Dominant-set clustering using multiple affinity matrices

Abstract

Pairwise (or graph-based) clustering algorithms typically assume the existence of a single affinity matrix, which describes the similarity between the objects to be clustered. In many practical applications, however, several similarity relations might be envisaged and the problem arises as to how properly select or combine them. In this paper we offer a solution to this problem for the case of dominant sets, a well-known formalization of the notion of a cluster, which generalizes the notion of maximal clique to edge-weighted graphs and has intriguing connections to evolutionary game theory. Specifically, it has been shown that dominant sets can be bijectively related to Evolutionary Stable Strategies (ESS) - a classic notion of equilibrium in the evolutionary game theory field - of a so-called “clustering game”. The clustering game is a non-cooperative game between two-players, where the objects to cluster form the set of strategies, while the affinity matrix provides the players’ payoffs. The proposed approach generalizes dominant sets to multiple affinities by extending the clustering game, which has a single payoff, to a multi-payoff game. Accordingly, dominant sets in the multi-affinity setting become equivalent to ESSs of a corresponding multi-payoff clustering game, which can be found by means of so-called Biased Replicator Dynamics. Experiments conducted over standard benchmark datasets consistently show that the proposed combination scheme allows one to substantially improve the performance of dominant-set clustering over its single-affinity counterpart.