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12.4 kB
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| import os | |
| from glob import glob | |
| from tqdm import tqdm | |
| import sys | |
| def Hbeta(D=np.array([]), beta=1.0): | |
| """ | |
| Compute the perplexity and the P-row for a specific value of the | |
| precision of a Gaussian distribution. | |
| Args: | |
| D (numpy.ndarray): Distance array. | |
| beta (float): Precision of the Gaussian distribution. | |
| Returns: | |
| tuple: A tuple containing perplexity (H) and the P-row (P). | |
| """ | |
| P = np.exp(-D.copy() * beta) | |
| sumP = sum(P) | |
| H = np.log(sumP) + beta * np.sum(D * P) / sumP | |
| P = P / sumP | |
| return H, P | |
| def pca(X=np.array([]), no_dims=50): | |
| # Runs PCA on the NxD array X in order to reduce its dimensionality to no_dims dimensions. | |
| (n, d) = X.shape | |
| X = X - np.tile(np.mean(X, 0), (n, 1)) | |
| (l, M) = np.linalg.eig(np.dot(X.T, X)) | |
| Y = np.dot(X, M[:, 0:no_dims]) | |
| return Y | |
| def x2p(X=np.array([]), tol=1e-5, perplexity=30.0): | |
| """ | |
| Performs a binary search to get P-values in such a way that each | |
| conditional Gaussian has the same perplexity. | |
| """ | |
| (n, d) = X.shape | |
| sum_X = np.sum(np.square(X), 1) | |
| D = np.add(np.add(-2 * np.dot(X, X.T), sum_X).T, sum_X) | |
| P = np.zeros((n, n)) | |
| beta = np.ones((n, 1)) | |
| logU = np.log(perplexity) | |
| # Loop over all datapoints | |
| for i in range(n): | |
| if i % 100 == 0: | |
| print("Computing P-values for point %d of %d..." % (i, n)) | |
| # Compute the Gaussian kernel and entropy for the current precision | |
| betamin = -np.inf | |
| betamax = np.inf | |
| Di = D[i, np.concatenate((np.r_[0:i], np.r_[i+1:n]))] | |
| (H, thisP) = Hbeta(Di, beta[i]) | |
| # Evaluate whether the perplexity is within tolerance | |
| Hdiff = H - logU | |
| tries = 0 | |
| while np.abs(Hdiff) > tol and tries < 50: | |
| # If not, increase or decrease precision | |
| if Hdiff > 0: | |
| betamin = beta[i].copy() | |
| if betamax == np.inf or betamax == -np.inf: | |
| beta[i] = beta[i] * 2. | |
| else: | |
| beta[i] = (beta[i] + betamax) / 2. | |
| else: | |
| betamax = beta[i].copy() | |
| if betamin == np.inf or betamin == -np.inf: | |
| beta[i] = beta[i] / 2. | |
| else: | |
| beta[i] = (beta[i] + betamin) / 2. | |
| # Recompute the values | |
| (H, thisP) = Hbeta(Di, beta[i]) | |
| Hdiff = H - logU | |
| tries += 1 | |
| # Set the final row of P | |
| P[i, np.concatenate((np.r_[0:i], np.r_[i+1:n]))] = thisP | |
| # Return final P-matrix | |
| print("Mean value of sigma: %f" % np.mean(np.sqrt(1 / beta))) | |
| return P | |
| def tsne(X=np.array([]), no_dims=2, initial_dims=50, perplexity=30.0): | |
| """ | |
| Runs t-SNE on the dataset in the NxD array X to reduce its | |
| dimensionality to no_dims dimensions. The syntaxis of the function is | |
| `Y = tsne.tsne(X, no_dims, perplexity), where X is an NxD NumPy array. | |
| """ | |
| if isinstance(no_dims, float): | |
| print("Error: array X should have type float.") | |
| return -1 | |
| if round(no_dims) != no_dims: | |
| print("Error: number of dimensions should be an integer.") | |
| return -1 | |
| X = pca(X, initial_dims).real | |
| (n, d) = X.shape | |
| max_iter = 1000 | |
| initial_momentum = 0.5 | |
| final_momentum = 0.8 | |
| eta = 500 | |
| min_gain = 0.01 | |
| Y = np.random.randn(n, no_dims) | |
| dY = np.zeros((n, no_dims)) | |
| iY = np.zeros((n, no_dims)) | |
| gains = np.ones((n, no_dims)) | |
| # Compute P-values | |
| P = x2p(X, 1e-5, perplexity) | |
| P = P + np.transpose(P) | |
| P = P / np.sum(P) | |
| P = P * 4. | |
| P = np.maximum(P, 1e-12) | |
| for iter in range(max_iter): | |
| # Compute pairwise affinities | |
| sum_Y = np.sum(np.square(Y), 1) | |
| num = -2. * np.dot(Y, Y.T) | |
| num = 1. / (1. + np.add(np.add(num, sum_Y).T, sum_Y)) # | |
| num[range(n), range(n)] = 0. | |
| Q = num / np.sum(num) | |
| Q = np.maximum(Q, 1e-12) | |
| # Compute gradient | |
| PQ = P - Q | |
| for i in range(n): | |
| dY[i, :] = np.sum(np.tile(PQ[:, i] * num[:, i], (no_dims, 1)).T * (Y[i, :] - Y), 0) | |
| # Perform the update | |
| if iter < 20: | |
| momentum = initial_momentum | |
| else: | |
| momentum = final_momentum | |
| gains = (gains + 0.2) * ((dY > 0.) != (iY > 0.)) + \ | |
| (gains * 0.8) * ((dY > 0.) == (iY > 0.)) | |
| gains[gains < min_gain] = min_gain | |
| iY = momentum * iY - eta * (gains * dY) | |
| Y = Y + iY | |
| Y = Y - np.tile(np.mean(Y, 0), (n, 1)) | |
| # Compute current value of cost function | |
| if (iter + 1) % 10 == 0: | |
| C = np.sum(P * np.log(P / Q)) | |
| print("Iteration %d: error is %f" % (iter + 1, C)) | |
| if iter == 100: | |
| P = P / 4. | |
| return Y | |
| import numpy as np | |
| import matplotlib.pyplot as plt | |
| import os | |
| from glob import glob | |
| from tqdm import tqdm | |
| import sys | |
| def Hbeta(D=np.array([]), beta=1.0): | |
| """ | |
| Compute the perplexity and the P-row for a specific value of the | |
| precision of a Gaussian distribution. | |
| Args: | |
| D (numpy.ndarray): Distance array. | |
| beta (float): Precision of the Gaussian distribution. | |
| Returns: | |
| tuple: A tuple containing perplexity (H) and the P-row (P). | |
| """ | |
| # Compute P-row and corresponding perplexity | |
| P = np.exp(-D.copy() * beta) | |
| sumP = np.sum(P) | |
| H = np.log(sumP) + beta * np.sum(D * P) / sumP | |
| P = P / sumP | |
| return H, P | |
| def pca(X=np.array([]), no_dims=50): | |
| """ | |
| Performs PCA on the NxD array X to reduce its dimensionality to no_dims dimensions. | |
| Args: | |
| X (numpy.ndarray): Input data array. | |
| no_dims (int): Number of dimensions to reduce to. | |
| Returns: | |
| numpy.ndarray: The reduced data array. | |
| """ | |
| (n, d) = X.shape | |
| X = X - np.tile(np.mean(X, axis=0), (n, 1)) | |
| (l, M) = np.linalg.eig(np.dot(X.T, X)) | |
| Y = np.dot(X, M[:, 0:no_dims]) | |
| return Y | |
| def x2p(X=np.array([]), tol=1e-5, perplexity=30.0): | |
| """ | |
| Performs a binary search to get P-values such that each | |
| conditional Gaussian has the same perplexity. | |
| Args: | |
| X (numpy.ndarray): Input data array. | |
| tol (float): Tolerance for the perplexity. | |
| perplexity (float): Desired perplexity. | |
| Returns: | |
| numpy.ndarray: The P-values matrix. | |
| """ | |
| (n, d) = X.shape | |
| sum_X = np.sum(np.square(X), axis=1) | |
| D = np.add(np.add(-2 * np.dot(X, X.T), sum_X).T, sum_X) | |
| P = np.zeros((n, n)) | |
| beta = np.ones((n, 1)) | |
| logU = np.log(perplexity) | |
| # Loop over all data points | |
| for i in range(n): | |
| if i % 100 == 0: | |
| print(f"Computing P-values for point {i} of {n}...") | |
| # Compute the Gaussian kernel and entropy for the current precision | |
| betamin = -np.inf | |
| betamax = np.inf | |
| Di = D[i, np.concatenate((np.r_[0:i], np.r_[i+1:n]))] | |
| (H, thisP) = Hbeta(Di, beta[i]) | |
| # Evaluate whether the perplexity is within tolerance | |
| Hdiff = H - logU | |
| tries = 0 | |
| while np.abs(Hdiff) > tol and tries < 50: | |
| # If not, adjust precision | |
| if Hdiff > 0: | |
| betamin = beta[i].copy() | |
| if betamax in [np.inf, -np.inf]: | |
| beta[i] *= 2 | |
| else: | |
| beta[i] = (beta[i] + betamax) / 2 | |
| else: | |
| betamax = beta[i].copy() | |
| if betamin in [np.inf, -np.inf]: | |
| beta[i] /= 2 | |
| else: | |
| beta[i] = (beta[i] + betamin) / 2 | |
| # Recompute the values | |
| (H, thisP) = Hbeta(Di, beta[i]) | |
| Hdiff = H - logU | |
| tries += 1 | |
| # Set the final row of P | |
| P[i, np.concatenate((np.r_[0:i], np.r_[i+1:n]))] = thisP | |
| print("Mean value of sigma: %f" % np.mean(np.sqrt(1 / beta))) | |
| return P | |
| def tsne(X=np.array([]), no_dims=2, initial_dims=50, perplexity=30.0): | |
| """ | |
| Runs t-SNE on the dataset in the NxD array X to reduce its | |
| dimensionality to no_dims dimensions. | |
| Args: | |
| X (numpy.ndarray): Input data array. | |
| no_dims (int): Number of dimensions to reduce to. | |
| initial_dims (int): Number of initial dimensions. | |
| perplexity (float): Desired perplexity. | |
| Returns: | |
| numpy.ndarray: The reduced data array. | |
| """ | |
| if isinstance(no_dims, float): | |
| print("Error: array X should have type float.") | |
| return -1 | |
| if round(no_dims) != no_dims: | |
| print("Error: number of dimensions should be an integer.") | |
| return -1 | |
| X = pca(X, initial_dims).real | |
| (n, d) = X.shape | |
| max_iter = 1000 | |
| initial_momentum = 0.5 | |
| final_momentum = 0.8 | |
| eta = 500 | |
| min_gain = 0.01 | |
| Y = np.random.randn(n, no_dims) | |
| dY = np.zeros((n, no_dims)) | |
| iY = np.zeros((n, no_dims)) | |
| gains = np.ones((n, no_dims)) | |
| # Compute P-values | |
| P = x2p(X, 1e-5, perplexity) | |
| P = P + np.transpose(P) # Ensure symmetry | |
| P = P / np.sum(P) # Normalize | |
| P = P * 4. # Early exaggeration | |
| P = np.maximum(P, 1e-12) # Avoid numerical issues | |
| for iter in range(max_iter): | |
| # Compute pairwise affinities | |
