[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Springer Nature Link
Log in

Nonconvex low-rank and sparse tensor representation for multi-view subspace clustering

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

Multi-view subspace clustering has attracted significant attention due to the popularity of multi-view datasets. The effectiveness of the existing multi-view clustering methods highly depends on the quality of the affinity matrix. To derive a high quality affinity matrix, tensor optimization has been explored for multi-view subspace clustering. However, only the global low-rank correlation information among views has been explored, and the local geometric structure has been ignored. In addition, for low-rank tensor approximation learning, the commonly used tensor nuclear norm cannot retain the main information of all views. In this paper, we propose a nonconvex low-rank and sparse tensor representation (NLRSTR) method, which retains the similarity information of the view dimension from global and local perspectives. Specifically, the proposed NLRSTR method imposes nonconvex function and sparse constraint on the self-representation tensor to characterize the high relationship among views. Based on the alternating direction method of multipliers, an effective algorithm is proposed to solve our NLRSTR model. The experimental results on eight datasets show the superiority of the proposed NLRSTR method compared with seventeen state-of-the-art methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Chao G, Sun S, Bi J (2021) A survey on multi-view clustering. IEEE Trans. Artif. Intell.

  2. Chao G, Sun J, Lu J, Wang A-L, Langleben DD, Li C-S, Bi J (2019) Multi-view cluster analysis with incomplete data to understand treatment effects. Inf. Sci., 494

  3. Vidal R, Tron R, Hartley R (2008) Multiframe motion segmentation with missing data using powerfactorization and gpca. Int. J. Comput. Vis. 79(1):85–105

    Article  Google Scholar 

  4. Rao X, Tron R, Vidal R, Ma Y (2009) Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. IEEE Trans. Pattern Anal. Mach. Intell. 32(10):1832–1845

    Article  Google Scholar 

  5. Wang X, Tang X (2004) A unified framework for subspace face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 26(9):1222–1228

    Article  MathSciNet  Google Scholar 

  6. Zhang H, Zhang Y, Huang TS (2013) Pose-robust face recognition via sparse representation. Pattern Recognit. 46(5):1511– 1521

    Article  Google Scholar 

  7. Nie F, Cai G, Li J, Li X (2017) Auto-weighted multi-view learning for image clustering and semi-supervised classification. IEEE Trans. Image Process. 27(3):1501–1511

    Article  MathSciNet  Google Scholar 

  8. Wang H, Yang Y, Liu B, Fujita H (2019) A study of graph-based system for multi-view clustering. Knowl-Based Syst. 163:1009–1019

    Article  Google Scholar 

  9. Zhang X, Yang Y, Li T, Zhang Y, Wang H, Fujita H (2021) Cmc: A consensus multi-view clustering model for predicting alzheimer?s disease progression. Comput Methods Prog Biomed 199:105895

    Article  Google Scholar 

  10. Xia R, Pan Y, Du L, Yin J (2014) Robust multi-view spectral clustering via low-rank and sparse decomposition. In: Proc. AAAI Conf. Artif. Intell., pp 2149–2155

  11. Deng T, Ye D, Ma R, Fujita H, Xiong L (2020) Low-rank local tangent space embedding for subspace clustering. Inf Sci 508:1–21

    Article  MathSciNet  Google Scholar 

  12. Abhadiomhen SE, Wang Z, Shen X (2021) Coupled low rank representation and subspace clustering. Appl. Intell., pp 1–17

  13. Chen Y, Wang S, Peng C, Hua Z, Zhou Y (2021) Generalized nonconvex low-rank tensor approximation for multi-view subspace clustering. IEEE Trans. Image Process. 30:4022–4035

    Article  MathSciNet  Google Scholar 

  14. Zhang Y, Yang Y, Li T, Fujita H (2019) A multitask multiview clustering algorithm in heterogeneous situations based on lle and le. Knowl-Based Syst. 163:776–786

    Article  Google Scholar 

  15. Yang X, Jiang X, Tian C, Wang P, Zhou F, Fujita H (2020) Inverse projection group sparse representation for tumor classification: A low rank variation dictionary approach. Knowl-Based Syst. 196:105768

    Article  Google Scholar 

  16. Yang S, Zhu W, Zhu Y (2020) Residual encoder-decoder network for deep subspace clustering. In: IEEE Int. Conf. Image Process., pp 2895–2899

  17. Chen Y, Xiao X, Zhou Y (2020) Multi-view subspace clustering via simultaneously learning the representation tensor and affinity matrix. Pattern Recognit. 106:107441

    Article  Google Scholar 

  18. Wang S, Chen Y, Zheng F (2021) Weighted low-rank tensor representation for multi-view subspace clustering. Frontiers in Physics 8:639

