Low rank matrix completion using truncated nuclear norm and sparse regularizer

2018 ◽  
Vol 68 ◽  
pp. 76-87 ◽  
Author(s):  
Jing Dong ◽  
Zhichao Xue ◽  
Jian Guan ◽  
Zi-Fa Han ◽  
Wenwu Wang
Keyword(s):  
Matrix Completion ◽  
Nuclear Norm ◽  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix ◽  
Truncated Nuclear Norm

scholarly journals Low-rank matrix completion and denoising under Poisson noise

2020 ◽  
Author(s):  
Andrew D McRae ◽  
Mark A Davenport
Keyword(s):  
Matrix Completion ◽  
Universal Constant ◽  
Poisson Noise ◽  
Nuclear Norm ◽  
Low Rank ◽  
Frobenius Norm ◽  
Rank Matrix ◽  
The Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix

Abstract This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe only a subset of the entries, this is a problem of matrix completion. In both cases, we exploit an assumption that the underlying matrix is low-rank. Specifically, we analyse several estimators, including a constrained nuclear-norm minimization program, nuclear-norm regularized least squares and a non-convex constrained low-rank optimization problem. We show that for all three estimators, with high probability, we have an upper error bound (in the Frobenius norm error metric) that depends on the matrix rank, the fraction of the elements observed and the maximal row and column sums of the true matrix. We furthermore show that the above results are minimax optimal (within a universal constant) in classes of matrices with low-rank and bounded row and column sums. We also extend these results to handle the case of matrix multinomial denoising and completion.

scholarly journals Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion

2011 ◽  
Vol 39 (5) ◽  
pp. 2302-2329 ◽  
Author(s):  
Vladimir Koltchinskii ◽  
Karim Lounici ◽  
Alexandre B. Tsybakov
Keyword(s):  
Matrix Completion ◽  
Nuclear Norm ◽  
Low Rank ◽  
Rank Matrix ◽  
Low Rank Matrix Completion ◽  
Low Rank Matrix
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