectiveness of Deep Image Embedding Clustering Methods on Tabular Data", "abstract": "  Deep learning methods in the literature are commonly benchmarked on image\ndata sets, which may not be suitable or effective baselines for non-image\ntabular data. In this paper, we take a data-centric view to perform one of the\nfirst studies on deep embedding clustering of tabular data. Eight clustering\nand state-of-the-art embedding clustering methods proposed for image data sets\nare tested on seven tabular data sets. Our results reveal that a traditional\nclustering method ranks second out of eight methods and is superior to most\ndeep embedding clustering baselines. Our observation aligns with the literature\nthat conventional machine learning of tabular data is still a robust approach\nagainst deep learning. Therefore, state-of-the-art embedding clustering methods\nshould consider data-centric customization of learning architectures to become\ncompetitive baselines for tabular data.\n", "date": "2022-12-28", "categories": []}
{"id": "2301.04451", "title": "Heterogeneous Tri-stream Clustering Network", "abstract": "  Contrastive deep clustering has recently gained significant attention with\nits ability of joint contrastive learning and clustering via deep neural\nnetworks. Despite the rapid progress, previous works mostly require both\npositive and negative sample pairs for contrastive clustering, which rely on a\nrelative large batch-size. Moreover, they typically adopt a two-stream\narchitecture with two augmented views, which overlook the possibility and\npotential benefits of multi-stream architectures (especially with heterogeneous\nor hybrid networks). In light of this, this paper presents a new end-to-end\ndeep clustering approach termed Heterogeneous Tri-stream Clustering Network\n(HTCN). The tri-stream architecture in HTCN consists of three main components,\nincluding two weight-sharing online networks and a target network, where the\nparameters of the target network are the exponential moving average of that of\nthe online networks. Notably, the two online networks are trained by\nsimultaneously (i) predicting the instance representations of the target\nnetwork and (ii) enforcing the consistency between the cluster representations\nof the target network and that of the two online networks. Experimental results\non four challenging image datasets demonstrate the superiority of HTCN over the\nstate-of-the-art deep clustering approaches. The code is available at\nhttps://github.com/dengxiaozhi/HTCN.\n", "date": "2023-01-11", "categories": []}
{"id": "2301.02814", "title": "Randomized Greedy Algorithms and Composable Coreset for k-Center\n  Clustering with Outliers", "abstract": "  In this paper, we study the problem of {\\em $k$-center clustering with\noutliers}. The problem has many important applications in real world, but the\npresence of outliers can significantly increase the computational complexity.\nThough a number of methods have been developed in the past decades, it is still\nquite challenging to design quality guaranteed algorithm with low complexity\nfor this problem. Our idea is inspired by the greedy method, Gonzalez's\nalgorithm, that was developed for solving the ordinary $k$-center clustering\nproblem. Based on some novel observations, we show that a simple randomized\nversion of this greedy strategy actually can handle outliers efficiently. We\nfurther show that this randomized greedy approach also yields small coreset for\nthe problem in doubling metrics (even if the doubling dimension is not given),\nwhich can greatly reduce the computational complexity. Moreover, together with\nthe partial clustering framework proposed in arXiv:1703.01539 , we prove that\nour coreset method can be applied to distributed data with a low communication\ncomplexity. The experimental results suggest that our algorithms can achieve\nnear optimal solutions and yield lower complexities comparing with the existing\nmethods.\n", "date": "2023-01-07", "categories": []}
{"id": "2301.02896", "title": "k-Means SubClustering: A Differentially Private Algorithm with Improved\n  Clustering Quality", "abstract": "  In today's data-driven world, the sensitivity of information has been a\nsignificant concern. With this data and additional information on the person's\nbackground, one can easily infer an individual's private data. Many\ndifferentially private iterative algorithms have been proposed in interactive\nsettings to protect an individual's privacy from these inference attacks. The\nexisting approaches adapt the method to compute differentially private(DP)\ncentroids by iterative Llyod's algorithm and perturbing the centroid with\nvarious DP mechanisms. These DP mechanisms do not guarantee convergence of\ndifferentially private iterative algorithms and degrade the quality of the\ncluster. Thus, in this work, we further extend the previous work on\n'Differentially Private k-Means Clustering With Convergence Guarantee' by\ntaking it as our baseline. The novelty of our approach is to sub-cluster the\nclusters and then select the centroid which has a higher probability of moving\nin the direction of the future centroid. At every Lloyd's step, the centroids\nare injected with the noise using the exponential DP mechanism. The results of\nthe experiments indicate that our approach outperforms the current\nstate-of-the-art method, i.e., the baseline algorithm, in terms of clustering\nquality while maintaining the same differential privacy requirements. The\nclustering quality significantly improved by 4.13 and 2.83 times than baseline\nfor the Wine and Breast_Cancer dataset, respectively.\n", "date": "2023-01-07", "categories": []}
{"id": "2301.02484", "title": "Graph-Collaborated Auto-Encoder Hashing for Multi-view Binary Clustering", "abstract": "  Unsupervised hashing methods have attracted widespread attention with the\nexplosive growth of large-scale data, which can greatly reduce storage and\ncomputation by learning compact binary codes. Existing unsupervised hashing\nmethods attempt to exploit the valuable information from samples, which fails\nto take the local geometric structure of unlabeled samples into consideration.\nMoreover, hashing based on auto-encoders aims to minimize the reconstruction\nloss between the input data and binary codes, which ignores the potential\nconsistency and complementarity of multiple sources data. To address the above\nissues, we propose a hashing algorithm based on auto-encoders for multi-view\nbinary clustering, which dynamically learns affinity graphs with low-rank\nconstraints and adopts collaboratively learning between auto-encoders and\naffinity graphs to learn a unified binary code, called Graph-Collaborated\nAuto-Encoder Hashing for Multi-view Binary Clustering (GCAE). Specifically, we\npropose a multi-view affinity graphs learning model with low-rank constraint,\nwhich can mine the underlying geometric information from multi-view data. Then,\nwe design an encoder-decoder paradigm to collaborate the multiple affinity\ngraphs, which can learn a unified binary code effectively. Notably, we impose\nthe decorrelation and code balance constraints on binary codes to reduce the\nquantization errors. Finally, we utilize an alternating iterative optimization\nscheme to obtain the multi-view clustering results. Extensive experimental\nresults on $5$ public datasets are provided to reveal the effectiveness of the\nalgorithm and its superior performance over other state-of-the-art\nalternatives.\n", "date": "2023-01-06", "categories": []}
{"id": "2301.00344", "title": "Semidefinite programming on population clustering: a global analysis", "abstract": "  In this paper, we consider the problem of partitioning a small data sample of\nsize $n$ drawn from a mixture of $2$ sub-gaussian distributions. Our work is\nmotivated by the application of clustering individuals according to their\npopulation of origin using markers, when the divergence between the two\npopulations is small. We are interested in the case that individual features\nare of low average quality $\\gamma$, and we want to use as few of them as\npossible to correctly partition the sample. We consider semidefinite relaxation\nof an integer quadratic program which is formulated essentially as finding the\nmaximum cut on a graph where edge weights in the cut represent dissimilarity\nscores between two nodes based on their features. A small simulation result in\nBlum, Coja-Oghlan, Frieze and Zhou (2007, 2009) shows that even when the sample\nsize $n$ is small, by increasing $p$ so that $np= \\Omega(1/\\gamma^2)$, one can\nclassify a mixture of two product populations using the spectral method therein\nwith success rate reaching an ``oracle'' curve. There the ``oracle'' was\ncomputed assuming that distributions were known, where success rate means the\nratio between correctly classified individuals and the sample size $n$. In this\nwork, we show the theoretical underpinning of this observed concentration of\nmeasure phenomenon in high dimensions, simultaneously for the semidefinite\noptimization goal and the spectral method, where the input is based on the gram\nmatrix computed from centered data. We allow a full range of tradeoffs between\nthe sample size and the number of features such that the product of these two\nis lower bounded by $1/{\\gamma^2}$ so long as the number of features $p$ is\nlower bounded by $1/\\gamma$.\n", "date": "2023-01-01", "categories": []}
{"id": "2301.01098", "title": "Cluster-guided Contrastive Graph Clustering Network", "abstract": "  Benefiting from the intrinsic supervision information exploitation\ncapability, contrastive learning has achieved promising performance in the\nfield of deep graph clustering recently. However, we observe that two drawbacks\nof the positive and negative sample construction mechanisms limit the\nperformance of existing algorithms from further improvement. 1) The quality of\npositive samples heavily depends on the carefully designed data augmentations,\nwhile inappropriate data augmentations would easily lead to the semantic drift\nand indiscriminative positive samples. 2) The constructed negative samples are\nnot reliable for ignoring important clustering information. To solve these\nproblems, we propose a Cluster-guided Contrastive deep Graph Clustering network\n(CCGC) by mining the intrinsic supervision information in the high-confidence\nclustering results. Specifically, instead of conducting complex node or edge\nperturbation, we construct two views of the graph by designing special Siamese\nencoders whose weights are not shared between the sibling sub-networks. Then,\nguided by the high-confidence clustering information, we carefully select and\nconstruct the positive samples from the same high-confidence cluster in two\nviews. Moreover, to construct semantic meaningful negative sample pairs, we\nregard the centers of different high-confidence clusters as negative samples,\nthus improving the discriminative capability and reliability of the constructed\nsample pairs. Lastly, we design an objective function to pull close the samples\nfrom the same cluster while pushing away those from other clusters by\nmaximizing and minimizing the cross-view cosine similarity between positive and\nnegative samples. Extensive experimental results on six datasets demonstrate\nthe effectiveness of CCGC compared with the existing state-of-the-art\nalgorithms.\n", "date": "2023-01-03", "categories": []}
{"id": "2301.00717", "title": "Robust Consensus Clustering and its Applications for Advertising\n  Forecasting", "abstract": "  Consensus clustering aggregates partitions in order to find a better fit by\nreconciling clustering results from different sources/executions. In practice,\nthere exist noise and outliers in clustering task, which, however, may\nsignificantly degrade the performance. To address this issue, we propose a\nnovel algorithm -- robust consensus clustering that can find common ground\ntruth among experts' opinions, which tends to be minimally affected by the bias\ncaused by the outliers. In particular, we formalize the robust consensus\nclustering problem as a constraint optimization problem, and then derive an\neffective algorithm upon alternating direction method of multipliers (ADMM)\nwith rigorous convergence guarantee. Our method outperforms the baselines on\nbenchmarks. We apply the proposed method to the real-world advertising campaign\nsegmentation and forecasting tasks using the proposed consensus clustering\nresults based on the similarity computed via Kolmogorov-Smirnov Statistics. The\naccurate clustering result is helpful for building the advertiser profiles so\nas to perform the forecasting.\n", "date": "2022-12-27", "categories": []}
{"id": "2212.14334", "title": "Constant Approximation for Normalized Modularity and Associations\n  Clustering", "abstract": "  We study the problem of graph clustering under a broad class of objectives in\nwhich the quality of a cluster is defined based on the ratio between the number\nof edges in the cluster, and the total weight of vertices in the cluster. We\nshow that our definition is closely related to popular clustering measures,\nnamely normalized associations, which is a dual of the normalized cut\nobjective, and normalized modularity. We give a linear time\nconstant-approximate algorithm for our objective, which implies the first\nconstant-factor approximation algorithms for normalized modularity and\nnormalized associations.\n", "date": "2022-12-29", "categories": []}
{"id": "2212.14345", "title": "On Learning the Structure of Clusters in Graphs", "abstract": "  Graph clustering is a fundamental problem in unsupervised learning, with\nnumerous applications in computer science and in analysing real-world data. In\nmany real-world applications, we find that the clusters have a significant\nhigh-level structure. This is often overlooked in the design and analysis of\ngraph clustering algorithms which make strong simplifying assumptions about the\nstructure of the graph. This thesis addresses the natural question of whether\nthe structure of clusters can be learned efficiently and describes four new\nalgorithmic results for learning such structure in graphs and hypergraphs.\n  All of the presented theoretical results are extensively evaluated on both\nsynthetic and real-word datasets of different domains, including image\nclassification and segmentation, migration networks, co-authorship networks,\nand natural language processing. These experimental results demonstrate that\nthe newly developed algorithms are practical, effective, and immediately\napplicable for learning the structure of clusters in real-world data.\n", "date": "2022-12-29", "categories": []}
{"id": "2212.14366", "title": "Deep Temporal Contrastive Clustering", "abstract": "  Recently the deep learning has shown its advantage in representation learning\nand clustering for time series data. Despite the considerable progress, the\nexisting deep time series clustering approaches mostly seek to train the deep\nneural network by some instance reconstruction based or cluster distribution\nbased objective, which, however, lack the ability to exploit the sample-wise\n(or augmentation-wise) contrastive information or even the higher-level (e.g.,\ncluster-level) contrastiveness for learning discriminative and\nclustering-friendly representations. In light of this, this paper presents a\ndeep temporal contrastive clustering (DTCC) approach, which for the first time,\nto our knowledge, incorporates the contrastive learning paradigm into the deep\ntime series clustering research. Specifically, with two parallel views\ngenerated from the original time series and their augmentations, we utilize two\nidentical auto-encoders to learn the corresponding representations, and in the\nmeantime perform the cluster distribution learning by incorporating a k-means\nobjective. Further, two levels of contrastive learning are simultaneously\nenforced to capture the instance-level and cluster-level contrastive\ninformation, respectively. With the reconstruction loss of the auto-encoder,\nthe cluster distribution loss, and the two levels of contrastive losses jointly\noptimized, the network architecture is trained in a self-supervised manner and\nthe clustering result can thereby be obtained. Experiments on a variety of time\nseries datasets demonstrate the superiority of our DTCC approach over the\nstate-of-the-art.\n", "date": "2022-12-29", "categories": []}
{"id": "2212.14467", "title": "Cluster-level Group Representativity Fairness in $k$-means Clustering", "abstract": "  There has been much interest recently in developing fair clustering\nalgorithms that seek to do justice to the representation of groups defined\nalong sensitive attributes such as race and gender. We observe that clustering\nalgorithms could generate clusters such that different groups are disadvantaged\nwithin different clusters. We develop a clustering algorithm, building upon the\ncentroid clustering paradigm pioneered by classical algorithms such as\n$k$-means, where we focus on mitigating the unfairness experienced by the\nmost-disadvantaged group within each cluster. Our method uses an iterative\noptimisation paradigm whereby an initial cluster assignment is modified by\nreassigning objects to clusters such that the worst-off sensitive group within\neach cluster is benefitted. We demonstrate the effectiveness of our method\nthrough extensive empirical evaluations over a novel evaluation metric on\nreal-world datasets. Specifically, we show that our method is effective in\nenhancing cluster-level group representativity fairness significantly at low\nimpact on cluster coherence.\n", "date": "2022-12-29", "categories": []}
{"id": "2212.14524", "title": "A novel cluster internal evaluation index based on hyper-balls", "abstract": "  It is crucial to evaluate the quality and determine the optimal number of\nclusters in cluster analysis. In this paper, the multi-granularity\ncharacterization of the data set is carried out to obtain the hyper-balls. The\ncluster internal evaluation index based on hyper-balls(HCVI) is defined.\nMoreover, a general method for determining the optimal number of clusters based\non HCVI is proposed. The proposed methods can evaluate the clustering results\nproduced by the several classic methods and determine the optimal cluster\nnumber for data sets containing noises and clusters with arbitrary shapes. The\nexperimental results on synthetic and real data sets indicate that the new\nindex outperforms existing ones.\n", "date": "2022-12-30", "categories": []}
{"id": "2212.14591", "title": "Mixture of von Mises-Fisher distribution with sparse prototypes", "abstract": "  Mixtures of von Mises-Fisher distributions can be used to cluster data on the\nunit hypersphere. This is particularly adapted for high-dimensional directional\ndata such as texts. We propose in this article to estimate a von Mises mixture\nusing a l 1 penalized likelihood. This leads to sparse prototypes that improve\nclustering interpretability. We introduce an expectation-maximisation (EM)\nalgorithm for this estimation and explore the trade-off between the sparsity\nterm and the likelihood one with a path following algorithm. The model's\nbehaviour is studied on simulated data and, we show the advantages of the\napproach on real data benchmark. We also introduce a new data set on financial\nreports and exhibit the benefits of our method for exploratory analysis.\n", "date": "2022-12-30", "categories": []}
{"id": "2212.14874", "title": "Comparative Analysis of Clustering Techniques for Personalized Food Kit\n  Distribution", "abstract": "  The Government of Kerala had increased the frequency of supply of free food\nkits owing to the pandemic, however, these items were static and not indicative\nof the personal preferences of the consumers. This paper conducts a comparative\nanalysis of various clustering techniques on a scaled-down version of a\nreal-world dataset obtained through a conjoint analysis-based survey.\nClustering carried out by centroid-based methods such as k means is analyzed\nand the results are plotted along with SVD, and finally, a conclusion is\nreached as to which among the two is better. Once the clusters have been\nformulated, commodities are also decided upon for each cluster. Also,\nclustering is further enhanced by reassignment, based on a specific cluster\nloss threshold. Thus, the most efficacious clustering technique for designing a\nfood kit tailored to the needs of individuals is finally obtained.\n", "date": "2022-12-30", "categories": []}
{"id": "2212.12379", "title": "Using MM principles to deal with incomplete data in K-means clustering", "abstract": "  Among many clustering algorithms, the K-means clustering algorithm is widely\nused because of its simple algorithm and fast convergence. However, this\nalgorithm suffers from incomplete data, where some samples have missed some of\ntheir attributes. To solve this problem, we mainly apply MM principles to\nrestore the symmetry of the data, so that K-means could work well. We give the\npseudo-code of the algorithm and use the standard datasets for experimental\nverification. The source code for the experiments is publicly available in the\nfollowing link:\n\\url{https://github.com/AliBeikmohammadi/MM-Optimization/blob/main/mini-project/MM%20K-means.ipynb}.\n", "date": "2022-12-23", "categories": []}
{"id": "2212.11725", "title": "Model Based Co-clustering of Mixed Numerical and Binary Data", "abstract": "  Co-clustering is a data mining technique used to extract the underlying block\nstructure between the rows and columns of a data matrix. Many approaches have\nbeen studied and have shown their capacity to extract such structures in\ncontinuous, binary or contingency tables. However, very little work has been\ndone to perform co-clustering on mixed type data. In this article, we extend\nthe latent block models based co-clustering to the case of mixed data\n(continuous and binary variables). We then evaluate the effectiveness of the\nproposed approach on simulated data and we discuss its advantages and potential\nlimits.\n", "date": "2022-12-22", "categories": []}
{"id": "2212.06642", "title": "AWT -- Clustering Meteorological Time Series Using an Aggregated Wavelet\n  Tree", "abstract": "  Both clustering and outlier detection play an important role for\nmeteorological measurements. We present the AWT algorithm, a clustering\nalgorithm for time series data that also performs implicit outlier detection\nduring the clustering. AWT integrates ideas of several well-known K-Means\nclustering algorithms. It chooses the number of clusters automatically based on\na user-defined threshold parameter, and it can be used for heterogeneous\nmeteorological input data as well as for data sets that exceed the available\nmemory size. We apply AWT to crowd sourced 2-m temperature data with an hourly\nresolution from the city of Vienna to detect outliers and to investigate if the\nfinal clusters show general similarities and similarities with urban land-use\ncharacteristics. It is shown that both the outlier detection and the implicit\nmapping to land-use characteristic is possible with AWT which opens new\npossible fields of application, specifically in the rapidly evolving field of\nurban climate and urban weather.\n", "date": "2022-12-13", "categories": []}
{"id": "2212.04009", "title": "A parallelizable model-based approach for marginal and multivariate\n  clustering", "abstract": "  This paper develops a clustering method that takes advantage of the\nsturdiness of model-based clustering, while attempting to mitigate some of its\npitfalls. First, we note that standard model-based clustering likely leads to\nthe same number of clusters per margin, which seems a rather artificial\nassumption for a variety of datasets. We tackle this issue by specifying a\nfinite mixture model per margin that allows each margin to have a different\nnumber of clusters, and then cluster the multivariate data using a strategy\ngame-inspired algorithm to which we call Reign-and-Conquer. Second, since the\nproposed clustering approach only specifies a model for the margins -- but\nleaves the joint unspecified -- it has the advantage of being partially\nparallelizable; hence, the proposed approach is computationally appealing as\nwell as more tractable for moderate to high dimensions than a `full' (joint)\nmodel-based clustering approach. A battery of numerical experiments on\nartificial data indicate an overall good performance of the proposed methods in\na variety of scenarios, and real datasets are used to showcase their\napplication in practice.\n", "date": "2022-12-07", "categories": []}
