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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 5, Pages 916–927 (Mi zvmmf145)  
This article is cited in 2 scientific papers (total in 2 papers)

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

A. G. D'yakonov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
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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.
Key words: pattern recognition, estimation algorithm, matrices of estimates, correct algorithm, algebra over algorithms, metric, Gram's matrix, minimal degree.
Received: 20.09.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 5, Pages 866–876
DOI: https://doi.org/10.1134/S0965542508050138
Bibliographic databases:
Document Type: Article
UDC: 519.712
Language: Russian
Citation: A. G. D'yakonov, “Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes”, Zh. Vychisl. Mat. Mat. Fiz., 48:5 (2008), 916–927; Comput. Math. Math. Phys., 48:5 (2008), 866–876
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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