Approaches for fully automated parameter estimation of mixtures of factor analysers

Mixture of factor analysers (MFA) are popular tools for dimension reduction and model-based clustering. The conventional method of parameter estimation for MFA is via maximum likelihood using the Expectation-Maximization (EM) algorithm. This typically assumes the number of components ( g ) and the number of factors ( q ) to be known a priori , which are often not known in practice. This article reviews different approaches for automatically inferring g and/or q from the data. A hybrid method, incremental automated MFA (IAMFA), is also proposed. We conduct a systematic comparison of these methods using simulated data and analyse their relative performance across various scenarios, looking at their ability to infer g and q correctly, the general model fit, clustering accuracy, and computation time.