On Unifying Multi-view Self-Representations for Clustering by Tensor Multi-rank Minimization

Xie, Y; Tao, D; Zhang, W; Liu, Y; Zhang, L; Qu, Y

On Unifying Multi-view Self-Representations for Clustering by Tensor Multi-rank Minimization

Xie, Y Tao, D

Zhang, W Liu, Y Zhang, L Qu, Y

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Publication Type:: Journal Article
Citation:: International Journal of Computer Vision, 2018, 126 (11), pp. 1157 - 1179
Issue Date:: 2018-11-01

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Field	Value	Language
dc.contributor.author	Xie, Y	en_US
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.contributor.author	Zhang, W	en_US
dc.contributor.author	Liu, Y	en_US
dc.contributor.author	Zhang, L	en_US
dc.contributor.author	Qu, Y	en_US
dc.date.issued	2018-11-01	en_US
dc.identifier.citation	International Journal of Computer Vision, 2018, 126 (11), pp. 1157 - 1179	en_US
dc.identifier.issn	0920-5691	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132395
dc.description.abstract	© 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to capture the low rank tensor subspace so that the refinement of the view-specific subspaces can be achieved, as well as the high order correlations underlying multi-view data can be explored. By introducing a recently proposed tensor factorization, namely tensor-Singular Value Decomposition (t-SVD) (Kilmer et al. in SIAM J Matrix Anal Appl 34(1):148–172, 2013), we can impose a new type of low-rank tensor constraint on the rotated tensor to ensure the consensus among multiple views. Different from traditional unfolding based tensor norm, this low-rank tensor constraint has optimality properties similar to that of matrix rank derived from SVD, so the complementary information can be explored and propagated among all the views more thoroughly and effectively. The established model, called t-SVD based Multi-view Subspace Clustering (t-SVD-MSC), falls into the applicable scope of augmented Lagrangian method, and its minimization problem can be efficiently solved with theoretical convergence guarantee and relatively low computational complexity. Extensive experimental testing on eight challenging image datasets shows that the proposed method has achieved highly competent objective performance compared to several state-of-the-art multi-view clustering methods.	en_US
dc.relation.ispartof	International Journal of Computer Vision	en_US
dc.relation.isbasedon	10.1007/s11263-018-1086-2	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	On Unifying Multi-view Self-Representations for Clustering by Tensor Multi-rank Minimization	en_US
dc.type	Journal Article
utslib.citation.volume	11	en_US
utslib.citation.volume	126	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	closed_access
pubs.issue	11	en_US
pubs.publication-status	Published	en_US
pubs.volume	126	en_US

Abstract:

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this paper, we address the multi-view subspace clustering problem. Our method utilizes the circulant algebra for tensor, which is constructed by stacking the subspace representation matrices of different views and then rotating, to capture the low rank tensor subspace so that the refinement of the view-specific subspaces can be achieved, as well as the high order correlations underlying multi-view data can be explored. By introducing a recently proposed tensor factorization, namely tensor-Singular Value Decomposition (t-SVD) (Kilmer et al. in SIAM J Matrix Anal Appl 34(1):148–172, 2013), we can impose a new type of low-rank tensor constraint on the rotated tensor to ensure the consensus among multiple views. Different from traditional unfolding based tensor norm, this low-rank tensor constraint has optimality properties similar to that of matrix rank derived from SVD, so the complementary information can be explored and propagated among all the views more thoroughly and effectively. The established model, called t-SVD based Multi-view Subspace Clustering (t-SVD-MSC), falls into the applicable scope of augmented Lagrangian method, and its minimization problem can be efficiently solved with theoretical convergence guarantee and relatively low computational complexity. Extensive experimental testing on eight challenging image datasets shows that the proposed method has achieved highly competent objective performance compared to several state-of-the-art multi-view clustering methods.

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http://hdl.handle.net/10453/132395