At1uri/topological-market-persistence-benchmarks

Topological Market Persistence Benchmarks

A high-precision benchmark dataset containing 1,000 multi-asset time-series windows mapped onto persistent homology manifolds ($H_0, H_1$) for benchmarking Topological Data Analysis (TDA) algorithms, market crash early warning systems, and geometric regime classifiers.

Part of the Institutional Quantitative AI Suite by At1uri.

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1. Dataset Overview

Each record captures an exact Takens delay coordinate embedding and Vietoris-Rips filtration over field $\mathbb{F}_2$:

• Takens Embedding: Reconstructs the multidimensional attractor $\mathbf{v}t = (x_t, x{t-\tau}, \dots, x_{t-(d-1)\tau})$.
• Persistent Homology Groups: Tracks the birth $b_i$ and death $d_i$ of connected components ($H_0$) and non-bounding 1-cycles ($H_1$).
• Topological Invariants:
  • Persistent Topological Entropy: $E(\text{Dgm}) = -\sum p_i \log_2 p_i$ measures structural diversity.
  • Max H1 Persistence: Distinguishes authentic geometric attractors from high-frequency market microstructure noise.
  • Topological Condensation Score: Measures the geometric collapse of the correlation manifold preceding financial turbulence.

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2. Schema Specification

Column	Type	Description
sample_id	int64	Unique sample identifier (0 to 999)
regime	string	Market dynamic regime (quiescent, chaotic, liquidity_spiral, covid_shock, hawkes_jump)
embedding_dim	int64	Takens embedding dimension $d \in {3, 4}$
tau_delay	int64	Embedding delay parameter $\tau \in {1, 2, 3}$
h0_features_count	int64	Number of 0-dimensional connected components
h1_features_count	int64	Number of 1-dimensional persistent cycles
max_persistence_h1	float64	Maximum lifetime $\ell = d - b$ across all 1-cycles
persistent_entropy_h0	float64	Persistent entropy of connected components (bits)
persistent_entropy_h1	float64	Persistent entropy of 1-cycles (bits)
total_topological_entropy	float64	Combined persistent topological entropy (bits)
topological_condensation_score	float64	Geometric condensation index $\in [0, 1]$
crash_probability	float64	Calibrated non-parametric crash risk probability
h0_intervals_json	string	JSON-encoded birth-death pairs for $H_0$
h1_intervals_json	string	JSON-encoded birth-death pairs for $H_1$

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3. Quickstart & Usage

from datasets import load_dataset
import pandas as pd
import json

# 1. Load dataset via Hugging Face Datasets
dataset = load_dataset("At1uri/topological-market-persistence-benchmarks")
df = dataset["train"].to_pandas()

print(f"Total benchmark windows: {len(df)}")
print(f"Mean Topological Entropy: {df['total_topological_entropy'].mean():.3f} bits")

# 2. Compare entropy across market regimes
print("\nEntropy by Market Regime:")
print(df.groupby("regime")[["total_topological_entropy", "max_persistence_h1", "crash_probability"]].mean())

# 3. Decode sample H1 persistence barcode
first_h1 = json.loads(df.iloc[0]["h1_intervals_json"])
print(f"\nFirst sample H1 intervals: {first_h1[:3]}")

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4. Associated Repositories

• Interactive Space: Topological Market Dynamics Studio
• Model Card: Topological Phase Transition Detector
• Collection: Institutional Quantitative AI Suite