Model-based clustering with sparse matrix mixture models

In recent years we are witnessing to an increased attention towards methods for clustering matrix-valued data. In this framework, matrix Gaussian mixture models constitute a natural extension of the model-based clustering strategies. Regrettably, the overparametrization issues, already affecting the vector-valued framework in high-dimensional scenarios, are even more troublesome for matrix mixtures. In this work we introduce a sparse model-based clustering procedure conceived for the matrix-variate context. We introduce a penalized estimation scheme which, by shrinking some of the parameters towards zero, produces parsimonious solutions when the dimensions increase. Moreover it allows cluster-wise sparsity, possibly easing the interpretation and providing richer insights on the analyzed dataset.