Discriminant Analysis by Gaussian Mixtures

SUMMARY Fisher-Rao linear discriminant analysis (LDA) is a valuable tool for multigroup classification. LDA is equivalent to maximum likelihood classification assuming Gaussian distributions for each class. In this paper, we fit Gaussian mixtures to each class to facilitate effective classification in non-normal settings, especially when the classes are clustered. Low dimensional views are an important by-product of LDA—our new techniques inherit this feature. We can control the within-class spread of the subclass centres relative to the between-class spread. Our technique for fitting these models permits a natural blend with nonparametric versions of LDA.