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 and real data.
latent Classes of Objects and Variable Selection / G. Galimberti; A. Montanari; C. Viroli. - STAMPA. - (2008), pp. 373-383. (Intervento presentato al convegno COMPSTAT 2008 - 18th Conference of IASC-ERS tenutosi a Porto - Portugal nel 24-29 Agosto 2008).
latent Classes of Objects and Variable Selection
GALIMBERTI, GIULIANO;MONTANARI, ANGELA;VIROLI, CINZIA
2008
Abstract
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 and real data.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.