Learning a multivariate Gaussian mixture model with the reversible jump MCMC algorithm

Authors:
Zhihua Zhang;Kap Luk Chan;Yiming Wu;Chibiao Chen
Affiliations:
Department of Computer Science, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. zhzhang@cs.ust.hk;School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798;School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798;School of Electrical and Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798
Venue:
Statistics and Computing
Year:
2004

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Abstract

This paper is a contribution to the methodology of fully Bayesian inference in a multivariate Gaussian mixture model using the reversible jump Markov chain Monte Carlo algorithm. To follow the constraints of preserving the first two moments before and after the split or combine moves, we concentrate on a simplified multivariate Gaussian mixture model, in which the covariance matrices of all components share a common eigenvector matrix. We then propose an approach to the construction of the reversible jump Markov chain Monte Carlo algorithm for this model. Experimental results on several data sets demonstrate the efficacy of our algorithm.