  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.
