Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Graph constraint-based robust latent space low-rank and sparse subspace clustering

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

Recently, low-rank and sparse representation-based methods have achieved great success in subspace clustering, which aims to cluster data lying in a union of subspaces. However, most methods fail if the data samples are corrupted by noise and outliers. To solve this problem, we propose a novel robust method that uses the F-norm for dealing with universal noise and the \(l_1\) norm or the \(l_{2,1}\) norm for capturing outliers. The proposed method can find a low-dimensional latent space and a low-rank and sparse representation simultaneously. To preserve the local manifold structure of the data, we have adopted a graph constraint in our model to obtain a discriminative latent space. Extensive experiments on several face benchmark datasets show that our proposed method performs better than state-of-the-art subspace clustering 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
$34.99 /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 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
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Explore related subjects

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

Notes

  1. https://www.sheffield.ac.uk/eee/research/iel/research/face.

  2. http://archive.ics.uci.edu/ml/datasets/cmu+face+images.

References

  1. Basri R, Jacobs D (2001) Lambertian reflectance and linear subspaces. In: ICCV

  2. Agarwal P, Mustafa N (2004) k-means projective clustering. In: ACM symposium on principles of database systems, pp 155–165

  3. Zhang T, Szlam A, Lerman G (2009) Median k-flats for hybrid linear modeling with many outliers. In: ICCV

  4. Zhang T, Szlam A, Wang Y, Lerman G (2012) Hybrid linear modeling via local best-fit flats. Int J Comput Vis 100(3):217–240

    Article  MathSciNet  Google Scholar 

  5. Huang K, Ma Y, Vidal R (2004) Minimum effective dimension for mixtures of subspaces: a robust GPCA algorithm and its applications. In: CVPR

  6. Ma Y, Yang AY, Derksen H, Fossum R (2008) Estimation of subspace arrangements with applications in modeling and segmenting mixed data. SIAM Rev 50(3):413–458

    Article  MathSciNet  Google Scholar 

  7. Vidal R, Ma Y, Sastry S (2005) Generalized principal component analysis (GPCA). IEEE Trans Pattern Anal Mach Intell 27(12):1–15

    Article  Google Scholar 

  8. Archambeau C, Delannay N, Verleysen M (2008) Mixtures of robust probabilistic principal component analyzers. Neurocomputing 71(7–9):1274–1282

    Article  Google Scholar 

  9. Gruber A, Weiss Y (2004) Multibody factorization with uncertainty and missing data using the EM algorithm. In: CVPR

  10. Ma Y, Derksen H, Hong W, Wright J (2007) Segmentation of multivariate mixed data via lossy coding and compression. IEEE Trans Pattern Anal Mach Intell 29(9):1546–1562

    Article  Google Scholar 

  11. Yang AY, Rao SR, Ma Y (2006) Robust statistical estimation and segmentation of multiple subspaces. In: CVPR

  12. Chen G, Lerman G (2009) Spectral curvature clustering (SCC). Int J Comput Vision 81(3):317–330

    Article  Google Scholar 

  13. Elhamifar E, Vidal R (2009) Sparse subspace clustering. In: CVPR

  14. 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 

  15. Favaro P, Vidal R, Ravichandran A (2011) A closed form solution to robust subspace estimation and clustering. In: CVPR

  16. Liu G, Lin Z, Yu Y (2010) Robust subspace segmentation by low-rank representation. In: ICML

  17. Liu G, Lin Z, Yan S, Sun J, 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 

  18. Lu C, Lin Z, Yan S (2013) Correlation adaptive subspace segmentation by trace lasso. In: ICCV

  19. Lu C, Min H, Zhao ZQ, Zhu L, Huang DS, Yan S (2012) Robust and efficient subspace segmentation via least squares regression. In: ECCV

  20. Vidal R, Favaro P (2014) Low rank subspace clustering (LRSC). Pattern Recognit Lett 43(1):47–61

    Article  Google Scholar 

  21. Wang YX, Xu H, Leng C (2013) Provable subspace clustering: when LRR meets SSC. In: NIPS

  22. Chen J, Yang J (2014) Robust subspace segmentation via low-rank representation. IEEE Trans Cybern 44(8):1432–1445

    Article  Google Scholar 

  23. Donoho DL, Elad M, Temlyakov VN (2006) Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans Inf Theory 52(1):6–18

    Article  MathSciNet  Google Scholar 

  24. Yang Y, Feng J, Jojic N, Yang J, Huang TS (2016) L0-sparse subspace clustering. In: ECCV

  25. Li J, Kong Y, Fu Y (2017) Sparse subspace clustering by learning approximation L0 codes. In: AAAI

  26. Yin M, Xie S, Wu Z, Zhang Y, Gao J (2018) Subspace clustering via learning an adaptive low-rank graph. IEEE Trans Image Process 27(8):3716–3728

    Article  MathSciNet  Google Scholar 

  27. Lu C, Feng J, Lin Z, Mei T, Yan S (2018) Subspace clustering by block diagonal representation. IEEE Trans Pattern Anal Mach Intell 41(2):487–501

