The asymptotic properties of a Σ-classifier for multiclass recognition problems with non-elliptic distribution of data

Abstract

The asymptotic properties of a Σ-classifier that does not require a priori information about the distribution or shape of a dividing curve are studied. A mathematical apparatus is built to solve multiclass recognition problems with a non-elliptic distribution of data on the basis of the majority voting method. The procedure is studied to determine the shapes of dividing curves of a Σ-classifier by the geometric structure of data that are the basis of the Σ-scheme. The conditions, under which the Σ-classifier is asymptotically equivalent to the Bayes rule, are defined.