PENALIZED DISCRIMINANT-ANALYSIS

Fisher's linear discriminant analysis (LDA) is a popular data-analytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly cor related predictors, such as those obtained by discretizing a function, or the grey-scale values of the pixels in a series of images. In case s such as these it is natural, efficient and sometimes essential to im pose a spatial smoothness constraint on the coefficients, both for imp roved prediction performance and interpretability. We cast the classif ication problem into a regression framework via optimal scoring. Using this, our proposal facilitates the use of any penalized regression te chnique in the classification setting. The technique is illustrated wi th examples in speech recognition and handwritten character recognitio n.