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A Game-Theoretic Approach to Hypergraph Clustering
June 2013 (vol. 35 no. 6)
pp. 1312-1327
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.
Index Terms:
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 and Machine Intelligence, vol. 35, no. 6, pp. 1312-1327, June 2013, doi:10.1109/TPAMI.2012.226
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