Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications
The problem of data recovery in multiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low-n-rank tensor with an unknown fraction of its entries being arbitra...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2014/914963 |
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| _version_ | 1832565110419226624 |
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| author | Huachun Tan Bin Cheng Jianshuai Feng Li Liu Wuhong Wang |
| author_facet | Huachun Tan Bin Cheng Jianshuai Feng Li Liu Wuhong Wang |
| author_sort | Huachun Tan |
| collection | DOAJ |
| description | The problem of data recovery in multiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low-n-rank tensor with an unknown fraction of its entries being arbitrarily corrupted. In the new algorithm, the tensor recovery problem is formulated as a mixture convex multilinear Robust Principal Component Analysis (RPCA) optimization problem by minimizing a sum of the nuclear norm and the ℓ1-norm. The problem is well structured in both the objective function and constraints. We apply augmented Lagrange multiplier method which can make use of the good structure for efficiently solving this problem. In the experiments, the algorithm is compared with the state-of-art algorithm both on synthetic data and real data including traffic data, image data, and video data. |
| format | Article |
| id | doaj-art-85f60e37edf44fde9e3981e840a76752 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-85f60e37edf44fde9e3981e840a767522025-02-03T01:09:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2014-01-01201410.1155/2014/914963914963Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its ApplicationsHuachun Tan0Bin Cheng1Jianshuai Feng2Li Liu3Wuhong Wang4Department of Transportation Engineering, Beijing Institute of Technology, Beijing 100081, ChinaDepartment of Transportation Engineering, Beijing Institute of Technology, Beijing 100081, ChinaIntegrated Information System Research Center, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, ChinaMarvell Semiconductor Inc., 5488 Marvell LN, Santa Clara, CA 95054, USADepartment of Transportation Engineering, Beijing Institute of Technology, Beijing 100081, ChinaThe problem of data recovery in multiway arrays (i.e., tensors) arises in many fields such as computer vision, image processing, and traffic data analysis. In this paper, we propose a scalable and fast algorithm for recovering a low-n-rank tensor with an unknown fraction of its entries being arbitrarily corrupted. In the new algorithm, the tensor recovery problem is formulated as a mixture convex multilinear Robust Principal Component Analysis (RPCA) optimization problem by minimizing a sum of the nuclear norm and the ℓ1-norm. The problem is well structured in both the objective function and constraints. We apply augmented Lagrange multiplier method which can make use of the good structure for efficiently solving this problem. In the experiments, the algorithm is compared with the state-of-art algorithm both on synthetic data and real data including traffic data, image data, and video data.http://dx.doi.org/10.1155/2014/914963 |
| spellingShingle | Huachun Tan Bin Cheng Jianshuai Feng Li Liu Wuhong Wang Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications Discrete Dynamics in Nature and Society |
| title | Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications |
| title_full | Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications |
| title_fullStr | Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications |
| title_full_unstemmed | Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications |
| title_short | Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications |
| title_sort | mixture augmented lagrange multiplier method for tensor recovery and its applications |
| url | http://dx.doi.org/10.1155/2014/914963 |
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