Optimal set features determination in discriminant analysis by the group method of data handling

It is shown analytically that the two schemes of the Group Method of Data Handling - with dividing of observations into the training and checking subsamples and proposed SL-scheme of sliding examination allow to solve the problem of discriminant analysis in the broad sense on the basis of finite samples of observations. For the both schemes, it is shown that there exists an optimal set of features corresponding to the maximum mathematical expectation of some generalized distance between the observations from two general sets. It is shown analytically that parameters of the general sets and samples sizes influence on a complexity of optimal discriminant function, and conditions under which the optimal discriminant function is simplified are exhibited.