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bin/cluster_kmeans_mahalanobis.py
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''' Un petit test pour faire du clustering avec une distance de mahalanobis From paper: Convergence problems of Mahalanobis distance-based k-means clustering Just one thing: Column and lines are inversed in this script. ''' import matplotlib.pyplot as plt import numpy as np # from sklearn.manifold import TSNE N = 50 # Number of individus d = 2 # Number of dimensions K = 3 # number of clusters def initialize_model(X, number_clusters): C = X[np.random.choice(X.shape[0], number_clusters)] L = np.zeros((K, d, d)) for k in range(K): L[k] = np.identity(d) return C, L X = np.random.rand(N, d) # Features C, L = initialize_model(X, K) def dist(a, b, l): ''' Distance euclidienne ''' a = np.reshape(a, (-1, 1)) b = np.reshape(b, (-1, 1)) result = np.transpose(a - b).dot(l).dot(a-b)[0][0] return result def plot_iteration(iteration, points, clusters, centers): fig = plt.figure() ax = fig.add_subplot(111) scatter = ax.scatter(points[:, 0], points[:, 1], c=clusters, s=50) for i, j in centers: ax.scatter(i, j, s=50, c='red', marker='+') ax.set_xlabel('x') ax.set_ylabel('y') plt.colorbar(scatter) plt.ylim(0, 1) plt.xlim(0, 1) plt.savefig("test_" + str(iteration) + ".pdf") end_algo = False i = 0 while not end_algo: if i == 10: exit(1) print("Iteration: ", i) # Calcul matrix distance distances = np.zeros((N, K)) for n in range(N): for k in range(K): distances[n][k] = dist(X[n], C[k], L[k]) print(distances) closest_cluster = np.argmin(distances, axis=1) if i % 1 == 0: # -- Debug tool ---------------------- # TSNE X_embedded = np.concatenate((X, C), axis=0) # X_embedded = TSNE(n_components=2).fit_transform(np.concatenate((X, C), axis=0)) # Then plot plot_iteration( i, X_embedded[:X.shape[0]], closest_cluster, X_embedded[X.shape[0]:] ) # ------------------------------------ end_algo = True for k in range(K): # Find subset of X with values closed to the centroid c_k. X_sub = np.where(closest_cluster == k) X_sub = np.take(X, X_sub[0], axis=0) np.mean(X_sub, axis=0) C_new = np.mean(X_sub, axis=0) # -- COMPUTE NEW LAMBDA (here named K) -- K_new = np.zeros((L.shape[1], L.shape[2])) for x in X_sub: x = np.reshape(x, (-1, 1)) c_tmp = np.reshape(C_new, (-1, 1)) K_new = K_new + (x - c_tmp).dot((x - c_tmp).transpose()) K_new = K_new / X_sub.shape[0] K_new = np.linalg.inv(K_new) if end_algo and (not (C[k] == C_new).all()): # If the same stop end_algo = False C[k] = C_new L[k] = K_new i = i + 1 plot_iteration( i, X_embedded[:X.shape[0]], closest_cluster, X_embedded[X.shape[0]:] ) |