  Recent advances on overfitting Bayesian mixture models provide a solid and
straightforward approach for inferring the underlying number of clusters and
model parameters in heterogeneous datasets. The applicability of such a
framework in clustering correlated high dimensional data is demonstrated. For
this purpose an overfitting mixture of factor analyzers is introduced, assuming
that the number of factors is fixed. A Markov chain Monte Carlo (MCMC) sampler
combined with a prior parallel tempering scheme is used to estimate the
posterior distribution of model parameters. The optimal number of factors is
estimated using information criteria. Identifiability issues related to the
label switching problem are dealt by post-processing the simulated MCMC sample
by relabelling algorithms. The method is benchmarked against state-of-the-art
software for maximum likelihood estimation of mixtures of factor analyzers
using an extensive simulation study. Finally, the applicability of the method
is illustrated in publicly available data.
