Skip to main content
SpringerLink
Log in

Self-Supervised Convolutional Subspace Clustering Network with the Block Diagonal Regularizer

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

The practical visual data do not necessarily lie in linear subspaces, so deep convolutional subspace clustering network is proposed to segment the practical visual data into multiple categories accurately. The original convolutional subspace clustering network contains the stacked convolutional encoder module, the stacked convolutional decoder module and the self-expression module. We firstly alter the self-expression module, i.e., add a new k-block diagonal regularizer to the weights of the self-expression module. It means that the \(\ell _1\) or \(\ell _2\) regularizer is abandoned. The k-block diagonal regularizer is proposed to directly pursue the block diagonal matrix, so introducing this regularizer to the self-expression module will make the learned representation matrix conform with the block diagonal matrix better. Secondly, we add a new spectral clustering module to this convolutional subspace clustering network, in which the spectral clustering result is used to supervise the learning of the representation matrix. This subspace structured regularizer is introduced to the spectral clustering module, which further refines the learned representation matrix. Experimental results on three challenging datasets have demonstrated that the proposed deep learning based subspace clustering method achieves the better clustering effect over the state-of-the-arts.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Elhamifar E, Vidal R (2009) Sparse subspace clustering. In CVPR. pp 2790–2797

  2. Hastie T, Simard PY (2000) Metrics and models for handwritten character recognition. Stat Sci 13(1)

  3. 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 

  4. Qian C, Brechon TP, Xu ZZ (2018) Clustering in pursuit of temporal correlation for human motion segmentation. Multimed Tools Appl 77(15):19615–19631

    Article  Google Scholar 

  5. Basri R, Jacobs DW (2003) Lambertian reflectance and linear subspaces. IEEE Trans Pattern Anal Recognit Mach Intell 25(2):218–233

    Article  Google Scholar 

  6. Elhamifar E, Vidal R (2010) Clustering disjoint subspaces via sparse representation. In: IEEE international conference on acoustics, speech, and signal processing. pp 1926–1929

  7. You C, Robinson D, Vidal R (2016) Scalable sparse subspace clustering by orthogonal matching pursuit. In: IEEE conference on computer vision and pattern recognition. pp 3918–3927

  8. Dyer EL, Studer C, Baraniuk RG (2013) Subspace clustering with dense representations. In: International conference on acoustics, speech and signal processing

  9. Ji P, Salzmann M, Li H (2014) Efficient dense subspace clustering. In: IEEE winter conference on applications of computer vision. IEEE, pp 461–468

  10. Favar P, Vidal R, Ravichandran A (2011) A closed form solution to robust subspace estimation and clustering. In: IEEE conference on computer vision and pattern recognition. pp 1801–1807

  11. Vidal R, Favaro P (2014) Low rank subspace clustering (LRSC). Pattern Recognit Lett 43:47–61

    Article  Google Scholar 

  12. Lu CY, Min H, Zhao ZQ, Zhu L, Huang DS, Yan S (2012) Robust and efficient subspace segmentation via least squares regression. European conference on computer vision. Springer, Berlin, Heidelberg, pp 347–360

    Google Scholar 

  13. Cheng B, Yang J, Yan S, Huang TS (2010) Learning with \(\ell _1\)-graph for image analysis. TIP, 19(Compendex). pp 858–866

  14. Liu G, Lin Z, Yu Y (2010) Robust subspace segmentation by low-rank representation. In: International conference on machine learning. pp 663-670

  15. 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 

  16. Lu C, Feng J, Lin Z, Yan S (2013) Correlation adaptive subspace segmentation by trace lasso. In: Proceedings of the IEEE international conference on computer vision. pp 1345–1352

  17. Xu J, Xu K, Chen K, Ruan JS (2015) Reweighted sparse subspace clustering. Comput Vis Image Underst 138:25–37

    Article  Google Scholar 

  18. Dong W, Wu XJ, Kittler J (2019) Sparse subspace clustering via smoothed \(\ell _p\) minimization. Pattern Recognit Lett 125:206–211

    Article  Google Scholar 

  19. Dong W, Wu XJ (2018) Robust affine subspace clustering via smoothed \(\ell _0\)-norm. Neural Process Lett 50(1):785–797

    Article  Google Scholar 

  20. Ng AY, Jordan MI, Weiss Y (2002) On spectral clustering: analysis and an algorithm. Adv Neural Inf Process Syst 14:849–856

    Google Scholar 

  21. Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Recognit Mach Intell 22(8):888–905

    Article  Google Scholar 

  22. Li CG, You C, Vidal R (2017) Structured sparse subspace clustering: a joint affinity learning and subspace clustering framework. IEEE Trans Image Process 26(6):2988–3001

    Article  MathSciNet  Google Scholar 

  23. Li CG, Vidal R (2015) Structured sparse subspace clustering: a unified optimization framework. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp 277–286

