Group-wise penalized estimation schemes in model-based clustering

Gaussian mixture models provide a probabilistically sound clustering approach. However, their tendency to be over-parameterized endangers their utility in high dimensions. To induce sparsity, penalized model-based clustering strategies have been explored. Some of these approaches, exploiting the link between Gaussian graphical models and mixtures, allow to handle large precision matrices, encoding variables relationships. By assuming similar components sparsity levels, these methods fall short when the dependence structures are group-dependent. Our proposal, by penalizing group-specific transformations of the precision matrices, automatically handles situations where under or over-connectivity between variables is witnessed. The performances of the method are shown via a real data experiment