Application of mixture models to large datasets

Abstract

Mixture distributions are commonly being applied for modelling and for discriminant and cluster analyses in a wide variety of situations. We first consider normal and t-mixture models. As they are highly parameterized, we review methods to enable them to be fitted to large datasets involving many observations and variables. Attention is then given to extensions of these mixture models to mixtures with skew normal and skew t-distributions for the segmentation of data into clusters of non-elliptical shape. The focus is then on the latter models in conjunction with the JCM (joint clustering and matching) procedure for an automated approach to the clustering of cells in a sample in flow cytometry where a large number of cells and their associated markers have been measured. For a class of multiple samples, we consider the use of JCM for matching the sample-specific clusters across the samples in the class and for improving the clustering of each individual sample. The supervised classification of a sample is also considered in the case where there are different classes of samples corresponding, for example, to different outcomes or treatment strategies for patients undergoing medical screening or treatment.