DISCRIMINANT-ANALYSIS WITH SINGULAR COVARIANCE MATRICES - METHODS ANDAPPLICATIONS TO SPECTROSCOPIC DATA

Currently popular techniques such as experimental spectroscopy and com puter-aided molecular modelling lead to data having very many variable s observed on each of relatively few individuals. A common objective i s discrimination between two or more groups, but the direct applicatio n of standard discriminant methodology fails because of singularity of covariance matrices. The problem has been circumvented in the past by prior selection of a few transformed variables, using either principa l component analysis or partial least squares. Although such selection ensures nonsingularity of matrices, the decision process is arbitrary and valuable information on group structure may be lost. We therefore consider some ways of estimating linear discriminant functions withou t such prior selection. Several spectroscopic data sets are analysed w ith each method, and questions of bias of assessment procedures are in vestigated. All proposed methods seem worthy of consideration in pract ice.