Document Type : Research Article
Department of Computer Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran
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.