Machine learning. A method of approximation of discriminant functions and two methods of estimation of a posterior probabilities of classes in the problem of classification

Abstract

The method of approximating a discriminant functions of the training set is proposed. The sign of the discriminant functions allows us to classify the point in one or another class. The approximation is constructed with greater precision in the neighborhood of zero values of the discriminant function. To estimate a posterior probability of a class of a point two methods are proposed: based on a series of discriminant functions constructed from the training set and a method in which for each point a personal approximation of the discriminant function is constructed that takes a zero value at a given point. At points where the discriminant function is zero a posterior probability of the class are the same and depend only on the ratio of the values of classification errors.