Fast population game dynamics for dominant sets and other quadratic optimization problems

  • Authors:
  • Samuel Rota Bulò;Immanuel M. Bomze;Marcello Pelillo

  • Affiliations:
  • Dipartimento di Informatica, Univ. of Venice, Italy;Department of Statistics and Decision Support Systems, Univ. of Vienna, Austria;Dipartimento di Informatica, Univ. of Venice, Italy

  • Venue:
  • SSPR&SPR'10 Proceedings of the 2010 joint IAPR international conference on Structural, syntactic, and statistical pattern recognition
  • Year:
  • 2010

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Abstract

We propose a fast population game dynamics, motivated by the analogy with infection and immunization processes within a population of "players," for finding dominant sets, a powerful graph-theoretical notion of a cluster. Each step of the proposed dynamics is shown to have a linear time/space complexity and we show that, under the assumption of symmetric affinities, the average population payoff is strictly increasing along any non-constant trajectory, thereby allowing us to prove that dominant sets are asymptotically stable (i.e., attractive) points for the proposed dynamics. The approach is general and can be applied to a large class of quadratic optimization problems arising in computer vision. Experimentally, the proposed dynamics is found to be orders of magnitude faster than and as accurate as standard algorithms.