Journal
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
Volume 35, Issue 6, Pages 1312-1327Publisher
IEEE COMPUTER SOC
DOI: 10.1109/TPAMI.2012.226
Keywords
Hypergraph clustering; evolutionary game theory; polynomial optimization; Baum-Eagon inequality; high-order replicator dynamics
Funding
- FET programme within EU FP7 under the SIMBAD project [213250]
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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.
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