Generalized competitive learning of Gaussian mixture models

Authors:
Zhiwu Lu;Horace H. S. Ip
Affiliations:
Department of Computer Science, City University of Hong Kong, Kowloon, Hong Kong;Dept. of Comp. Sci., City Univ. of Hong Kong, Kowloon, Hong Kong and Centre for Innovative Applications of Internet and Multimedia Technologie, City Univ. of Hong Kong, Kowloon, Hong Kong
Venue:
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics - Special issue on cybernetics and cognitive informatics
Year:
2009

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Abstract

When fitting Gaussian mixtures to multivariate data, it is crucial to select the appropriate number of Gaussians, which is generally referred to as the model selection problem. Under regularization theory, we aim to solve this model selection problem through developing an entropy regularized likelihood (ERL) learning on Gaussian mixtures. We further present a gradient algorithm for this ERL learning. Through some theoretic analysis, we have shown a mechanism of generalized competitive learning that is inherent in the ERL learning, which can lead to automatic model selection on Gaussian mixtures and also make our ERL learning algorithm less sensitive to the initialization as compared to the standard expectation-maximization algorithm. The experiments on simulated data using our algorithm verified our theoretic analysis. Moreover, our ERL learning algorithm has been shown to outperform other competitive learning algorithms in the application of unsupervised image segmentation.