Penalized Model-Based Clustering with Group-Dependent Shrinkage Estimation

Gaussian mixture models (GMM) are the most-widely employed approach to perform model-based clustering of continuous features. Grievously, with the increasing availability of high-dimensional datasets, their direct applicability is put at stake: GMMs suffer from the curse of dimensionality issue, as the number of parameters grows quadratically with the number of variables. To this extent, a methodological link between Gaussian mixtures and Gaussian graphical models has recently been established in order to provide a framework for performing penalized model-based clustering in presence of large precision matrices. Notwithstanding, current methodologies do not account for the fact that groups may be under or over-connected, thus implicitly assuming similar levels of sparsity across clusters. We overcome this limitation by defining data-driven and component specific penalty factors, automatically accounting for different degrees of connections within groups. A real data experiment on handwritten digits recognition showcases the validity of our proposal.