Optimal feature extraction based on the minimization of the increase in risk of misclassification

A general approach is presented for finding the optimal finite dimensional subspace of a prescribed dimension onto which to project the data belonging to a (higher dimensional) observation space. The approach is based on the use of suitable approximations of the functions involved, so that a variational technique may be used for the solution of the problem. The optimality criterion used is the minimization of the increase in the Bayes risk of misclassification araising from the dimensionality reduction. As an illustration of this approach, the case of two Gaussian pattern classes is considered in some detail.