EM algorithm with split and merge operations for mixture models

The maximum likelihood estimate of a mixture model is usually found by using the EM algorithm. However, the EM algorithm suffers from a local optima problem and therefore we cannot obtain the potential performance of mixture models in practice. In the case of mixture models, local maxima often have 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 proposed a new variant of the Ehl algorithm in which simultaneous split and merge operations are repeatedly performed by using a new criterion for efficiently selecting the split and merge candidates. We apply the proposed algorithm to the training of Gaussian mixtures and the dimensionality reduction based on a mixture of factor analyzers using synthetic and real data and show that the proposed algorithm can markedly improve the ML estimates.