Skip to main content
SpringerLink
Log in

Auto-Weighted Graph Regularization and Residual Compensation for Multi-view Subspace Clustering

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

Multi-view clustering has attractive intensive attention and proved to be more effective than single-view clustering. The mining and effective utilization of information complementarity is core of multi-view clustering. In this paper, we propose a novel Auto-Weighted Graph Regularization and Residual Compensation for Multi-view Subspace Clustering (ARMSC) method, which adopts residual representation information to compensate the globally low rank consensus representation. The auto-weighted multi-view graph regularization term is constructed to preserve the local manifold structure of multiple features, which can automatically adjust the weights and the learned weights are adopt to measure the importance of each view’s residual representation for final representation. Specifically, we formulate the graph regularized consistent representation using nuclear norm and a set of group effect residual compensation using Frobenius norm. Finally, we introduce a convex relaxation and alternating direction method to optimize the problem. Comprehensive and ablation experiments on seven real-world data sets illustrate the effectiveness and superiority of the proposed ARMSC over several state-of-the-art multi-view clustering approaches.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Notes

  1. http://mlg.ucd.ie/datasets/segment.html.

  2. http://mlg.ucd.ie/datasets/segment.html.

  3. http://mlg.ucd.ie/datasets/3sources.html.

  4. http://www.uk.research.att.com/facedatabase.html.

  5. https://archive.ics.uci.edu/ml/datasets.

  6. http://lig-membres.imag.fr/grimal/data.html.

  7. http://www.vision.caltech.edu.

References

  1. Rao S, Tron R, Vidal R, Ma Y (2010) Motion segmentation in the presence of outlying, incomplete, or corrupted trajectories. IEEE Trans Pattern Anal Mach Intell 32(10):1832–1845. https://doi.org/10.1109/TPAMI.2009.191

    Article  Google Scholar 

  2. Chen X, Wang Q, Zhuang S (2021) Ensemble dimension reduction based on spectral disturbance for subspace clustering. Knowl-Based Syst 227:107182

  3. Abavisani M, Patel VM (2018) Multimodal sparse and low-rank subspace clustering. Inf Fus 39:168–177. https://doi.org/10.1016/j.inffus.2017.05.002

    Article  Google Scholar 

  4. Tu B, Yang X, Li N, Zhou C, He D (2020) Hyperspectral anomaly detection via density peak clustering. Pattern Recogn Lett 129:144–149. https://doi.org/10.1016/j.patrec.2019.11.022

    Article  Google Scholar 

  5. Chao G, Sun S, Bi J (2021) A survey on multi-view clustering. IEEE Trans Artif Intell 2:146–168. https://doi.org/10.1109/TAI.2021.3065894

    Article  Google Scholar 

  6. Elhamifar E, Vidal R (2012) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781. https://doi.org/10.1109/TPAMI.2013.57

    Article  Google Scholar 

  7. 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. https://doi.org/10.1109/TPAMI.2012.88

    Article  Google Scholar 

  8. Lu CY, Min H, Zhao ZQ, Zhu L, Huang DS, Yan S (2014) Robust and efficient subspace segmentation via least squares regression. Comput Sci. https://doi.org/10.1007/978-3-642-33786-4_26

  9. 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 494:278–293

    Article  MathSciNet  Google Scholar 

  10. Yu H, Zhang T, Chen J, Guo C, Lian Y (2018) Web items recommendation based on multi-view clustering. In: 2018 IEEE 42nd annual computer software and applications conference (COMPSAC), vol 1. IEEE, pp 420–425

  11. Xia, R., Pan, Y., Du, L., Yin, J.: Robust multi-view spectral clustering via low-rank and sparse decomposition. In: Proceedings of the national conference on artificial intelligence, pp 2149–2155 (2014)

  12. Li S, Shao M, Fu Y (2018) Multi-view low-rank analysis with applications to outlier detection. ACM Trans Knowl Discov Data 12(3):1–22. https://doi.org/10.1145/3168363

    Article  Google Scholar 

  13. Brbić M, Kopriva I (2017) Multi-view low-rank sparse subspace clustering. Pattern Recogn 73:247–258. https://doi.org/10.1016/j.patcog.2017.08.024

    Article  Google Scholar 

  14. Wang X, Guo X, Lei Z, Zhang C, Li S (2017) Exclusivity-consistency regularized multi-view subspace clustering, pp 1–9. https://doi.org/10.1109/CVPR.2017.8

  15. Luo S, Zhang C, Zhang W (2018) Consistent and specific multi-view subspace clustering. In: 32nd AAAI conference on artificial intelligence, pp 3730–3737 (2018)

  16. Nie F, Cai G, Li X (2017) Multi-view clustering and semi-supervised classification with adaptive neighbours. In: Proceedings of the AAAI conference on artificial intelligence, pp 2408–2414 (2017)

  17. Lin, Z., Liu, R., Su, Z.: Linearized alternating direction method with adaptive penalty for low-rank representation. arXiv preprint arXiv:1109.0367 (2011)

  18. Chaudhuri K, Kakade S, Livescu K, Sridharan K (2009) Multi-view clustering via canonical correlation analysis. In: Proceedings of the 26th annual international conference on machine learning, pp 129–136. https://doi.org/10.1145/1553374.1553391

