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We consider the problem of performing interpretable classification in the high-dimensional setting, in which the number of features is very large and the number of observations is limited. This setting has been studied extensively in the chemometrics literature, and more recently has become commonplace in biological and medical applications. In this setting, a traditional approach involves performing feature selection before classification. We propose sparse discriminant analysis, a method for performing linear discriminant analysis with a sparseness criterion imposed such that classification and feature selection are performed simultaneously. Sparse discriminant analysis is based on the optimal scoring interpretation of linear discriminant analysis, and can be extended to perform sparse discrimination via mixtures of Gaussians if boundaries between classes are nonlinear or if subgroups are present within each class. Our proposal also provides low-dimensional views of the discriminative directions. [ABSTRACT FROM AUTHOR]

Fisher's linear discriminant analysis is a valuable tool for multigroup classification With a large number of predictors, one can find a reduced number of discriminant coordinate functions that are "optimal' for separating the groups With two such functions, one can produce a classification map that partitions the reduced space into regions that are identified with group membership, and the decision boundaries are linear This article is about richer nonlinear classification schemes Linear discriminant analysis is equivalent to multiresponse linear regression using optimal scorings to represent the groups In this paper, we obtain nonparametnc versions of discriminant analysis by replacing linear regression by any nonparameinc regression method In this way, any multiresponse regression technique (such as MARS or neural networks) can be postprocessed to improve its classification performance. [ABSTRACT FROM AUTHOR]