Group-Wise Shrinkage Estimation in Penalized Model-Based Clustering

Abstract Finite Gaussian mixture models provide a powerful and widely employed probabilistic approach for clustering multivariate continuous data. However, the practical usefulness of these is jeopardized in high-dimensional spaces, where they tend to be over-parameterized. As consequence, different solutions have been proposed, often relying on matrix decompositions or variable selection strategies. Recently, methodological link between graphical finite mixtures has established, paving way penalized model-based presence large precision matrices. Notwithstanding, current methodologies implicitly assume similar levels sparsity across classes, not accounting degrees association variables groups. We overcome this limitation by deriving group-wise penalty factors, which automatically enforce under over-connectivity estimated graphs. The entirely data-driven does require additional hyper-parameter specification. Analyses synthetic real data showcase validity our proposal.