  19. Liang Y, Huang D, Wang C-D (2019) Consistency meets inconsistency: a unified graph learning framework for multi-view clustering. In: 2019 IEEE international conference on data mining (ICDM). IEEE, pp 1204–1209

  20. Nie F, Li J, Li X (2016) Parameter-free auto-weighted multiple graph learning: a framework for multiview clustering and semi-supervised classification. In: Proceedings of the 25h international joint conference on artificial intelligence, pp 1881–1887

  21. Nie F, Li J, Li X (2017) Self-weighted multiview clustering with multiple graphs. In: 16th international joint conference on artificial intelligence, pp 2564–2570. https://doi.org/10.24963/ijcai.2017/357

  22. Nie F, Wang X, Jordan M, Huang H (2016) The constrained Laplacian rank algorithm for graph-based clustering. In: The 30th AAAI conference on artificial intelligence, pp 1969–1976. https://doi.org/10.5555/3016100.3016174

  23. Hao W, Yan Y, Bing L, Hamido F (2019) A study of graph-based system for multi-view clustering. Knowl-Based Syst 163:1009–1019

    Article  Google Scholar 

  24. Zheng Q, Zhu J, Li Z, Pang S, Wang L, Jun Y (2019) Feature concatenation multi-view subspace clustering. Knowl-Based Syst 379:89–102. https://doi.org/10.1016/j.neucom.2019.10.074

    Article  Google Scholar 

  25. Xia R, Pan Y, Du L, Yin J (2014) Robust multi-view spectral clustering via low-rank and sparse decomposition. In: Proceedings of the AAAI conference on artificial intelligence, vol 28

  26. Zhang C, Fu H, Hu Q, Cao X, Yuan X, Tao D, Dong X (2018) Generalized latent multi-view subspace clustering. IEEE Trans Pattern Anal Mach Intell 42:86–99

    Article  Google Scholar 

  27. Zhang C, Hu Q, Fu H, Zhu P, Cao X (2017) Latent multi-view subspace clustering. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 4279–4287

  28. Chen Y, Wang S, Zheng F, Cen Y (2020) Graph-regularized least squares regression for multi-view subspace clustering. Knowl-Based Syst 194:105482. https://doi.org/10.1016/j.knosys.2020.105482

    Article  Google Scholar 

  29. Zhang G-Y, Chen X-W, Zhou Y-R, Wang C-D, Huang D (2021) Consistency-and inconsistency-aware multi-view subspace clustering. In: International conference on database systems for advanced applications. Springer, pp 291–306

  30. Ji P, Zhang T, Li H, Salzmann M, Reid I (2017) Deep subspace clustering network. In: Advances in neural information processing systems, pp 24–33

  31. Zhu W, Peng B (2020) Sparse and low-rank regularized deep subspace clustering. Knowl-Based Syst. https://doi.org/10.1016/j.knosys.2020.106199

  32. Abavisani M, Patel VM (2018) Deep multimodal subspace clustering networks. IEEE J Sel Top Signal Process 12(6):1601–1614

    Article  Google Scholar 

  33. Cai D, Chen X (2014) Large scale spectral clustering via landmark-based sparse representation. IEEE Trans Cybern 45(8):1669–1680

    Google Scholar 

  34. Huang D, Wang C-D, Wu J-S, Lai J-H, Kwoh C-K (2019) Ultra-scalable spectral clustering and ensemble clustering. IEEE Trans Knowl Data Eng 32(6):1212–1226

    Article  Google Scholar 

  35. Ng AY, Jordan MI, Weiss Y (2001) On spectral clustering: Analysis and an algorithm. In: Proceedings of the 14th international conference on neural information processing systems: natural and synthetic, pp 849–856

  36. Nie F, Wang X, Huang H. (2014) Clustering and projected clustering with adaptive neighbors. In: ACM SIGKDD international conference on knowledge discovery data mining, pp 977–986. https://doi.org/10.1145/2623330.2623726

  37. You C, Li C-G, Robinson DP, Vidal R (2016) Oracle based active set algorithm for scalable elastic net subspace clustering. In: Proceedings of the IEEE conference on computer vision and pattern recognition, pp 3928–3937

  38. Lin Z, Liu R, Su Z (2011) Linearized alternating direction method with adaptive penalty for low-rank representation. In: Advances in neural information processing systems, pp 612–620

  39. Lu CS (2007) Solution of the matrix equation \(ax+xb = c\). Electron Lett 7(8):185–186

    Article  MathSciNet  Google Scholar 

  40. Yang J, Yin W, Zhang Y, Wang Y (2009) A fast algorithm for edge-preserving variational multichannel image restoration. SIAM J Imag Sci 2(2):569–592

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350116, China

    Qiaoping Wang, Xiaoyun Chen & Wenjian Chen

Authors
  1. Qiaoping Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoyun Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenjian Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoyun Chen.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Q., Chen, X. & Chen, W. Auto-Weighted Graph Regularization and Residual Compensation for Multi-view Subspace Clustering. Neural Process Lett 54, 3851–3871 (2022). https://doi.org/10.1007/s11063-022-10789-7

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-022-10789-7

Keywords

Search

Navigation