{"id": "2212.03589", "title": "On the Global Solution of Soft k-Means", "abstract": "  This paper presents an algorithm to solve the Soft k-Means problem globally.\nUnlike Fuzzy c-Means, Soft k-Means (SkM) has a matrix factorization-type\nobjective and has been shown to have a close relation with the popular\nprobability decomposition-type clustering methods, e.g., Left Stochastic\nClustering (LSC). Though some work has been done for solving the Soft k-Means\nproblem, they usually use an alternating minimization scheme or the projected\ngradient descent method, which cannot guarantee global optimality since the\nnon-convexity of SkM. In this paper, we present a sufficient condition for a\nfeasible solution of Soft k-Means problem to be globally optimal and show the\noutput of the proposed algorithm satisfies it. Moreover, for the Soft k-Means\nproblem, we provide interesting discussions on stability, solutions\nnon-uniqueness, and connection with LSC. Then, a new model, named Minimal\nVolume Soft k-Means (MVSkM), is proposed to address the solutions\nnon-uniqueness issue. Finally, experimental results support our theoretical\nresults.\n", "date": "2022-12-07", "categories": []}
{"id": "2211.02883", "title": "Unified Multi-View Orthonormal Non-Negative Graph Based Clustering\n  Framework", "abstract": "  Spectral clustering is an effective methodology for unsupervised learning.\nMost traditional spectral clustering algorithms involve a separate two-step\nprocedure and apply the transformed new representations for the final\nclustering results. Recently, much progress has been made to utilize the\nnon-negative feature property in real-world data and to jointly learn the\nrepresentation and clustering results. However, to our knowledge, no previous\nwork considers a unified model that incorporates the important multi-view\ninformation with those properties, which severely limits the performance of\nexisting methods. In this paper, we formulate a novel clustering model, which\nexploits the non-negative feature property and, more importantly, incorporates\nthe multi-view information into a unified joint learning framework: the unified\nmulti-view orthonormal non-negative graph based clustering framework\n(Umv-ONGC). Then, we derive an effective three-stage iterative solution for the\nproposed model and provide analytic solutions for the three sub-problems from\nthe three stages. We also explore, for the first time, the multi-model\nnon-negative graph-based approach to clustering data based on deep features.\nExtensive experiments on three benchmark data sets demonstrate the\neffectiveness of the proposed method.\n", "date": "2022-11-03", "categories": []}
{"id": "2212.00996", "title": "Clustering through Feature Space Sequence Discovery and Analysis", "abstract": "  Identifying high-dimensional data patterns without a priori knowledge is an\nimportant task of data science. This paper proposes a simple and efficient\nnoparametric algorithm: Data Convert to Sequence Analysis, DCSA, which\ndynamically explore each point in the feature space without repetition, and a\nDirected Hamilton Path will be found. Based on the change point analysis\ntheory, The sequence corresponding to the path is cut into several fragments to\nachieve clustering. The experiments on real-world datasets from different\nfields with dimensions ranging from 4 to 20531 confirm that the method in this\nwork is robust and has visual interpretability in result analysis.\n", "date": "2022-12-02", "categories": []}
{"id": "2212.01159", "title": "Clustering individuals based on multivariate EMA time-series data", "abstract": "  In the field of psychopathology, Ecological Momentary Assessment (EMA)\nmethodological advancements have offered new opportunities to collect\ntime-intensive, repeated and intra-individual measurements. This way, a large\namount of data has become available, providing the means for further exploring\nmental disorders. Consequently, advanced machine learning (ML) methods are\nneeded to understand data characteristics and uncover hidden and meaningful\nrelationships regarding the underlying complex psychological processes. Among\nother uses, ML facilitates the identification of similar patterns in data of\ndifferent individuals through clustering. This paper focuses on clustering\nmultivariate time-series (MTS) data of individuals into several groups. Since\nclustering is an unsupervised problem, it is challenging to assess whether the\nresulting grouping is successful. Thus, we investigate different clustering\nmethods based on different distance measures and assess them for the stability\nand quality of the derived clusters. These clustering steps are illustrated on\na real-world EMA dataset, including 33 individuals and 15 variables. Through\nevaluation, the results of kernel-based clustering methods appear promising to\nidentify meaningful groups in the data. So, efficient representations of EMA\ndata play an important role in clustering.\n", "date": "2022-12-02", "categories": []}
{"id": "2212.01248", "title": "Clustering -- Basic concepts and methods", "abstract": "  We review clustering as an analysis tool and the underlying concepts from an\nintroductory perspective. What is clustering and how can clusterings be\nrealised programmatically? How can data be represented and prepared for a\nclustering task? And how can clustering results be validated?\nConnectivity-based versus prototype-based approaches are reflected in the\ncontext of several popular methods: single-linkage, spectral embedding,\nk-means, and Gaussian mixtures are discussed as well as the density-based\nprotocols (H)DBSCAN, Jarvis-Patrick, CommonNN, and density-peaks.\n", "date": "2022-12-01", "categories": []}
{"id": "2212.00206", "title": "Clustering and Analysis of GPS Trajectory Data using Distance-based\n  Features", "abstract": "  The proliferation of smartphones has accelerated mobility studies by largely\nincreasing the type and volume of mobility data available. One such source of\nmobility data is from GPS technology, which is becoming increasingly common and\nhelps the research community understand mobility patterns of people. However,\nthere lacks a standardized framework for studying the different mobility\npatterns created by the non-Work, non-Home locations of Working and Nonworking\nusers on Workdays and Offdays using machine learning methods. We propose a new\nmobility metric, Daily Characteristic Distance, and use it to generate features\nfor each user together with Origin-Destination matrix features. We then use\nthose features with an unsupervised machine learning method, $k$-means\nclustering, and obtain three clusters of users for each type of day (Workday\nand Offday). Finally, we propose two new metrics for the analysis of the\nclustering results, namely User Commonality and Average Frequency. By using the\nproposed metrics, interesting user behaviors can be discerned and it helps us\nto better understand the mobility patterns of the users.\n", "date": "2022-12-01", "categories": []}
{"id": "2212.00288", "title": "Locally Adaptive Hierarchical Cluster Termination With Application To\n  Individual Tree Delineation", "abstract": "  A clustering termination procedure which is locally adaptive (with respect to\nthe hierarchical tree of sets representative of the agglomerative merging) is\nproposed, for agglomerative hierarchical clustering on a set equipped with a\ndistance function. It represents a multi-scale alternative to conventional\nscale dependent threshold based termination criteria.\n", "date": "2022-12-01", "categories": []}
{"id": "2209.13763", "title": "Clustering-Induced Generative Incomplete Image-Text Clustering (CIGIT-C)", "abstract": "  The target of image-text clustering (ITC) is to find correct clusters by\nintegrating complementary and consistent information of multi-modalities for\nthese heterogeneous samples. However, the majority of current studies analyse\nITC on the ideal premise that the samples in every modality are complete. This\npresumption, however, is not always valid in real-world situations. The missing\ndata issue degenerates the image-text feature learning performance and will\nfinally affect the generalization abilities in ITC tasks. Although a series of\nmethods have been proposed to address this incomplete image text clustering\nissue (IITC), the following problems still exist: 1) most existing methods\nhardly consider the distinct gap between heterogeneous feature domains. 2) For\nmissing data, the representations generated by existing methods are rarely\nguaranteed to suit clustering tasks. 3) Existing methods do not tap into the\nlatent connections both inter and intra modalities. In this paper, we propose a\nClustering-Induced Generative Incomplete Image-Text Clustering(CIGIT-C) network\nto address the challenges above. More specifically, we first use\nmodality-specific encoders to map original features to more distinctive\nsubspaces. The latent connections between intra and inter-modalities are\nthoroughly explored by using the adversarial generating network to produce one\nmodality conditional on the other modality. Finally, we update the\ncorresponding modalityspecific encoders using two KL divergence losses.\nExperiment results on public image-text datasets demonstrated that the\nsuggested method outperforms and is more effective in the IITC job.\n", "date": "2022-09-28", "categories": []}
{"id": "2211.17036", "title": "High-Dimensional Wide Gap $k$-Means Versus Clustering Axioms", "abstract": "  Kleinberg's axioms for distance based clustering proved to be contradictory.\n  Various efforts have been made to overcome this problem.\n  Here we make an attempt to handle the issue by embedding in high-dimensional\nspace and granting wide gaps between clusters.\n", "date": "2022-11-30", "categories": []}
{"id": "2207.08779", "title": "Simplifying Clustering with Graph Neural Networks", "abstract": "  The objective functions used in spectral clustering are usually composed of\ntwo terms: i) a term that minimizes the local quadratic variation of the\ncluster assignments on the graph and; ii) a term that balances the clustering\npartition and helps avoiding degenerate solutions. This paper shows that a\ngraph neural network, equipped with suitable message passing layers, can\ngenerate good cluster assignments by optimizing only a balancing term. Results\non attributed graph datasets show the effectiveness of the proposed approach in\nterms of clustering performance and computation time.\n", "date": "2022-07-18", "categories": []}
{"id": "2211.14987", "title": "Dual Information Enhanced Multi-view Attributed Graph Clustering", "abstract": "  Multi-view attributed graph clustering is an important approach to partition\nmulti-view data based on the attribute feature and adjacent matrices from\ndifferent views. Some attempts have been made in utilizing Graph Neural Network\n(GNN), which have achieved promising clustering performance. Despite this, few\nof them pay attention to the inherent specific information embedded in multiple\nviews. Meanwhile, they are incapable of recovering the latent high-level\nrepresentation from the low-level ones, greatly limiting the downstream\nclustering performance. To fill these gaps, a novel Dual Information enhanced\nmulti-view Attributed Graph Clustering (DIAGC) method is proposed in this\npaper. Specifically, the proposed method introduces the Specific Information\nReconstruction (SIR) module to disentangle the explorations of the consensus\nand specific information from multiple views, which enables GCN to capture the\nmore essential low-level representations. Besides, the Mutual Information\nMaximization (MIM) module maximizes the agreement between the latent high-level\nrepresentation and low-level ones, and enables the high-level representation to\nsatisfy the desired clustering structure with the help of the Self-supervised\nClustering (SC) module. Extensive experiments on several real-world benchmarks\ndemonstrate the effectiveness of the proposed DIAGC method compared with the\nstate-of-the-art baselines.\n", "date": "2022-11-28", "categories": []}
{"id": "2209.11927", "title": "Self-supervised Image Clustering from Multiple Incomplete Views via\n  Constrastive Complementary Generation", "abstract": "  Incomplete Multi-View Clustering aims to enhance clustering performance by\nusing data from multiple modalities. Despite the fact that several approaches\nfor studying this issue have been proposed, the following drawbacks still\npersist: 1) It's difficult to learn latent representations that account for\ncomplementarity yet consistency without using label information; 2) and thus\nfails to take full advantage of the hidden information in incomplete data\nresults in suboptimal clustering performance when complete data is scarce. In\nthis paper, we propose Contrastive Incomplete Multi-View Image Clustering with\nGenerative Adversarial Networks (CIMIC-GAN), which uses GAN to fill in\nincomplete data and uses double contrastive learning to learn consistency on\ncomplete and incomplete data. More specifically, considering diversity and\ncomplementary information among multiple modalities, we incorporate\nautoencoding representation of complete and incomplete data into double\ncontrastive learning to achieve learning consistency. Integrating GANs into the\nautoencoding process can not only take full advantage of new features of\nincomplete data, but also better generalize the model in the presence of high\ndata missing rates. Experiments conducted on \\textcolor{black}{four}\nextensively-used datasets show that CIMIC-GAN outperforms state-of-the-art\nincomplete multi-View clustering methods.\n", "date": "2022-09-24", "categories": []}
{"id": "2211.12511", "title": "Scalable and Effective Conductance-based Graph Clustering", "abstract": "  Conductance-based graph clustering has been recognized as a fundamental\noperator in numerous graph analysis applications. Despite the significant\nsuccess of conductance-based graph clustering, existing algorithms are either\nhard to obtain satisfactory clustering qualities, or have high time and space\ncomplexity to achieve provable clustering qualities. To overcome these\nlimitations, we devise a powerful \\textit{peeling}-based graph clustering\nframework \\textit{PCon}. We show that many existing solutions can be reduced to\nour framework. Namely, they first define a score function for each vertex, then\niteratively remove the vertex with the smallest score. Finally, they output the\nresult with the smallest conductance during the peeling process. Based on our\nframework, we propose two novel algorithms \\textit{PCon\\_core} and\n\\emph{PCon\\_de} with linear time and space complexity, which can efficiently\nand effectively identify clusters from massive graphs with more than a few\nbillion edges. Surprisingly, we prove that \\emph{PCon\\_de} can identify\nclusters with near-constant approximation ratio, resulting in an important\ntheoretical improvement over the well-known quadratic Cheeger bound. Empirical\nresults on real-life and synthetic datasets show that our algorithms can\nachieve 5$\\sim$42 times speedup with a high clustering accuracy, while using\n1.4$\\sim$7.8 times less memory than the baseline algorithms.\n", "date": "2022-11-22", "categories": []}
{"id": "2211.10015", "title": "Asymptotics for The $k$-means", "abstract": "  The $k$-means is one of the most important unsupervised learning techniques\nin statistics and computer science. The goal is to partition a data set into\nmany clusters, such that observations within clusters are the most homogeneous\nand observations between clusters are the most heterogeneous. Although it is\nwell known, the investigation of the asymptotic properties is far behind,\nleading to difficulties in developing more precise $k$-means methods in\npractice. To address this issue, a new concept called clustering consistency is\nproposed. Fundamentally, the proposed clustering consistency is more\nappropriate than the previous criterion consistency for the clustering methods.\nUsing this concept, a new $k$-means method is proposed. It is found that the\nproposed $k$-means method has lower clustering error rates and is more robust\nto small clusters and outliers than existing $k$-means methods. When $k$ is\nunknown, using the Gap statistics, the proposed method can also identify the\nnumber of clusters. This is rarely achieved by existing $k$-means methods\nadopted by many software packages.\n", "date": "2022-11-18", "categories": []}
{"id": "2211.08184", "title": "Improved Coresets for Euclidean $k$-Means", "abstract": "  Given a set of $n$ points in $d$ dimensions, the Euclidean $k$-means problem\n(resp. the Euclidean $k$-median problem) consists of finding $k$ centers such\nthat the sum of squared distances (resp. sum of distances) from every point to\nits closest center is minimized. The arguably most popular way of dealing with\nthis problem in the big data setting is to first compress the data by computing\na weighted subset known as a coreset and then run any algorithm on this subset.\nThe guarantee of the coreset is that for any candidate solution, the ratio\nbetween coreset cost and the cost of the original instance is less than a\n$(1\\pm \\varepsilon)$ factor. The current state of the art coreset size is\n$\\tilde O(\\min(k^{2} \\cdot \\varepsilon^{-2},k\\cdot \\varepsilon^{-4}))$ for\nEuclidean $k$-means and $\\tilde O(\\min(k^{2} \\cdot \\varepsilon^{-2},k\\cdot\n\\varepsilon^{-3}))$ for Euclidean $k$-median. The best known lower bound for\nboth problems is $\\Omega(k \\varepsilon^{-2})$. In this paper, we improve the\nupper bounds $\\tilde O(\\min(k^{3/2} \\cdot \\varepsilon^{-2},k\\cdot\n\\varepsilon^{-4}))$ for $k$-means and $\\tilde O(\\min(k^{4/3} \\cdot\n\\varepsilon^{-2},k\\cdot \\varepsilon^{-3}))$ for $k$-median. In particular, ours\nis the first provable bound that breaks through the $k^2$ barrier while\nretaining an optimal dependency on $\\varepsilon$.\n", "date": "2022-11-15", "categories": []}
{"id": "2211.08302", "title": "Solving clustering as ill-posed problem: experiments with K-Means\n  algorithm", "abstract": "  In this contribution, the clustering procedure based on K-Means algorithm is\nstudied as an inverse problem, which is a special case of the illposed\nproblems. The attempts to improve the quality of the clustering inverse problem\ndrive to reduce the input data via Principal Component Analysis (PCA). Since\nthere exists a theorem by Ding and He that links the cardinality of the optimal\nclusters found with K-Means and the cardinality of the selected informative PCA\ncomponents, the computational experiments tested the theorem between two\nquantitative features selection methods: Kaiser criteria (based on imperative\ndecision) versus Wishart criteria (based on random matrix theory). The results\nsuggested that PCA reduction with features selection by Wishart criteria leads\nto a low matrix condition number and satisfies the relation between clusters\nand components predicts by the theorem. The data used for the computations are\nfrom a neuroscientific repository: it regards healthy and young subjects that\nperformed a task-oriented functional Magnetic Resonance Imaging (fMRI)\nparadigm.\n", "date": "2022-11-15", "categories": []}
{"id": "2206.10801", "title": "Automated Cancer Subtyping via Vector Quantization Mutual Information\n  Maximization", "abstract": "  Cancer subtyping is crucial for understanding the nature of tumors and\nproviding suitable therapy. However, existing labelling methods are medically\ncontroversial, and have driven the process of subtyping away from teaching\nsignals. Moreover, cancer genetic expression profiles are high-dimensional,\nscarce, and have complicated dependence, thereby posing a serious challenge to\nexisting subtyping models for outputting sensible clustering. In this study, we\npropose a novel clustering method for exploiting genetic expression profiles\nand distinguishing subtypes in an unsupervised manner. The proposed method\nadaptively learns categorical correspondence from latent representations of\nexpression profiles to the subtypes output by the model. By maximizing the\nproblem -- agnostic mutual information between input expression profiles and\noutput subtypes, our method can automatically decide a suitable number of\nsubtypes. Through experiments, we demonstrate that our proposed method can\nrefine existing controversial labels, and, by further medical analysis, this\nrefinement is proven to have a high correlation with cancer survival rates.\n", "date": "2022-06-22", "categories": []}
{"id": "2211.06780", "title": "Inv-SENnet: Invariant Self Expression Network for clustering under\n  biased data", "abstract": "  Subspace clustering algorithms are used for understanding the cluster\nstructure that explains the dataset well. These methods are extensively used\nfor data-exploration tasks in various areas of Natural Sciences. However, most\nof these methods fail to handle unwanted biases in datasets. For datasets where\na data sample represents multiple attributes, naively applying any clustering\napproach can result in undesired output. To this end, we propose a novel\nframework for jointly removing unwanted attributes (biases) while learning to\ncluster data points in individual subspaces. Assuming we have information about\nthe bias, we regularize the clustering method by adversarially learning to\nminimize the mutual information between the data and the unwanted attributes.\nOur experimental result on synthetic and real-world datasets demonstrate the\neffectiveness of our approach.\n", "date": "2022-11-13", "categories": []}
{"id": "2211.07000", "title": "Online Correlation Clustering for Dynamic Complete Signed Graphs", "abstract": "  In the correlation clustering problem for complete signed graphs, the input\nis a complete signed graph with edges weighted as $+1$ (denote recommendation\nto put this pair in the same cluster) or $-1$ (recommending to put this pair of\nvertices in separate clusters) and the target is to cluster the set of vertices\nsuch that the number of disagreements with these recommendations is minimized.\n  In this paper, we consider the problem of correlation clustering for dynamic\ncomplete signed graphs where (1) a vertex can be added or deleted, and (2) the\nsign of an edge can be flipped. In the proposed online scheme, the offline\napproximation algorithm in [CALM+21] for correlation clustering is used. Up to\nthe author's knowledge, this is the first online algorithm for dynamic graphs\nwhich allows a full set of graph editing operations.\n  The proposed approach is rigorously analyzed and compared with a baseline\nmethod, which runs the original offline algorithm on each time step. Our\nresults show that the dynamic operations have local effects on the neighboring\nvertices and we employ this locality to reduce the dependency of the running\ntime in the Baseline to the summation of the degree of all vertices in $G_t$,\nthe graph after applying the graph edit operation at time step $t$, to the\nsummation of the degree of the changing vertices (e.g. two endpoints of an\nedge) and the number of clusters in the previous time step. Moreover, the\nrequired working memory is reduced to the square of the summation of the degree\nof the modified edge endpoints rather than the total number of vertices in the\ngraph.\n", "date": "2022-11-13", "categories": []}
{"id": "2208.07678", "title": "FEC: Fast Euclidean Clustering for Point Cloud Segmentation", "abstract": "  Segmentation from point cloud data is essential in many applications such as\nremote sensing, mobile robots, or autonomous cars. However, the point clouds\ncaptured by the 3D range sensor are commonly sparse and unstructured,\nchallenging efficient segmentation. In this paper, we present a fast solution\nto point cloud instance segmentation with small computational demands. To this\nend, we propose a novel fast Euclidean clustering (FEC) algorithm which applies\na pointwise scheme over the clusterwise scheme used in existing works. Our\napproach is conceptually simple, easy to implement (40 lines in C++), and\nachieves two orders of magnitudes faster against the classical segmentation\nmethods while producing high-quality results.\n", "date": "2022-08-16", "categories": []}
