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UCL

SMEM Algorithm for Mixture Models

Naonori Ueda, Ryohei Nakano
NTT Communication Science Laboratories
Hikaridai, Seika-cho, Soraku-gun
Kyoto 619-0237, Japan

Zoubin Ghahramani, Geoffrey Hinton
Gatsby Computational Neuroscience Unit
University College London
17 Queen Square,  Alexandra House
London WC1N 3AR, UK

Abstract

We Present a split and merge EM (SMEM) algorithm to overcome the local maxima problem in parameter estimation of finite mixture models.  In the case of mixture models, local maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely separated part of the space.   To escape from such configurations we repeatedly perform simultaneous split and merge operations using a new criterion for efficiently selecting the split and merge candidates.  We apply the proposed algorithm to the training of Gaussian mixtures and mixtures of factor analyzers using synthetic and real data and show the effectiveness of using the split and merge operations to improve the likelihood of both the training data and of held-out test data.  We also show the practical usefulness of the proposed algorithm by applying it to image compression and pattern recognition problems.

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Neural Computation (in press)

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