An elementary algorithm for classifying digital objects based on the variational principle

TL;DR

This paper introduces a simple algorithm for classifying digital objects using the variational principle, involving a modified Uzawa's method to handle polyhedral vertices in noisy data scenarios.

Contribution

It presents a novel modification of Uzawa's method for efficiently computing polyhedral vertices in classification problems based on histograms.

Findings

Effective classification of digital objects demonstrated.

Algorithm handles noisy data with improved accuracy.

Computational efficiency of the method shown.

Abstract

When using the maximin principle to solve the problem of classifying digital objects according to histograms, generated by this objects, it becomes necessary to take into account all the vertices of the polyhedron, generated by inequalities - restrictions in which the objective function takes maximum values or values close to maximum, if the data is noisy. In the proposed work, to obtain coordinates of all vertices mentioned polyhedron, a modification of H.Uzawa's method is used, which is obtained by replacing vectors and matrices with functions defined on finite sets of a special type.