EM algorithm for clustering an ensemble of graphs with comb matching

Abstract

In this paper we address the unsupervised clustering of an ensemble of graphs. We adapt to the domain of graphs the Asymmetric Clustering Model (ACM). Firstly, we use an improvement of our Comb algorithm for graph matching, a population-based method which performs multi-point explorations of the discrete space of feasible solutions. Given this algorithm we define an incremental method to obtain a prototypical graph by fusing the elements of the ensemble weighted by their prior probabilities of belonging to the class. Graph-matching and incremental fusion are integrated in a EM clustering algorithm: In the E-step we re-estimate the class-membership variables by computing the distances of input graphs to current prototypes through graph-matching, and in the M-step we re-estimate the prototypes by considering the latter class-membership variables in order to perform graph fusions. We introduce adaptation: The algorithm starts with a high number of classes and in each epoch tries to fuse the two classes with closer prototypes. We present several results of Comb-matching, incremental fusion and clustering. © Springer-Verlag Berlin Heidelberg 2003.