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This article is cited in 5 scientific papers (total in 5 papers)
General numerical methods
Low-rank approximation algorithms for matrix completion with random sampling
O. S. Lebedevaa, A. I. Osinskiib, S. V. Petrova a Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
b Skolkovo Institute of Science and Technology (Skoltech), 121205, Moscow, Russia
Abstract:
The possibility of accelerating a projection algorithm onto dominant singular spaces in the problem of recovering a low-rank matrix from a small number of its entries is explored. The underlying idea is to replace best approximation procedures in the Frobenius norm by fast approximation algorithms. Two methods for computing such approximations are considered: (a) projection onto random subspaces and (b) the cross approximation method. Theorems on the geometric convergence of the algorithms with approximate projections are proved. Numerical experiments are described that demonstrate the efficiency of both variants as compared with the exact projection.
Key words:
low-rank matrices, matrix completion, singular value projection, cross approximation method, random subspaces.
Received: 24.11.2020 Revised: 24.11.2020 Accepted: 14.01.2021
Citation:
O. S. Lebedeva, A. I. Osinskii, S. V. Petrov, “Low-rank approximation algorithms for matrix completion with random sampling”, Zh. Vychisl. Mat. Mat. Fiz., 61:5 (2021), 827–844; Comput. Math. Math. Phys., 61:5 (2021), 799–815
Linking options:
https://www.mathnet.ru/eng/zvmmf11241 https://www.mathnet.ru/eng/zvmmf/v61/i5/p827
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