    Article  Google Scholar 

  19. Lu C-Y, Min H, Zhao Z-Q, Zhu L, Huang D-S, Yan S (2012) Robust and efficient subspace segmentation via least squares regression. In: Proc. Eur. Conf. Comput. Vis., Springer, pp 347–360

  20. Liu M, Wang Y, Sun J, Ji Z (2020) Structured block diagonal representation for subspace clustering. Appl. Intell. 50(8):2523–2536

    Article  Google Scholar 

  21. Elhamifar E, Vidal R (2013) Sparse subspace clustering: Algorithm, theory, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 35(11):2765–2781

    Article  Google Scholar 

  22. Patel VM, Vidal R (2014) Kernel sparse subspace clustering. In: IEEE Int. Conf. Image Process., pp 2849–2853

  23. Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2013) Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(1):171–184

    Article  Google Scholar 

  24. Cao X, Zhang C, Fu H, Liu S, Zhang H (2015) Diversity-induced multi-view subspace clustering. In: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pp 586–594

  25. Wang X, Guo X, Lei Z, Zhang C, Li SZ (2017) Exclusivity-consistency regularized multi-view subspace clustering. In: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pp 923–931

  26. Zhang C, Fu H, Hu Q, Cao X, Xie Y, Tao D, Xu D (2020) Generalized latent multi-view subspace clustering. IEEE Trans. Pattern Anal. Mach. Intell. 42(1):86–99

    Article  Google Scholar 

  27. Tang Y, Xie Y, Zhang C, Zhang Z, Zhang W (2021) One-step multiview subspace segmentation via joint skinny tensor learning and latent clustering. IEEE Trans. Cybern.

  28. Tang Y, Xie Y, Zhang C, Zhang W (2021) Constrained tensor representation learning for multi-view semi-supervised subspace clustering. IEEE Trans. on Multimedia

  29. Zhang C, Fu H, Liu S, Liu G, Cao X (2015) Low-rank tensor constrained multiview subspace clustering. In: Proc. IEEE Int. Conf. Comput. Vis., pp 1582–1590

  30. Xie Y, Tao D, Zhang W, Liu Y, Zhang L, Qu Y (2018) On unifying multi-view self-representations for clustering by tensor multi-rank minimization. Int. J. Comput. Vis. 126(11):1157–1179

    Article  MathSciNet  Google Scholar 

  31. Wu J, Lin Z, Zha H (2019) Essential tensor learning for multi-view spectral clustering. IEEE Trans. Image Process. 28(12):5910–5922

    Article  MathSciNet  Google Scholar 

  32. Kang Z, Peng C, Cheng J, Cheng Q (2015) Logdet rank minimization with application to subspace clustering. Comput. Intell. Neurosci. 2015:68

    Article  Google Scholar 

  33. Chen Y, Wang Y, Li M, He G (2017) Augmented lagrangian alternating direction method for low-rank minimization via non-convex approximation. Signal Image Video Process. 11(7):1271–1278

    Article  Google Scholar 

  34. Gu S, Xie Q, Meng D, Zuo W, Feng X, Zhang L (2017) Weighted nuclear norm minimization and its applications to low level vision. Int. J. Comput. Vis. 121(2):183–208

    Article  Google Scholar 

  35. Chao G (2018) Discriminative k-means laplacian clustering. Neural Process. Lett., pp 1–13

  36. Zheng M, Bu J, Chen C, Wang C, Zhang L, Qiu G, Cai D (2011) Graph regularized sparse coding for image representation. IEEE Trans. Image Process. 20(5):1327–1336

    Article  MathSciNet  Google Scholar 

  37. Gao S, Tsang I W-H, Chia L-T (2012) Laplacian sparse coding, hypergraph laplacian sparse coding, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 35(1):92–104

    Article  Google Scholar 

  38. Yin M, Gao J, Lin Z (2016) Laplacian regularized low-rank representation and its applications. IEEE Trans. Pattern Anal. Mach. Intell. 38(3):504–517

    Article  Google Scholar 

  39. Xie Y, Zhang W, Qu Y (2020) Hyper-laplacian regularized multilinear multiview self-representations for clustering and semisupervised learning. IEEE Trans. Cybern. 93(2):572–586

    Article  Google Scholar 

  40. Chen Y, Xiao X, Peng C, Lu G, Zhou Y (2021) Low-rank tensor graph learning for multi-view subspace clustering. IEEE Trans. Circuits Syst. Video Technol., https://doi.org/10.1109/TCSVT.2021.3055625

