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

Research output: Journal article publicationJournal articleAcademic researchpeer-review

110 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1157-1179
Number of pages23
JournalInternational Journal of Computer Vision
Issue number11
Publication statusPublished - 1 Nov 2018


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

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence


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