{"id": "2211.05183", "title": "An Empirical Study on Clustering Pretrained Embeddings: Is Deep Strictly\n  Better?", "abstract": "  Recent research in clustering face embeddings has found that unsupervised,\nshallow, heuristic-based methods -- including $k$-means and hierarchical\nagglomerative clustering -- underperform supervised, deep, inductive methods.\nWhile the reported improvements are indeed impressive, experiments are mostly\nlimited to face datasets, where the clustered embeddings are highly\ndiscriminative or well-separated by class (Recall@1 above 90% and often nearing\nceiling), and the experimental methodology seemingly favors the deep methods.\nWe conduct a large-scale empirical study of 17 clustering methods across three\ndatasets and obtain several robust findings. Notably, deep methods are\nsurprisingly fragile for embeddings with more uncertainty, where they match or\neven perform worse than shallow, heuristic-based methods. When embeddings are\nhighly discriminative, deep methods do outperform the baselines, consistent\nwith past results, but the margin between methods is much smaller than\npreviously reported. We believe our benchmarks broaden the scope of supervised\nclustering methods beyond the face domain and can serve as a foundation on\nwhich these methods could be improved. To enable reproducibility, we include\nall necessary details in the appendices, and plan to release the code.\n", "date": "2022-11-09", "categories": []}
{"id": "2211.03956", "title": "Significance-Based Categorical Data Clustering", "abstract": "  Although numerous algorithms have been proposed to solve the categorical data\nclustering problem, how to access the statistical significance of a set of\ncategorical clusters remains unaddressed. To fulfill this void, we employ the\nlikelihood ratio test to derive a test statistic that can serve as a\nsignificance-based objective function in categorical data clustering.\nConsequently, a new clustering algorithm is proposed in which the\nsignificance-based objective function is optimized via a Monte Carlo search\nprocedure. As a by-product, we can further calculate an empirical $p$-value to\nassess the statistical significance of a set of clusters and develop an\nimproved gap statistic for estimating the cluster number. Extensive\nexperimental studies suggest that our method is able to achieve comparable\nperformance to state-of-the-art categorical data clustering algorithms.\nMoreover, the effectiveness of such a significance-based formulation on\nstatistical cluster validation and cluster number estimation is demonstrated\nthrough comprehensive empirical results.\n", "date": "2022-11-08", "categories": []}
{"id": "2211.02765", "title": "Clustering above Exponential Families with Tempered Exponential Measures", "abstract": "  The link with exponential families has allowed $k$-means clustering to be\ngeneralized to a wide variety of data generating distributions in exponential\nfamilies and clustering distortions among Bregman divergences. Getting the\nframework to work above exponential families is important to lift roadblocks\nlike the lack of robustness of some population minimizers carved in their\naxiomatization. Current generalisations of exponential families like\n$q$-exponential families or even deformed exponential families fail at\nachieving the goal. In this paper, we provide a new attempt at getting the\ncomplete framework, grounded in a new generalisation of exponential families\nthat we introduce, tempered exponential measures (TEM). TEMs keep the maximum\nentropy axiomatization framework of $q$-exponential families, but instead of\nnormalizing the measure, normalize a dual called a co-distribution. Numerous\ninteresting properties arise for clustering such as improved and controllable\nrobustness for population minimizers, that keep a simple analytic form.\n", "date": "2022-11-04", "categories": []}
{"id": "2211.00409", "title": "Oracle-guided Contrastive Clustering", "abstract": "  Deep clustering aims to learn a clustering representation through deep\narchitectures. Most of the existing methods usually conduct clustering with the\nunique goal of maximizing clustering performance, that ignores the personalized\ndemand of clustering tasks.% and results in unguided clustering solutions.\nHowever, in real scenarios, oracles may tend to cluster unlabeled data by\nexploiting distinct criteria, such as distinct semantics (background, color,\nobject, etc.), and then put forward personalized clustering tasks. To achieve\ntask-aware clustering results, in this study, Oracle-guided Contrastive\nClustering(OCC) is then proposed to cluster by interactively making pairwise\n``same-cluster\" queries to oracles with distinctive demands. Specifically,\ninspired by active learning, some informative instance pairs are queried, and\nevaluated by oracles whether the pairs are in the same cluster according to\ntheir desired orientation. And then these queried same-cluster pairs extend the\nset of positive instance pairs for contrastive learning, guiding OCC to extract\norientation-aware feature representation. Accordingly, the query results,\nguided by oracles with distinctive demands, may drive the OCC's clustering\nresults in a desired orientation. Theoretically, the clustering risk in an\nactive learning manner is given with a tighter upper bound, that guarantees\nactive queries to oracles do mitigate the clustering risk. Experimentally,\nextensive results verify that OCC can cluster accurately along the specific\norientation and it substantially outperforms the SOTA clustering methods as\nwell. To the best of our knowledge, it is the first deep framework to perform\npersonalized clustering.\n", "date": "2022-11-01", "categories": []}
{"id": "2210.15507", "title": "How To Overcome Richness Axiom Fallacy", "abstract": "  The paper points at the grieving problems implied by the richness axiom in\nthe Kleinberg's axiomatic system and suggests resolutions. The richness induces\nlearnability problem in general and leads to conflicts with consistency axiom.\nAs a resolution, learnability constraints and usage of centric consistency or\nrestriction of the domain of considered clusterings to super-ball-clusterings\nis proposed.\n", "date": "2022-10-27", "categories": []}
{"id": "2210.12638", "title": "Tucker-O-Minus Decomposition for Multi-view Tensor Subspace Clustering", "abstract": "  With powerful ability to exploit latent structure of self-representation\ninformation, different tensor decompositions have been employed into low rank\nmulti-view clustering (LRMVC) models for achieving significant performance.\nHowever, current approaches suffer from a series of problems related to those\ntensor decomposition, such as the unbalanced matricization scheme, rotation\nsensitivity, deficient correlations capture and so forth. All these will lead\nto LRMVC having insufficient access to global information, which is contrary to\nthe target of multi-view clustering. To alleviate these problems, we propose a\nnew tensor decomposition called Tucker-O-Minus Decomposition (TOMD) for\nmulti-view clustering. Specifically, based on the Tucker format, we\nadditionally employ the O-minus structure, which consists of a circle with an\nefficient bridge linking two weekly correlated factors. In this way, the core\ntensor in Tucker format is replaced by the O-minus architecture with a more\nbalanced structure, and the enhanced capacity of capturing the global low rank\ninformation will be achieved. The proposed TOMD also provides more compact and\npowerful representation abilities for the self-representation tensor,\nsimultaneously. The alternating direction method of multipliers is used to\nsolve the proposed model TOMD-MVC. Numerical experiments on six benchmark data\nsets demonstrate the superiority of our proposed method in terms of F-score,\nprecision, recall, normalized mutual information, adjusted rand index, and\naccuracy.\n", "date": "2022-10-23", "categories": []}
{"id": "2210.12778", "title": "Local and Global Structure Preservation Based Spectral Clustering", "abstract": "  Spectral Clustering (SC) is widely used for clustering data on a nonlinear\nmanifold. SC aims to cluster data by considering the preservation of the local\nneighborhood structure on the manifold data. This paper extends Spectral\nClustering to Local and Global Structure Preservation Based Spectral Clustering\n(LGPSC) that incorporates both global structure and local neighborhood\nstructure simultaneously. For this extension, LGPSC proposes two models to\nextend local structures preservation to local and global structures\npreservation: Spectral clustering guided Principal component analysis model and\nMultilevel model. Finally, we compare the experimental results of the\nstate-of-the-art methods with our two models of LGPSC on various data sets such\nthat the experimental results confirm the effectiveness of our LGPSC models to\ncluster nonlinear data.\n", "date": "2022-10-23", "categories": []}
{"id": "2210.11680", "title": "Twin Contrastive Learning for Online Clustering", "abstract": "  This paper proposes to perform online clustering by conducting twin\ncontrastive learning (TCL) at the instance and cluster level. Specifically, we\nfind that when the data is projected into a feature space with a dimensionality\nof the target cluster number, the rows and columns of its feature matrix\ncorrespond to the instance and cluster representation, respectively. Based on\nthe observation, for a given dataset, the proposed TCL first constructs\npositive and negative pairs through data augmentations. Thereafter, in the row\nand column space of the feature matrix, instance- and cluster-level contrastive\nlearning are respectively conducted by pulling together positive pairs while\npushing apart the negatives. To alleviate the influence of intrinsic\nfalse-negative pairs and rectify cluster assignments, we adopt a\nconfidence-based criterion to select pseudo-labels for boosting both the\ninstance- and cluster-level contrastive learning. As a result, the clustering\nperformance is further improved. Besides the elegant idea of twin contrastive\nlearning, another advantage of TCL is that it could independently predict the\ncluster assignment for each instance, thus effortlessly fitting online\nscenarios. Extensive experiments on six widely-used image and text benchmarks\ndemonstrate the effectiveness of TCL. The code will be released on GitHub.\n", "date": "2022-10-21", "categories": []}
{"id": "2210.09507", "title": "An enhanced method of initial cluster center selection for K-means\n  algorithm", "abstract": "  Clustering is one of the widely used techniques to find out patterns from a\ndataset that can be applied in different applications or analyses. K-means, the\nmost popular and simple clustering algorithm, might get trapped into local\nminima if not properly initialized and the initialization of this algorithm is\ndone randomly. In this paper, we propose a novel approach to improve initial\ncluster selection for K-means algorithm. This algorithm is based on the fact\nthat the initial centroids must be well separated from each other since the\nfinal clusters are separated groups in feature space. The Convex Hull algorithm\nfacilitates the computing of the first two centroids and the remaining ones are\nselected according to the distance from previously selected centers. To ensure\nthe selection of one center per cluster, we use the nearest neighbor technique.\nTo check the robustness of our proposed algorithm, we consider several\nreal-world datasets. We obtained only 7.33%, 7.90%, and 0% clustering error in\nIris, Letter, and Ruspini data respectively which proves better performance\nthan other existing systems. The results indicate that our proposed method\noutperforms the conventional K means approach by accelerating the computation\nwhen the number of clusters is greater than 2.\n", "date": "2022-10-18", "categories": []}
{"id": "2210.09523", "title": "Agglomerative Hierarchical Clustering with Dynamic Time Warping for\n  Household Load Curve Clustering", "abstract": "  Energy companies often implement various demand response (DR) programs to\nbetter match electricity demand and supply by offering the consumers incentives\nto reduce their demand during critical periods. Classifying clients according\nto their consumption patterns enables targeting specific groups of consumers\nfor DR. Traditional clustering algorithms use standard distance measurement to\nfind the distance between two points. The results produced by clustering\nalgorithms such as K-means, K-medoids, and Gaussian Mixture Models depend on\nthe clustering parameters or initial clusters. In contrast, our methodology\nuses a shape-based approach that combines Agglomerative Hierarchical Clustering\n(AHC) with Dynamic Time Warping (DTW) to classify residential households' daily\nload curves based on their consumption patterns. While DTW seeks the optimal\nalignment between two load curves, AHC provides a realistic initial clusters\ncenter. In this paper, we compare the results with other clustering algorithms\nsuch as K-means, K-medoids, and GMM using different distance measures, and we\nshow that AHC using DTW outperformed other clustering algorithms and needed\nfewer clusters.\n", "date": "2022-10-18", "categories": []}
{"id": "2210.09786", "title": "Bagged $k$-Distance for Mode-Based Clustering Using the Probability of\n  Localized Level Sets", "abstract": "  In this paper, we propose an ensemble learning algorithm named \\textit{bagged\n$k$-distance for mode-based clustering} (\\textit{BDMBC}) by putting forward a\nnew measurement called the \\textit{probability of localized level sets}\n(\\textit{PLLS}), which enables us to find all clusters for varying densities\nwith a global threshold. On the theoretical side, we show that with a properly\nchosen number of nearest neighbors $k_D$ in the bagged $k$-distance, the\nsub-sample size $s$, the bagging rounds $B$, and the number of nearest\nneighbors $k_L$ for the localized level sets, BDMBC can achieve optimal\nconvergence rates for mode estimation. It turns out that with a relatively\nsmall $B$, the sub-sample size $s$ can be much smaller than the number of\ntraining data $n$ at each bagging round, and the number of nearest neighbors\n$k_D$ can be reduced simultaneously. Moreover, we establish optimal convergence\nresults for the level set estimation of the PLLS in terms of Hausdorff\ndistance, which reveals that BDMBC can find localized level sets for varying\ndensities and thus enjoys local adaptivity. On the practical side, we conduct\nnumerical experiments to empirically verify the effectiveness of BDMBC for mode\nestimation and level set estimation, which demonstrates the promising accuracy\nand efficiency of our proposed algorithm.\n", "date": "2022-10-18", "categories": []}
{"id": "2210.09911", "title": "Leveraging Cluster Analysis to Understand Educational Game Player\n  Experiences and Support Design", "abstract": "  The ability for an educational game designer to understand their audience's\nplay styles and resulting experience is an essential tool for improving their\ngame's design. As a game is subjected to large-scale player testing, the\ndesigners require inexpensive, automated methods for categorizing patterns of\nplayer-game interactions. In this paper we present a simple, reusable process\nusing best practices for data clustering, feasible for use within a small\neducational game studio. We utilize the method to analyze a real-time strategy\ngame, processing game telemetry data to determine categories of players based\non their in-game actions, the feedback they received, and their progress\nthrough the game. An interpretive analysis of these clusters results in\nactionable insights for the game's designers.\n", "date": "2022-10-18", "categories": []}
{"id": "2210.06300", "title": "Generalised Mutual Information for Discriminative Clustering", "abstract": "  In the last decade, recent successes in deep clustering majorly involved the\nmutual information (MI) as an unsupervised objective for training neural\nnetworks with increasing regularisations. While the quality of the\nregularisations have been largely discussed for improvements, little attention\nhas been dedicated to the relevance of MI as a clustering objective. In this\npaper, we first highlight how the maximisation of MI does not lead to\nsatisfying clusters. We identified the Kullback-Leibler divergence as the main\nreason of this behaviour. Hence, we generalise the mutual information by\nchanging its core distance, introducing the generalised mutual information\n(GEMINI): a set of metrics for unsupervised neural network training. Unlike MI,\nsome GEMINIs do not require regularisations when training. Some of these\nmetrics are geometry-aware thanks to distances or kernels in the data space.\nFinally, we highlight that GEMINIs can automatically select a relevant number\nof clusters, a property that has been little studied in deep clustering context\nwhere the number of clusters is a priori unknown.\n", "date": "2022-10-12", "categories": []}
{"id": "2210.08798", "title": "Cluster Explanation via Polyhedral Descriptions", "abstract": "  Clustering is an unsupervised learning problem that aims to partition\nunlabelled data points into groups with similar features. Traditional\nclustering algorithms provide limited insight into the groups they find as\ntheir main focus is accuracy and not the interpretability of the group\nassignments. This has spurred a recent line of work on explainable machine\nlearning for clustering. In this paper we focus on the cluster description\nproblem where, given a dataset and its partition into clusters, the task is to\nexplain the clusters. We introduce a new approach to explain clusters by\nconstructing polyhedra around each cluster while minimizing either the\ncomplexity of the resulting polyhedra or the number of features used in the\ndescription. We formulate the cluster description problem as an integer program\nand present a column generation approach to search over an exponential number\nof candidate half-spaces that can be used to build the polyhedra. To deal with\nlarge datasets, we introduce a novel grouping scheme that first forms smaller\ngroups of data points and then builds the polyhedra around the grouped data, a\nstrategy which out-performs simply sub-sampling data. Compared to state of the\nart cluster description algorithms, our approach is able to achieve competitive\ninterpretability with improved description accuracy.\n", "date": "2022-10-17", "categories": []}
{"id": "2210.08972", "title": "A new nonparametric interpoint distance-based measure for assessment of\n  clustering", "abstract": "  A new interpoint distance-based measure is proposed to identify the optimal\nnumber of clusters present in a data set. Designed in nonparametric approach,\nit is independent of the distribution of given data. Interpoint distances\nbetween the data members make our cluster validity index applicable to\nunivariate and multivariate data measured on arbitrary scales, or having\nobservations in any dimensional space where the number of study variables can\nbe even larger than the sample size. Our proposed criterion is compatible with\nany clustering algorithm, and can be used to determine the unknown number of\nclusters or to assess the quality of the resulting clusters for a data set.\nDemonstration through synthetic and real-life data establishes its superiority\nover the well-known clustering accuracy measures of the literature.\n", "date": "2022-10-01", "categories": []}
{"id": "2209.06975", "title": "Wasserstein $K$-means for clustering probability distributions", "abstract": "  Clustering is an important exploratory data analysis technique to group\nobjects based on their similarity. The widely used $K$-means clustering method\nrelies on some notion of distance to partition data into a fewer number of\ngroups. In the Euclidean space, centroid-based and distance-based formulations\nof the $K$-means are equivalent. In modern machine learning applications, data\noften arise as probability distributions and a natural generalization to handle\nmeasure-valued data is to use the optimal transport metric. Due to non-negative\nAlexandrov curvature of the Wasserstein space, barycenters suffer from\nregularity and non-robustness issues. The peculiar behaviors of Wasserstein\nbarycenters may make the centroid-based formulation fail to represent the\nwithin-cluster data points, while the more direct distance-based $K$-means\napproach and its semidefinite program (SDP) relaxation are capable of\nrecovering the true cluster labels. In the special case of clustering Gaussian\ndistributions, we show that the SDP relaxed Wasserstein $K$-means can achieve\nexact recovery given the clusters are well-separated under the $2$-Wasserstein\nmetric. Our simulation and real data examples also demonstrate that\ndistance-based $K$-means can achieve better classification performance over the\nstandard centroid-based $K$-means for clustering probability distributions and\nimages.\n", "date": "2022-09-14", "categories": []}
{"id": "2210.06795", "title": "Subspace-Contrastive Multi-View Clustering", "abstract": "  Most multi-view clustering methods are limited by shallow models without\nsound nonlinear information perception capability, or fail to effectively\nexploit complementary information hidden in different views. To tackle these\nissues, we propose a novel Subspace-Contrastive Multi-View Clustering (SCMC)\napproach. Specifically, SCMC utilizes view-specific auto-encoders to map the\noriginal multi-view data into compact features perceiving its nonlinear\nstructures. Considering the large semantic gap of data from different\nmodalities, we employ subspace learning to unify the multi-view data into a\njoint semantic space, namely the embedded compact features are passed through\nmultiple self-expression layers to learn the subspace representations,\nrespectively. In order to enhance the discriminability and efficiently excavate\nthe complementarity of various subspace representations, we use the contrastive\nstrategy to maximize the similarity between positive pairs while differentiate\nnegative pairs. Thus, a weighted fusion scheme is developed to initially learn\na consistent affinity matrix. Furthermore, we employ the graph regularization\nto encode the local geometric structure within varying subspaces for further\nfine-tuning the appropriate affinities between instances. To demonstrate the\neffectiveness of the proposed model, we conduct a large number of comparative\nexperiments on eight challenge datasets, the experimental results show that\nSCMC outperforms existing shallow and deep multi-view clustering methods.\n", "date": "2022-10-13", "categories": []}
{"id": "2207.11839", "title": "A Deep Dive into Deep Cluster", "abstract": "  Deep Learning has demonstrated a significant improvement against traditional\nmachine learning approaches in different domains such as image and speech\nrecognition. Their success on benchmark datasets is transferred to the\nreal-world through pretrained models by practitioners. Pretraining visual\nmodels using supervised learning requires a significant amount of expensive\ndata annotation. To tackle this limitation, DeepCluster - a simple and scalable\nunsupervised pretraining of visual representations - has been proposed.\nHowever, the underlying work of the model is not yet well understood. In this\npaper, we analyze DeepCluster internals and exhaustively evaluate the impact of\nvarious hyperparameters over a wide range of values on three different\ndatasets. Accordingly, we propose an explanation of why the algorithm works in\npractice. We also show that DeepCluster convergence and performance highly\ndepend on the interplay between the quality of the randomly initialized filters\nof the convolutional layer and the selected number of clusters. Furthermore, we\ndemonstrate that continuous clustering is not critical for DeepCluster\nconvergence. Therefore, early stopping of the clustering phase will reduce the\ntraining time and allow the algorithm to scale to large datasets. Finally, we\nderive plausible hyperparameter selection criteria in a semi-supervised\nsetting.\n", "date": "2022-07-24", "categories": []}
