Systems and Means of Informatics
2023, Volume 33, Issue 1, pp 7889
EFFICIENT COMPUTATIONS IN MATRIX FACTORIZATION WITH MISSING COMPONENTS
Abstract
The paper is devoted to the effective implementation of matrix factorization in the presence of missing components into a product of two lower rank matrices. The problem of estimating the parameters of the adopted data model is solved by multidimensional optimization. In practice, the large sizes of the matrices and vectors included in iterative algorithms give rise to the curse of dimensionality. It is proposed to drastically reduce the complexity of matrix operations by presenting them in blockdiagonal form. The article substantiates the possibility of casting individual matrices to a blockdiagonal form and describes the rules for blockbyblock singular value decomposition of matrices. The results of blockbyblock processing are illustrated by the example of data matrix factorization of different sizes and with different probabilities of missing components. The time for estimating parameters can be reduced by several orders of magnitude compared to the processing of matrices in the usual representation.
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[+] About this article
Title
EFFICIENT COMPUTATIONS IN MATRIX FACTORIZATION WITH MISSING COMPONENTS
Journal
Systems and Means of Informatics
Volume 33, Issue 1, pp 7889
Cover Date
20230511
DOI
10.14357/08696527230108
Print ISSN
08696527
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
lower rank matrix approximation; singular decomposition; missing data; ALS algorithm; blockdiagonal representation of a matrix
Authors
M. P. Krivenko
Author Affiliations
Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 442 Vavilov Str., Moscow 119333, Russian Federation
