Dirichlet Process Mixtures of Factor Analysers

Mixture of factor analysers (MFA) is a well-known model that combines the dimensionality reduction technique of Factor Analysis (FA) with mixture modeling. The key issue in MFA is deciding on the latent dimension and the number of mixture components to be used. The Bayesian treatment of MFA has been considered by Beal and Ghahramani (2000) using variational approximation and by Fokoué and Titterington (2003) using birth-and –death Markov chain Monte Carlo (MCMC). Here, we present the nonparametric MFA model utilizing a Dirichlet process (DP) prior on the component parameters (that is, the factor loading matrix and the mean vector of each component) and describe an MCMC scheme for inference. The clustering property of the DP provides automatic selection of the number of mixture components. The latent dimensionality of each component is inferred by automatic relevance determination (ARD). Identifying the action potentials of individual neurons from extracellular recordings, known as spike sorting, is a challenging clustering problem. We apply our model for clustering the waveforms recorded from the cortex of a macaque monkey