The Discrimination Subspace Model

Abstract

For a p-variate normal random vector measured in two populations, we propose a method of discrimination under the constraint that all differences between the two populations occur in a subspace of dimension q < p. This method of classification is based on the discrimination subspace model, denoted by DSM(q), and is intermediate between linear and quadratic discrimination. It combines the ideas of dimension reduction and constraints on the parameter space, thus substantially reducing the number of parameters to be estimated. The maximum likelihood estimators of the model are presented, and the performance of DSM(q) versus quadratic and linear discrimination is assessed via simulation. It is generally shown that discrimination based on DSM(q) consistently yields noticeably lower expected actual error rates relative to the traditional methods. The method is illustrated with a real data example and is compared to linear and quadratic discrimination using a leave-one-out method. The example confirms the simulation results in that the DSM(q) discrimination function misclassified approximately one-half as many observations.