Linear dimension reduction and Bayes classification

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 was developed. The Bayes population assignment of X and TX were shown to be equivalent for a compression matrix T explicitly calculated as a function of the means and covariances of the given populations.