Algebraic methods for solving recognition problems with non-crossing classes

TL;DR

This paper introduces algebraic methods for pattern recognition, defining recognizing operators and decision rules, and constructs algorithms with guaranteed completeness for non-crossing classes.

Contribution

It proposes a novel algebraic framework for recognition models using operators and decision rules, enabling the creation of comprehensive recognizing algorithms.

Findings

Developed algebraic operations on recognizing operators

Constructed algorithms ensuring model completeness

Provided upper estimates guaranteeing extension completeness

Abstract

In this paper, we propose to consider various models of pattern recognition. At the same time, it is proposed to consider models in the form of two operators: a recognizing operator and a decision rule. Algebraic operations are introduced on recognizing operators, and based on the application of these operators, a family of recognizing algorithms is created. An upper estimate is constructed for the model, which guarantees the completeness of the extension.