{"id": "2210.05314", "title": "Client Error Clustering Approaches in Content Delivery Networks (CDN)", "abstract": "  Content delivery networks (CDNs) are the backbone of the Internet and are key\nin delivering high quality video on demand (VoD), web content and file services\nto billions of users. CDNs usually consist of hierarchically organized content\nservers positioned as close to the customers as possible. CDN operators face a\nsignificant challenge when analyzing billions of web server and proxy logs\ngenerated by their systems. The main objective of this study was to analyze the\napplicability of various clustering methods in CDN error log analysis. We\nworked with real-life CDN proxy logs, identified key features included in the\nlogs (e.g., content type, HTTP status code, time-of-day, host) and clustered\nthe log lines corresponding to different host types offering live TV, video on\ndemand, file caching and web content. Our experiments were run on a dataset\nconsisting of proxy logs collected over a 7-day period from a single, physical\nCDN server running multiple types of services (VoD, live TV, file). The dataset\nconsisted of 2.2 billion log lines. Our analysis showed that CDN error\nclustering is a viable approach towards identifying recurring errors and\nimproving overall quality of service.\n", "date": "2022-10-11", "categories": []}
{"id": "2210.04142", "title": "Deep Clustering: A Comprehensive Survey", "abstract": "  Cluster analysis plays an indispensable role in machine learning and data\nmining. Learning a good data representation is crucial for clustering\nalgorithms. Recently, deep clustering, which can learn clustering-friendly\nrepresentations using deep neural networks, has been broadly applied in a wide\nrange of clustering tasks. Existing surveys for deep clustering mainly focus on\nthe single-view fields and the network architectures, ignoring the complex\napplication scenarios of clustering. To address this issue, in this paper we\nprovide a comprehensive survey for deep clustering in views of data sources.\nWith different data sources and initial conditions, we systematically\ndistinguish the clustering methods in terms of methodology, prior knowledge,\nand architecture. Concretely, deep clustering methods are introduced according\nto four categories, i.e., traditional single-view deep clustering,\nsemi-supervised deep clustering, deep multi-view clustering, and deep transfer\nclustering. Finally, we discuss the open challenges and potential future\nopportunities in different fields of deep clustering.\n", "date": "2022-10-09", "categories": []}
{"id": "2210.01679", "title": "Detection and Evaluation of Clusters within Sequential Data", "abstract": "  Motivated by theoretical advancements in dimensionality reduction techniques\nwe use a recent model, called Block Markov Chains, to conduct a practical study\nof clustering in real-world sequential data. Clustering algorithms for Block\nMarkov Chains possess theoretical optimality guarantees and can be deployed in\nsparse data regimes. Despite these favorable theoretical properties, a thorough\nevaluation of these algorithms in realistic settings has been lacking.\n  We address this issue and investigate the suitability of these clustering\nalgorithms in exploratory data analysis of real-world sequential data. In\nparticular, our sequential data is derived from human DNA, written text, animal\nmovement data and financial markets. In order to evaluate the determined\nclusters, and the associated Block Markov Chain model, we further develop a set\nof evaluation tools. These tools include benchmarking, spectral noise analysis\nand statistical model selection tools. An efficient implementation of the\nclustering algorithm and the new evaluation tools is made available together\nwith this paper.\n  Practical challenges associated to real-world data are encountered and\ndiscussed. It is ultimately found that the Block Markov Chain model assumption,\ntogether with the tools developed here, can indeed produce meaningful insights\nin exploratory data analyses despite the complexity and sparsity of real-world\ndata.\n", "date": "2022-10-04", "categories": []}
{"id": "2210.00064", "title": "CEREAL: Few-Sample Clustering Evaluation", "abstract": "  Evaluating clustering quality with reliable evaluation metrics like\nnormalized mutual information (NMI) requires labeled data that can be expensive\nto annotate. We focus on the underexplored problem of estimating clustering\nquality with limited labels. We adapt existing approaches from the few-sample\nmodel evaluation literature to actively sub-sample, with a learned surrogate\nmodel, the most informative data points for annotation to estimate the\nevaluation metric. However, we find that their estimation can be biased and\nonly relies on the labeled data. To that end, we introduce CEREAL, a\ncomprehensive framework for few-sample clustering evaluation that extends\nactive sampling approaches in three key ways. First, we propose novel NMI-based\nacquisition functions that account for the distinctive properties of clustering\nand uncertainties from a learned surrogate model. Next, we use ideas from\nsemi-supervised learning and train the surrogate model with both the labeled\nand unlabeled data. Finally, we pseudo-label the unlabeled data with the\nsurrogate model. We run experiments to estimate NMI in an active sampling\npipeline on three datasets across vision and language. Our results show that\nCEREAL reduces the area under the absolute error curve by up to 57% compared to\nthe best sampling baseline. We perform an extensive ablation study to show that\nour framework is agnostic to the choice of clustering algorithm and evaluation\nmetric. We also extend CEREAL from clusterwise annotations to pairwise\nannotations. Overall, CEREAL can efficiently evaluate clustering with limited\nhuman annotations.\n", "date": "2022-09-30", "categories": []}
{"id": "2209.15143", "title": "Double Graphs Regularized Multi-view Subspace Clustering", "abstract": "  Recent years have witnessed a growing academic interest in multi-view\nsubspace clustering. In this paper, we propose a novel Double Graphs\nRegularized Multi-view Subspace Clustering (DGRMSC) method, which aims to\nharness both global and local structural information of multi-view data in a\nunified framework. Specifically, DGRMSC firstly learns a latent representation\nto exploit the global complementary information of multiple views. Based on the\nlearned latent representation, we learn a self-representation to explore its\nglobal cluster structure. Further, Double Graphs Regularization (DGR) is\nperformed on both latent representation and self-representation to take\nadvantage of their local manifold structures simultaneously. Then, we design an\niterative algorithm to solve the optimization problem effectively. Extensive\nexperimental results on real-world datasets demonstrate the effectiveness of\nthe proposed method.\n", "date": "2022-09-30", "categories": []}
{"id": "2209.15399", "title": "Parea: multi-view ensemble clustering for cancer subtype discovery", "abstract": "  Multi-view clustering methods are essential for the stratification of\npatients into sub-groups of similar molecular characteristics. In recent years,\na wide range of methods has been developed for this purpose. However, due to\nthe high diversity of cancer-related data, a single method may not perform\nsufficiently well in all cases. We present Parea, a multi-view hierarchical\nensemble clustering approach for disease subtype discovery. We demonstrate its\nperformance on several machine learning benchmark datasets. We apply and\nvalidate our methodology on real-world multi-view cancer patient data. Parea\noutperforms the current state-of-the-art on six out of seven analysed cancer\ntypes. We have integrated the Parea method into our developed Python package\nPyrea (https://github.com/mdbloice/Pyrea), which enables the effortless and\nflexible design of ensemble workflows while incorporating a wide range of\nfusion and clustering algorithms.\n", "date": "2022-09-30", "categories": []}
{"id": "2209.12005", "title": "Contrastive learning for unsupervised medical image clustering and\n  reconstruction", "abstract": "  The lack of large labeled medical imaging datasets, along with significant\ninter-individual variability compared to clinically established disease\nclasses, poses significant challenges in exploiting medical imaging information\nin a precision medicine paradigm, where in principle dense patient-specific\ndata can be employed to formulate individual predictions and/or stratify\npatients into finer-grained groups which may follow more homogeneous\ntrajectories and therefore empower clinical trials. In order to efficiently\nexplore the effective degrees of freedom underlying variability in medical\nimages in an unsupervised manner, in this work we propose an unsupervised\nautoencoder framework which is augmented with a contrastive loss to encourage\nhigh separability in the latent space. The model is validated on (medical)\nbenchmark datasets. As cluster labels are assigned to each example according to\ncluster assignments, we compare performance with a supervised transfer learning\nbaseline. Our method achieves similar performance to the supervised\narchitecture, indicating that separation in the latent space reproduces expert\nmedical observer-assigned labels. The proposed method could be beneficial for\npatient stratification, exploring new subdivisions of larger classes or\npathological continua or, due to its sampling abilities in a variation setting,\ndata augmentation in medical image processing.\n", "date": "2022-09-24", "categories": []}
{"id": "2209.12553", "title": "Clustering by Direct Optimization of the Medoid Silhouette", "abstract": "  The evaluation of clustering results is difficult, highly dependent on the\nevaluated data set and the perspective of the beholder. There are many\ndifferent clustering quality measures, which try to provide a general measure\nto validate clustering results. A very popular measure is the Silhouette. We\ndiscuss the efficient medoid-based variant of the Silhouette, perform a\ntheoretical analysis of its properties, and provide two fast versions for the\ndirect optimization. We combine ideas from the original Silhouette with the\nwell-known PAM algorithm and its latest improvements FasterPAM. One of the\nversions guarantees equal results to the original variant and provides a run\nspeedup of $O(k^2)$. In experiments on real data with 30000 samples and\n$k$=100, we observed a 10464$\\times$ speedup compared to the original PAMMEDSIL\nalgorithm.\n", "date": "2022-09-26", "categories": []}
{"id": "2209.12621", "title": "Improving Image Clustering through Sample Ranking and Its Application to\n  remote--sensing images", "abstract": "  Image clustering is a very useful technique that is widely applied to various\nareas, including remote sensing. Recently, visual representations by\nself-supervised learning have greatly improved the performance of image\nclustering. To further improve the well-trained clustering models, this paper\nproposes a novel method by first ranking samples within each cluster based on\nthe confidence in their belonging to the current cluster and then using the\nranking to formulate a weighted cross-entropy loss to train the model. For\nranking the samples, we developed a method for computing the likelihood of\nsamples belonging to the current clusters based on whether they are situated in\ndensely populated neighborhoods, while for training the model, we give a\nstrategy for weighting the ranked samples. We present extensive experimental\nresults that demonstrate that the new technique can be used to improve the\nState-of-the-Art image clustering models, achieving accuracy performance gains\nranging from $2.1\\%$ to $15.9\\%$. Performing our method on a variety of\ndatasets from remote sensing, we show that our method can be effectively\napplied to remote--sensing images.\n", "date": "2022-09-26", "categories": []}
{"id": "2209.10578", "title": "Algorithm-Agnostic Interpretations for Clustering", "abstract": "  A clustering outcome for high-dimensional data is typically interpreted via\npost-processing, involving dimension reduction and subsequent visualization.\nThis destroys the meaning of the data and obfuscates interpretations. We\npropose algorithm-agnostic interpretation methods to explain clustering\noutcomes in reduced dimensions while preserving the integrity of the data. The\npermutation feature importance for clustering represents a general framework\nbased on shuffling feature values and measuring changes in cluster assignments\nthrough custom score functions. The individual conditional expectation for\nclustering indicates observation-wise changes in the cluster assignment due to\nchanges in the data. The partial dependence for clustering evaluates average\nchanges in cluster assignments for the entire feature space. All methods can be\nused with any clustering algorithm able to reassign instances through soft or\nhard labels. In contrast to common post-processing methods such as principal\ncomponent analysis, the introduced methods maintain the original structure of\nthe features.\n", "date": "2022-09-21", "categories": []}
{"id": "2209.10838", "title": "High-order Multi-view Clustering for Generic Data", "abstract": "  Graph-based multi-view clustering has achieved better performance than most\nnon-graph approaches. However, in many real-world scenarios, the graph\nstructure of data is not given or the quality of initial graph is poor.\nAdditionally, existing methods largely neglect the high-order neighborhood\ninformation that characterizes complex intrinsic interactions. To tackle these\nproblems, we introduce an approach called high-order multi-view clustering\n(HMvC) to explore the topology structure information of generic data. Firstly,\ngraph filtering is applied to encode structure information, which unifies the\nprocessing of attributed graph data and non-graph data in a single framework.\nSecondly, up to infinity-order intrinsic relationships are exploited to enrich\nthe learned graph. Thirdly, to explore the consistent and complementary\ninformation of various views, an adaptive graph fusion mechanism is proposed to\nachieve a consensus graph. Comprehensive experimental results on both non-graph\nand attributed graph data show the superior performance of our method with\nrespect to various state-of-the-art techniques, including some deep learning\nmethods.\n", "date": "2022-09-22", "categories": []}
{"id": "2209.11125", "title": "A Bibliographic View on Constrained Clustering", "abstract": "  A keyword search on constrained clustering on Web-of-Science returned just\nunder 3,000 documents. We ran automatic analyses of those, and compiled our own\nbibliography of 183 papers which we analysed in more detail based on their\ntopic and experimental study, if any. This paper presents general trends of the\narea and its sub-topics by Pareto analysis, using citation count and year of\npublication. We list available software and analyse the experimental sections\nof our reference collection. We found a notable lack of large comparison\nexperiments. Among the topics we reviewed, applications studies were most\nabundant recently, alongside deep learning, active learning and ensemble\nlearning.\n", "date": "2022-09-22", "categories": []}
{"id": "2209.10042", "title": "Sanity Check for External Clustering Validation Benchmarks using\n  Internal Validation Measures", "abstract": "  We address the lack of reliability in benchmarking clustering techniques\nbased on labeled datasets. A standard scheme in external clustering validation\nis to use class labels as ground truth clusters, based on the assumption that\neach class forms a single, clearly separated cluster. However, as such\ncluster-label matching (CLM) assumption often breaks, the lack of conducting a\nsanity check for the CLM of benchmark datasets casts doubt on the validity of\nexternal validations. Still, evaluating the degree of CLM is challenging. For\nexample, internal clustering validation measures can be used to quantify CLM\nwithin the same dataset to evaluate its different clusterings but are not\ndesigned to compare clusterings of different datasets. In this work, we propose\na principled way to generate between-dataset internal measures that enable the\ncomparison of CLM across datasets. We first determine four axioms for\nbetween-dataset internal measures, complementing Ackerman and Ben-David's\nwithin-dataset axioms. We then propose processes to generalize internal\nmeasures to fulfill these new axioms, and use them to extend the widely used\nCalinski-Harabasz index for between-dataset CLM evaluation. Through\nquantitative experiments, we (1) verify the validity and necessity of the\ngeneralization processes and (2) show that the proposed between-dataset\nCalinski-Harabasz index accurately evaluates CLM across datasets. Finally, we\ndemonstrate the importance of evaluating CLM of benchmark datasets before\nconducting external validation.\n", "date": "2022-09-20", "categories": []}
{"id": "2209.09670", "title": "Explainable Clustering via Exemplars: Complexity and Efficient\n  Approximation Algorithms", "abstract": "  Explainable AI (XAI) is an important developing area but remains relatively\nunderstudied for clustering. We propose an explainable-by-design clustering\napproach that not only finds clusters but also exemplars to explain each\ncluster. The use of exemplars for understanding is supported by the\nexemplar-based school of concept definition in psychology. We show that finding\na small set of exemplars to explain even a single cluster is computationally\nintractable; hence, the overall problem is challenging. We develop an\napproximation algorithm that provides provable performance guarantees with\nrespect to clustering quality as well as the number of exemplars used. This\nbasic algorithm explains all the instances in every cluster whilst another\napproximation algorithm uses a bounded number of exemplars to allow simpler\nexplanations and provably covers a large fraction of all the instances.\nExperimental results show that our work is useful in domains involving\ndifficult to understand deep embeddings of images and text.\n", "date": "2022-09-20", "categories": []}
{"id": "2208.02973", "title": "An Efficient Person Clustering Algorithm for Open Checkout-free\n  Groceries", "abstract": "  Open checkout-free grocery is the grocery store where the customers never\nhave to wait in line to check out. Developing a system like this is not trivial\nsince it faces challenges of recognizing the dynamic and massive flow of\npeople. In particular, a clustering method that can efficiently assign each\nsnapshot to the corresponding customer is essential for the system. In order to\naddress the unique challenges in the open checkout-free grocery, we propose an\nefficient and effective person clustering method. Specifically, we first\npropose a Crowded Sub-Graph (CSG) to localize the relationship among massive\nand continuous data streams. CSG is constructed by the proposed\nPick-Link-Weight (PLW) strategy, which \\textbf{picks} the nodes based on\ntime-space information, \\textbf{links} the nodes via trajectory information,\nand \\textbf{weighs} the links by the proposed von Mises-Fisher (vMF) similarity\nmetric. Then, to ensure that the method adapts to the dynamic and unseen person\nflow, we propose Graph Convolutional Network (GCN) with a simple Nearest\nNeighbor (NN) strategy to accurately cluster the instances of CSG. GCN is\nadopted to project the features into low-dimensional separable space, and NN is\nable to quickly produce a result in this space upon dynamic person flow. The\nexperimental results show that the proposed method outperforms other\nalternative algorithms in this scenario. In practice, the whole system has been\nimplemented and deployed in several real-world open checkout-free groceries.\n", "date": "2022-08-05", "categories": []}
{"id": "2209.09030", "title": "SMIXS: Novel efficient algorithm for non-parametric mixture\n  regression-based clustering", "abstract": "  We investigate a novel non-parametric regression-based clustering algorithm\nfor longitudinal data analysis. Combining natural cubic splines with Gaussian\nmixture models (GMM), the algorithm can produce smooth cluster means that\ndescribe the underlying data well. However, there are some shortcomings in the\nalgorithm: high computational complexity in the parameter estimation procedure\nand a numerically unstable variance estimator. Therefore, to further increase\nthe usability of the method, we incorporated approaches to reduce its\ncomputational complexity, we developed a new, more stable variance estimator,\nand we developed a new smoothing parameter estimation procedure. We show that\nthe developed algorithm, SMIXS, performs better than GMM on a synthetic dataset\nin terms of clustering and regression performance. We demonstrate the impact of\nthe computational speed-ups, which we formally prove in the new framework.\nFinally, we perform a case study by using SMIXS to cluster vertical atmospheric\nmeasurements to determine different weather regimes.\n", "date": "2022-09-19", "categories": []}
{"id": "2209.07715", "title": "Comments on \"Iteratively Re-weighted Algorithm for Fuzzy c-Means\"", "abstract": "  In this comment, we present a simple alternate derivation to the IRW-FCM\nalgorithm presented in \"Iteratively Re-weighted Algorithm for Fuzzy c-Means\"\nfor Fuzzy c-Means problem. We show that the iterative steps derived for IRW-FCM\nalgorithm are nothing but steps of the popular Majorization Minimization (MM)\nalgorithm. The derivation presented in this note is much simpler and\nstraightforward and, unlike the derivation of IRW-FCM, the derivation here does\nnot involve introduction of any auxiliary variable. Moreover, by showing the\nsteps of IRW-FCM as the MM algorithm, the inner loop of the IRW-FCM algorithm\ncan be eliminated and the algorithm can be effectively run as a \"single loop\"\nalgorithm. More precisely, the new MM-based derivation deduces that a single\ninner loop of IRW-FCM is sufficient to decrease the Fuzzy c-means objective\nfunction, which speeds up the IRW-FCM algorithm.\n", "date": "2022-09-16", "categories": []}
{"id": "2209.06941", "title": "Joint Debiased Representation and Image Clustering Learning with\n  Self-Supervision", "abstract": "  Contrastive learning is among the most successful methods for visual\nrepresentation learning, and its performance can be further improved by jointly\nperforming clustering on the learned representations. However, existing methods\nfor joint clustering and contrastive learning do not perform well on\nlong-tailed data distributions, as majority classes overwhelm and distort the\nloss of minority classes, thus preventing meaningful representations to be\nlearned. Motivated by this, we develop a novel joint clustering and contrastive\nlearning framework by adapting the debiased contrastive loss to avoid\nunder-clustering minority classes of imbalanced datasets. We show that our\nproposed modified debiased contrastive loss and divergence clustering loss\nimproves the performance across multiple datasets and learning tasks. The\nsource code is available at\nhttps://anonymous.4open.science/r/SSL-debiased-clustering\n", "date": "2022-09-14", "categories": []}
{"id": "2209.06582", "title": "A Clustering Method Based on Information Entropy Payload", "abstract": "  Existing clustering algorithms such as K-means often need to preset\nparameters such as the number of categories K, and such parameters may lead to\nthe failure to output objective and consistent clustering results. This paper\nintroduces a clustering method based on the information theory, by which\nclusters in the clustering result have maximum average information entropy\n(called entropy payload in this paper). This method can bring the following\nbenefits: firstly, this method does not need to preset any super parameter such\nas category number or other similar thresholds, secondly, the clustering\nresults have the maximum information expression efficiency. it can be used in\nimage segmentation, object classification, etc., and could be the basis of\nunsupervised learning.\n", "date": "2022-09-13", "categories": []}