    Article  Google Scholar 

  28. Jolliffe IT (2002) Principal component analysis, 2nd edn. Springer, New York

    MATH  Google Scholar 

  29. Bingham E, Mannila H (2001) Random projection in dimensionality reduction: applications to image and text data. In: ACM SIGKDD international conference on knowledge discovery and data mining, pp 245–250

  30. Patel VM, Nguyen HV, Vidal R (2013) Latent space sparse subspace clustering. In: ICCV

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

    Article  Google Scholar 

  32. Wei L, Wu A, Yin J (2015) Latent space robust subspace segmentation based on low-rank and locality constraints. Expert Syst Appl 42(19):6598–6608

    Article  Google Scholar 

  33. He X, Niyogi P (2004) Locality preserving projections. In: NIPS

  34. He X, Yan S, Hu Y, Niyogi P, Zhang H (2005) Face recognition using laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):328–340

    Article  Google Scholar 

  35. Tang K, Su Z, Jiang W, Zhang J, Sun X, Luo X (2018) Robust subspace learning-based low-rank representation for manifold. Neural Comput Appl 29:329

    Article  Google Scholar 

  36. Jalali A, Sujay S, Ruan C, Ravikumar PK (2010) A dirty model for multi-task learning. In: NIPS

  37. Wang D, Liu Q, Xia Y, Dong P, Luo J, Huang Q, Feng DD (2013) Dictionary learning based impulse noise removal via L1–L1 minimization. Signal Process 93(9):2696–2708

    Article  Google Scholar 

  38. Chen Z, Wu Y (2013) Robust dictionary learning by error source decomposition. In: ICCV

  39. Zhang H, Wang S, Zhao M, Xu X, Ye Y (2018) Locality reconstruction models for book representation. IEEE Trans Knowl Data Eng 30(10):1873–1886

    Article  Google Scholar 

  40. Zhang H, Wang S, Xu X, Chow TWS, Wu QMJ (2018) Tree2Vector: learning a vectorial representation for tree-structured data. IEEE Trans Neural Netw Learn Syst 29(11):5304–5318

    Article  MathSciNet  Google Scholar 

  41. Boyd S, Parikh N, Chu E, Peleato B, Eckstein J (2011) Distributed optimization and statistical learning via the alternating direction method of multipliers. Found Trends Mach Learn 3(1):1–122

    Article  Google Scholar 

  42. Lin Z, Chen M, Wu L, Ma Y (2009) The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. Technical report, UIUC technical report UILU-ENG-09-2215

  43. Ng AY, Jordan MI, Weiss Y (2002) On spectral clustering: analysis and an algorithm. In: NIPS

  44. Zelnik-Manor L, Perona P (2005) Self-tuning spectral clustering. In: NIPS

  45. Cai D, He X (2005) Orthogonal locality preserving indexing. In: Proceedings of the 28th annual international ACM SIGIR conference on research and development in information retrieval, pp 3–10

  46. Kokiopoulou E, Saad Y (2007) Orthogonal neighborhood preserving projections: a projection-based dimensionality reduction technique. IEEE Trans Pattern Anal Mach Intell 29(12):2143–2156

    Article  Google Scholar 

  47. Cai D, He X, Han J, Zhang H (2006) Orthogonal laplacianfaces for face recognition. IEEE Trans Image Process 15(11):3608–3614

    Article  Google Scholar 

  48. Hale E, Yin W, Zhang Y (2008) Fixed-point continuation for l1-minimization: methodology and convergence. SIAM J Optim 19(3):1107–1130

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  50. Cai D, He X, Han J (2007) Spectral regression: a unified approach for sparse subspace learning. In: ICDM

  51. Samaria FS, Harter AC (1994) Parameterisation of a stochastic model for human face identification. In: IEEE workshop on applications of computer vision

  52. Phillips J, Bruce V, Soulie FF (1999) In face recognition: from theory to applications. Springer, Berlin

    Book  Google Scholar 

  53. Maaten LVD, Hinton G (2008) Visualizing data using T-SNE. J Mach Learn Res 9:2579–2605

    MATH  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (61402181, 61502174), the Natural Science Foundation of Guangdong Province (2015A030313215, 2017A030313358, 2017A030313355), the Science and Technology Planning Project of Guangdong Province (2016A040403046), the Guangzhou Science and Technology Planning Project (201704030051).

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, South China University of Technology, Guangzhou, China

    Yunjun Xiao, Jia Wei, Jiabing Wang & Qianli Ma

  2. School of Computing, University of Utah, Salt Lake City, USA

    Shandian Zhe

  3. Scientific Computing and Imaging Institute, University of Utah, Salt Lake City, USA

    Tolga Tasdizen

Authors
  1. Yunjun Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jia Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jiabing Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qianli Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shandian Zhe
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Tolga Tasdizen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jia Wei.

Ethics declarations

Conflict of interest

We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

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

Xiao, Y., Wei, J., Wang, J. et al. Graph constraint-based robust latent space low-rank and sparse subspace clustering. Neural Comput & Applic 32, 8187–8204 (2020). https://doi.org/10.1007/s00521-019-04317-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-019-04317-3

Keywords