On Minimizing the Probability of Misclassification for Linear Feature Selection

Abstract

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 $k k \times n$ 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 $\mathbf{B}$. The use of this exression in a computational procedure for obtaining a $\mathbf{B}$ which minimizes the probability of misclassification in the case of two populations is discussed.