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IEEE Trans Pattern Anal Mach Intell. 2013 Jun;35(6):1312-27. doi: 10.1109/TPAMI.2012.226.

A game-theoretic approach to hypergraph clustering.

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Dipartimento di Scienze Ambientali, Informatica e Statistica, Università Cà Foscari di Venezia, via Torino 155, Venezia-Mestre 30172, Italy.


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.

[Indexed for MEDLINE]

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