On Minimizing the Probability of Misclassification for Linear Feature Selection

We describe an approach to linear feature selection for n-dimensional normally distributed observation vectors which belong to one of m populations. More specifically, we consider the problem of finding a rank k k × n matrix B which minimizes the probability of misclassification with respect to the k-dimensional transformed density functions when a Bayes optimal (maximum likelihood) classification scheme is used. Theoretical results are presented which, for the case $k = 1$, give rise to a numerically tractable expression for the variation in the probability of misclassification with respect to B. The use of this exression in a computational procedure for obtaining a B which minimizes the probability of misclassification in the case of two populations is discussed.