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Clustering Games

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Registration and Recognition in Images and Videos

Part of the book series: Studies in Computational Intelligence ((SCI,volume 532))

Abstract

Clustering refers to the process of extracting maximally coherent groups from a set of objects using pairwise, or high-order, 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 chapter, we provide a brief review of our recent work which offers a radically different view of the problem. In contrast to the classical approach, in fact, 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. To this end, we formulate the clustering problem in terms of a non-cooperative “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 dynamics to perform this optimization, based on the Baum-Eagon inequality. Experiments on real-world data are presented which show the superiority of our approach over the state of the art.

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Authors and Affiliations

  1. DAIS, Università Ca’ Foscari Venezia, Via Torino, 155, Venezia Mestre, Italy

    Marcello Pelillo & Samuel Rota Bulò

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  1. Marcello Pelillo
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  2. Samuel Rota Bulò
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Correspondence to Marcello Pelillo .

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Editors and Affiliations

  1. University of Cambridge Department of Engineering, Cambridge, United Kingdom

    Roberto Cipolla

  2. Università di Catania Dipartimento di Matematica e Informatica, Catania, Catania, Italy

    Sebastiano Battiato

  3. Università di Catania Dipartimento di Matematica e Informatica, Catania, Italy

    Giovanni Maria Farinella

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Pelillo, M., Bulò, S.R. (2014). Clustering Games. In: Cipolla, R., Battiato, S., Farinella, G. (eds) Registration and Recognition in Images and Videos. Studies in Computational Intelligence, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-44907-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-44907-9_8

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