Carleton University
Technical Report TR-01-03
January 2001
On Opitmal Pairwise Linear Classifiers for Normal Distributions: The d-Dimensional Case
Luis Rueda & B. John Oommen
Abstract
We consider the well-studied Pattern Recognition (PR) problem of designing linear classifi ers. When dealing with normally distributed classes, it is well known that the optimal Bayes classifi er is linear only when the covariance matrices are equal. This was the only known condition for classifi er linearity. In a previous work, we presented the theoretical framework for optimal pairwise linear classifi ers for two- dimensional normally distributed random vectors. We derived the necessary and sufficient conditions that the distributions have to satisfy so as to yield the optimal linear classifi er as a pair of straight lines.