Linear dimension reduction and Bayes classification

摘要

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.