Fast Monte Carlo Algorithms for Matrices II: Computing a Low-Rank Approximation to a Matrix
SIAM Journal on Computing
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
Interior-Point Method for Nuclear Norm Approximation with Application to System Identification
SIAM Journal on Matrix Analysis and Applications
Low-rank matrix completion with noisy observations: a quantitative comparison
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
ADMiRA: atomic decomposition for minimum rank approximation
IEEE Transactions on Information Theory
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Convergence of Fixed-Point Continuation Algorithms for Matrix Rank Minimization
Foundations of Computational Mathematics
Fixed point and Bregman iterative methods for matrix rank minimization
Mathematical Programming: Series A and B
Fast communication: Constraint removal for sparse signal recovery
Signal Processing
Low-rank Matrix Recovery via Iteratively Reweighted Least Squares Minimization
SIAM Journal on Optimization
Iterative reweighted algorithms for matrix rank minimization
The Journal of Machine Learning Research
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This paper proposes a new matrix shrinkage algorithm for matrix rank minimization problems. The proposed algorithm provides a low rank solution by estimating a matrix rank and shrinking non-dominant singular values iteratively. We study the convergence properties of the algorithm, which indicate that the algorithm gives approximate low-rank solutions. Numerical results show that the proposed algorithm works efficiently for hard problems with low computing time.