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A quantitative measure of compactness and similarity in a competitive space

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Abstract

Measures of similarity between objects in a metric space and a competitive space are described. The function of rival similarity is proposed as a similarity measure used in the problems of classification and pattern recognition. This function enables us to develop effective algorithms for solving all major problems of data mining, to obtain a quantitative estimate of pattern compactness and informativity of the feature space, and to construct simply interpreted decision rules. The method is applicable to the problems with arbitrary number of patterns and any character of their distributions, and it can be also used for solving ill-conditioned problems.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    N. G. Zagoruiko, I. A. Borisova, V. V. Dyubanov & O. A. Kutnenko

Authors
  1. N. G. Zagoruiko
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  2. I. A. Borisova
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  3. V. V. Dyubanov
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  4. O. A. Kutnenko
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Correspondence to N. G. Zagoruiko.

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Original Russian Text © N.G. Zagoruiko, I.A. Borisova, V.V. Dyubanov, O.A. Kutnenko, 2010, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2010, Vol. XIII, No. 1, pp. 59–71.

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Zagoruiko, N.G., Borisova, I.A., Dyubanov, V.V. et al. A quantitative measure of compactness and similarity in a competitive space. J. Appl. Ind. Math. 5, 144–154 (2011). https://doi.org/10.1134/S1990478911010157

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  • DOI: https://doi.org/10.1134/S1990478911010157

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