Linear dimension reduction and Bayes classification

This paper develops an explicit expression for a compression matrix T of smallest possible left dimension k consistent with preserving the n-variate normal Bayes assignment of X to a given one of a finite number of populations and the k-variate Bayes assignment of TX to that population. The Bayes population assignment of X and TX are shown to be equivalent for a compression matrix T explicitly calculated as a function of the means and covariances (known) of the given populations. 1. Mathematics Department, University of Houston 2. Programs in Mathematical Sciences, Univ. of Texas at Dallas 3. Department of Mathematics, University of Tulsa This work was partially supported by Johnson Space Center Contract'NAS-9-15000.