  24. Li CG, Vidal R (2016) A structured sparse plus structured low-rank framework for subspace clustering and completion. IEEE Trans Signal Process 64(24):6557–6570

    Article  MathSciNet  Google Scholar 

  25. Chen H, Wang W, Feng X (2018) Structured sparse subspace clustering with within-cluster grouping. Pattern Recognit 83:107–118

    Article  Google Scholar 

  26. Chen H, Wang W, Feng X, He R (2018) Discriminative and coherent subspace clustering. Neurocomputing 284:177–186

    Article  Google Scholar 

  27. Lu C, Feng J, Lin Z, Mei T, Yan S (2019) Subspace clustering by block diagonal representation. IEEE Trans Pattern Anal Mach Intell 41(2):487–501

    Article  Google Scholar 

  28. Zhang Z, Xu Y, Shao L, Yang J (2018) Discriminative block-diagonal representation learning for image recognition. IEEE Trans Neural Netw Learn Syst 29(7):3111–3125

    Article  MathSciNet  Google Scholar 

  29. Xie X, Guo X, Liu G, Wang J (2018) Implicit block diagonal low-rank representation. IEEE Trans Image Process 27(1):477–489

    Article  MathSciNet  Google Scholar 

  30. Patel VM, Vidal R (2014) Kernel sparse subspace clustering. In: IEEE international conference on image processing. pp 2849–2853

  31. Patel VM, Nguyen HV, Vidal R (2015) Latent space sparse and low-rank subspace clustering. IEEE J Sel Topics in Signal Process 9(4):691–701

    Article  Google Scholar 

  32. Patel VM, Nguyen HV, Vidal R (2013) Latent space sparse subspace clustering

  33. Kang Z, Peng C, Cheng Q et al (2020) Structured graph learning for clustering and semi-supervised classification. Pattern Recognit 110:107627

    Article  Google Scholar 

  34. Ji P, Reid I, Garg R, et al (2017) Adaptive low-rank kernel subspace clustering. arXiv:1707.04974v4

  35. Xiao S, Tan M, Xu D et al (2016) Robust kernel low-rank representation. IEEE Trans Neural Netw Learn Syst 27(11):2268–2281

    Article  MathSciNet  Google Scholar 

  36. Saba T, Khan MA, Rehman A et al (2019) Region extraction and classification of skin cancer: a heterogeneous framework of deep CNN features fusion and reduction. J Med Syst 43(9):1–19

    Article  Google Scholar 

  37. Hassan MM, Alam MGR, Uddin MZ et al (2019) Human emotion recognition using deep belief network architecture. Inf Fusion 51:10–18

    Article  Google Scholar 

  38. Peng X, Xiao S, Feng J, Yau WY, Yi Z (2016) Deep subspace clustering with sparsity prior. In: International Joint conference on artificial intelligence. pp. 1925–1931

  39. Peng X, Feng J, Xiao S, et al (2017) Deep sparse subspace clustering. arXiv preprint arXiv:1709.08374

  40. Ji P, Zhang T, Li H, Salzmann M (2017) Deep subspace clustering networks. arXiv preprint arXiv:1709.02508

  41. Kang Z, Lu X, Liang J et al (2020) Relation-guided representation learning. Neural Netw 131:93–102

    Article  Google Scholar 

  42. Kang Z, Pan H, Hoi SC et al (2019) Robust graph learning from noisy data. IEEE Trans Cybern 50(5):1833–1843

    Article  Google Scholar 

  43. Zhang J, Li CG, You C, et al (2019) Self-supervised convolutional subspace clustering network. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp 5473–5482

  44. Huang D, Wang CD, Lai JH (2017) Locally weighted ensemble clustering. IEEE Trans Cybern 48(5):1460–1473

    Article  Google Scholar 

  45. Huang D, Wang CD, Peng H, et al (2018) Enhanced ensemble clustering via fast propagation of cluster-wise similarities. IEEE Trans Syst Man Cybern Syst

  46. Huang D, Wang CD, Wu JS et al (2019) Ultra-scalable spectral clustering and ensemble clustering. IEEE Trans Knowl Data Eng 32(6):1212–1226

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Key R&D Program of China (Project Number: 2018YFB1701903) and the National Natural Science Foundation of China (Project No: 61973138).

Author information

Authors and Affiliations

  1. Engineering Research Center of Internet of Things Technology Applications, Ministry of Education, Jiangnan University, No 1800, Lihu Avenue, Wuxi, Jiangsu, 214122, China

    Maoshan Liu, Yan Wang & Zhicheng Ji

Authors
  1. Maoshan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhicheng Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Wang.

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

Liu, M., Wang, Y. & Ji, Z. Self-Supervised Convolutional Subspace Clustering Network with the Block Diagonal Regularizer. Neural Process Lett 53, 3849–3875 (2021). https://doi.org/10.1007/s11063-021-10563-1

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10563-1

Keywords

Search

Navigation