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, we propose a constrained procedure which maintains the eigenvalues of the covariance structure into suitable ranges. Applications of this approach in robust clustering is then outlined.