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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2005, Volume 45, Number 9, Pages 1720–1727 (Mi zvmmf604)  
On the properties of optimal point configurations for a family of comparison functionals for metric configurations

A. I. Maysuradze

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Leninskie gory, Moscow, 119992, Russia
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Abstract: The problem of searching for an optimal point configuration (i.e., a set of points such that the distances between them best fit a given metric configuration) is considered. An upper bound is obtained for the dimension of a space in which any metric configuration can be represented exactly or approximately by an optimal point configuration. It is shown that, if there is no point configuration that exactly represents a given metric configuration, then, for a natural family of comparison functionals for metric configurations, the dimension of a space in which there is an optimal point configuration is lower than the dimension required in the general case for representing a metric configuration of a given cardinality.
Key words: pattern recognition, data mining, geometry of distances, multidimensional scaling, error estimation.
Received: 09.06.2004
Bibliographic databases:
Document Type: Article
UDC: 519.7
Language: Russian
Citation: A. I. Maysuradze, “On the properties of optimal point configurations for a family of comparison functionals for metric configurations”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005), 1720–1727; Comput. Math. Math. Phys., 45:9 (2005), 1660–1666
Citation in format AMSBIB
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\by A.~I.~Maysuradze
\paper On the properties of optimal point configurations for a family of comparison functionals for metric configurations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 9
\pages 1720--1727
\mathnet{http://mi.mathnet.ru/zvmmf604}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2216078}
\zmath{https://zbmath.org/?q=an:1087.68103}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 9
\pages 1660--1666
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