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A Fast and Accurate Matrix Completion Method Based on QR Decomposition and $L_{2,1}$ -Norm Minimization.
- Source :
- IEEE Transactions on Neural Networks & Learning Systems; Mar2019, Vol. 30 Issue 3, p803-817, 15p
- Publication Year :
- 2019
-
Abstract
- Low-rank matrix completion aims to recover matrices with missing entries and has attracted considerable attention from machine learning researchers. Most of the existing methods, such as weighted nuclear-norm-minimization-based methods and Qatar Riyal (QR)-decomposition-based methods, cannot provide both convergence accuracy and convergence speed. To investigate a fast and accurate completion method, an iterative QR-decomposition-based method is proposed for computing an approximate singular value decomposition. This method can compute the largest $r (r>0)$ singular values of a matrix by iterative QR decomposition. Then, under the framework of matrix trifactorization, a method for computing an approximate SVD based on QR decomposition (CSVD-QR)-based $L_{2,1}$ -norm minimization method (LNM-QR) is proposed for fast matrix completion. Theoretical analysis shows that this QR-decomposition-based method can obtain the same optimal solution as a nuclear norm minimization method, i.e., the $L_{2,1}$ -norm of a submatrix can converge to its nuclear norm. Consequently, an LNM-QR-based iteratively reweighted $L_{2,1}$ -norm minimization method (IRLNM-QR) is proposed to improve the accuracy of LNM-QR. Theoretical analysis shows that IRLNM-QR is as accurate as an iteratively reweighted nuclear norm minimization method, which is much more accurate than the traditional QR-decomposition-based matrix completion methods. Experimental results obtained on both synthetic and real-world visual data sets show that our methods are much faster and more accurate than the state-of-the-art methods. [ABSTRACT FROM AUTHOR]
- Subjects :
- LOW-rank matrices
MACHINE learning
DECOMPOSITION method
Subjects
Details
- Language :
- English
- ISSN :
- 2162237X
- Volume :
- 30
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- IEEE Transactions on Neural Networks & Learning Systems
- Publication Type :
- Periodical
- Accession number :
- 134886706
- Full Text :
- https://doi.org/10.1109/TNNLS.2018.2851957