RESULTS ON THE TWO POPULATION FEATURE SELECTION PROBLEM USING PROBABILITY OF CORRECT CLASSIFICATION AS A CRITERION

摘要

We present the variational equations for maximizing the probability of correct classification as a function of a l*n feature selection matrix B for the two population problem. For the special case of equal covariance matrices the optimal B is unique up to scalar multiples and ranks one sufficient. For equal population means, the best l*n B is an eigenvector corresponding either to the largest or smallest eigenvalues of where £1 and Σ2 are the n*n covariance matrices of the two populations. The transformed probability of correct classification depends only on the eigenvalues. Finally, a procedure is proposed for constructing an optimal or nearly optimal k*n matrix of rank k without solving the k-dimensional variational equation.