Linear Discriminant Analysis: Loss of Discriminating Power When a Variate is Omitted

where a is the probability of misclassification, A' is the iMahalanobis' distance, Pi = (HA g')/o is the normalized difference of the expectations of the ith variate in the populations A and B, and p is the number of variates. However, this procedure requires too much computing. Approximate algorithms have been suggested (Weiner and Dunn [1966]) but they also require large computers. Only in special cases (namely, when the correlation matrix has some specified properties) are more simple techniques to select the best variates available (Cochran [1964]). In some situations a more particular problem is of interest: estimation of the reduction of the discriminating power when a single variate from the complete set of p variates is excluded after the discriminant function has been formed. 2. Let A = ai i be a symmetric square matrix. If we cross out the kth line and the kth column of this matrix, the elements of the new inverse matrix Aiwill be connected with the elements of the matrix A-' by an equality: