Variable selection for model–based high– dimensional clustering and its application to microarray data

Summary. Variable selection in high-dimensional clustering analysis is an important yet challenging prob-lem. In this article, we propose two methods that simultaneously separate data points into similar clusters and select informative variables that contribute to the clustering. Our methods are in the framework of pe-nalized model-based clustering. Unlike the classical L1-norm penalization, the penalty terms that we propose make use of the fact that parameters belonging to one variable should be treated as a natural “group. ” Nu-merical results indicate that the two new methods tend to remove noninformative variables more effectively and provide better clustering results than the L1-norm approach. Key words: EM algorithm; High-dimension low sample size; Microarray; Model-based clustering; Regu-larization; Variable selection