Title :

A Fast and Accurate Matrix Completion Method based on QR Decomposition and L 2,1-Norm Minimization

Author(s) :

Liu, Qing [Auteur]
Nanjing University of Science and Technology [NJUST]
Davoine, Franck [Auteur]
Heuristique et Diagnostic des Systèmes Complexes [Compiègne] [Heudiasyc]
Yang, Jian [Auteur]
Nanjing University of Science and Technology [NJUST]
Cui, Ying [Auteur]
Zhejiang University of Technology
Zhong, Jin [Auteur]
Nanjing University of Science and Technology [NJUST]
Han, Fei [Auteur]
JiangSu University

Journal title :

IEEE Transactions on Neural Networks and Learning Systems

Pages :

803-817

Publisher :

IEEE

Publication date :

2019-03

ISSN :

2162-237X

English keyword(s) :

Qatar Riyal (QR) decomposition
Iteratively Reweighted L21-Norm
QR Decomposition
Matrix Completion

HAL domain(s) :

Informatique [cs]/Vision par ordinateur et reconnaissance de formes [cs.CV]
Informatique [cs]/Traitement des images [eess.IV]

English abstract : [en]

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 ...
Show more >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 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 (CSVD-QR). This method can compute the largest r(r > 0) singular values of a matrix by iterative QR decomposition. Then, under the framework of matrix tri-factorization, a CSVD-QR-based L2,1-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 L2,1-norm of a submatrix can converge to its nuclear norm. Consequently, an LNM-QR-based iteratively reweighted L2,1-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 datasets show that our methods are much faster and more accurate than the state-of-the-art methods.Show less >

Language :

Anglais

Popular science :

Non

ANR Project :

Sorbonne Universités à Paris pour l'Enseignement et la Recherche

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL