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Zh. Vychisl. Mat. Mat. Fiz., 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

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.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:5, 866–876

Bibliographic databases:

UDC: 519.712
Received: 20.09.2007

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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\paper Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2008
\vol 48
\issue 5
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\pages 866--876
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. G. D'yakonov, “Theory of equivalence systems for describing algebraic closures of a generalized estimation model. II”, Comput. Math. Math. Phys., 51:3 (2011), 490–504  mathnet  crossref  mathscinet  isi
    2. A. G. Dyakonov, “Criteria for the singularity of a pairwise $l_1$-distance matrix and their generalizations”, Izv. Math., 76:3 (2012), 517–534  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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