The problem of obtaining optimal projections for performing discriminant analysis with Gaussian class densities is studied. Unlike in most existing approaches to the problem, the focus of the optimisation is on the multinomial likelihood based on posterior probability estimates, which directly captures discriminability of classes. In addition to the more commonly considered problem, in this context, of classification, the unsupervised clustering counterpart is also considered. 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 considerable promise for both classification and clustering. Code to implement the proposed method is available in the form of an R package from https://github.com/DavidHofmeyr/OPGD.
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