  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.
