Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Spoken Language Identification for Indian Languages Using Split and Merge EM Algorithm

Performance of Language Identification (LID) System using Gaussian Mixture Models (GMM) is limited by the convergence of Expectation Maximization (EM) algorithm to local maxima. In this paper an LID system is described using Gaussian Mixture Models for the extracted features which are then trained using Split and Merge Expectation Maximization Algorithm that improves the global convergence of E...

A Note on the Article ’ Inference for multivariate normal mixtures ’

Gaussian mixture models provide a flexible tool for data modeling, clustering and classification. We consider the problem of estimating the parameters of a multivariate Gaussian mixture with K components by maximizing the likelihood function. This approach has a theoretical drawback: the likelihood function is unbounded, and the interesting maxima are local maxima in the interior of the paramet...

Split and Merge EM Algorithm for Improving Gaussian Mixture Density Estimates

The EM algorithm for Gaussian mixture models often gets caught in local maxima of the likelihood which involve having too many Gaussians in one part of the space and too few in another, widely separated part of the space. We present a new EM algorithm which performs split and merge operations on the Gaussians to escape from these configurations. This algorithm uses two novel criteria for effici...

Critical Lines in Symmetry of Mixture Models and its Application to Component Splitting

We show the existence of critical points as lines for the likelihood function of mixture-type models. They are given by embedding of a critical point for models with less components. A sufficient condition that the critical line gives local maxima or saddle points is also derived. Based on this fact, a component-split method is proposed for a mixture of Gaussian components, and its effectivenes...