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Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes

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Abstract

It is shown that, in the pattern recognition problem with two nonoverlapping classes, the matrices of estimates of the object closeness are described by a metric. The transition to the algebraic closure of the model of recognizing operators of finite degree corresponds to the application of a special transformation of this metric. It is proved that the minimal degree correct algorithm can be found as a polynomial of a special form. A simple criterion for testing classification implementations is obtained.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia

    A. G. D’yakonov

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  1. A. G. D’yakonov
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Correspondence to A. G. D’yakonov.

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Original Russian Text © A.G. D’yakonov, 2008, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2008, Vol. 48, No. 5, pp. 916–927.

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D’yakonov, A.G. Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes. Comput. Math. and Math. Phys. 48, 866–876 (2008). https://doi.org/10.1134/S0965542508050138

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