From 5eb3a27646632055665ec5fde59add00dbe7547a Mon Sep 17 00:00:00 2001
From: Mathias Quillot <mathiasquillot@gmail.com>
Date: Wed, 11 Sep 2019 22:11:48 +0200
Subject: [PATCH] Implementation of kmeans with mahalanobis distance

---
 bin/cluster_kmeans_mahalanobis.py | 113 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 113 insertions(+)
 create mode 100644 bin/cluster_kmeans_mahalanobis.py

diff --git a/bin/cluster_kmeans_mahalanobis.py b/bin/cluster_kmeans_mahalanobis.py
new file mode 100644
index 0000000..96e6921
--- /dev/null
+++ b/bin/cluster_kmeans_mahalanobis.py
@@ -0,0 +1,113 @@
+'''
+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]:]
+)
-- 
1.8.2.3