Graphical tools for model-based mixture discriminant analysis

The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we consider the case of mixture of mixture models with varying parametrization which allow for parsimonious models. The approach is an extension of an existing work on reducing dimensionality for model-based clustering based on Gaussian mixtures. Information on the dimension reduction subspace is provided by the variation on class locations and, depending on the estimated mixture model, on the variation on class dispersions. Projections along the estimated directions provide summary plots which help to visualize the structure of the classes and their characteristics. A suitable modification of the method allows us to recover the most discriminant directions, i.e., those that show maximal separation among classes. The approach is illustrated using simulated and real data.