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
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.
pattern recognition, estimation algorithm, matrices of estimates, correct algorithm, algebra over algorithms, metric, Gram's matrix, minimal degree.
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Computational Mathematics and Mathematical Physics, 2008, 48:5, 866–876
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
\paper Metrics of algebraic closures in pattern recognition problems with two nonoverlapping classes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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This publication is cited in the following articles:
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
A. G. Dyakonov, “Criteria for the singularity of a pairwise $l_1$-distance matrix and their generalizations”, Izv. Math., 76:3 (2012), 517–534
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