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An Improved Structured Low-Rank Representation for Disjoint Subspace Segmentation

  • Lai Wei
  • Yan Zhang
  • Jun Yin
  • Rigui Zhou
  • Changming Zhu
  • Xiafeng Zhang
Article
  • 68 Downloads

Abstract

Low-rank representation (LRR) and its extensions have shown prominent performances in subspace segmentation tasks. Among these algorithms, structured-constrained low-rank representation (SCLRR) is proved to be superior to classical LRR because of its usage of structure information of data sets. Compared with LRR, in the objective function of SCLRR, an additional constraint term is added to compel the obtained coefficient matrices to reveal the subspace structures of data sets more precisely. However, it is very difficult to determine the best value for the corresponding parameter of the constraint term, and an improper value will decrease the performance of SCLRR sharply. For the sake of alleviating the problem in SCLRR, in this paper, we proposed an improved structured low-rank representation (ISLRR). Our proposed method introduces the structure information of data sets into the equality constraint term of LRR. Hence, ISLRR avoids the adjustment of the extra parameter. Experiments conducted on some benchmark databases showed that the proposed algorithm was superior to the related algorithms.

Keywords

Subspace segmentation Spectral clustering Low-rank representation Structure constraint 

Notes

Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments on this paper.

Compliance with Ethical Standards

Conflict of interest

The authors declared that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled.

