Testing hypotheses on discriminant space in the mixture model of Gaussian distributions

When clustering multivariate observations adhering the mixture model of Gaussian distributions, rather frequently projections of the observations onto a linear subspace of less dimensionality, called discriminant space (DS), contain all statistical information about the cluster structure of the model. In this case, the actual reduction of data dimensionality substantially facilitates a solution of various classification problems. In the paper, attention is devoted to statistical testing of hypotheses about DS and its dimension. The characterization of DS and methods of its identification are also briefly discussed.