This article is cited in 2 papers

Optimization, System Analysis, and Operations Research

Entropy-randomized projection

Yu. S. Popkov^ab, Yu. A. Dubnov^ac, A. Yu. Popkov<sup>a

a</sup> 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

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.

Presented by the member of Editorial Board: A. I. Kibzun

Received: 12.07.2020
Revised: 23.09.2020
Accepted: 28.10.2020

DOI: 10.31857/S0005231021030090

 English version: Automation and Remote Control, 2021, 82:3, 490–505

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