Flexible Discriminant Analysis

Fisher's linear discriminant analysis is a valuable tool for multi- group classification. With large number of predictors, one can find a reduced number of descriminant 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 that are identified with group membership, and the decision boundaries are linear. This paper is about richer nonlinear classification schemes. There is a well known correspondence between discriminant analysis and canonical correlation analysis, which isn this case amounts to multi-response linear regression using optimal scalings to represent the groups.