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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2010, Volume 50, Number 7, Pages 1315–1326
(Mi zvmmf4911)
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On a scheme for constructing algorithms for correcting a local perturbation in a finite semi-metric
I. A. Gromov Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333 Russia
Abstract:
A three-step scheme for constructing algorithms for transforming metric information in data mining is proposed and investigated. The correction problem of a local perturbation of a semimetric on a finite set of objects is considered. In the framework of the proposed scheme, algorithms correcting the changes of the distance between a pair of objects by a given quantity that preserve the metric properties are examined. Sufficient conditions under which the correction of semimetrics using the proposed three-step scheme actually completes in two steps and in some special cases even after the first step are obtained. Semimetric similarity functionals are considered, and the correction algorithms are matched to those functionals.
Key words:
data mining, preprocessing of metric information, metric recognition algorithms, semimetric on a finite set, similarity of semimetrics.
Received: 25.05.2009 Revised: 21.12.2009
Citation:
I. A. Gromov, “On a scheme for constructing algorithms for correcting a local perturbation in a finite semi-metric”, Zh. Vychisl. Mat. Mat. Fiz., 50:7 (2010), 1315–1326; Comput. Math. Math. Phys., 50:7 (2010), 1249–1259
Linking options:
https://www.mathnet.ru/eng/zvmmf4911 https://www.mathnet.ru/eng/zvmmf/v50/i7/p1315
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Abstract page: | 185 | Full-text PDF : | 66 | References: | 35 | First page: | 11 |
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