Repulsive mixture models for high-dimensional data

Model-based clustering is customarily achieved in the Bayesian setting through finite or infinite mixture models, assuming that the p-dimensional data are iid generated from homogeneous populations, represented by parametric densities. The poor performance of Bayesian mixtures in the large-p setting is known and they may lead to inconsistent cluster estimates when p increases to infinity. We build on a class of mixtures of latent factor models, similar to the model in [4], mixing over the latent parameters. Our main contribution to the model is the assumption of a repulsive point process as mixing measure. The matrix of factor loadings drives the anisotropic behavior, so that separation is indeed induced between the high-dimensional centers of different clusters. We also propose a MCMC algorithm which extends a conditional algorithm for repulsive mixture models, introduced previously in the literature.