A mixture of common skew‐t factor analysers

Abstract A mixture of common skew‐ t factor analysers model is introduced for model‐based clustering of high‐dimensional data. By assuming common factors, this model allows clustering to be performed in the presence of a large number of mixture components or when the number of dimensions is too large to be well modelled by the mixture of factor analysers model or a variant thereof. Furthermore, assuming that the component densities follow a skew‐ t distribution allows robust clustering of data with asymmetric clusters. This paper is the first time that skewed common factors have been used, and it marks an important step in robust clustering and classification of high‐dimensional data. The alternating expectation–conditional maximization algorithm is employed for parameter estimation. We demonstrate excellent clustering performance when our mixture of common skew‐ t factor analysers model is applied to real and simulated data. Copyright © 2014 John Wiley & Sons, Ltd