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Godaz, Reza, Monsefi, Reza, Toutounian, Faezeh, Hosseini, Reshad. (1401). Accurate and fast matrix factorization for low-rank learning. فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), 263-278. doi: 10.22124/jmm.2021.19892.1723
Reza Godaz; Reza Monsefi; Faezeh Toutounian; Reshad Hosseini. "Accurate and fast matrix factorization for low-rank learning". فیزیولوژی و بیوتکنولوژی آبزیان, 10, 2, 1401, 263-278. doi: 10.22124/jmm.2021.19892.1723
Godaz, Reza, Monsefi, Reza, Toutounian, Faezeh, Hosseini, Reshad. (1401). 'Accurate and fast matrix factorization for low-rank learning', فیزیولوژی و بیوتکنولوژی آبزیان, 10(2), pp. 263-278. doi: 10.22124/jmm.2021.19892.1723
Godaz, Reza, Monsefi, Reza, Toutounian, Faezeh, Hosseini, Reshad. Accurate and fast matrix factorization for low-rank learning. فیزیولوژی و بیوتکنولوژی آبزیان, 1401; 10(2): 263-278. doi: 10.22124/jmm.2021.19892.1723

Accurate and fast matrix factorization for low-rank learning

Journal of Mathematical Modeling
دوره 10، شماره 2، شهریور 2022، صفحه 263-278    اصل مقاله (404.24 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2021.19892.1723
نویسندگان
Reza Godaz1؛ Reza Monsefi* 1؛ Faezeh Toutounian2؛ Reshad Hosseini3
1Department of Computer Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
2Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
3Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
چکیده
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.
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