{"id": "2209.05757", "title": "Genie: A new, fast, and outlier-resistant hierarchical clustering\n  algorithm", "abstract": "  The time needed to apply a hierarchical clustering algorithm is most often\ndominated by the number of computations of a pairwise dissimilarity measure.\nSuch a constraint, for larger data sets, puts at a disadvantage the use of all\nthe classical linkage criteria but the single linkage one. However, it is known\nthat the single linkage clustering algorithm is very sensitive to outliers,\nproduces highly skewed dendrograms, and therefore usually does not reflect the\ntrue underlying data structure -- unless the clusters are well-separated. To\novercome its limitations, we propose a new hierarchical clustering linkage\ncriterion called Genie. Namely, our algorithm links two clusters in such a way\nthat a chosen economic inequity measure (e.g., the Gini- or Bonferroni-index)\nof the cluster sizes does not drastically increase above a given threshold. The\npresented benchmarks indicate a high practical usefulness of the introduced\nmethod: it most often outperforms the Ward or average linkage in terms of the\nclustering quality while retaining the single linkage's speed. The Genie\nalgorithm is easily parallelizable and thus may be run on multiple threads to\nspeed up its execution even further. Its memory overhead is small: there is no\nneed to precompute the complete distance matrix to perform the computations in\norder to obtain a desired clustering. It can be applied on arbitrary spaces\nequipped with a dissimilarity measure, e.g., on real vectors, DNA or protein\nsequences, images, rankings, informetric data, etc. A reference implementation\nof the algorithm has been included in the open source 'genie' package for R.\nSee also https://genieclust.gagolewski.com for a new implementation\n(genieclust) -- available for both R and Python.\n", "date": "2022-09-13", "categories": []}
{"id": "2207.10469", "title": "Fast Data Driven Estimation of Cluster Number in Multiplex Images using\n  Embedded Density Outliers", "abstract": "  The usage of chemical imaging technologies is becoming a routine\naccompaniment to traditional methods in pathology. Significant technological\nadvances have developed these next generation techniques to provide rich,\nspatially resolved, multidimensional chemical images. The rise of digital\npathology has significantly enhanced the synergy of these imaging modalities\nwith optical microscopy and immunohistochemistry, enhancing our understanding\nof the biological mechanisms and progression of diseases. Techniques such as\nimaging mass cytometry provide labelled multidimensional (multiplex) images of\nspecific components used in conjunction with digital pathology techniques.\nThese powerful techniques generate a wealth of high dimensional data that\ncreate significant challenges in data analysis. Unsupervised methods such as\nclustering are an attractive way to analyse these data, however, they require\nthe selection of parameters such as the number of clusters. Here we propose a\nmethodology to estimate the number of clusters in an automatic data-driven\nmanner using a deep sparse autoencoder to embed the data into a lower\ndimensional space. We compute the density of regions in the embedded space, the\nmajority of which are empty, enabling the high density regions to be detected\nas outliers and provide an estimate for the number of clusters. This framework\nprovides a fully unsupervised and data-driven method to analyse\nmultidimensional data. In this work we demonstrate our method using 45\nmultiplex imaging mass cytometry datasets. Moreover, our model is trained using\nonly one of the datasets and the learned embedding is applied to the remaining\n44 images providing an efficient process for data analysis. Finally, we\ndemonstrate the high computational efficiency of our method which is two orders\nof magnitude faster than estimating via computing the sum squared distances as\na function of cluster number.\n", "date": "2022-07-21", "categories": []}
{"id": "2209.02513", "title": "Semi-Supervised Clustering via Dynamic Graph Structure Learning", "abstract": "  Most existing semi-supervised graph-based clustering methods exploit the\nsupervisory information by either refining the affinity matrix or directly\nconstraining the low-dimensional representations of data points. The affinity\nmatrix represents the graph structure and is vital to the performance of\nsemi-supervised graph-based clustering. However, existing methods adopt a\nstatic affinity matrix to learn the low-dimensional representations of data\npoints and do not optimize the affinity matrix during the learning process. In\nthis paper, we propose a novel dynamic graph structure learning method for\nsemi-supervised clustering. In this method, we simultaneously optimize the\naffinity matrix and the low-dimensional representations of data points by\nleveraging the given pairwise constraints. Moreover, we propose an alternating\nminimization approach with proven convergence to solve the proposed nonconvex\nmodel. During the iteration process, our method cyclically updates the\nlow-dimensional representations of data points and refines the affinity matrix,\nleading to a dynamic affinity matrix (graph structure). Specifically, for the\nupdate of the affinity matrix, we enforce the data points with remarkably\ndifferent low-dimensional representations to have an affinity value of 0.\nFurthermore, we construct the initial affinity matrix by integrating the local\ndistance and global self-representation among data points. Experimental results\non eight benchmark datasets under different settings show the advantages of the\nproposed approach.\n", "date": "2022-09-06", "categories": []}
{"id": "2208.01261", "title": "Are Cluster Validity Measures (In)valid?", "abstract": "  Internal cluster validity measures (such as the Calinski-Harabasz, Dunn, or\nDavies-Bouldin indices) are frequently used for selecting the appropriate\nnumber of partitions a dataset should be split into. In this paper we consider\nwhat happens if we treat such indices as objective functions in unsupervised\nlearning activities. Is the optimal grouping with regards to, say, the\nSilhouette index really meaningful? It turns out that many cluster (in)validity\nindices promote clusterings that match expert knowledge quite poorly. We also\nintroduce a new, well-performing variant of the Dunn index that is built upon\nOWA operators and the near-neighbour graph so that subspaces of higher density,\nregardless of their shapes, can be separated from each other better.\n", "date": "2022-08-02", "categories": []}
{"id": "2208.14390", "title": "k-MS: A novel clustering algorithm based on morphological reconstruction", "abstract": "  This work proposes a clusterization algorithm called k-Morphological Sets\n(k-MS), based on morphological reconstruction and heuristics. k-MS is faster\nthan the CPU-parallel k-Means in worst case scenarios and produces enhanced\nvisualizations of the dataset as well as very distinct clusterizations. It is\nalso faster than similar clusterization methods that are sensitive to density\nand shapes such as Mitosis and TRICLUST. In addition, k-MS is deterministic and\nhas an intrinsic sense of maximal clusters that can be created for a given\ninput sample and input parameters, differing from k-Means and other\nclusterization algorithms. In other words, given a constant k, a structuring\nelement and a dataset, k-MS produces k or less clusters without using random/\npseudo-random functions. Finally, the proposed algorithm also provides a\nstraightforward means for removing noise from images or datasets in general.\n", "date": "2022-08-30", "categories": []}
{"id": "2208.12808", "title": "Adaptively-weighted Integral Space for Fast Multiview Clustering", "abstract": "  Multiview clustering has been extensively studied to take advantage of\nmulti-source information to improve the clustering performance. In general,\nmost of the existing works typically compute an n * n affinity graph by some\nsimilarity/distance metrics (e.g. the Euclidean distance) or learned\nrepresentations, and explore the pairwise correlations across views. But\nunfortunately, a quadratic or even cubic complexity is often needed, bringing\nabout difficulty in clustering largescale datasets. Some efforts have been made\nrecently to capture data distribution in multiple views by selecting view-wise\nanchor representations with k-means, or by direct matrix factorization on the\noriginal observations. Despite the significant success, few of them have\nconsidered the view-insufficiency issue, implicitly holding the assumption that\neach individual view is sufficient to recover the cluster structure. Moreover,\nthe latent integral space as well as the shared cluster structure from multiple\ninsufficient views is not able to be simultaneously discovered. In view of\nthis, we propose an Adaptively-weighted Integral Space for Fast Multiview\nClustering (AIMC) with nearly linear complexity. Specifically, view generation\nmodels are designed to reconstruct the view observations from the latent\nintegral space with diverse adaptive contributions. Meanwhile, a centroid\nrepresentation with orthogonality constraint and cluster partition are\nseamlessly constructed to approximate the latent integral space. An alternate\nminimizing algorithm is developed to solve the optimization problem, which is\nproved to have linear time complexity w.r.t. the sample size. Extensive\nexperiments conducted on several realworld datasets confirm the superiority of\nthe proposed AIMC method compared with the state-of-the-art methods.\n", "date": "2022-08-25", "categories": []}
{"id": "2208.13217", "title": "Leachable Component Clustering", "abstract": "  Clustering attempts to partition data instances into several distinctive\ngroups, while the similarities among data belonging to the common partition can\nbe principally reserved. Furthermore, incomplete data frequently occurs in many\nrealworld applications, and brings perverse influence on pattern analysis. As a\nconsequence, the specific solutions to data imputation and handling are\ndeveloped to conduct the missing values of data, and independent stage of\nknowledge exploitation is absorbed for information understanding. In this work,\na novel approach to clustering of incomplete data, termed leachable component\nclustering, is proposed. Rather than existing methods, the proposed method\nhandles data imputation with Bayes alignment, and collects the lost patterns in\ntheory. Due to the simple numeric computation of equations, the proposed method\ncan learn optimized partitions while the calculation efficiency is held.\nExperiments on several artificial incomplete data sets demonstrate that, the\nproposed method is able to present superior performance compared with other\nstate-of-the-art algorithms.\n", "date": "2022-08-28", "categories": []}
{"id": "2208.12636", "title": "Four Algorithms for Correlation Clustering: A Survey", "abstract": "  In the Correlation Clustering problem, we are given a set of objects with\npairwise similarity information. Our aim is to partition these objects into\nclusters that match this information as closely as possible. More specifically,\nthe pairwise information is given as a weighted graph $G$ with its edges\nlabelled as ``similar\" or ``dissimilar\" by a binary classifier. The goal is to\nproduce a clustering that minimizes the weight of ``disagreements\": the sum of\nthe weights of similar edges across clusters and dissimilar edges within\nclusters. In this exposition we focus on the case when $G$ is complete and\nunweighted. We explore four approximation algorithms for the Correlation\nClustering problem under this assumption. In particular, we describe the\nfollowing algorithms: (i) the $17429-$approximation algorithm by Bansal, Blum,\nand Chawla, (ii) the $4-$approximation algorithm by Charikar, Guruswami, and\nWirth (iii) the $3-$approximation algorithm by Ailon, Charikar, and Newman (iv)\nthe $2.06-$approximation algorithm by Chawla, Makarychev, Schramm, and\nYaroslavtsev.\n", "date": "2022-08-24", "categories": []}
{"id": "2208.12160", "title": "Clustering Egocentric Images in Passive Dietary Monitoring with\n  Self-Supervised Learning", "abstract": "  In our recent dietary assessment field studies on passive dietary monitoring\nin Ghana, we have collected over 250k in-the-wild images. The dataset is an\nongoing effort to facilitate accurate measurement of individual food and\nnutrient intake in low and middle income countries with passive monitoring\ncamera technologies. The current dataset involves 20 households (74 subjects)\nfrom both the rural and urban regions of Ghana, and two different types of\nwearable cameras were used in the studies. Once initiated, wearable cameras\ncontinuously capture subjects' activities, which yield massive amounts of data\nto be cleaned and annotated before analysis is conducted. To ease the data\npost-processing and annotation tasks, we propose a novel self-supervised\nlearning framework to cluster the large volume of egocentric images into\nseparate events. Each event consists of a sequence of temporally continuous and\ncontextually similar images. By clustering images into separate events,\nannotators and dietitians can examine and analyze the data more efficiently and\nfacilitate the subsequent dietary assessment processes. Validated on a held-out\ntest set with ground truth labels, the proposed framework outperforms baselines\nin terms of clustering quality and classification accuracy.\n", "date": "2022-08-25", "categories": []}
{"id": "2208.09643", "title": "The computational complexity of some explainable clustering problems", "abstract": "  We study the computational complexity of some explainable clustering problems\nin the framework proposed by [Dasgupta et al., ICML 2020], where explainability\nis achieved via axis-aligned decision trees. We consider the $k$-means,\n$k$-medians, $k$-centers and the spacing cost functions. We prove that the\nfirst three are hard to optimize while the latter can be optimized in\npolynomial time.\n", "date": "2022-08-20", "categories": []}
{"id": "2208.10095", "title": "Socially Fair Center-based and Linear Subspace Clustering", "abstract": "  Center-based clustering (e.g., $k$-means, $k$-medians) and clustering using\nlinear subspaces are two most popular techniques to partition real-world data\ninto smaller clusters. However, when the data consists of sensitive demographic\ngroups, significantly different clustering cost per point for different\nsensitive groups can lead to fairness-related harms (e.g., different\nquality-of-service). The goal of socially fair clustering is to minimize the\nmaximum cost of clustering per point over all groups. In this work, we propose\na unified framework to solve socially fair center-based clustering and linear\nsubspace clustering, and give practical, efficient approximation algorithms for\nthese problems. We do extensive experiments to show that on multiple benchmark\ndatasets our algorithms either closely match or outperform state-of-the-art\nbaselines.\n", "date": "2022-08-22", "categories": []}
{"id": "2208.04313", "title": "AUTOSHAPE: An Autoencoder-Shapelet Approach for Time Series Clustering", "abstract": "  Time series shapelets are discriminative subsequences that have been recently\nfound effective for time series clustering (TSC). The shapelets are convenient\nfor interpreting the clusters. Thus, the main challenge for TSC is to discover\nhigh-quality variable-length shapelets to discriminate different clusters. In\nthis paper, we propose a novel autoencoder-shapelet approach (AUTOSHAPE), which\nis the first study to take the advantage of both autoencoder and shapelet for\ndetermining shapelets in an unsupervised manner. An autoencoder is specially\ndesigned to learn high-quality shapelets. More specifically, for guiding the\nlatent representation learning, we employ the latest self-supervised loss to\nlearn the unified embeddings for variable-length shapelet candidates (time\nseries subsequences) of different variables, and propose the diversity loss to\nselect the discriminating embeddings in the unified space. We introduce the\nreconstruction loss to recover shapelets in the original time series space for\nclustering. Finally, we adopt Davies Bouldin index (DBI) to inform AUTOSHAPE of\nthe clustering performance during learning. We present extensive experiments on\nAUTOSHAPE. To evaluate the clustering performance on univariate time series\n(UTS), we compare AUTOSHAPE with 15 representative methods using UCR archive\ndatasets. To study the performance of multivariate time series (MTS), we\nevaluate AUTOSHAPE on 30 UEA archive datasets with 5 competitive methods. The\nresults validate that AUTOSHAPE is the best among all the methods compared. We\ninterpret clusters with shapelets, and can obtain interesting intuitions about\nclusters in two UTS case studies and one MTS case study, respectively.\n", "date": "2022-08-06", "categories": []}
{"id": "2208.08040", "title": "A Survey on Incomplete Multi-view Clustering", "abstract": "  Conventional multi-view clustering seeks to partition data into respective\ngroups based on the assumption that all views are fully observed. However, in\npractical applications, such as disease diagnosis, multimedia analysis, and\nrecommendation system, it is common to observe that not all views of samples\nare available in many cases, which leads to the failure of the conventional\nmulti-view clustering methods. Clustering on such incomplete multi-view data is\nreferred to as incomplete multi-view clustering. In view of the promising\napplication prospects, the research of incomplete multi-view clustering has\nnoticeable advances in recent years. However, there is no survey to summarize\nthe current progresses and point out the future research directions. To this\nend, we review the recent studies of incomplete multi-view clustering.\nImportantly, we provide some frameworks to unify the corresponding incomplete\nmulti-view clustering methods, and make an in-depth comparative analysis for\nsome representative methods from theoretical and experimental perspectives.\nFinally, some open problems in the incomplete multi-view clustering field are\noffered for researchers.\n", "date": "2022-08-17", "categories": []}
{"id": "2208.04720", "title": "Clustering Optimisation Method for Highly Connected Biological Data", "abstract": "  Currently, data-driven discovery in biological sciences resides in finding\nsegmentation strategies in multivariate data that produce sensible descriptions\nof the data. Clustering is but one of several approaches and sometimes falls\nshort because of difficulties in assessing reasonable cutoffs, the number of\nclusters that need to be formed or that an approach fails to preserve\ntopological properties of the original system in its clustered form. In this\nwork, we show how a simple metric for connectivity clustering evaluation leads\nto an optimised segmentation of biological data.\n  The novelty of the work resides in the creation of a simple optimisation\nmethod for clustering crowded data. The resulting clustering approach only\nrelies on metrics derived from the inherent properties of the clustering. The\nnew method facilitates knowledge for optimised clustering, which is easy to\nimplement.\n  We discuss how the clustering optimisation strategy corresponds to the viable\ninformation content yielded by the final segmentation. We further elaborate on\nhow the clustering results, in the optimal solution, corresponds to prior\nknowledge of three different data sets.\n", "date": "2022-08-08", "categories": []}
{"id": "2208.05561", "title": "SSDBCODI: Semi-Supervised Density-Based Clustering with Outliers\n  Detection Integrated", "abstract": "  Clustering analysis is one of the critical tasks in machine learning.\nTraditionally, clustering has been an independent task, separate from outlier\ndetection. Due to the fact that the performance of clustering can be\nsignificantly eroded by outliers, a small number of algorithms try to\nincorporate outlier detection in the process of clustering. However, most of\nthose algorithms are based on unsupervised partition-based algorithms such as\nk-means. Given the nature of those algorithms, they often fail to deal with\nclusters of complex, non-convex shapes. To tackle this challenge, we have\nproposed SSDBCODI, a semi-supervised density-based algorithm. SSDBCODI combines\nthe advantage of density-based algorithms, which are capable of dealing with\nclusters of complex shapes, with the semi-supervised element, which offers\nflexibility to adjust the clustering results based on a few user labels. We\nalso merge an outlier detection component with the clustering process.\nPotential outliers are detected based on three scores generated during the\nprocess: (1) reachability-score, which measures how density-reachable a point\nis to a labeled normal object, (2) local-density-score, which measures the\nneighboring density of data objects, and (3) similarity-score, which measures\nthe closeness of a point to its nearest labeled outliers. Then in the following\nstep, instance weights are generated for each data instance based on those\nthree scores before being used to train a classifier for further clustering and\noutlier detection. To enhance the understanding of the proposed algorithm, for\nour evaluation, we have run our proposed algorithm against some of the\nstate-of-art approaches on multiple datasets and separately listed the results\nof outlier detection apart from clustering. Our results indicate that our\nalgorithm can achieve superior results with a small percentage of labels.\n", "date": "2022-08-10", "categories": []}
{"id": "2208.04537", "title": "Automating DBSCAN via Deep Reinforcement Learning", "abstract": "  DBSCAN is widely used in many scientific and engineering fields because of\nits simplicity and practicality. However, due to its high sensitivity\nparameters, the accuracy of the clustering result depends heavily on practical\nexperience. In this paper, we first propose a novel Deep Reinforcement Learning\nguided automatic DBSCAN parameters search framework, namely DRL-DBSCAN. The\nframework models the process of adjusting the parameter search direction by\nperceiving the clustering environment as a Markov decision process, which aims\nto find the best clustering parameters without manual assistance. DRL-DBSCAN\nlearns the optimal clustering parameter search policy for different feature\ndistributions via interacting with the clusters, using a weakly-supervised\nreward training policy network. In addition, we also present a recursive search\nmechanism driven by the scale of the data to efficiently and controllably\nprocess large parameter spaces. Extensive experiments are conducted on five\nartificial and real-world datasets based on the proposed four working modes.\nThe results of offline and online tasks show that the DRL-DBSCAN not only\nconsistently improves DBSCAN clustering accuracy by up to 26% and 25%\nrespectively, but also can stably find the dominant parameters with high\ncomputational efficiency. The code is available at\nhttps://github.com/RingBDStack/DRL-DBSCAN.\n", "date": "2022-08-09", "categories": []}
{"id": "2208.01724", "title": "A Tighter Analysis of Spectral Clustering, and Beyond", "abstract": "  This work studies the classical spectral clustering algorithm which embeds\nthe vertices of some graph $G=(V_G, E_G)$ into $\\mathbb{R}^k$ using $k$\neigenvectors of some matrix of $G$, and applies $k$-means to partition $V_G$\ninto $k$ clusters. Our first result is a tighter analysis on the performance of\nspectral clustering, and explains why it works under some much weaker condition\nthan the ones studied in the literature. For the second result, we show that,\nby applying fewer than $k$ eigenvectors to construct the embedding, spectral\nclustering is able to produce better output for many practical instances; this\nresult is the first of its kind in spectral clustering. Besides its conceptual\nand theoretical significance, the practical impact of our work is demonstrated\nby the empirical analysis on both synthetic and real-world datasets, in which\nspectral clustering produces comparable or better results with fewer than $k$\neigenvectors.\n", "date": "2022-08-02", "categories": []}
