Adaptive Tensor Rank Approximation for Multi-View Subspace Clustering

SUN Xiaoli; HAI Yang; ZHANG Xiujun; XU Chen

doi:10.23919/cje.2022.00.180

Volume 32 Issue 4

Jul. 2023

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Article Navigation > Chinese Journal of Electronics > 2023 > 32(4): 840-853

SUN Xiaoli, HAI Yang, ZHANG Xiujun, et al., “Adaptive Tensor Rank Approximation for Multi-View Subspace Clustering,” Chinese Journal of Electronics, vol. 32, no. 4, pp. 840-853, 2023, doi: 10.23919/cje.2022.00.180

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SUN Xiaoli, HAI Yang, ZHANG Xiujun, et al., “Adaptive Tensor Rank Approximation for Multi-View Subspace Clustering,” Chinese Journal of Electronics, vol. 32, no. 4, pp. 840-853, 2023, doi: 10.23919/cje.2022.00.180

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Adaptive Tensor Rank Approximation for Multi-View Subspace Clustering

doi: 10.23919/cje.2022.00.180

SUN Xiaoli^1
,,
HAI Yang^1
,,
ZHANG Xiujun^2
,,
XU Chen^{1, 3
,}

1.
College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
2.
School of Electronic and Communication Engineering, Shenzhen Polytechnic, Shenzhen 518055, China
3.
National Center for Applied Mathematics Shenzhen (NCAMS), Shenzhen 518055, China

Funds: This work was supported by the National Natural Science Foundation of China (61872429, 62272313, 12101415, 62202018) and the Project of Educational Commission of Guangdong Province (2022KTSCX106)

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Author Bio:
Xiaoli SUN received the Ph.D. degree in applied mathematics from Xidian University in 2007. She is currently an Associate Professor at the College of Mathematics and Statistics, Shenzhen University, Shenzhen. Her research interests include subspace clustering, saliency detection, and computer vision. (Email: xlsun@szu.edu.cn)

Yang HAI received the B.S. degree in mathematics and applied mathematics from Jiangxi Normol University in 2019. She is currently a master student at the College of Mathematics and Statistics, Shenzhen University, Shenzhen, China. Her research interests are in the fields of pattern recognition and intelligent computing. (Email: 2060201016@email.szu.edu.cn)

Xiujun ZHANG (corresponding author) received the B.S. degree and M.S. degree in electrical engineering from Xidian University, Xi’an, China, in 2002 and 2005, respectively, and received the Ph.D. degree from Shenzhen University, Shenzhen, China in 2016. He is now working at the School of Electronic and Communication Engineering, Shenzhen Polytechnic, Shenzhen. His current research interests include saliency detection, subspace clustering, sparse and low-rank representation in image processing. (Email: zhangxiujun@szpt.edu.cn)

Chen XU received the B.S. and M.S. degrees in Mathematics from Xidian University in 1986 and 1989, the Ph.D. degree in Mathematics from Xi’an Jiaotong University in 1992 respectively. He is currently a Professor of mathematics and Ph.D. Supervisor at Shenzhen University, Shenzhen. His research fields are information and computational science, analysis and application of wavelet. (Email: xuchen_szu@szu.edu.com)
Received Date: 2022-06-27
Accepted Date: 2022-11-07

Available Online: 2022-11-21

Publish Date: 2023-07-05

Abstract

Abstract

Multi-view subspace clustering under a tensor framework remains a challenging problem, which can be potentially applied to image classification, impainting, denoising, etc. There are some existing tensor-based multi-view subspace clustering models mainly making use of the consistency in different views through tensor nuclear norm (TNN). The diversity which means the intrinsic difference in individual view is always ignored. In this paper, a new tensorial multi-view subspace clustering model is proposed, which jointly exploits both the consistency and diversity in each view. The view representation is decomposed into view-consistent part (low-rank part) and view-specific part (diverse part). A tensor adaptive log-determinant regularization (TALR) is imposed on the low-rank part to better relax the tensor multi-rank, and a view-specific sparsity regularization is applied on the diverse part to ensure connectedness property. Although the TALR minimization is not convex, it has a closed-form analytical solution and its convergency is validated mathematically. Extensive evaluations on six widely used clustering datasets are executed and our model is demonstrated to have the superior performance.
- Diversity,
- Multi-view subspace clustering,
- Tensor adaptive log-determinant,
- View-specific sparsity,
- Self-representation

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References(41)

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