Abstract
The use of principal components to reduce the number of dimensions is an optimum procedure for data representation, but may involve the loss of valuable information for discriminant analysis. In this paper a simple approach is proposed to improve the discrimination based on a given number (k) of principal components, without requiring the calculation of additional ones. This is achieved by introducing a metric which is a linear combination of the Mahalanobis distance in the subspace of the first k components and the euclidean distance in its orthogonal complement. This concept, applied to Fisher's linear discriminant function, yields an optimum combination of the two distances mentioned. The empirical performance of this procedure for estimated parameters is investigated by a simulation study. Some suggestions for further extensions of this method to nonlinear discrimination are briefly discussed.
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