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Recent advances on overfitting Bayesian mixture models provide a solid andstraightforward approach for inferring the underlying number of clusters andmodel parameters in heterogeneous datasets. The applicability of such aframework in clustering correlated high dimensional data is demonstrated. Forthis purpose an overfitting mixture of factor analyzers is introduced, assumingthat the number of factors is fixed. A Markov chain Monte Carlo (MCMC) samplercombined with a prior parallel tempering scheme is used to estimate theposterior distribution of model parameters. The optimal number of factors isestimated using information criteria. Identifiability issues related to thelabel switching problem are dealt by post-processing the simulated MCMC sampleby relabelling algorithms. The method is benchmarked against state-of-the-artsoftware for maximum likelihood estimation of mixtures of factor analyzersusing an extensive simulation study. Finally, the applicability of the methodis illustrated in publicly available data.

Overfitting Bayesian Mixtures of Factor Analyzers with an Unknown Number of Components