Optimal projections for Gaussian discriminants

Abstract

We study the problem of obtaining optimal projections for performing discriminant analysis with Gaussian class densities. Unlike in most existing approaches to the problem, we focus on the optimisation of the multinomial likelihood based on posterior probability estimates, which directly captures discriminability of classes. Finding optimal projections offers utility for dimension reduction and regularisation, as well as instructive visualisation for better model interpretability. Practical applications of the proposed approach show that it is highly competitive with existing Gaussian discriminant models. Code to implement the proposed method is available in the form of an R package from https://github.com/DavidHofmeyr/OPGD.