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Avtomatika i Telemekhanika, 2021, Issue 3, Pages 149–168
DOI: https://doi.org/10.31857/S0005231021030090 (Mi at15516) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Optimization, System Analysis, and Operations Research

Entropy-randomized projection

Yu. S. Popkovab, Yu. A. Dubnovac, A. Yu. Popkova

a Federal Research Center “Computer Science and Control,” Russian Academy of Sciences, Moscow, 119333 Russia
b Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia
c National Research University Higher School of Economics, Moscow, 101000 Russia
Full-text PDF (280 kB) Citations (2)
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DOI: https://doi.org/10.31857/S0005231021030090
Abstract: We propose a new randomized projection method based on entropy optimization of random projection matrices (the ERP method). The concept of compactness indicator of a data matrix, which is stored in projection matrices, is introduced. An ERP algorithm is formulated in the form of a conditional maximization problem for an entropy functional defined on the probability density functions of the projection matrices. A discrete version of this problem is considered, and conditions are obtained for the existence and uniqueness of its positive solution. Procedures are developed for the implementation of entropy-optimal projection matrices by sampling the probability density functions.
Keywords: random projection, compression and expansion of data matrix, projection matrix, compactness indicator, density function sampling, variance set, interquartile set.
Funding agency Grant number
Russian Foundation for Basic Research 20-07-00470
This work was supported by the Russian Foundation for Basic Research, project no. 20-07-00470.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 12.07.2020
Revised: 23.09.2020
Accepted: 28.10.2020
English version:
Automation and Remote Control, 2021, Volume 82, Issue 3, Pages 490–505
DOI: https://doi.org/10.1134/S0005117921030097
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Yu. S. Popkov, Yu. A. Dubnov, A. Yu. Popkov, “Entropy-randomized projection”, Avtomat. i Telemekh., 2021, no. 3, 149–168; Autom. Remote Control, 82:3 (2021), 490–505
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/at15516
  • https://www.mathnet.ru/eng/at/y2021/i3/p149
    • This publication is cited in the following 2 articles:
    1. A. V. Kvasnov, A. A. Baranenko, E. Yu. Butyrskii, U. P. Zaranik, “O vliyanii tsentralnoi tendentsii na kharakter plotnosti raspredeleniya maksimalnoi entropii v mashinnom obuchenii”, Vestn. S.-Peterburg. un-ta. Ser. 10. Prikl. matem. Inform. Prots. upr., 19:2 (2023), 176–184  mathnet  crossref
    2. Xiao Xu, Hao Yan, Xiaolei Wang, Punit Gupta, “Research on Postproduction of Film and Television Based on Computer Multimedia Technology”, Scientific Programming, 2022 (2022), 1  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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