Mixture augmented lagrange multiplier method for tensor recovery

Huachun Tan; Bin Cheng; Jianshuai Feng; Guangdong Feng; Wuhong Wang; Yu Jin Zhang

doi:10.1142/9789814417747_0069

Mixture augmented lagrange multiplier method for tensor recovery

Huachun Tan, Bin Cheng, Jianshuai Feng, Guangdong Feng, Wuhong Wang, Yu Jin Zhang

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

摘要

The problem of data recovery in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. 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 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.

源语言	英语
主期刊名	World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.
出版商	World Scientific Publishing Co. Pte Ltd
页	430-435
页数	6
ISBN（印刷版）	9789814417730
DOI	https://doi.org/10.1142/9789814417747_0069
出版状态	已出版 - 2012
活动	10th International Fuzzy Logic and Intelligent Technologies inNuclear Science Conference, FLINS 2012 - Istanbul, 土耳其期限: 26 8月 2012 → 29 8月 2012

出版系列

姓名	World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.
卷	7

会议

会议	10th International Fuzzy Logic and Intelligent Technologies inNuclear Science Conference, FLINS 2012
国家/地区	土耳其
市	Istanbul
时期	26/08/12 → 29/08/12

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10.1142/9789814417747_0069

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Tan, H., Cheng, B., Feng, J., Feng, G., Wang, W., & Zhang, Y. J. (2012). Mixture augmented lagrange multiplier method for tensor recovery. 在 World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf. (页码 430-435). (World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.; 卷 7). World Scientific Publishing Co. Pte Ltd. https://doi.org/10.1142/9789814417747_0069

Tan, Huachun ; Cheng, Bin ; Feng, Jianshuai 等. / Mixture augmented lagrange multiplier method for tensor recovery. World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.. World Scientific Publishing Co. Pte Ltd, 2012. 页码 430-435 (World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.).

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title = "Mixture augmented lagrange multiplier method for tensor recovery",

abstract = "The problem of data recovery in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. 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 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.",

author = "Huachun Tan and Bin Cheng and Jianshuai Feng and Guangdong Feng and Wuhong Wang and Zhang, {Yu Jin}",

year = "2012",

doi = "10.1142/9789814417747_0069",

language = "English",

isbn = "9789814417730",

series = "World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.",

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pages = "430--435",

booktitle = "World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.",

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note = "10th International Fuzzy Logic and Intelligent Technologies inNuclear Science Conference, FLINS 2012 ; Conference date: 26-08-2012 Through 29-08-2012",

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Tan, H, Cheng, B, Feng, J, Feng, G, Wang, W & Zhang, YJ 2012, Mixture augmented lagrange multiplier method for tensor recovery. 在 World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.. World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf., 卷 7, World Scientific Publishing Co. Pte Ltd, 页码 430-435, 10th International Fuzzy Logic and Intelligent Technologies inNuclear Science Conference, FLINS 2012, Istanbul, 土耳其, 26/08/12. https://doi.org/10.1142/9789814417747_0069

Mixture augmented lagrange multiplier method for tensor recovery. / Tan, Huachun; Cheng, Bin; Feng, Jianshuai 等.
World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.. World Scientific Publishing Co. Pte Ltd, 2012. 页码 430-435 (World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.; 卷 7).

科研成果: 书/报告/会议事项章节 › 会议稿件 › 同行评审

TY - GEN

T1 - Mixture augmented lagrange multiplier method for tensor recovery

AU - Tan, Huachun

AU - Cheng, Bin

AU - Feng, Jianshuai

AU - Feng, Guangdong

AU - Wang, Wuhong

AU - Zhang, Yu Jin

PY - 2012

Y1 - 2012

N2 - The problem of data recovery in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. 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 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.

AB - The problem of data recovery in multi-way arrays (i.e., tensors) arises in many fields such as image processing and computer vision, etc. 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 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.

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U2 - 10.1142/9789814417747_0069

DO - 10.1142/9789814417747_0069

M3 - Conference contribution

AN - SCOPUS:84892655189

SN - 9789814417730

T3 - World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.

SP - 430

EP - 435

BT - World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.

PB - World Scientific Publishing Co. Pte Ltd

T2 - 10th International Fuzzy Logic and Intelligent Technologies inNuclear Science Conference, FLINS 2012

Y2 - 26 August 2012 through 29 August 2012

ER -

Tan H, Cheng B, Feng J, Feng G, Wang W, Zhang YJ. Mixture augmented lagrange multiplier method for tensor recovery. 在 World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.. World Scientific Publishing Co. Pte Ltd. 2012. 页码 430-435. (World Scientific Proc. Series on Computer Engineering and Information Science 7; Uncertainty Modeling in Knowledge Engineering and Decision Making - Proceedings of the 10th International FLINS Conf.). doi: 10.1142/9789814417747_0069

Mixture augmented lagrange multiplier method for tensor recovery

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