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A Game-Theoretic Approach to Hypergraph Clustering (2009)
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BibTeX
@MISC{Bulò09agame-theoretic,
author = {Samuel Rota Bulò and Marcello Pelillo},
title = {A Game-Theoretic Approach to Hypergraph Clustering},
year = {2009}
}
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Abstract
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.
Keyphrases
hypergraph clustering game-theoretic approach user-defined number traditional approach game theory classical approach state-of-the-art hypergraph input data clustering game computational viewpoint standard simplex unexplored perspective polynomial function discrete-time dynamic partitioning process coherent group meaningful formalization different perspective classical game-theoretic equilibrium concept non-cooperative multi-player clustering game
