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bin/cluster_kmeans_constrained_mahalanobis.py
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Implementation of...
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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,
Itshak Lapidot
Just one thing: Column and lines are inversed in this script.
TODO: Random selection from the set
'''
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):
rand = np.random.choice(X.shape[0], number_clusters)
C = X[rand]
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 gaussian(x, c, l):
'''
G function
'''
p1 = np.power(np.linalg.det(l), 0.5) / np.power((2 * np.pi), d/2)
p2 = np.exp(np.transpose(x - c).dot(1/2).dot(l).dot(x - c))
return (p1 * p2).reshape(1)
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))
# -- Calcul closest cluster
for n in range(N):
for k in range(K):
distances[n][k] = dist(X[n], C[k], L[k])
closest_cluster = np.argmin(distances, axis=1)
# -- Debug tool ----------------------
if i % 1 == 0:
# 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 = K_new / np.power(np.linalg.det(K_new), 1/d)
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]:]
)
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