Discriminant principal components analysis

Abstract When the number of variables exceeds the number of samples, one method of multivariate discrimination is to use principal components analysis to reduce the dimensionality and then to perform canonical variates analysis (PC–CVA). This paper proposes an alternative approach in which discriminant analysis is carried out by a weighted principal component analysis of the group means (DPCA). This method does not require prior data reduction and produces discriminant factors that are orthogonal in the original data space. The theory and performance of the two methods are compared. Although the individual factors of DPCA are found to be less discriminating than PC–CVA, the overall discrimination, calculated by multivariate analysis of variance, and the predictive value, estimated by the leaving‐one‐out error rate, are broadly comparable.