Journal of Mathematical Modeling, Year (2021-10)

Title : ( Accurate and fast matrix factorization for low-rank learning )

Authors: Reza Godaz , Reza Monsefi , Faezeh Toutounian Mashhad , Reshad Hosseini ,

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In this paper, we tackle two important problems in low-rank learning, which are partial singular value decomposition and numerical rank estimation of huge matrices. By using the concepts of Krylov subspaces such as Golub-Kahan bidiagonalization (GK-bidiagonalization) as well as Ritz vectors, we propose two methods for solving these problems in a fast and accurate way. Our experiments show the advantages of the proposed methods compared to the traditional and randomized singular value decomposition methods. The proposed methods are appropriate for applications involving huge matrices where the accuracy of the desired singular values and also all of their corresponding singular vectors are essential. As a real application, we evaluate the performance of our methods on the problem of Riemannian similarity learning between two different image datasets of MNIST and USPS.


, Krylov subspace, Ritz vectors, Golub-Kahan bidiagonalization, Riemannian optimization, low-rank learning.
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author = {Godaz, Reza and Monsefi, Reza and Toutounian Mashhad, Faezeh and Reshad Hosseini},
title = {Accurate and fast matrix factorization for low-rank learning},
journal = {Journal of Mathematical Modeling},
year = {2021},
month = {October},
issn = {2345-394X},
keywords = {Krylov subspace; Ritz vectors; Golub-Kahan bidiagonalization; Riemannian optimization; low-rank learning.},


%0 Journal Article
%T Accurate and fast matrix factorization for low-rank learning
%A Godaz, Reza
%A Monsefi, Reza
%A Toutounian Mashhad, Faezeh
%A Reshad Hosseini
%J Journal of Mathematical Modeling
%@ 2345-394X
%D 2021