Penalized mixtures of factor analyzers with application to clustering high-dimensional microarray data

Abstract

Motivation: Model-based clustering has been widely used, e.g. in microarray data analysis. Since for high-dimensional data variable selection is necessary, several penalized model-based clustering methods have been proposed tørealize simultaneous variable selection and clustering. However, the existing methods all assume that the variables are independent with the use of diagonal covariance matrices.

Results: To model non-independence of variables (e.g. correlated gene expressions) while alleviating the problem with the large number of unknown parameters associated with a general non-diagonal covariance matrix, we generalize the mixture of factor analyzers to that with penalization, which, among others, can effectively realize variable selection. We use simulated data and real microarray data to illustrate the utility and advantages of the proposed method over several existing ones.

Fig. 1.

Clusters identified by PMFA (right panels) and PMND (left panels) from a dataset in simulation set-up 4. Three informative variables (X3, X6 and X16) were plotted. The five types of the symbols represent the cluster-memberships in the five clusters identified by PMND in left panels, while the two types of the symbols represent the true cluster memberships in right panels.

Fig. 2.

Survival curves for the clusters identified by PMFA and PMND for the lung cancer data.