Affinity Propagation preferences initialization

Question

I need to perform clustering without knowing in advance the number of clusters. The number of cluster may be from 1 to 5, since I may find cases where all the samples belong to the same instance, or to a limited number of group. I thought affinity propagation could be my choice, since I could control the number of clusters by setting the preference parameter. However, if I have a single cluster artificially generated and I set preference to the minimal euclidean distance among nodes (to minimize number of clusters), I get terrible over clustering.

"""
=================================================
Demo of affinity propagation clustering algorithm
=================================================

Reference:
Brendan J. Frey and Delbert Dueck, "Clustering by Passing Messages
Between Data Points", Science Feb. 2007

"""
print(__doc__)
import numpy as np
from sklearn.cluster import AffinityPropagation
from sklearn import metrics
from sklearn.datasets.samples_generator import make_blobs
from scipy.spatial.distance import pdist

##############################################################################
# Generate sample data
centers = [[0,0],[1,1]]
X, labels_true = make_blobs(n_samples=300, centers=centers, cluster_std=0.5,
                            random_state=0)
init = np.min(pdist(X))

##############################################################################
# Compute Affinity Propagation
af = AffinityPropagation(preference=init).fit(X)
cluster_centers_indices = af.cluster_centers_indices_
labels = af.labels_

n_clusters_ = len(cluster_centers_indices)

print('Estimated number of clusters: %d' % n_clusters_)
print("Homogeneity: %0.3f" % metrics.homogeneity_score(labels_true, labels))
print("Completeness: %0.3f" % metrics.completeness_score(labels_true, labels))
print("V-measure: %0.3f" % metrics.v_measure_score(labels_true, labels))
print("Adjusted Rand Index: %0.3f"
      % metrics.adjusted_rand_score(labels_true, labels))
print("Adjusted Mutual Information: %0.3f"
      % metrics.adjusted_mutual_info_score(labels_true, labels))
print("Silhouette Coefficient: %0.3f"
      % metrics.silhouette_score(X, labels, metric='sqeuclidean'))

##############################################################################
# Plot result
import matplotlib.pyplot as plt
from itertools import cycle

plt.close('all')
plt.figure(1)
plt.clf()

colors = cycle('bgrcmykbgrcmykbgrcmykbgrcmyk')
for k, col in zip(range(n_clusters_), colors):
    class_members = labels == k
    cluster_center = X[cluster_centers_indices[k]]
    plt.plot(X[class_members, 0], X[class_members, 1], col + '.')
    plt.plot(cluster_center[0], cluster_center[1], 'o', markerfacecolor=col,
             markeredgecolor='k', markersize=14)
    for x in X[class_members]:
        plt.plot([cluster_center[0], x[0]], [cluster_center[1], x[1]], col)

plt.title('Estimated number of clusters: %d' % n_clusters_)
plt.show()

Is there any flaw in my approach of using Affinity Propagation? Conversely, is Affinity Propagation unsuited for this task, so should I use something else?

Answer 1

No, there is no flaw. AP does not use distances, but requires you to specify a similarity. I don't know the scikit implementation so well, but according to what I read, it uses negative squared Euclidean distances by default to compute the similarity matrix. If you set the input preference to the minimal Euclidean distance, you get a positive value, while all similarities are negative. So this will typically result in as many clusters as you have samples (note: the higher the input preference, the more clusters). I'd rather suggest to set the input preference to the minimal negative squared distance, i.e. -1 times the square of the largest distance in the data set. This will give you a much smaller number of clusters, but not necessarily one single cluster. I don't know whether the preferenceRange() function exists also in the scikit implementation. There is Matlab code on the AP homepage and it is also implemented in the R package 'apcluster' that I am maintaining. This function allows for determining meaningful bounds for the input preference parameter. I hope that helps.