Latent classes of objects and variable selection

In this paper we present a model based clustering approach which contextually performs dimension reduction and variable selection. In particular we assume that the data have been generated by a linear factor model with latent variables modeled as gaussian mixtures (thus obtaining dimension reduction) and. we shrink the factor loadings, resorting to a penalized likelihood method, with an L1 penalty (thus realizing automatic variable selection). We derive an EM algorithm to obtain the penalized model estimates and a modified BIC criterion to select the penalization parameter. We evaluate the performance of the proposed method on simulated data.