Approaches to construction of linear classifiers in the case of many classes

Abstract

Some approaches to the problem of constructing linear classifiers, including embedded ones, are studied for the case of many classes. Sufficient conditions for linear separability of classes are formulated, and specifics of the problem statement when sets are not linearly separable are considered. Different approaches to construction of optimal linear classifiers are studied, and the results of numerical experiments are presented. The properties of embedded (convex piecewise linear) classifiers are studied. It is shown that, for an arbitrary family of finite nonintersecting sets, there is an embedded linear classifier that correctly separates the points of these sets.