{"id": "2208.01152", "title": "Interpretable Time Series Clustering Using Local Explanations", "abstract": "  This study focuses on exploring the use of local interpretability methods for\nexplaining time series clustering models. Many of the state-of-the-art\nclustering models are not directly explainable. To provide explanations for\nthese clustering algorithms, we train classification models to estimate the\ncluster labels. Then, we use interpretability methods to explain the decisions\nof the classification models. The explanations are used to obtain insights into\nthe clustering models. We perform a detailed numerical study to test the\nproposed approach on multiple datasets, clustering models, and classification\nmodels. The analysis of the results shows that the proposed approach can be\nused to explain time series clustering models, specifically when the underlying\nclassification model is accurate. Lastly, we provide a detailed analysis of the\nresults, discussing how our approach can be used in a real-life scenario.\n", "date": "2022-08-01", "categories": []}
{"id": "2208.01198", "title": "Late Fusion Multi-view Clustering via Global and Local Alignment\n  Maximization", "abstract": "  Multi-view clustering (MVC) optimally integrates complementary information\nfrom different views to improve clustering performance. Although demonstrating\npromising performance in various applications, most of existing approaches\ndirectly fuse multiple pre-specified similarities to learn an optimal\nsimilarity matrix for clustering, which could cause over-complicated\noptimization and intensive computational cost. In this paper, we propose late\nfusion MVC via alignment maximization to address these issues. To do so, we\nfirst reveal the theoretical connection of existing k-means clustering and the\nalignment between base partitions and the consensus one. Based on this\nobservation, we propose a simple but effective multi-view algorithm termed\nLF-MVC-GAM. It optimally fuses multiple source information in partition level\nfrom each individual view, and maximally aligns the consensus partition with\nthese weighted base ones. Such an alignment is beneficial to integrate\npartition level information and significantly reduce the computational\ncomplexity by sufficiently simplifying the optimization procedure. We then\ndesign another variant, LF-MVC-LAM to further improve the clustering\nperformance by preserving the local intrinsic structure among multiple\npartition spaces. After that, we develop two three-step iterative algorithms to\nsolve the resultant optimization problems with theoretically guaranteed\nconvergence. Further, we provide the generalization error bound analysis of the\nproposed algorithms. Extensive experiments on eighteen multi-view benchmark\ndatasets demonstrate the effectiveness and efficiency of the proposed\nLF-MVC-GAM and LF-MVC-LAM, ranging from small to large-scale data items. The\ncodes of the proposed algorithms are publicly available at\nhttps://github.com/wangsiwei2010/latefusionalignment.\n", "date": "2022-08-02", "categories": []}
{"id": "2207.14375", "title": "Expanding the class of global objective functions for\n  dissimilarity-based hierarchical clustering", "abstract": "  Recent work on dissimilarity-based hierarchical clustering has led to the\nintroduction of global objective functions for this classical problem. Several\nstandard approaches, such as average linkage, as well as some new heuristics\nhave been shown to provide approximation guarantees. Here we introduce a broad\nnew class of objective functions which satisfy desirable properties studied in\nprior work. Many common agglomerative and divisive clustering methods are shown\nto be greedy algorithms for these objectives, which are inspired by related\nconcepts in phylogenetics.\n", "date": "2022-07-28", "categories": []}
{"id": "2207.14431", "title": "Learning idempotent representation for subspace clustering", "abstract": "  The critical point for the successes of spectral-type subspace clustering\nalgorithms is to seek reconstruction coefficient matrices which can faithfully\nreveal the subspace structures of data sets. An ideal reconstruction\ncoefficient matrix should have two properties: 1) it is block diagonal with\neach block indicating a subspace; 2) each block is fully connected. Though\nthere are various spectral-type subspace clustering algorithms have been\nproposed, some defects still exist in the reconstruction coefficient matrices\nconstructed by these algorithms. We find that a normalized membership matrix\nnaturally satisfies the above two conditions. Therefore, in this paper, we\ndevise an idempotent representation (IDR) algorithm to pursue reconstruction\ncoefficient matrices approximating normalized membership matrices. IDR designs\na new idempotent constraint for reconstruction coefficient matrices. And by\ncombining the doubly stochastic constraints, the coefficient matrices which are\nclosed to normalized membership matrices could be directly achieved. We present\nthe optimization algorithm for solving IDR problem and analyze its computation\nburden as well as convergence. The comparisons between IDR and related\nalgorithms show the superiority of IDR. Plentiful experiments conducted on both\nsynthetic and real world datasets prove that IDR is an effective and efficient\nsubspace clustering algorithm.\n", "date": "2022-07-29", "categories": []}
{"id": "2207.14589", "title": "Stochastic Parallelizable Eigengap Dilation for Large Graph Clustering", "abstract": "  Large graphs commonly appear in social networks, knowledge graphs,\nrecommender systems, life sciences, and decision making problems. Summarizing\nlarge graphs by their high level properties is helpful in solving problems in\nthese settings. In spectral clustering, we aim to identify clusters of nodes\nwhere most edges fall within clusters and only few edges fall between clusters.\nThis task is important for many downstream applications and exploratory\nanalysis. A core step of spectral clustering is performing an\neigendecomposition of the corresponding graph Laplacian matrix (or\nequivalently, a singular value decomposition, SVD, of the incidence matrix).\nThe convergence of iterative singular value decomposition approaches depends on\nthe eigengaps of the spectrum of the given matrix, i.e., the difference between\nconsecutive eigenvalues. For a graph Laplacian corresponding to a\nwell-clustered graph, the eigenvalues will be non-negative but very small (much\nless than $1$) slowing convergence. This paper introduces a parallelizable\napproach to dilating the spectrum in order to accelerate SVD solvers and in\nturn, spectral clustering. This is accomplished via polynomial approximations\nto matrix operations that favorably transform the spectrum of a matrix without\nchanging its eigenvectors. Experiments demonstrate that this approach\nsignificantly accelerates convergence, and we explain how this transformation\ncan be parallelized and stochastically approximated to scale with available\ncompute.\n", "date": "2022-07-29", "categories": []}
{"id": "2207.13364", "title": "Deep Clustering with Features from Self-Supervised Pretraining", "abstract": "  A deep clustering model conceptually consists of a feature extractor that\nmaps data points to a latent space, and a clustering head that groups data\npoints into clusters in the latent space. Although the two components used to\nbe trained jointly in an end-to-end fashion, recent works have proved it\nbeneficial to train them separately in two stages. In the first stage, the\nfeature extractor is trained via self-supervised learning, which enables the\npreservation of the cluster structures among the data points. To preserve the\ncluster structures even better, we propose to replace the first stage with\nanother model that is pretrained on a much larger dataset via self-supervised\nlearning. The method is simple and might suffer from domain shift. Nonetheless,\nwe have empirically shown that it can achieve superior clustering performance.\nWhen a vision transformer (ViT) architecture is used for feature extraction,\nour method has achieved clustering accuracy 94.0%, 55.6% and 97.9% on CIFAR-10,\nCIFAR-100 and STL-10 respectively. The corresponding previous state-of-the-art\nresults are 84.3%, 47.7% and 80.8%. Our code will be available online with the\npublication of the paper.\n", "date": "2022-07-27", "categories": []}
{"id": "2207.11559", "title": "Tensor-based Multi-view Spectral Clustering via Shared Latent Space", "abstract": "  Multi-view Spectral Clustering (MvSC) attracts increasing attention due to\ndiverse data sources. However, most existing works are prohibited in\nout-of-sample predictions and overlook model interpretability and exploration\nof clustering results. In this paper, a new method for MvSC is proposed via a\nshared latent space from the Restricted Kernel Machine framework. Through the\nlens of conjugate feature duality, we cast the weighted kernel principal\ncomponent analysis problem for MvSC and develop a modified weighted conjugate\nfeature duality to formulate dual variables. In our method, the dual variables,\nplaying the role of hidden features, are shared by all views to construct a\ncommon latent space, coupling the views by learning projections from\nview-specific spaces. Such single latent space promotes well-separated clusters\nand provides straightforward data exploration, facilitating visualization and\ninterpretation. Our method requires only a single eigendecomposition, whose\ndimension is independent of the number of views. To boost higher-order\ncorrelations, tensor-based modelling is introduced without increasing\ncomputational complexity. Our method can be flexibly applied with out-of-sample\nextensions, enabling greatly improved efficiency for large-scale data with\nfixed-size kernel schemes. Numerical experiments verify that our method is\neffective regarding accuracy, efficiency, and interpretability, showing a sharp\neigenvalue decay and distinct latent variable distributions.\n", "date": "2022-07-23", "categories": []}
{"id": "2207.11895", "title": "On Mitigating Hard Clusters for Face Clustering", "abstract": "  Face clustering is a promising way to scale up face recognition systems using\nlarge-scale unlabeled face images. It remains challenging to identify small or\nsparse face image clusters that we call hard clusters, which is caused by the\nheterogeneity, \\ie, high variations in size and sparsity, of the clusters.\nConsequently, the conventional way of using a uniform threshold (to identify\nclusters) often leads to a terrible misclassification for the samples that\nshould belong to hard clusters. We tackle this problem by leveraging the\nneighborhood information of samples and inferring the cluster memberships (of\nsamples) in a probabilistic way. We introduce two novel modules,\nNeighborhood-Diffusion-based Density (NDDe) and Transition-Probability-based\nDistance (TPDi), based on which we can simply apply the standard Density Peak\nClustering algorithm with a uniform threshold. Our experiments on multiple\nbenchmarks show that each module contributes to the final performance of our\nmethod, and by incorporating them into other advanced face clustering methods,\nthese two modules can boost the performance of these methods to a new\nstate-of-the-art. Code is available at:\nhttps://github.com/echoanran/On-Mitigating-Hard-Clusters.\n", "date": "2022-07-25", "categories": []}
{"id": "2207.12279", "title": "Orthogonalization of data via Gromov-Wasserstein type feedback for\n  clustering and visualization", "abstract": "  In this paper we propose an adaptive approach for clustering and\nvisualization of data by an orthogonalization process. Starting with the data\npoints being represented by a Markov process using the diffusion map framework,\nthe method adaptively increase the orthogonality of the clusters by applying a\nfeedback mechanism inspired by the Gromov-Wasserstein distance. This mechanism\niteratively increases the spectral gap and refines the orthogonality of the\ndata to achieve a clustering with high specificity. By using the diffusion map\nframework and representing the relation between data points using transition\nprobabilities, the method is robust with respect to both the underlying\ndistance, noise in the data and random initialization. We prove that the method\nconverges globally to a unique fixpoint for certain parameter values. We also\npropose a related approach where the transition probabilities in the Markov\nprocess are required to be doubly stochastic, in which case the method\ngenerates a minimizer to a nonconvex optimization problem. We apply the method\non cryo-electron microscopy image data from biopharmaceutical manufacturing\nwhere we can confirm biologically relevant insights related to therapeutic\nefficacy. We consider an example with morphological variations of gene\npackaging and confirm that the method produces biologically meaningful\nclustering results consistent with human expert classification.\n", "date": "2022-07-25", "categories": []}
{"id": "2206.04583", "title": "Clustering with Queries under Semi-Random Noise", "abstract": "  The seminal paper by Mazumdar and Saha \\cite{MS17a} introduced an extensive\nline of work on clustering with noisy queries. Yet, despite significant\nprogress on the problem, the proposed methods depend crucially on knowing the\nexact probabilities of errors of the underlying fully-random oracle. In this\nwork, we develop robust learning methods that tolerate general semi-random\nnoise obtaining qualitatively the same guarantees as the best possible methods\nin the fully-random model.\n  More specifically, given a set of $n$ points with an unknown underlying\npartition, we are allowed to query pairs of points $u,v$ to check if they are\nin the same cluster, but with probability $p$, the answer may be adversarially\nchosen. We show that information theoretically $O\\left(\\frac{nk \\log n}\n{(1-2p)^2}\\right)$ queries suffice to learn any cluster of sufficiently large\nsize. Our main result is a computationally efficient algorithm that can\nidentify large clusters with $O\\left(\\frac{nk \\log n} {(1-2p)^2}\\right) +\n\\text{poly}\\left(\\log n, k, \\frac{1}{1-2p} \\right)$ queries, matching the\nguarantees of the best known algorithms in the fully-random model. As a\ncorollary of our approach, we develop the first parameter-free algorithm for\nthe fully-random model, answering an open question by \\cite{MS17a}.\n", "date": "2022-06-09", "categories": []}
{"id": "2207.10625", "title": "A Dynamical Systems Algorithm for Clustering in Hyperspectral Imagery", "abstract": "  In this paper we present a new dynamical systems algorithm for clustering in\nhyperspectral images. The main idea of the algorithm is that data points are\n\\`pushed\\' in the direction of increasing density and groups of pixels that end\nup in the same dense regions belong to the same class. This is essentially a\nnumerical solution of the differential equation defined by the gradient of the\ndensity of data points on the data manifold. The number of classes is automated\nand the resulting clustering can be extremely accurate. In addition to\nproviding a accurate clustering, this algorithm presents a new tool for\nunderstanding hyperspectral data in high dimensions. We evaluate the algorithm\non the Urban (Available at www.tec.ary.mil/Hypercube/) scene comparing\nperformance against the k-means algorithm using pre-identified classes of\nmaterials as ground truth.\n", "date": "2022-07-21", "categories": []}
{"id": "2207.07949", "title": "A Nearly Tight Analysis of Greedy k-means++", "abstract": "  The famous $k$-means++ algorithm of Arthur and Vassilvitskii [SODA 2007] is\nthe most popular way of solving the $k$-means problem in practice. The\nalgorithm is very simple: it samples the first center uniformly at random and\neach of the following $k-1$ centers is then always sampled proportional to its\nsquared distance to the closest center so far. Afterward, Lloyd's iterative\nalgorithm is run. The $k$-means++ algorithm is known to return a $\\Theta(\\log\nk)$ approximate solution in expectation.\n  In their seminal work, Arthur and Vassilvitskii [SODA 2007] asked about the\nguarantees for its following \\emph{greedy} variant: in every step, we sample\n$\\ell$ candidate centers instead of one and then pick the one that minimizes\nthe new cost. This is also how $k$-means++ is implemented in e.g. the popular\nScikit-learn library [Pedregosa et al.; JMLR 2011].\n  We present nearly matching lower and upper bounds for the greedy $k$-means++:\nWe prove that it is an $O(\\ell^3 \\log^3 k)$-approximation algorithm. On the\nother hand, we prove a lower bound of $\\Omega(\\ell^3 \\log^3 k / \\log^2(\\ell\\log\nk))$. Previously, only an $\\Omega(\\ell \\log k)$ lower bound was known\n[Bhattacharya, Eube, R\\\"oglin, Schmidt; ESA 2020] and there was no known upper\nbound.\n", "date": "2022-07-16", "categories": []}
{"id": "2206.00380", "title": "Strongly Augmented Contrastive Clustering", "abstract": "  Deep clustering has attracted increasing attention in recent years due to its\ncapability of joint representation learning and clustering via deep neural\nnetworks. In its latest developments, the contrastive learning has emerged as\nan effective technique to substantially enhance the deep clustering\nperformance. However, the existing contrastive learning based deep clustering\nalgorithms mostly focus on some carefully-designed augmentations (often with\nlimited transformations to preserve the structure), referred to as weak\naugmentations, but cannot go beyond the weak augmentations to explore the more\nopportunities in stronger augmentations (with more aggressive transformations\nor even severe distortions). In this paper, we present an end-to-end deep\nclustering approach termed Strongly Augmented Contrastive Clustering (SACC),\nwhich extends the conventional two-augmentation-view paradigm to multiple views\nand jointly leverages strong and weak augmentations for strengthened deep\nclustering. Particularly, we utilize a backbone network with triply-shared\nweights, where a strongly augmented view and two weakly augmented views are\nincorporated. Based on the representations produced by the backbone, the\nweak-weak view pair and the strong-weak view pairs are simultaneously exploited\nfor the instance-level contrastive learning (via an instance projector) and the\ncluster-level contrastive learning (via a cluster projector), which, together\nwith the backbone, can be jointly optimized in a purely unsupervised manner.\nExperimental results on five challenging image datasets have shown the\nsuperiority of our SACC approach over the state-of-the-art. The code is\navailable at https://github.com/dengxiaozhi/SACC.\n", "date": "2022-06-01", "categories": []}
{"id": "2207.06041", "title": "Multiple Kernel Clustering with Dual Noise Minimization", "abstract": "  Clustering is a representative unsupervised method widely applied in\nmulti-modal and multi-view scenarios. Multiple kernel clustering (MKC) aims to\ngroup data by integrating complementary information from base kernels. As a\nrepresentative, late fusion MKC first decomposes the kernels into orthogonal\npartition matrices, then learns a consensus one from them, achieving promising\nperformance recently. However, these methods fail to consider the noise inside\nthe partition matrix, preventing further improvement of clustering performance.\nWe discover that the noise can be disassembled into separable dual parts, i.e.\nN-noise and C-noise (Null space noise and Column space noise). In this paper,\nwe rigorously define dual noise and propose a novel parameter-free MKC\nalgorithm by minimizing them. To solve the resultant optimization problem, we\ndesign an efficient two-step iterative strategy. To our best knowledge, it is\nthe first time to investigate dual noise within the partition in the kernel\nspace. We observe that dual noise will pollute the block diagonal structures\nand incur the degeneration of clustering performance, and C-noise exhibits\nstronger destruction than N-noise. Owing to our efficient mechanism to minimize\ndual noise, the proposed algorithm surpasses the recent methods by large\nmargins.\n", "date": "2022-07-13", "categories": []}
{"id": "2207.05376", "title": "Optimal Clustering with Noisy Queries via Multi-Armed Bandit", "abstract": "  Motivated by many applications, we study clustering with a faulty oracle. In\nthis problem, there are $n$ items belonging to $k$ unknown clusters, and the\nalgorithm is allowed to ask the oracle whether two items belong to the same\ncluster or not. However, the answer from the oracle is correct only with\nprobability $\\frac{1}{2}+\\frac{\\delta}{2}$. The goal is to recover the hidden\nclusters with minimum number of noisy queries. Previous works have shown that\nthe problem can be solved with $O(\\frac{nk\\log n}{\\delta^2} +\n\\text{poly}(k,\\frac{1}{\\delta}, \\log n))$ queries, while\n$\\Omega(\\frac{nk}{\\delta^2})$ queries is known to be necessary. So, for any\nvalues of $k$ and $\\delta$, there is still a non-trivial gap between upper and\nlower bounds. In this work, we obtain the first matching upper and lower bounds\nfor a wide range of parameters. In particular, a new polynomial time algorithm\nwith $O(\\frac{n(k+\\log n)}{\\delta^2} + \\text{poly}(k,\\frac{1}{\\delta}, \\log\nn))$ queries is proposed. Moreover, we prove a new lower bound of\n$\\Omega(\\frac{n\\log n}{\\delta^2})$, which, combined with the existing\n$\\Omega(\\frac{nk}{\\delta^2})$ bound, matches our upper bound up to an additive\n$\\text{poly}(k,\\frac{1}{\\delta},\\log n)$ term. To obtain the new results, our\nmain ingredient is an interesting connection between our problem and\nmulti-armed bandit, which might provide useful insights for other similar\nproblems.\n", "date": "2022-07-12", "categories": []}
{"id": "2206.12925", "title": "Vision Transformer for Contrastive Clustering", "abstract": "  Vision Transformer (ViT) has shown its advantages over the convolutional\nneural network (CNN) with its ability to capture global long-range dependencies\nfor visual representation learning. Besides ViT, contrastive learning is\nanother popular research topic recently. While previous contrastive learning\nworks are mostly based on CNNs, some recent studies have attempted to combine\nViT and contrastive learning for enhanced self-supervised learning. Despite the\nconsiderable progress, these combinations of ViT and contrastive learning\nmostly focus on the instance-level contrastiveness, which often overlook the\nglobal contrastiveness and also lack the ability to directly learn the\nclustering result (e.g., for images). In view of this, this paper presents a\nnovel deep clustering approach termed Vision Transformer for Contrastive\nClustering (VTCC), which for the first time, to our knowledge, unifies the\nTransformer and the contrastive learning for the image clustering task.\nSpecifically, with two random augmentations performed on each image, we utilize\na ViT encoder with two weight-sharing views as the backbone. To remedy the\npotential instability of the ViT, we incorporate a convolutional stem to split\neach augmented sample into a sequence of patches, which uses multiple stacked\nsmall convolutions instead of a big convolution in the patch projection layer.\nBy learning the feature representations for the sequences of patches via the\nbackbone, an instance projector and a cluster projector are further utilized to\nperform the instance-level contrastive learning and the global clustering\nstructure learning, respectively. Experiments on eight image datasets\ndemonstrate the stability (during the training-from-scratch) and the\nsuperiority (in clustering performance) of our VTCC approach over the\nstate-of-the-art.\n", "date": "2022-06-26", "categories": []}
{"id": "2207.04050", "title": "Few-Example Clustering via Contrastive Learning", "abstract": "  We propose Few-Example Clustering (FEC), a novel algorithm that performs\ncontrastive learning to cluster few examples. Our method is composed of the\nfollowing three steps: (1) generation of candidate cluster assignments, (2)\ncontrastive learning for each cluster assignment, and (3) selection of the best\ncandidate. Based on the hypothesis that the contrastive learner with the\nground-truth cluster assignment is trained faster than the others, we choose\nthe candidate with the smallest training loss in the early stage of learning in\nstep (3). Extensive experiments on the \\textit{mini}-ImageNet and CUB-200-2011\ndatasets show that FEC outperforms other baselines by about 3.2% on average\nunder various scenarios. FEC also exhibits an interesting learning curve where\nclustering performance gradually increases and then sharply drops.\n", "date": "2022-07-08", "categories": []}
{"id": "2207.04261", "title": "Fuzzy Clustering by Hyperbolic Smoothing", "abstract": "  We propose a novel method for building fuzzy clusters of large data sets,\nusing a smoothing numerical approach. The usual sum-of-squares criterion is\nrelaxed so the search for good fuzzy partitions is made on a continuous space,\nrather than a combinatorial space as in classical methods \\cite{Hartigan}. The\nsmoothing allows a conversion from a strongly non-differentiable problem into\ndifferentiable subproblems of optimization without constraints of low\ndimension, by using a differentiable function of infinite class. For the\nimplementation of the algorithm we used the statistical software $R$ and the\nresults obtained were compared to the traditional fuzzy $C$--means method,\nproposed by Bezdek.\n", "date": "2022-07-09", "categories": []}
{"id": "2207.03600", "title": "Individual Preference Stability for Clustering", "abstract": "  In this paper, we propose a natural notion of individual preference (IP)\nstability for clustering, which asks that every data point, on average, is\ncloser to the points in its own cluster than to the points in any other\ncluster. Our notion can be motivated from several perspectives, including game\ntheory and algorithmic fairness. We study several questions related to our\nproposed notion. We first show that deciding whether a given data set allows\nfor an IP-stable clustering in general is NP-hard. As a result, we explore the\ndesign of efficient algorithms for finding IP-stable clusterings in some\nrestricted metric spaces. We present a polytime algorithm to find a clustering\nsatisfying exact IP-stability on the real line, and an efficient algorithm to\nfind an IP-stable 2-clustering for a tree metric. We also consider relaxing the\nstability constraint, i.e., every data point should not be too far from its own\ncluster compared to any other cluster. For this case, we provide polytime\nalgorithms with different guarantees. We evaluate some of our algorithms and\nseveral standard clustering approaches on real data sets.\n", "date": "2022-07-07", "categories": []}
{"id": "2207.02846", "title": "Local Sample-weighted Multiple Kernel Clustering with Consensus\n  Discriminative Graph", "abstract": "  Multiple kernel clustering (MKC) is committed to achieving optimal\ninformation fusion from a set of base kernels. Constructing precise and local\nkernel matrices is proved to be of vital significance in applications since the\nunreliable distant-distance similarity estimation would degrade clustering\nper-formance. Although existing localized MKC algorithms exhibit improved\nperformance compared to globally-designed competi-tors, most of them widely\nadopt KNN mechanism to localize kernel matrix by accounting for {\\tau} -nearest\nneighbors. However, such a coarse manner follows an unreasonable strategy that\nthe ranking importance of different neighbors is equal, which is impractical in\napplications. To alleviate such problems, this paper proposes a novel local\nsample-weighted multiple kernel clustering (LSWMKC) model. We first construct a\nconsensus discriminative affinity graph in kernel space, revealing the latent\nlocal structures. Further, an optimal neighborhood kernel for the learned\naffinity graph is output with naturally sparse property and clear block\ndiagonal structure. Moreover, LSWMKC im-plicitly optimizes adaptive weights on\ndifferent neighbors with corresponding samples. Experimental results\ndemonstrate that our LSWMKC possesses better local manifold representation and\noutperforms existing kernel or graph-based clustering algo-rithms. The source\ncode of LSWMKC can be publicly accessed from\nhttps://github.com/liliangnudt/LSWMKC.\n", "date": "2022-07-05", "categories": []}
{"id": "2207.00966", "title": "An Empirical Evaluation of $k$-Means Coresets", "abstract": "  Coresets are among the most popular paradigms for summarizing data. In\nparticular, there exist many high performance coresets for clustering problems\nsuch as $k$-means in both theory and practice. Curiously, there exists no work\non comparing the quality of available $k$-means coresets.\n  In this paper we perform such an evaluation. There currently is no algorithm\nknown to measure the distortion of a candidate coreset. We provide some\nevidence as to why this might be computationally difficult. To complement this,\nwe propose a benchmark for which we argue that computing coresets is\nchallenging and which also allows us an easy (heuristic) evaluation of\ncoresets. Using this benchmark and real-world data sets, we conduct an\nexhaustive evaluation of the most commonly used coreset algorithms from theory\nand practice.\n", "date": "2022-07-03", "categories": []}
{"id": "2207.01178", "title": "An Improved Probability Propagation Algorithm for Density Peak\n  Clustering Based on Natural Nearest Neighborhood", "abstract": "  Clustering by fast search and find of density peaks (DPC) (Since, 2014) has\nbeen proven to be a promising clustering approach that efficiently discovers\nthe centers of clusters by finding the density peaks. The accuracy of DPC\ndepends on the cutoff distance ($d_c$), the cluster number ($k$) and the\nselection of the centers of clusters. Moreover, the final allocation strategy\nis sensitive and has poor fault tolerance. The shortcomings above make the\nalgorithm sensitive to parameters and only applicable for some specific\ndatasets. To overcome the limitations of DPC, this paper presents an improved\nprobability propagation algorithm for density peak clustering based on the\nnatural nearest neighborhood (DPC-PPNNN). By introducing the idea of natural\nnearest neighborhood and probability propagation, DPC-PPNNN realizes the\nnonparametric clustering process and makes the algorithm applicable for more\ncomplex datasets. In experiments on several datasets, DPC-PPNNN is shown to\noutperform DPC, K-means and DBSCAN.\n", "date": "2022-07-04", "categories": []}
{"id": "2207.00510", "title": "Enhancing cluster analysis via topological manifold learning", "abstract": "  We discuss topological aspects of cluster analysis and show that inferring\nthe topological structure of a dataset before clustering it can considerably\nenhance cluster detection: theoretical arguments and empirical evidence show\nthat clustering embedding vectors, representing the structure of a data\nmanifold instead of the observed feature vectors themselves, is highly\nbeneficial. To demonstrate, we combine manifold learning method UMAP for\ninferring the topological structure with density-based clustering method\nDBSCAN. Synthetic and real data results show that this both simplifies and\nimproves clustering in a diverse set of low- and high-dimensional problems\nincluding clusters of varying density and/or entangled shapes. Our approach\nsimplifies clustering because topological pre-processing consistently reduces\nparameter sensitivity of DBSCAN. Clustering the resulting embeddings with\nDBSCAN can then even outperform complex methods such as SPECTACL and\nClusterGAN. Finally, our investigation suggests that the crucial issue in\nclustering does not appear to be the nominal dimension of the data or how many\nirrelevant features it contains, but rather how \\textit{separable} the clusters\nare in the ambient observation space they are embedded in, which is usually the\n(high-dimensional) Euclidean space defined by the features of the data. Our\napproach is successful because we perform the cluster analysis after projecting\nthe data into a more suitable space that is optimized for separability, in some\nsense.\n", "date": "2022-07-01", "categories": []}
{"id": "2206.14233", "title": "Gaussian Latent Dirichlet Allocation for Discrete Human State Discovery", "abstract": "  In this article we propose and validate an unsupervised probabilistic model,\nGaussian Latent Dirichlet Allocation (GLDA), for the problem of discrete state\ndiscovery from repeated, multivariate psychophysiological samples collected\nfrom multiple, inherently distinct, individuals. Psychology and medical\nresearch heavily involves measuring potentially related but individually\ninconclusive variables from a cohort of participants to derive diagnosis,\nnecessitating clustering analysis. Traditional probabilistic clustering models\nsuch as Gaussian Mixture Model (GMM) assume a global mixture of component\ndistributions, which may not be realistic for observations from different\npatients. The GLDA model borrows the individual-specific mixture structure from\na popular topic model Latent Dirichlet Allocation (LDA) in Natural Language\nProcessing and merges it with the Gaussian component distributions of GMM to\nsuit continuous type data. We implemented GLDA using STAN (a probabilistic\nmodeling language) and applied it on two datasets, one containing Ecological\nMomentary Assessments (EMA) and the other heart measures from electrocardiogram\nand impedance cardiograph. We found that in both datasets the GLDA-learned\nclass weights achieved significantly higher correlations with clinically\nassessed depression, anxiety, and stress scores than those produced by the\nbaseline GMM. Our findings demonstrate the advantage of GLDA over conventional\nfinite mixture models for human state discovery from repeated multivariate\ndata, likely due to better characterization of potential underlying\nbetween-participant differences. Future work is required to validate the\nutility of this model on a broader range of applications.\n", "date": "2022-06-28", "categories": []}
{"id": "2206.05928", "title": "Compressive Clustering with an Optical Processing Unit", "abstract": "  We explore the use of Optical Processing Units (OPU) to compute random\nFourier features for sketching, and adapt the overall compressive clustering\npipeline to this setting. We also propose some tools to help tuning a critical\nhyper-parameter of compressive clustering.\n", "date": "2022-06-13", "categories": []}
{"id": "2206.13813", "title": "Sublinear-Time Clustering Oracle for Signed Graphs", "abstract": "  Social networks are often modeled using signed graphs, where vertices\ncorrespond to users and edges have a sign that indicates whether an interaction\nbetween users was positive or negative. The arising signed graphs typically\ncontain a clear community structure in the sense that the graph can be\npartitioned into a small number of polarized communities, each defining a\nsparse cut and indivisible into smaller polarized sub-communities. We provide a\nlocal clustering oracle for signed graphs with such a clear community\nstructure, that can answer membership queries, i.e., \"Given a vertex $v$, which\ncommunity does $v$ belong to?\", in sublinear time by reading only a small\nportion of the graph. Formally, when the graph has bounded maximum degree and\nthe number of communities is at most $O(\\log n)$, then with\n$\\tilde{O}(\\sqrt{n}\\operatorname{poly}(1/\\varepsilon))$ preprocessing time, our\noracle can answer each membership query in\n$\\tilde{O}(\\sqrt{n}\\operatorname{poly}(1/\\varepsilon))$ time, and it correctly\nclassifies a $(1-\\varepsilon)$-fraction of vertices w.r.t. a set of hidden\nplanted ground-truth communities. Our oracle is desirable in applications where\nthe clustering information is needed for only a small number of vertices.\nPreviously, such local clustering oracles were only known for unsigned graphs;\nour generalization to signed graphs requires a number of new ideas and gives a\nnovel spectral analysis of the behavior of random walks with signs. We evaluate\nour algorithm for constructing such an oracle and answering membership queries\non both synthetic and real-world datasets, validating its performance in\npractice.\n", "date": "2022-06-28", "categories": []}
{"id": "2206.12417", "title": "Deep embedded clustering algorithm for clustering PACS repositories", "abstract": "  Creating large datasets of medical radiology images from several sources can\nbe challenging because of the differences in the acquisition and storage\nstandards. One possible way of controlling and/or assessing the image selection\nprocess is through medical image clustering. This, however, requires an\nefficient method for learning latent image representations. In this paper, we\ntackle the problem of fully-unsupervised clustering of medical images using\npixel data only. We test the performance of several contemporary approaches,\nbuilt on top of a convolutional autoencoder (CAE) - convolutional deep embedded\nclustering (CDEC) and convolutional improved deep embedded clustering (CIDEC) -\nand three approaches based on preset feature extraction - histogram of oriented\ngradients (HOG), local binary pattern (LBP) and principal component analysis\n(PCA). CDEC and CIDEC are end-to-end clustering solutions, involving\nsimultaneous learning of latent representations and clustering assignments,\nwhereas the remaining approaches rely on k-means clustering from fixed\nembeddings. We train the models on 30,000 images, and test them using a\nseparate test set consisting of 8,000 images. We sampled the data from the PACS\nrepository archive of the Clinical Hospital Centre Rijeka. For evaluation, we\nuse silhouette score, homogeneity score and normalised mutual information (NMI)\non two target parameters, closely associated with commonly occurring DICOM tags\n- Modality and anatomical region (adjusted BodyPartExamined tag). CIDEC attains\nan NMI score of 0.473 with respect to anatomical region, and CDEC attains an\nNMI score of 0.645 with respect to the tag Modality - both outperforming other\ncommonly used feature descriptors.\n", "date": "2022-06-24", "categories": []}
{"id": "2206.12959", "title": "Probabilistic PolarGMM: Unsupervised Cluster Learning of Very Noisy\n  Projection Images of Unknown Pose", "abstract": "  A crucial step in single particle analysis (SPA) of cryogenic electron\nmicroscopy (Cryo-EM), 2D classification and alignment takes a collection of\nnoisy particle images to infer orientations and group similar images together.\nAveraging these aligned and clustered noisy images produces a set of clean\nimages, ready for further analysis such as 3D reconstruction. Fourier-Bessel\nsteerable principal component analysis (FBsPCA) enables an efficient,\nadaptable, low-rank rotation operator. We extend the FBsPCA to additionally\nhandle translations. In this extended FBsPCA representation, we use a\nprobabilistic polar-coordinate Gaussian mixture model to learn soft clusters in\nan unsupervised fashion using an expectation maximization (EM) algorithm. The\nobtained rotational clusters are thus additionally robust to the presence of\npairwise alignment imperfections. Multiple benchmarks from simulated Cryo-EM\ndatasets show probabilistic PolarGMM's improved performance in comparisons with\nstandard single-particle Cryo-EM tools, EMAN2 and RELION, in terms of various\nclustering metrics and alignment errors.\n", "date": "2022-06-26", "categories": []}
{"id": "2206.12190", "title": "SECLEDS: Sequence Clustering in Evolving Data Streams via Multiple\n  Medoids and Medoid Voting", "abstract": "  Sequence clustering in a streaming environment is challenging because it is\ncomputationally expensive, and the sequences may evolve over time. K-medoids or\nPartitioning Around Medoids (PAM) is commonly used to cluster sequences since\nit supports alignment-based distances, and the k-centers being actual data\nitems helps with cluster interpretability. However, offline k-medoids has no\nsupport for concept drift, while also being prohibitively expensive for\nclustering data streams. We therefore propose SECLEDS, a streaming variant of\nthe k-medoids algorithm with constant memory footprint. SECLEDS has two unique\nproperties: i) it uses multiple medoids per cluster, producing stable\nhigh-quality clusters, and ii) it handles concept drift using an intuitive\nMedoid Voting scheme for approximating cluster distances. Unlike existing\nadaptive algorithms that create new clusters for new concepts, SECLEDS follows\na fundamentally different approach, where the clusters themselves evolve with\nan evolving stream. Using real and synthetic datasets, we empirically\ndemonstrate that SECLEDS produces high-quality clusters regardless of drift,\nstream size, data dimensionality, and number of clusters. We compare against\nthree popular stream and batch clustering algorithms. The state-of-the-art\nBanditPAM is used as an offline benchmark. SECLEDS achieves comparable F1 score\nto BanditPAM while reducing the number of required distance computations by\n83.7%. Importantly, SECLEDS outperforms all baselines by 138.7% when the stream\ncontains drift. We also cluster real network traffic, and provide evidence that\nSECLEDS can support network bandwidths of up to 1.08 Gbps while using the\n(expensive) dynamic time warping distance.\n", "date": "2022-06-24", "categories": []}
{"id": "2206.10860", "title": "Bregman Power k-Means for Clustering Exponential Family Data", "abstract": "  Recent progress in center-based clustering algorithms combats poor local\nminima by implicit annealing, using a family of generalized means. These\nmethods are variations of Lloyd's celebrated $k$-means algorithm, and are most\nappropriate for spherical clusters such as those arising from Gaussian data. In\nthis paper, we bridge these algorithmic advances to classical work on hard\nclustering under Bregman divergences, which enjoy a bijection to exponential\nfamily distributions and are thus well-suited for clustering objects arising\nfrom a breadth of data generating mechanisms. The elegant properties of Bregman\ndivergences allow us to maintain closed form updates in a simple and\ntransparent algorithm, and moreover lead to new theoretical arguments for\nestablishing finite sample bounds that relax the bounded support assumption\nmade in the existing state of the art. Additionally, we consider thorough\nempirical analyses on simulated experiments and a case study on rainfall data,\nfinding that the proposed method outperforms existing peer methods in a variety\nof non-Gaussian data settings.\n", "date": "2022-06-22", "categories": []}
{"id": "2206.11079", "title": "Noisy $\\ell^{0}$-Sparse Subspace Clustering on Dimensionality Reduced\n  Data", "abstract": "  Sparse subspace clustering methods with sparsity induced by $\\ell^{0}$-norm,\nsuch as $\\ell^{0}$-Sparse Subspace Clustering\n($\\ell^{0}$-SSC)~\\citep{YangFJYH16-L0SSC-ijcv}, are demonstrated to be more\neffective than its $\\ell^{1}$ counterpart such as Sparse Subspace Clustering\n(SSC)~\\citep{ElhamifarV13}. However, the theoretical analysis of $\\ell^{0}$-SSC\nis restricted to clean data that lie exactly in subspaces. Real data often\nsuffer from noise and they may lie close to subspaces. In this paper, we show\nthat an optimal solution to the optimization problem of noisy $\\ell^{0}$-SSC\nachieves subspace detection property (SDP), a key element with which data from\ndifferent subspaces are separated, under deterministic and semi-random model.\nOur results provide theoretical guarantee on the correctness of noisy\n$\\ell^{0}$-SSC in terms of SDP on noisy data for the first time, which reveals\nthe advantage of noisy $\\ell^{0}$-SSC in terms of much less restrictive\ncondition on subspace affinity. In order to improve the efficiency of noisy\n$\\ell^{0}$-SSC, we propose Noisy-DR-$\\ell^{0}$-SSC which provably recovers the\nsubspaces on dimensionality reduced data. Noisy-DR-$\\ell^{0}$-SSC first\nprojects the data onto a lower dimensional space by random projection, then\nperforms noisy $\\ell^{0}$-SSC on the projected data for improved efficiency.\nExperimental results demonstrate the effectiveness of Noisy-DR-$\\ell^{0}$-SSC.\n", "date": "2022-06-22", "categories": []}
{"id": "2206.11130", "title": "Multi-View Clustering for Open Knowledge Base Canonicalization", "abstract": "  Open information extraction (OIE) methods extract plenty of OIE triples <noun\nphrase, relation phrase, noun phrase> from unstructured text, which compose\nlarge open knowledge bases (OKBs). Noun phrases and relation phrases in such\nOKBs are not canonicalized, which leads to scattered and redundant facts. It is\nfound that two views of knowledge (i.e., a fact view based on the fact triple\nand a context view based on the fact triple's source context) provide\ncomplementary information that is vital to the task of OKB canonicalization,\nwhich clusters synonymous noun phrases and relation phrases into the same group\nand assigns them unique identifiers. However, these two views of knowledge have\nso far been leveraged in isolation by existing works. In this paper, we propose\nCMVC, a novel unsupervised framework that leverages these two views of\nknowledge jointly for canonicalizing OKBs without the need of manually\nannotated labels. To achieve this goal, we propose a multi-view CH K-Means\nclustering algorithm to mutually reinforce the clustering of view-specific\nembeddings learned from each view by considering their different clustering\nqualities. In order to further enhance the canonicalization performance, we\npropose a training data optimization strategy in terms of data quantity and\ndata quality respectively in each particular view to refine the learned\nview-specific embeddings in an iterative manner. Additionally, we propose a\nLog-Jump algorithm to predict the optimal number of clusters in a data-driven\nway without requiring any labels. We demonstrate the superiority of our\nframework through extensive experiments on multiple real-world OKB data sets\nagainst state-of-the-art methods.\n", "date": "2022-06-22", "categories": []}
{"id": "2206.11210", "title": "Constant-Factor Approximation Algorithms for Socially Fair\n  $k$-Clustering", "abstract": "  We study approximation algorithms for the socially fair $(\\ell_p,\nk)$-clustering problem with $m$ groups, whose special cases include the\nsocially fair $k$-median ($p=1$) and socially fair $k$-means ($p=2$) problems.\nWe present (1) a polynomial-time $(5+2\\sqrt{6})^p$-approximation with at most\n$k+m$ centers (2) a $(5+2\\sqrt{6}+\\epsilon)^p$-approximation with $k$ centers\nin time $n^{2^{O(p)}\\cdot m^2}$, and (3) a $(15+6\\sqrt{6})^p$ approximation\nwith $k$ centers in time $k^{m}\\cdot\\text{poly}(n)$. The first result is\nobtained via a refinement of the iterative rounding method using a sequence of\nlinear programs. The latter two results are obtained by converting a solution\nwith up to $k+m$ centers to one with $k$ centers using sparsification methods\nfor (2) and via an exhaustive search for (3). We also compare the performance\nof our algorithms with existing bicriteria algorithms as well as exactly $k$\ncenter approximation algorithms on benchmark datasets, and find that our\nalgorithms also outperform existing methods in practice.\n", "date": "2022-06-22", "categories": []}
