Oracle Complexity and Nontransitivity in Pattern Recognition

TL;DR

This paper models pattern recognition algorithms as oracle computations on Turing machines, linking recognition process comparison to oracle complexity, and reveals nontransitive preference relations among algorithms.

Contribution

It introduces a novel framework connecting pattern recognition with recursion theory and demonstrates nontransitivity in algorithm preferences.

Findings

Recognition algorithms modeled as oracle computations.

Preference relations among algorithms are nontransitive.

Connection established between recognition complexity and oracle information volume.

Abstract

Different mathematical models of recognition processes are known. In the present paper we consider a pattern recognition algorithm as an oracle computation on a Turing machine. Such point of view seems to be useful in pattern recognition as well as in recursion theory. Use of recursion theory in pattern recognition shows connection between a recognition algorithm comparison problem and complexity problems of oracle computation. That is because in many cases we can take into account only the number of sign computations or in other words volume of oracle information needed. Therefore, the problem of recognition algorithm preference can be formulated as a complexity optimization problem of oracle computation. Furthermore, introducing a certain "natural" preference relation on a set of recognizing algorithms, we discover it to be nontransitive. This relates to the well known nontransitivity paradox in probability theory. Keywords: Pattern Recognition, Recursion Theory, Nontransitivity, Preference Relation