Issue No. 06 - June (2013 vol. 35)
Samuel Rota Bulò , Universita Ca Foscari di Venezia, Venezia Mestre
Marcello Pelillo , Universita Ca Foscari di Venezia, Venezia Mestre
Hypergraph clustering refers to the process of extracting maximally coherent groups from a set of objects using high-order (rather than pairwise) similarities. Traditional approaches to this problem are based on the idea of partitioning the input data into a predetermined number of classes, thereby obtaining the clusters as a by-product of the partitioning process. In this paper, we offer a radically different view of the problem. In contrast to the classical approach, we attempt to provide a meaningful formalization of the very notion of a cluster and we show that game theory offers an attractive and unexplored perspective that serves our purpose well. To this end, we formulate the hypergraph clustering problem in terms of a noncooperative multiplayer “clustering game,” and show that a natural notion of a cluster turns out to be equivalent to a classical (evolutionary) game-theoretic equilibrium concept. We prove that the problem of finding the equilibria of our clustering game is equivalent to locally optimizing a polynomial function over the standard simplex, and we provide a discrete-time high-order replicator dynamics to perform this optimization, based on the Baum-Eagon inequality. Experiments over synthetic as well as real-world data are presented which show the superiority of our approach over the state of the art.
Sociology, Statistics, Game theory, Games, Standards, Clustering algorithms, Partitioning algorithms,high-order replicator dynamics, Hypergraph clustering, evolutionary game theory, polynomial optimization, Baum-Eagon inequality
Samuel Rota Bulò, Marcello Pelillo, "A Game-Theoretic Approach to Hypergraph Clustering", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 35, no. , pp. 1312-1327, June 2013, doi:10.1109/TPAMI.2012.226