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Matematicheskoe modelirovanie, 2020, Volume 32, Number 9, Pages 35–52
DOI: https://doi.org/10.20948/mm-2020-09-03 (Mi mm4212) 		 
Cross-entropy reduction of data matrix with restriction on information capacity of projectors and their norms

Y. S. Popkovab, A. Y. Popkovb, Y. A. Dubnovbc

a Institute of Control Sciences of RAS, Moscow
b Federal Research Center “Computer Science and Control” of RAS, Moscow
c National Research University Higher School of Economics, Moscow
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DOI: https://doi.org/10.20948/mm-2020-09-03
Abstract: We develop a new method of dimensionality reduction based on direct and inverse projection of data matrix and calculation of projectors minimizing cross-entropy functional. Concept of information capacity of matrix which is used as a restriction in a problem of optimal reduction is introduced. We conduct a comparison of proposed method with known ones based on binary classification.
Keywords: dimensionality reduction, entropy, cross-entropy, classification.
Funding agency Grant number
Russian Foundation for Basic Research 17-29-03119_офи_м
20-07-00470
Received: 15.01.2020
Revised: 12.03.2020
Accepted: 20.04.2020
English version:
Mathematical Models and Computer Simulations, 2021, Volume 13, Issue 3, Pages 382–394
DOI: https://doi.org/10.1134/S2070048221030145
Document Type: Article
Language: Russian
Citation: Y. S. Popkov, A. Y. Popkov, Y. A. Dubnov, “Cross-entropy reduction of data matrix with restriction on information capacity of projectors and their norms”, Matem. Mod., 32:9 (2020), 35–52; Math. Models Comput. Simul., 13:3 (2021), 382–394
Citation in format AMSBIB
\Bibitem{PopPopDub20}
\by Y.~S.~Popkov, A.~Y.~Popkov, Y.~A.~Dubnov
\paper Cross-entropy reduction of data matrix with restriction on information capacity of projectors and their norms
\jour Matem. Mod.
\yr 2020
\vol 32
\issue 9
\pages 35--52
\mathnet{http://mi.mathnet.ru/mm4212}
\crossref{https://doi.org/10.20948/mm-2020-09-03}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 3
\pages 382--394
\crossref{https://doi.org/10.1134/S2070048221030145}
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    		Математическое моделирование
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