Iterative Reconstrained Low-Rank Representation via Weighted Nonconvex Regularizer
Benefiting from the joint consideration of geometric structures and low-rank constraint, graph low-rank representation (GLRR) method has led to the state-of-the-art results in many applications. However, it faces the limitations that the structure of errors should be known a prior, the isolated cons...
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| Published in: | IEEE access Vol. 6; pp. 51693 - 51707 |
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| Format: | Journal Article |
| Language: | English |
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01.01.2018
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| ISSN: | 2169-3536, 2169-3536 |
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| Abstract | Benefiting from the joint consideration of geometric structures and low-rank constraint, graph low-rank representation (GLRR) method has led to the state-of-the-art results in many applications. However, it faces the limitations that the structure of errors should be known a prior, the isolated construction of graph Laplacian matrix, and the over shrinkage of the leading rank components. To improve GLRR in these regards, this paper proposes a new LRR model, namely iterative reconstrained LRR via weighted nonconvex regularization, using three distinguished properties on the concerned representation matrix. The first characterizes various distributions of the errors into an adaptively learned weight factor for more flexibility of noise suppression. The second generates an accurate graph matrix from weighted observations for less afflicted by noisy features. The third employs a parameterized rational function to reveal the importance of different rank components for better approximation to the intrinsic subspace structure. Following a deep exploration of automatic thresholding, parallel update, and partial SVD operation, we derive a computationally efficient low-rank representation algorithm using an iterative reconstrained framework and accelerated proximal gradient method. Comprehensive experiments are conducted on synthetic data, image clustering, and background subtraction to achieve several quantitative benchmarks as clustering accuracy, normalized mutual information, and execution time. Results demonstrate the robustness and efficiency of IRWNR compared with other state-of-the-art models. |
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| AbstractList | Benefiting from the joint consideration of geometric structures and low-rank constraint, graph low-rank representation (GLRR) method has led to the state-of-the-art results in many applications. However, it faces the limitations that the structure of errors should be known a prior, the isolated construction of graph Laplacian matrix, and the over shrinkage of the leading rank components. To improve GLRR in these regards, this paper proposes a new LRR model, namely iterative reconstrained LRR via weighted nonconvex regularization, using three distinguished properties on the concerned representation matrix. The first characterizes various distributions of the errors into an adaptively learned weight factor for more flexibility of noise suppression. The second generates an accurate graph matrix from weighted observations for less afflicted by noisy features. The third employs a parameterized rational function to reveal the importance of different rank components for better approximation to the intrinsic subspace structure. Following a deep exploration of automatic thresholding, parallel update, and partial SVD operation, we derive a computationally efficient low-rank representation algorithm using an iterative reconstrained framework and accelerated proximal gradient method. Comprehensive experiments are conducted on synthetic data, image clustering, and background subtraction to achieve several quantitative benchmarks as clustering accuracy, normalized mutual information, and execution time. Results demonstrate the robustness and efficiency of IRWNR compared with other state-of-the-art models. |
| Author | Zheng, Jianwei Lu, Cheng Yu, Hongchuan Chen, Shengyong Wang, Wanliang |
| Author_xml | – sequence: 1 givenname: Jianwei orcidid: 0000-0001-6017-0552 surname: Zheng fullname: Zheng, Jianwei organization: School of Computer Science and Engineering, Zhejiang University of Technology, Hangzhou, China – sequence: 2 givenname: Cheng surname: Lu fullname: Lu, Cheng organization: School of Computer Science and Engineering, Zhejiang University of Technology, Hangzhou, China – sequence: 3 givenname: Hongchuan surname: Yu fullname: Yu, Hongchuan organization: National Centre for Computer Animation, Bournemouth University, Poole, U.K – sequence: 4 givenname: Wanliang surname: Wang fullname: Wang, Wanliang email: wwl@zjut.edu.cn organization: School of Computer Science and Engineering, Zhejiang University of Technology, Hangzhou, China – sequence: 5 givenname: Shengyong surname: Chen fullname: Chen, Shengyong organization: School of Computer Science and Engineering, Zhejiang University of Technology, Hangzhou, China |
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| SubjectTerms | accelerated proximal gradient Adaptation models Algorithms Approximation algorithms Clustering Cost function Graphical representations Iterative methods Laplace equations Low-rank representation (LRR) Noise generation Noise measurement power method Rational functions Regularization Robustness singular value thresholding Subtraction weighted nonconvex constraint |
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| Title | Iterative Reconstrained Low-Rank Representation via Weighted Nonconvex Regularizer |
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