The matrix completion problem consists in the recovery of a low-rank or approximately low-rank matrix from a sampling of its entries. The solution rank is typically unknown, and this makes the problem even more challenging. However, for a broad class of interesting matrices with so-called displacement structure, the originally ill-posed completion problem can find an acceptable solution by exploiting the knowledge of the associated displacement rank. The goal of this paper is to propose a variational non-convex formulation for the low-rank matrix completion problem with low-rank displacement and to apply it to important classes of medium-large scale structured matrices. Experimental results show the effectiveness and efficiency of the proposed approach for Toeplitz and Hankel matrix completion problems
Matrix completion for matrices with low-rank displacement / Lazzaro, Damiana; Morigi, Serena. - In: ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. - ISSN 1068-9613. - ELETTRONICO. - 53:(2020), pp. 481-499. [10.1553/etna_vol53s481]
Matrix completion for matrices with low-rank displacement
Lazzaro, Damiana;Morigi, Serena
2020
Abstract
The matrix completion problem consists in the recovery of a low-rank or approximately low-rank matrix from a sampling of its entries. The solution rank is typically unknown, and this makes the problem even more challenging. However, for a broad class of interesting matrices with so-called displacement structure, the originally ill-posed completion problem can find an acceptable solution by exploiting the knowledge of the associated displacement rank. The goal of this paper is to propose a variational non-convex formulation for the low-rank matrix completion problem with low-rank displacement and to apply it to important classes of medium-large scale structured matrices. Experimental results show the effectiveness and efficiency of the proposed approach for Toeplitz and Hankel matrix completion problemsFile | Dimensione | Formato | |
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