A Truncated Nuclear Norm Regularization Method Based on Weighted Residual Error for Matrix Completion

Low-rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision. Most existing methods formulate the task as a low-rank matrix approximation problem. A truncated nuclear norm has recently been proposed as a better...

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Veröffentlicht in:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. - 1992. - 25(2016), 1 vom: 01. Jan., Seite 316-30
1. Verfasser: Qing Liu (VerfasserIn)
Weitere Verfasser: Zhihui Lai, Zongwei Zhou, Fangjun Kuang, Zhong Jin
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2016
Zugriff auf das übergeordnete Werk:IEEE transactions on image processing : a publication of the IEEE Signal Processing Society
Schlagworte:Journal Article Research Support, Non-U.S. Gov't
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520 |a Low-rank matrix completion aims to recover a matrix from a small subset of its entries and has received much attention in the field of computer vision. Most existing methods formulate the task as a low-rank matrix approximation problem. A truncated nuclear norm has recently been proposed as a better approximation to the rank of matrix than a nuclear norm. The corresponding optimization method, truncated nuclear norm regularization (TNNR), converges better than the nuclear norm minimization-based methods. However, it is not robust to the number of subtracted singular values and requires a large number of iterations to converge. In this paper, a TNNR method based on weighted residual error (TNNR-WRE) for matrix completion and its extension model (ETNNR-WRE) are proposed. TNNR-WRE assigns different weights to the rows of the residual error matrix in an augmented Lagrange function to accelerate the convergence of the TNNR method. The ETNNR-WRE is much more robust to the number of subtracted singular values than the TNNR-WRE, TNNR alternating direction method of multipliers, and TNNR accelerated proximal gradient with Line search methods. Experimental results using both synthetic and real visual data sets show that the proposed TNNR-WRE and ETNNR-WRE methods perform better than TNNR and Iteratively Reweighted Nuclear Norm (IRNN) methods 
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700 1 |a Zhihui Lai  |e verfasserin  |4 aut 
700 1 |a Zongwei Zhou  |e verfasserin  |4 aut 
700 1 |a Fangjun Kuang  |e verfasserin  |4 aut 
700 1 |a Zhong Jin  |e verfasserin  |4 aut 
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