Tensor LRR and Sparse Coding-Based Subspace Clustering

Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sam...

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Published in:	IEEE transaction on neural networks and learning systems Vol. 27; no. 10; pp. 2120 - 2133
Main Authors:	Yifan Fu, Junbin Gao, Tien, David, Zhouchen Lin, Xia Hong
Format:	Journal Article
Language:	English
Published:	United States IEEE 01.10.2016 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Automobile industry Clustering algorithms Correlation Data models Dictionaries Dictionary learning Robustness sparse coding (SC) Sparse matrices subspace clustering Tensile stress tensor low-rank representation (TLRR)
ISSN:	2162-237X, 2162-2388, 2162-2388
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Abstract	Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established stateof- the-art methods.
AbstractList	Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established stateof- the-art methods. Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established stateof- the-art methods.Subspace clustering groups a set of samples from a union of several linear subspaces into clusters, so that the samples in the same cluster are drawn from the same linear subspace. In the majority of the existing work on subspace clustering, clusters are built based on feature information, while sample correlations in their original spatial structure are simply ignored. Besides, original high-dimensional feature vector contains noisy/redundant information, and the time complexity grows exponentially with the number of dimensions. To address these issues, we propose a tensor low-rank representation (TLRR) and sparse coding-based (TLRRSC) subspace clustering method by simultaneously considering feature information and spatial structures. TLRR seeks the lowest rank representation over original spatial structures along all spatial directions. Sparse coding learns a dictionary along feature spaces, so that each sample can be represented by a few atoms of the learned dictionary. The affinity matrix used for spectral clustering is built from the joint similarities in both spatial and feature spaces. TLRRSC can well capture the global structure and inherent feature information of data and provide a robust subspace segmentation from corrupted data. Experimental results on both synthetic and real-world data sets show that TLRRSC outperforms several established stateof- the-art methods.
Author	Xia Hong Yifan Fu Zhouchen Lin Junbin Gao Tien, David
Author_xml	– sequence: 1 surname: Yifan Fu fullname: Yifan Fu email: fuyf939@gmail.com organization: Sch. of Comput. & Math., Charles Sturt Univ., Bathurst, NSW, Australia – sequence: 2 surname: Junbin Gao fullname: Junbin Gao email: junbin.gao@sydney.edu.au organization: Discipline of Bus. Analytics, Bus. Sch., Univ. of Sydney, Sydney, NSW, Australia – sequence: 3 givenname: David surname: Tien fullname: Tien, David email: dtien@csu.edu.au organization: Sch. of Comput. & Math., Charles Sturt Univ., Bathurst, NSW, Australia – sequence: 4 surname: Zhouchen Lin fullname: Zhouchen Lin email: zlin@pku.edu.cn organization: Sch. of Electron. Eng. & Comput. Sci., Peking Univ., Beijing, China – sequence: 5 surname: Xia Hong fullname: Xia Hong email: x.hong@reading.ac.uk organization: Dept. of Comput. Sci., Univ. of Reading, Reading, UK
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SubjectTerms	Automobile industry Clustering algorithms Correlation Data models Dictionaries Dictionary learning Robustness sparse coding (SC) Sparse matrices subspace clustering Tensile stress tensor low-rank representation (TLRR)
Title	Tensor LRR and Sparse Coding-Based Subspace Clustering
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