| sum_Y = np.sum(np.square(Y), axis=1) | |
| num = -2. * np.dot(Y, Y.T) | |
| num = 1. / (1. + np.add(np.add(num, sum_Y).T, sum_Y)) | |
| num[np.arange(n), np.arange(n)] = 0. # Avoid self-affinity | |
| Q = num / np.sum(num) | |
| Q = np.maximum(Q, 1e-12) # Avoid numerical issues | |
| # Compute gradient | |
| PQ = P - Q | |
| for i in range(n): | |
| dY[i, :] = np.sum(np.tile(PQ[:, i] * num[:, i], (no_dims, 1)).T * (Y[i, :] - Y), axis=0) | |
| # Perform the update | |
| momentum = initial_momentum if iter < 20 else final_momentum | |
| gains = (gains + 0.2) * ((dY > 0.) != (iY > 0.)) + (gains * 0.8) * ((dY > 0.) == (iY > 0.)) | |
| gains[gains < min_gain] = min_gain | |
| iY = momentum * iY - eta * (gains * dY) | |
| Y = Y + iY | |
| Y -= np.tile(np.mean(Y, axis=0), (n, 1)) # Center the data | |
| # Compute current value of cost function | |
| if (iter + 1) % 10 == 0: | |
| C = np.sum(P * np.log(P / Q)) | |
| print(f"Iteration {iter + 1}: error is {C:.6f}") | |
| if iter == 100: | |
| P /= 4. # Decrease early exaggeration | |
| return Y | |
| if __name__ == '__main__': | |
| task = sys.argv[2] | |
| if sys.argv[1] == "gnss": | |
| task_class = {0: 3, 1: 5, 2: 7, 3: 9, 4: 11} | |
| colors = {0: "#1f77b4", 1: "#ff7f0e", 2: "#2ca02c", 3: "#d62728", | |
| 4: "#9467bd", 5: "#8c564b", 6: "#e377c2", 7: "#7f7f7f", | |
| 8: "#bcbd22", 9: "#17becf", 10: "#000000"} | |
| elif sys.argv[1] == "cifar": | |
| task_class = {0: 4, 1: 6, 2: 8, 3: 10} | |
| colors = {0: "#1f77b4", 1: "#ff7f0e", 2: "#2ca02c", 3: "#d62728", | |
| 4: "#9467bd", 5: "#8c564b", 6: "#e377c2", 7: "#7f7f7f", | |
| 8: "#bcbd22", 9: "#17becf"} | |
| else: | |
| raise Exception("Please provide the name of the dataset.") | |
| # Load embeddings and ground truth of a task | |
| emb_file = f"embeddings_{task}.npy" | |
| ground_truth_file = f"predictions_{task}_tr_pr.npy" | |
| points = np.load(emb_file) | |
| ground_truth = np.load(ground_truth_file) | |
| size = points.shape[1] | |
| labels = ground_truth[:, 0] | |
| # Check if t-SNE embeddings are already computed | |
| tsne_file = f"tsne_embeddings/emb_tsne_{task}.npy" | |
| if not os.path.isfile(tsne_file): | |
| tsne_embs = tsne(points, 2, size, 30.0) | |
| np.save(tsne_file, tsne_embs) | |
| tsne_embs = np.load(tsne_file, allow_pickle=True) | |
| x = tsne_embs | |
| print('t-SNE embeddings shape:', x.shape) | |
| y = labels | |
| colors_list = [colors[cy] for cy in y] | |
| # Plotting the t-SNE results | |
| plt.figure(figsize=(5, 4)) | |
| for key, val in colors.items(): | |
| if key == task_class[int(task)]: | |
| break | |
| cur_x = x[y == key] | |
| plt.scatter(cur_x[:, 0], cur_x[:, 1], s=8, color=val, label=f"Class: {key}") | |
| # Add legend and save the plot | |
| plt.legend(fontsize=10, loc="lower left", ncol=2, labelspacing=0.03, columnspacing=0.03, | |
| handletextpad=0.03) | |
| plt.tight_layout() | |
| plt.xticks([], []) | |
| plt.yticks([], []) | |
| plt.savefig(f"tsne_plots/tsne_{task}.pdf", dpi=1200) | |
| plt.close() | |