On Bayesian analysis of a finite generalized Dirichlet mixture via a Metropolis-within-Gibbs sampling

Authors:
Nizar Bouguila;Djemel Ziou;Riad I. Hammoud
Affiliations:
Concordia University, Concordia Institute for Information Systems Engineering (CIISE), H3G 1T7, Montreal, QC, Canada;Université de Sherbrooke, Département d’Informatique, J1K 2R1, Sherbrooke, QC, Canada;Delphi Corporation, Delphi Electronics and Safety, Kokomo, IN, USA
Venue:
Pattern Analysis & Applications
Year:
2009

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Abstract

In this paper, we present a fully Bayesian approach for generalized Dirichlet mixtures estimation and selection. The estimation of the parameters is based on the Monte Carlo simulation technique of Gibbs sampling mixed with a Metropolis-Hastings step. Also, we obtain a posterior distribution which is conjugate to a generalized Dirichlet likelihood. For the selection of the number of clusters, we used the integrated likelihood. The performance of our Bayesian algorithm is tested and compared with the maximum likelihood approach by the classification of several synthetic and real data sets. The generalized Dirichlet mixture is also applied to the problems of IR eye modeling and introduced as a probabilistic kernel for Support Vector Machines.