FLEXIBLE DISCRIMINANT-ANALYSIS BY OPTIMAL SCORING

Fisher's linear discriminant analysis is a valuable tool for multigrou p classification. With a large number of predictors, one can find a re duced number of discriminant coordinate functions that are ''optimal'' for separating the groups. With two such functions, one can produce a classification map that partitions the reduced space into regions tha t are identified with group membership, and the decision boundaries ar e linear. This article is about richer nonlinear classification scheme s. Linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups. In this pap er, we obtain nonparametric versions of discriminant analysis by repla cing linear regression by any nonparametric regression method. In this way, any multiresponse regression technique (such as MARS or neural n etworks) can be postprocessed to improve its classification performanc e.