Unsupervised learning of finite mixture models using mean field games

Sergio Pequito*, A. Pedro Aguiar, Bruno Sinopoli, Diogo Gomes

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

In this paper we develop a dynamic continuous solution to the clustering problem of data characterized by a mixture of K distributions, where K is given a priori. The proposed solution resorts to game theory tools, in particular mean field games and can be interpreted as the continuous version of a generalized Expectation-Maximization (GEM) algorithm. The main contributions of this paper are twofold: first, we prove that the proposed solution is a GEM algorithm; second, we derive closed-form solution for a Gaussian mixture model and show that the proposed algorithm converges exponentially fast to a maximum of the log-likelihood function, improving significantly over the state of the art. We conclude the paper by presenting simulation results for the Gaussian case that indicate better performance of the proposed algorithm in term of speed of convergence and with respect to the overlap problem.

Original languageEnglish (US)
Title of host publication2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
Pages321-328
Number of pages8
DOIs
StatePublished - Dec 1 2011
Event2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011 - Monticello, IL, United States
Duration: Sep 28 2011Sep 30 2011

Publication series

Name2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011

Other

Other2011 49th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2011
CountryUnited States
CityMonticello, IL
Period09/28/1109/30/11

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

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