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International Journal of Computer Vision

, Volume 126, Issue 11, pp 1157–1179 | Cite as

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

  • Yuan Xie
  • Dacheng Tao
  • Wensheng Zhang
  • Yan Liu
  • Lei Zhang
  • Yanyun Qu
Article

Abstract

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.

Keywords

T-SVD Tensor multi-rank Multi-view features Subspace clustering 

Notes

Acknowledgements

The authors would like to thank editor and anonymous reviewers who gave valuable suggestion that has helped to improve the quality of the paper. This work was supported in part by the National Natural Science Foundation of China under Grants 61772524, 61402480, 61373077, 61602482; by the Beijing Natural Science Foundation under Grant 4182067; by the Australian Research Council Projects FL-170100117, DP-180103424, DP-140102164, LP-150100671; by the HK RGC General Research Fund (PolyU 152135/16E).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research Center of Precision Sensing and Control, Institute of AutomationChinese Academy of SciencesBeijingChina
  2. 2.UBTECH Sydney Artificial Intelligence Centre, School of Information Technologies, Faculty of Engineering and Information TechnologiesUniversity of SydneyDarlingtonAustralia
  3. 3.Department of ComputingThe Hong Kong Polytechnic UniversityHong KongChina
  4. 4.School of Information Science and TechnologyXiamen UniversityFujianChina

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