DISCRIMINANT-ANALYSIS WHEN THE CLASSES ARISE FROM A CONTINUUM

Sometimes two class linear discriminant analysis is applied to situati ons in which the classes are formed by partitioning an underlying cont inuum. In such cases, a reasonable assumption is that the underlying c ontinuous ''response'' variable forms a joint multivariate normal dist ribution with the predictors. We compare the error rate of linear disc riminant analysis with that of the optimal classification rule under t hese conditions, showing that linear discriminant analysis leads to a decision surface parallel to, but shifted from, the decision surface o f the optimal rule and that the two rules can lead to very different e rror rates. (C) 1998 Pattern Recognition Society. Published by Elsevie r Science Ltd. All rights reserved.