Discrimination on latent components with respect to patterns. Application to multicollinear data

A new presentation of discriminant analysis is discussed. It consists in setting up patterns associated to the various groups and deriving latent variables in such a way that scores in each group are as highly clustered about their pattern as possible. When the conformity between observations and group patterns is investigated by means of the coefficient of correlation, Fisher's canonical discriminant analysis is retrieved. If the covariance is used instead of the coefficient of correlation, then a new and simple formalization of PLS discriminant analysis is achieved. The potential of the general approach is discussed and the methods of analysis are illustrated on the basis of a real data set.