Commit 5eb3a27646632055665ec5fde59add00dbe7547a
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Implementation of kmeans with mahalanobis distance
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bin/cluster_kmeans_mahalanobis.py
| File was created | 1 | ''' | |
| 2 | Un petit test pour faire du clustering | ||
| 3 | avec une distance de mahalanobis | ||
| 4 | From paper: | ||
| 5 | Convergence problems of Mahalanobis distance-based k-means clustering | ||
| 6 | |||
| 7 | Just one thing: Column and lines are inversed in this script. | ||
| 8 | ''' | ||
| 9 | |||
| 10 | import matplotlib.pyplot as plt | ||
| 11 | import numpy as np | ||
| 12 | # from sklearn.manifold import TSNE | ||
| 13 | |||
| 14 | |||
| 15 | N = 50 # Number of individus | ||
| 16 | d = 2 # Number of dimensions | ||
| 17 | K = 3 # number of clusters | ||
| 18 | |||
| 19 | |||
| 20 | def initialize_model(X, number_clusters): | ||
| 21 | C = X[np.random.choice(X.shape[0], number_clusters)] | ||
| 22 | L = np.zeros((K, d, d)) | ||
| 23 | for k in range(K): | ||
| 24 | L[k] = np.identity(d) | ||
| 25 | return C, L | ||
| 26 | |||
| 27 | |||
| 28 | X = np.random.rand(N, d) # Features | ||
| 29 | |||
| 30 | C, L = initialize_model(X, K) | ||
| 31 | |||
| 32 | |||
| 33 | def dist(a, b, l): | ||
| 34 | ''' | ||
| 35 | Distance euclidienne | ||
| 36 | ''' | ||
| 37 | a = np.reshape(a, (-1, 1)) | ||
| 38 | b = np.reshape(b, (-1, 1)) | ||
| 39 | result = np.transpose(a - b).dot(l).dot(a-b)[0][0] | ||
| 40 | return result | ||
| 41 | |||
| 42 | |||
| 43 | def plot_iteration(iteration, points, clusters, centers): | ||
| 44 | fig = plt.figure() | ||
| 45 | ax = fig.add_subplot(111) | ||
| 46 | scatter = ax.scatter(points[:, 0], points[:, 1], c=clusters, s=50) | ||
| 47 | for i, j in centers: | ||
| 48 | ax.scatter(i, j, s=50, c='red', marker='+') | ||
| 49 | ax.set_xlabel('x') | ||
| 50 | ax.set_ylabel('y') | ||
| 51 | plt.colorbar(scatter) | ||
| 52 | plt.ylim(0, 1) | ||
| 53 | plt.xlim(0, 1) | ||
| 54 | plt.savefig("test_" + str(iteration) + ".pdf") | ||
| 55 | |||
| 56 | |||
| 57 | end_algo = False | ||
| 58 | i = 0 | ||
| 59 | while not end_algo: | ||
| 60 | if i == 10: | ||
| 61 | exit(1) | ||
| 62 | print("Iteration: ", i) | ||
| 63 | # Calcul matrix distance | ||
| 64 | distances = np.zeros((N, K)) | ||
| 65 | |||
| 66 | for n in range(N): | ||
| 67 | for k in range(K): | ||
| 68 | distances[n][k] = dist(X[n], C[k], L[k]) | ||
| 69 | print(distances) | ||
| 70 | closest_cluster = np.argmin(distances, axis=1) | ||
| 71 | if i % 1 == 0: | ||
| 72 | # -- Debug tool ---------------------- | ||
| 73 | # TSNE | ||
| 74 | X_embedded = np.concatenate((X, C), axis=0) | ||
| 75 | # X_embedded = TSNE(n_components=2).fit_transform(np.concatenate((X, C), axis=0)) | ||
| 76 | # Then plot | ||
| 77 | plot_iteration( | ||
| 78 | i, | ||
| 79 | X_embedded[:X.shape[0]], | ||
| 80 | closest_cluster, | ||
| 81 | X_embedded[X.shape[0]:] | ||
| 82 | ) | ||
| 83 | # ------------------------------------ | ||
| 84 | |||
| 85 | end_algo = True | ||
| 86 | for k in range(K): | ||
| 87 | # Find subset of X with values closed to the centroid c_k. | ||
| 88 | X_sub = np.where(closest_cluster == k) | ||
| 89 | X_sub = np.take(X, X_sub[0], axis=0) | ||
| 90 | np.mean(X_sub, axis=0) | ||
| 91 | C_new = np.mean(X_sub, axis=0) | ||
| 92 | |||
| 93 | # -- COMPUTE NEW LAMBDA (here named K) -- | ||
| 94 | K_new = np.zeros((L.shape[1], L.shape[2])) | ||
| 95 | for x in X_sub: | ||
| 96 | x = np.reshape(x, (-1, 1)) | ||
| 97 | c_tmp = np.reshape(C_new, (-1, 1)) | ||
| 98 | K_new = K_new + (x - c_tmp).dot((x - c_tmp).transpose()) | ||
| 99 | K_new = K_new / X_sub.shape[0] | ||
| 100 | K_new = np.linalg.inv(K_new) | ||
| 101 | |||
| 102 | if end_algo and (not (C[k] == C_new).all()): # If the same stop | ||
| 103 | end_algo = False | ||
| 104 | C[k] = C_new | ||
| 105 | L[k] = K_new | ||
| 106 | i = i + 1 | ||
| 107 | |||
| 108 | plot_iteration( | ||
| 109 | i, | ||
| 110 | X_embedded[:X.shape[0]], | ||
| 111 | closest_cluster, | ||
| 112 | X_embedded[X.shape[0]:] | ||
| 113 | ) | ||
| 114 |