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

By Yuan Xie, Dacheng Tao, Wensheng Zhang, Yan Liu, Lei Zhang, Yanyun Qu. International Journal of Computer Vision, 2016

468 citations recorded by the source corpus.

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.

Subfields: Computational Mathematics, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/600f06d9b16772053a984cbe257a7375d92ee52b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mathematics

1. Yimin Wei
2. Liqun Qi
3. Yun Miao
4. Changqing Zhang
5. Xiaochun Cao
6. Yuan Xie
7. Dacheng Tao
8. Hongyuan Zha

In Computational Mechanics

1. Changqing Zhang
2. Huan Fu
3. Xiaochun Cao
4. Hongyuan Zha
5. Jianlong Wu
6. Dacheng Tao
7. Yuan Xie
8. Qinghua Hu

In Computer Vision and Pattern Recognition

1. Dacheng Tao
2. Huan Fu
3. Xiaochun Cao
4. Changqing Zhang
5. Zhouchen Lin
6. Jianlong Wu
7. Yuan Xie
8. Qinghua Hu

Citations in the corpus

• Essential Tensor Learning for Multi-View Spectral Clustering (2018, methodology): “ECMSC [7] consists of position-aware exclusivity term and consistency term for regularization. t-SVD-MSC [24] uses the t-SVD based tensor nuclear norm to learn optimal subspace.”
• Generalized tensor function via the tensor singular value decomposition based on the T-product (2019, methodology): “…has been established and proved to be a useful tool in many areas, such as image processing [27, 28, 40, 44, 46, 56], computer vision [4, 16, 49, 51], signal processing [9, 33, 36, 45], low rank tensor recovery and robust tensor PCA [31, 33], data completion and denoising [11, 24, 25, 34,…”
• Generalized Latent Multi-View Subspace Clustering (2020, background): “and t-SVD-MSC [58], while the performance of gLMSC is”
• T-Jordan Canonical Form and T-Drazin Inverse Based on the T-Product (2019, background): “veloped by Stanimirovic et al. [56] The tensor T-product introduced by Kilmer [34] has been proved to be of great use in many areas, such as image processing [33, 34, 49, 55, 59, 70], computer vision [20, 64], signal processing [12, 41, 44, 58], low rank tensor recovery and robust tensor PCA [39, 41”