{"id": "2206.08982", "title": "ck-means, a novel unsupervised learning method that combines fuzzy and\n  crispy clustering methods to extract intersecting data", "abstract": "  Clustering data is a popular feature in the field of unsupervised machine\nlearning. Most algorithms aim to find the best method to extract consistent\nclusters of data, but very few of them intend to cluster data that share the\nsame intersections between two features or more. This paper proposes a method\nto do so. The main idea of this novel method is to generate fuzzy clusters of\ndata using a Fuzzy C-Means (FCM) algorithm. The second part involves applying a\nfilter that selects a range of minimum and maximum membership values,\nemphasizing the border data. A {\\mu} parameter defines the amplitude of this\nrange. It finally applies a k-means algorithm using the membership values\ngenerated by the FCM. Naturally, the data having similar membership values will\nregroup in a new crispy cluster. The algorithm is also able to find the optimal\nnumber of clusters for the FCM and the k-means algorithm, according to the\nconsistency of the clusters given by the Silhouette Index (SI). The result is a\nlist of data and clusters that regroup data sharing the same intersection,\nintersecting two features or more. ck-means allows extracting the very similar\ndata that does not naturally fall in the same cluster but at the intersection\nof two clusters or more. The algorithm also always finds itself the optimal\nnumber of clusters.\n", "date": "2022-06-17", "categories": []}
{"id": "2206.09483", "title": "An Analysis of the Admissibility of the Objective Functions Applied in\n  Evolutionary Multi-objective Clustering", "abstract": "  A variety of clustering criteria has been applied as an objective function in\nEvolutionary Multi-Objective Clustering approaches (EMOCs). However, most EMOCs\ndo not provide detailed analysis regarding the choice and usage of the\nobjective functions. Aiming to support a better choice and definition of the\nobjectives in the EMOCs, this paper proposes an analysis of the admissibility\nof the clustering criteria in evolutionary optimization by examining the search\ndirection and its potential in finding optimal results. As a result, we\ndemonstrate how the admissibility of the objective functions can influence the\noptimization. Furthermore, we provide insights regarding the combinations and\nusage of the clustering criteria in the EMOCs.\n", "date": "2022-06-19", "categories": []}
{"id": "2206.09827", "title": "A Distributional Approach for Soft Clustering Comparison and Evaluation", "abstract": "  The development of external evaluation criteria for soft clustering (SC) has\nreceived limited attention: existing methods do not provide a general approach\nto extend comparison measures to SC, and are unable to account for the\nuncertainty represented in the results of SC algorithms. In this article, we\npropose a general method to address these limitations, grounding on a novel\ninterpretation of SC as distributions over hard clusterings, which we call\n\\emph{distributional measures}. We provide an in-depth study of complexity- and\nmetric-theoretic properties of the proposed approach, and we describe\napproximation techniques that can make the calculations tractable. Finally, we\nillustrate our approach through a simple but illustrative experiment.\n", "date": "2022-06-20", "categories": []}
{"id": "2206.10019", "title": "flow-based clustering and spectral clustering: a comparison", "abstract": "  We propose and study a novel graph clustering method for data with an\nintrinsic network structure. Similar to spectral clustering, we exploit an\nintrinsic network structure of data to construct Euclidean feature vectors.\nThese feature vectors can then be fed into basic clustering methods such as\nk-means or Gaussian mixture model (GMM) based soft clustering. What sets our\napproach apart from spectral clustering is that we do not use the eigenvectors\nof a graph Laplacian to construct the feature vectors. Instead, we use the\nsolutions of total variation minimization problems to construct feature vectors\nthat reflect connectivity between data points. Our motivation is that the\nsolutions of total variation minimization are piece-wise constant around a\ngiven set of seed nodes. These seed nodes can be obtained from domain knowledge\nor by simple heuristics that are based on the network structure of data. Our\nresults indicate that our clustering methods can cope with certain graph\nstructures that are challenging for spectral clustering methods.\n", "date": "2022-06-20", "categories": []}
{"id": "2206.08646", "title": "Scalable Differentially Private Clustering via Hierarchically Separated\n  Trees", "abstract": "  We study the private $k$-median and $k$-means clustering problem in $d$\ndimensional Euclidean space. By leveraging tree embeddings, we give an\nefficient and easy to implement algorithm, that is empirically competitive with\nstate of the art non private methods. We prove that our method computes a\nsolution with cost at most $O(d^{3/2}\\log n)\\cdot OPT + O(k d^2 \\log^2 n /\n\\epsilon^2)$, where $\\epsilon$ is the privacy guarantee. (The dimension term,\n$d$, can be replaced with $O(\\log k)$ using standard dimension reduction\ntechniques.) Although the worst-case guarantee is worse than that of state of\nthe art private clustering methods, the algorithm we propose is practical, runs\nin near-linear, $\\tilde{O}(nkd)$, time and scales to tens of millions of\npoints. We also show that our method is amenable to parallelization in\nlarge-scale distributed computing environments. In particular we show that our\nprivate algorithms can be implemented in logarithmic number of MPC rounds in\nthe sublinear memory regime. Finally, we complement our theoretical analysis\nwith an empirical evaluation demonstrating the algorithm's efficiency and\naccuracy in comparison to other privacy clustering baselines.\n", "date": "2022-06-17", "categories": []}
{"id": "2206.07579", "title": "A Comprehensive Survey on Deep Clustering: Taxonomy, Challenges, and\n  Future Directions", "abstract": "  Clustering is a fundamental machine learning task which has been widely\nstudied in the literature. Classic clustering methods follow the assumption\nthat data are represented as features in a vectorized form through various\nrepresentation learning techniques. As the data become increasingly complicated\nand complex, the shallow (traditional) clustering methods can no longer handle\nthe high-dimensional data type. With the huge success of deep learning,\nespecially the deep unsupervised learning, many representation learning\ntechniques with deep architectures have been proposed in the past decade.\nRecently, the concept of Deep Clustering, i.e., jointly optimizing the\nrepresentation learning and clustering, has been proposed and hence attracted\ngrowing attention in the community. Motivated by the tremendous success of deep\nlearning in clustering, one of the most fundamental machine learning tasks, and\nthe large number of recent advances in this direction, in this paper we conduct\na comprehensive survey on deep clustering by proposing a new taxonomy of\ndifferent state-of-the-art approaches. We summarize the essential components of\ndeep clustering and categorize existing methods by the ways they design\ninteractions between deep representation learning and clustering. Moreover,\nthis survey also provides the popular benchmark datasets, evaluation metrics\nand open-source implementations to clearly illustrate various experimental\nsettings. Last but not least, we discuss the practical applications of deep\nclustering and suggest challenging topics deserving further investigations as\nfuture directions.\n", "date": "2022-06-15", "categories": []}
{"id": "2206.04686", "title": "Unsupervised Deep Discriminant Analysis Based Clustering", "abstract": "  This work presents an unsupervised deep discriminant analysis for clustering.\nThe method is based on deep neural networks and aims to minimize the\nintra-cluster discrepancy and maximize the inter-cluster discrepancy in an\nunsupervised manner. The method is able to project the data into a nonlinear\nlow-dimensional latent space with compact and distinct distribution patterns\nsuch that the data clusters can be effectively identified. We further provide\nan extension of the method such that available graph information can be\neffectively exploited to improve the clustering performance. Extensive\nnumerical results on image and non-image data with or without graph information\ndemonstrate the effectiveness of the proposed methods.\n", "date": "2022-06-09", "categories": []}
{"id": "2206.04958", "title": "Self-Supervised Deep Subspace Clustering with Entropy-norm", "abstract": "  Auto-Encoder based deep subspace clustering (DSC) is widely used in computer\nvision, motion segmentation and image processing. However, it suffers from the\nfollowing three issues in the self-expressive matrix learning process: the\nfirst one is less useful information for learning self-expressive weights due\nto the simple reconstruction loss; the second one is that the construction of\nthe self-expression layer associated with the sample size requires\nhigh-computational cost; and the last one is the limited connectivity of the\nexisting regularization terms. In order to address these issues, in this paper\nwe propose a novel model named Self-Supervised deep Subspace Clustering with\nEntropy-norm (S$^{3}$CE). Specifically, S$^{3}$CE exploits a self-supervised\ncontrastive network to gain a more effetive feature vector. The local structure\nand dense connectivity of the original data benefit from the self-expressive\nlayer and additional entropy-norm constraint. Moreover, a new module with data\nenhancement is designed to help S$^{3}$CE focus on the key information of data,\nand improve the clustering performance of positive and negative instances\nthrough spectral clustering. Extensive experimental results demonstrate the\nsuperior performance of S$^{3}$CE in comparison to the state-of-the-art\napproaches.\n", "date": "2022-06-10", "categories": []}
{"id": "2206.05050", "title": "Improved Approximation for Fair Correlation Clustering", "abstract": "  Correlation clustering is a ubiquitous paradigm in unsupervised machine\nlearning where addressing unfairness is a major challenge. Motivated by this,\nwe study Fair Correlation Clustering where the data points may belong to\ndifferent protected groups and the goal is to ensure fair representation of all\ngroups across clusters. Our paper significantly generalizes and improves on the\nquality guarantees of previous work of Ahmadi et al. and Ahmadian et al. as\nfollows.\n  - We allow the user to specify an arbitrary upper bound on the representation\nof each group in a cluster.\n  - Our algorithm allows individuals to have multiple protected features and\nensure fairness simultaneously across them all.\n  - We prove guarantees for clustering quality and fairness in this general\nsetting. Furthermore, this improves on the results for the special cases\nstudied in previous work. Our experiments on real-world data demonstrate that\nour clustering quality compared to the optimal solution is much better than\nwhat our theoretical result suggests.\n", "date": "2022-06-09", "categories": []}
{"id": "2206.05215", "title": "A new distance measurement and its application in K-Means Algorithm", "abstract": "  K-Means clustering algorithm is one of the most commonly used clustering\nalgorithms because of its simplicity and efficiency. K-Means clustering\nalgorithm based on Euclidean distance only pays attention to the linear\ndistance between samples, but ignores the overall distribution structure of the\ndataset (i.e. the fluid structure of dataset). Since it is difficult to\ndescribe the internal structure of two data points by Euclidean distance in\nhigh-dimensional data space, we propose a new distance measurement, namely,\nview-distance, and apply it to the K-Means algorithm. On the classical manifold\nlearning datasets, S-curve and Swiss roll datasets, not only this new distance\ncan cluster the data according to the structure of the data itself, but also\nthe boundaries between categories are neat dividing lines. Moreover, we also\ntested the classification accuracy and clustering effect of the K-Means\nalgorithm based on view-distance on some real-world datasets. The experimental\nresults show that, on most datasets, the K-Means algorithm based on\nview-distance has a certain degree of improvement in classification accuracy\nand clustering effect.\n", "date": "2022-06-10", "categories": []}
{"id": "2606.21743", "title": "Cohort Organized Learning: Clustering Through Agreement", "abstract": "In this article we describe Cohort Organized Learning (CoOL), a method for clustering data without explicit distance or similarity computations. Herein, we will describe CoOL, derive the gradients determined by expectation maximization to train the networks, show how to monitor convergence during training and evaluate the clusters after training, and discuss a series of examples and use cases. We also discuss CoOL's limitations and future prospects on related tasks. Because CoOL uses neural networks to estimate the clusters, it can be used to cluster any data that can be made compatible and we illustrate this on vector data and images.", "date": "2026-06-19", "categories": []}
{"id": "2606.23199", "title": "Bridge the Gaps: Heterogeneous Attributed Graph Clustering via Quaternion Representation Learning", "abstract": "Attributed graph clustering partitions nodes by jointly exploiting node attributes and graph topology. It remains challenging due to attribute heterogeneity and representation degradation during graph learning. Real-world datasets often contain heterogeneous attributes, i.e., numerical and categorical attributes, complicating unified representation learning. This challenge becomes more complex in attributed graphs, where constructing a clustering-friendly graph structure from attributes and topology remains difficult. Under deep graph architectures, repeated graph propagation causes node embeddings to become overly similar, leading to the over-smoothing (OS) effect. Meanwhile, graph representation learning amplifies topological influence, making discriminative attribute information harder to exploit for clustering, an effect we refer to as over-dominating (OD). To bridge these gaps, an end-to-end framework, Any-type attributed Graph REpresentation lEarning (AGREE), is proposed. It unifies attributed graphs and any-type attributed data through multi-level alignment and similarity-based graph construction. Quaternion-based graph convolution strengthens attribute interaction to alleviate OD, while shallow graph architectures help relieve OS. The learned embeddings are jointly optimized for graph reconstruction and clustering, without requiring a predefined number of clusters during training. Experiments on diverse benchmarks show that AGREE achieves strong overall performance in accuracy, robustness, and adaptability.", "date": "2026-06-22", "categories": []}
{"id": "2606.24094", "title": "Universal Guideline-Driven Image Clustering via a Hybrid LLM Agent", "abstract": "Unifying image clustering across different clustering scenarios remains challenging due to fundamental gaps among tasks. We introduce a Guideline-Driven Image Clustering Agent, the first universal framework that bridges these gaps through textual guidelines. To incorporate complex guidelines without task-specific training, we propose Generative Concept Proxy Modeling, which generates guideline-aware embeddings via concept proxy extraction. For scenarios requiring automatic cluster discovery, we introduce LLM Traversal based on Minimum Spanning Tree that selectively applies LLM reasoning for complex semantic judgments. Our method generalizes across diverse clustering scenarios spanning from general to fine-grained categorization, from global to local criteria, and from balanced to long-tail distributions. Our framework consistently outperforms specialized methods across diverse clustering tasks.", "date": "2026-06-23", "categories": []}
{"id": "2606.27061", "title": "How to evaluate clustering with ground truth?", "abstract": "External indexes can be used for cluster evaluation when ground truth is available. We review the most common external validity indexes focusing on set-matching-based measures. We recommend centroid index (CI), because it is an intuitive cluster-level measure with an explainable result. If we need a more fine-tuned, point-level measure, there are more choices. Pair-set index (PSI) provides a normalized score which is not biased by cluster sizes. If all points should matter equally, then clustering accuracy (ACC) or any other set-matching measure is suitable.", "date": "2026-06-25", "categories": []}
{"id": "2606.27984", "title": "Dual-Learning based Penalized Multi-Align Clustering for Multi-View Incomplete and Disorderly Data", "abstract": "Multimodal feature fusion can effectively capture complex patterns in real-world data by integrating complementary information from different modalities. However, in many applications, such as boiler combustion monitoring, equipment failure, inconsistent sensor sampling frequencies, and network delays often cause missing modalities and temporal asynchrony. These issues lead to incomplete and disorderly multimodal data. To address them, previous studies have proposed several data fusion methods that align cluster centers before fusion. However, these methods have two key limitations. First, they cannot guarantee accurate sample-level alignment of data pairs. Second, they do not address significant discrepancies in data sizes across different classes, which may affect subsequent fusion performance.\n  To address these problems, we propose a dual-learning based penalized multi-align clustering model, named DLPMAC. The dual-learning mechanism enables the model to learn prior knowledge from each modality, including semantic and structural information. This helps preserve semantic consistency and structural similarity across modalities at both local and global levels. In addition, the penalized multi-align module performs multi-to-multi data alignment through a penalty mechanism. It allows one sample to form data pairs with different samples from other modalities, thereby improving data-pair alignment accuracy. The penalty mechanism also prevents data aggregation, avoiding the case where excessive samples are linked to a single sample. Experimental results demonstrate the effectiveness of DLPMAC in addressing data alignment and fusion challenges from both sampling and clustering perspectives.", "date": "2026-06-26", "categories": []}
{"id": "2606.28048", "title": "DG^VoiC: Speaker Clustering for Fraud Investigation under Real Call-Centre Conditions", "abstract": "Insurance fraud remains costly and operationally difficult, particularly in call-centre workflows where many customer interactions begin at FNOL. While recent fraud detection methods mainly rely on structured data, text, or images, repeated speaker identity across calls remains underused as an investigative signal. This paper presents DG^VoiC, a voice clustering framework for customer verification and cross-profile speaker linking on anonymised real call-centre audio. The approach combines sensitive information-aligned anonymisation, speech-focused preprocessing, sliding-window speaker embedding extraction, and cosine similarity based clustering to identify repeated speakers under real telephony conditions. The method was evaluated on 121 recordings, with a curated reference subset of 56 samples in 22 human-agreed speaker clusters. used for validation. The best configuration achieved 96% AMI, 95% ARI, 98% completeness, 100% homogeneity, and 99% V-measure. These results show that speaker clustering can provide a strong additional signal for fraud investigation by helping analysts verify speaker consistency and surface repeated voices across customers.", "date": "2026-06-26", "categories": []}
{"id": "2606.29261", "title": "Nonlinear mixture model motivated subspace clustering", "abstract": "We derive the linear union-of-subspaces (UoS) model for subspace clustering (SC) from the nonlinear mixture model (NMM) used in blind source separation (BSS) to represent a D-dimensional observation vector as an unknown multivariate nonlinear mapping of C latent variables. Assuming the mapping is differentiable up to an unknown order K, we approximate NMM by a K-th order Taylor expansion, yielding a model equivalent to the linear UoS framework underlying SC. This establishes that: (i) the smoothness order K corresponds to the unknown subspace dimension d; (ii) KC equals the number of anchors; and (iii) the sparsity of the representation vector equals K (i.e., d). These relationships enable estimation of bounds on subspace dimension, and that is validated on six benchmark datasets using five established SC algorithms. Established theoretical results are important for post-processing of self-representation matrices estimated by SC algorithms.", "date": "2026-06-28", "categories": []}
{"id": "2606.30035", "title": "Consensus Clustering of Free-Viewing Gaze Data: New Insights into Human-Information Interaction", "abstract": "Free-viewing gaze data provides a rich, task-free window into human visual attention. Conventional exploratory data analysis of the data provides user attention patterns through fixations and areas of interest. However, despite the richness of this gaze data, its human-information interaction (HII) patterns are understudied. We address this gap using consensus clustering of gaze data with respect to users and stimulus characteristics. We present a novel end-to-end unsupervised ensemble learning system for consensus clustering of free-viewing gaze datasets, EnsembleGaze. With a goal of characterizing the user behavior and stimulus type, we propose a feature engineering step based on statistical descriptors of fixation-based distributions. EnsembleGaze involves consensus voting of selected clustering methods implemented on the feature vector to compute the co-association matrix. Using the separate consensus clustering of users and stimuli as a baseline, we further propose two high-dimensional clustering strategies for determining gaze clusters based on joint user and image characterization. They are consensus subspace clustering and spectral biclustering. Clustering performance is evaluated using selected standard metrics and is further interpreted through image-level properties. Our system provides a replicable method for the unsupervised analysis of fixation behavior in scene perception research. Our results show that image stimuli groupings are highly consistent across methods, reflecting a robust ambient-versus-focal viewing mode distinction, whereas user groupings are image-context-dependent, a structure that only biclustering and the two-step conditional approaches are architecturally capable of recovering. Testing on the publicly available datasets revealed dataset-specific patterns, with each offering complementary insights through distinct clustering strategies.", "date": "2026-06-29", "categories": []}
{"id": "2606.31253", "title": "MNAR-$k$-means: A $k$-means Clustering for Data Missing Not at Random with Magnitude-Decaying Probability", "abstract": "The classical $k$-means clustering, based on distances computed from all data features, cannot be directly applied to incomplete data with missing values. A natural extension of $k$-means to missing data is to involve only the observed positions in clustering, which is equivalent to imputing missing values by corresponding cluster means. However, for data missing not at random (MNAR), since missingness is related to data values, such a mean-imputation-based method may lead to the distortion of estimated cluster centers, resulting in a poor clustering result. Since MNAR mechanisms are very common in reality, it is necessary to improve the performance of $k$-means-based clustering methods for such data. In this paper, we focus on a magnitude-decaying MNAR scenario where data is more likely to be missing at positions with smaller absolute values, and we propose a novel $k$-means clustering method based on the constraint of the size of imputation values, which enjoys a good mathematical interpretation. Moreover, we establish the statistical consistency of the estimated cluster centers of the proposed method to the true cluster centers of fully observed data, and solve the optimization of the proposed loss function via an alternative minimization algorithm. Simulation experiments verify the effect of the proposed method in improving clustering results and reducing the bias of estimated cluster centers. Applications to real-world missing data further show the utility of the proposed method.", "date": "2026-06-30", "categories": []}