  41. Zhang Z, Ely G, Aeron S, Hao N, Kilmer M (2014) Novel methods for multilinear data completion and de-noising based on tensor-svd. In: Proc. IEEE Conf. Comput. Vis. Pattern Recognit., pp 3842–3849

  42. Piao X, Hu Y, Gao J, Sun Y, Lin Z, Yin B (2016) Tensor sparse and low-rank based submodule clustering method for multi-way data. arXiv:1601.00149

  43. Chen Y, Xiao X, Zhou Y (2019) Jointly learning kernel representation tensor and affinity matrix for multi-view clustering. IEEE Trans. on Multimedia 22(8):1985–1997

    Article  Google Scholar 

  44. Zhou P, Lu C, Feng J, Lin Z, Yan S (2019) Tensor low-rank representation for data recovery and clustering. IEEE Trans. Pattern Anal. Mach. Intell. 43(5):1718–1732

    Article  Google Scholar 

  45. Wang S, Chen Y, Ce Y, Zhang L, Voronin V (2021) Low-rank and sparse tensor representation for multi-view subspace clustering. In: 2021 IEEE International Conference on Image Processing (ICIP), pp 1534–1538

  46. Wang S, Chen Y, Jin Y, Cen Y, Li Y, Zhang L (2021) Error-robust low-rank tensor approximation for multi-view clustering. Knowl-Based Syst. 215:106745

    Article  Google Scholar 

  47. Gaïffas S, Lecué G (2011) Weighted algorithms for compressed sensing and matrix completion. arXiv:1107.1638

  48. Tang Y, Xie Y, Yang X, Niu J, Zhang W (2021) Tensor multi-elastic kernel self-paced learning for time series clustering. IEEE Trans. Knowl. Data Eng. 33:1223–1237

    Google Scholar 

  49. Chen Y, Wang S, Zheng F, Cen Y (2020) Graph-regularized least squares regression for multi-view subspace clustering. Knowl-Based Syst. 194:105482

    Article  Google Scholar 

  50. Chen M-S, Huang L, Wang C-D, Huang D (2020) Multi-view clustering in latent embedding space. In: Proc. AAAI Conf. Artif. Intell., vol 34, pp 3513–3520

  51. Zhao H, Ding Z, Fu Y (2017) Multi-view clustering via deep matrix factorization. In: Proc. AAAI Conf. Artif. Intell.

  52. Zhu P, Hui B, Zhang C, Du D, Wen L, Hu Q (2019) Multi-view deep subspace clustering networks. arXiv:1908.01978

  53. Li R, Zhang C, Fu H, Peng X, Zhou T, Hu Q (2019) Reciprocal multi-layer subspace learning for multi-view clustering. In: Proc. IEEE Int. Conf. Comput. Vis., pp 8172–8180

Download references

Acknowledgements

This work was supported in part by the National Key R&D Program of China 2021YFE0110500, in part by the National Natural Science Foundation of China under Grant 61872034, 62062021,62106063, 62072024 and 62011530042, in part by the Beijing Municipal Natural Science Foundation under Grant 4202055, in part by the RFBR and NSFC according to the research project 20-57-53012 and by project under Grant NoFSFS-2020-0031, in part by the Shenzhen College Stability Support Plan under Grant GXWD20201230155427003-20200824113231001, in part by the Fundamental Research Funds for the Central Universities (2021YJS025).

Author information

Authors and Affiliations

  1. Institute of Information Science, Beijing Jiaotong University, Beijing, China

    Shuqin Wang & Yigang Cen

  2. Beijing Key Laboratory of Advanced Information Science and Network Technology, Beijing, China

    Shuqin Wang & Yigang Cen

  3. School of Computer Science and Technology, Harbin Institute of Technology, Shenzhen, China

    Yongyong Chen

  4. College of Mechanical Engineering, Guizhou University, Guiyang, China

    Linna Zhang

  5. School of Science, Beijing University of Civil Engineering and Architecture, Beijing, China

    Hengyou Wang

  6. Center for Cognitive Technology and Machine Vision, Moscow State University of Technology “STANKIN”, Moscow, Russian Federation

    Viacheslav Voronin

Authors
  1. Shuqin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongyong Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yigang Cen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Linna Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Hengyou Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Viacheslav Voronin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yigang Cen.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article belongs to the Topical Collection: Special Issue on Multi-view Learning

Guest Editors: Guoqing Chao, Xingquan Zhu, Weiping Ding, Jinbo Bi and Shiliang Sun

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, S., Chen, Y., Cen, Y. et al. Nonconvex low-rank and sparse tensor representation for multi-view subspace clustering. Appl Intell 52, 14651–14664 (2022). https://doi.org/10.1007/s10489-022-03406-6

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-022-03406-6

Keywords

Search

Navigation