Constrained EM Algorithms for Gaussian Mixtures of Factor Analyzers

Mixtures of factor analyzers are becoming more and more popular in the area of model based clustering of high-dimensional data. In data modeling, according to the likelihood approach, it is well known that the loglikelihood function may present spurious maxima and singularities and this is due to specific patterns of the estimated covariance structure. To reduce such drawbacks, in this paper we introduce and implement a procedure for the parameter estimation of mixtures of factor analyzers, which maximizes the likelihood function in a constrained parameter space, having no singularities and a reduced number of spurious local maxima.We then analyze and measure its performance, compared to the usual non-constrained approach, via some simulations and applications to real data sets.