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 user-defined number of classes, thereby obtaining the clusters as a by-product of the partitioning process. In this paper, we provide a radically different perspective to 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 well our purpose. Specifically, we show that the hypergraph clustering problem can be naturally cast into a non-cooperative multi-player ``clustering game, whereby the notion of a cluster is equivalent to a classical game-theoretic equilibrium concept. From the computational viewpoint, we show 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 dynamics to perform this optimization. Experiments are presented which show the superiority of our approach over state-of-the-art hypergraph clustering techniques.
Samuel Rota Bulò (Università Ca' Foscari)
Marcello Pelillo (Università Ca' Foscari di Venezia)
More from the Same Authors
2012 Poster: Context-Sensitive Decision Forests for Object Detection »
Peter Kontschieder · Samuel Rota Bulò · Antonio Criminisi · Pushmeet Kohli · Marcello Pelillo · Horst Bischof
2011 Workshop: Philosophy and Machine Learning »
Marcello Pelillo · Joachim M Buhmann · Tiberio Caetano · Bernhard Schölkopf · Larry Wasserman