References

  1. 1.
    Hong W, Wright J, Huang K, Ma Y (2006) Multi-scale hybrid linear models for lossy image representation. IEEE Trans Image Process 15(12):3655–3671MathSciNetCrossRefGoogle Scholar
  2. 2.
    Costeira J, Kanade T (1998) A multibody factorization method for independently moving objects. Int J Comput Vis 29(3):159–179CrossRefGoogle Scholar
  3. 3.
    Kanatani K (2001) Motion segmentation by subspace separation and model selection. In: IEEE international conference on computer vision, vol 2, pp 586–591Google Scholar
  4. 4.
    Yan J, Pollefeys M (2006) A general framework for motion segmentation: independent, articulated, rigid, non-rigid, degenerate and nondegenerate. In: European Conference on Computer Vision, pp 94–106Google Scholar
  5. 5.
    Zelnik-Manor L, Irani M (2003) Degeneracies, dependencies and their implications in multi-body and multi-sequence factorization. In: IEEE conference on computer vision and pattern recognition, vol 2, pp 287–293Google Scholar
  6. 6.
    Vidal R, Favaro P (2014) Low rank subspace clustering. Pattern Recognit Lett 43:47–61CrossRefGoogle Scholar
  7. 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 35:171–184CrossRefGoogle Scholar
  8. 8.
    Wei L, Wang X, Yin J, Wu A (2016) Spectral clustering steered low-rank representation for subspace segmentation]. J Vis Commun Image Represent 38:386–395CrossRefGoogle Scholar
  9. 9.
    Huang K, Ma Y, Vidal R (2004) Minimum effective dimension for mixtures of subspaces: a robust GPCA algorithm and its applications. In: IEEE conference on computer vision and pattern recognition (CVPR), pp 631–638Google Scholar
  10. 10.
    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):413–458MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Zhang T, Szlam A, Wang Y, Lerman G (2012) Hybrid linear modeling via local bestfit flats. Int J Comput Vis 100(3):217–240MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Bradley PS, Mangasarian OL (2000) K-plane clustering. J Glob Optim 16(1):23–32MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Leonardis A, Bischof H, Maver J (2002) Multiple eigenspaces. Pattern Recogn 35(11):2613–2627CrossRefzbMATHGoogle Scholar
  14. 14.
    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):1546–1562CrossRefGoogle Scholar
  15. 15.
    Elhamifar E, Vidal R (2009) Sparse subspace clustering. In: CVPRGoogle Scholar
  16. 16.
    Patel VM, Nguyen HV, Vidal R (2013) Latent space sparse subspace clustering. In: ICCV, pp 225–232Google Scholar
  17. 17.
    Lu C, Tang J, Lin M, Lin L, Yan S, Lin Z (2013) Correntropy induced L2 graph for robust subspace clustering. In: ICCV, pp 1801–1808Google Scholar
  18. 18.
    Liu G, Lin Z, Yu Y (2010) Robust subspace segmentation by low-rank representation. In: ICML-10, Haifa, Israel, pp 663–670Google Scholar
  19. 19.
    Wei L, Wu A, Yin J (2015) Latent space robust subspace segmentation based on low rank and locality constraints. Expert Syst Appl 42:6598–6608CrossRefGoogle Scholar
  20. 20.
    Elhamifar E, Vidal R (2013) Sparse subspace clustering: algorithm, theory, and applications. IEEE Trans Pattern Anal Mach Intell 35(11):2765–2781CrossRefGoogle Scholar
  21. 21.
    Wei L, Wang X, Yin J, Wu A (2017) Self-regularized fixed-rank representation for subspace segmentation. Inf Sci 412–413:194–209MathSciNetCrossRefGoogle Scholar
  22. 22.
    Shi J, Malik J (2000) Normalized cuts and image segmentation. IEEE Trans Pattern Anal Mach Intell 22:888–905CrossRefGoogle Scholar
  23. 23.
    Wright J, Yang A, Ganesh A, Sastry SS, Ma Y (2009) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31(2):210–227CrossRefGoogle Scholar
  24. 24.
    Wang Y, Xu C, You S, Xu C, Tao D (2017) DCT regularized extreme visual recovery. IEEE Trans Image Process 26(7):3360–3371MathSciNetCrossRefGoogle Scholar
  25. 25.
    Liu Q, Lai Z, Zhou Z, Kuang F, Jin Z (2015) A truncated nuclear norm regularization method based on weighted residual error for matrix completion. IEEE Trans Image Process 25(1):316–330MathSciNetCrossRefGoogle Scholar
  26. 26.
    Wang Y, Xu C, Xu C, Tao D (2017) Beyond RPCA: flattening complex noise in the frequency domain In: AAAI conference on artificial intelligenceGoogle Scholar
  27. 27.
    Hu Y, Zhang D, Ye J, Li X, He X (2013) Fast and accurate matrix completion via truncated nuclear norm regularization. IEEE Trans Pattern Anal Mach Intell 35(9):2117–2130CrossRefGoogle Scholar
  28. 28.
    Li J, Xu C, Yang W, Sun C, Tao D (2017) Discriminative multi-view interactive image re-ranking. IEEE Trans Image Process 26(7):3113–3127MathSciNetCrossRefGoogle Scholar
  29. 29.
    Li J, Xu C, Yang W, Sun C (2017) SPA: spatially pooled attributes for image retrieval. Neurocomputing 257:47–58CrossRefGoogle Scholar
  30. 30.
    Chen J, Zhang H, Mao H, Sang Y, Yi Z (2014) Symmetric low-rank representation for subspace clustering. Neurocomputing 173(3):1192–1202Google Scholar
  31. 31.
    Zhuang L, Wang J, Lin Z, Yang AY, Ma Y, Yu N (2016) Locality-preserving low-rank representation for graph construction from nonlinear manifolds. Neurocomputing 175:715–722CrossRefGoogle Scholar
  32. 32.
    Zhang YL, Jiang Z, Larry S (2013) Learning structured low-rank representations for image classification. In: Computer vision and pattern recognition, pp 676–683Google Scholar
  33. 33.
    Zhuang L, Gao H, Lin Z, Ma Y, Zhang X, Yu N (2012) Non-negative low rank and sparse graph for semi-supervised learning, In: CVPR, pp 2328–2335Google Scholar
  34. 34.
    Tang K, Liu R, Su Z, Zhang J (2014) Structure-constrained low-rank representation. IEEE Trans Neural Netw Learn Syst 25(12):2167–2179CrossRefGoogle Scholar
  35. 35.
    Li X, Li X, Liu C, Liu H (2016) Structure-constrained low-rank and partial sparse representation with sample selection for image classification. Pattern Recognit 59:5–13CrossRefGoogle Scholar
  36. 36.
    Wu T, Gurram P, Rao RM, Bajwa W (2016) Clustering-aware structure-constrained low-rank representation model for learning human action attributes. In: Image, video, and multidimensional signal processing workshop. IEEE, pp 1–5Google Scholar
  37. 37.
    Xiao H, Rasul K, Vollgraf R (2017) Fashion-MNIST: a novel image dataset for benchmarking machine learning algorithms. arXiv:1708.07747
  38. 38.
    Zhang X (2004) Matrix analysis and applications. Springer, New YorkGoogle Scholar
  39. 39.
    Cai JF, Candès EJ, Shen Z (2008) A singular value thresholding algorithm for matrix completion. SIAM J Optim 20(4):1956–1982MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    Lin Z, Chen M, Wu L, Ma Y (2009) The augmented Lagrange multiplier method for exact recovery of corrupted low-rank matrices. In: UIUC, Champaign, IL, USA, Technical Report UILU-ENG-09-2215Google Scholar
  41. 41.
    Eckstein J, Bertsekas DP (1992) On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators. Math Program 55(1–3):293–318MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    Tron R, Vidal R (2007) A benchmark for the comparison of 3-D motion segmentation algorithms. In: IEEE international conference on computer vision and pattern recognition (ICCV)Google Scholar
  43. 43.
    Samaria F, Harter A (1994) Parameterisation of a stochastic model for human face identification. In: Proceedings of 2nd IEEE workshop applications of computer visionGoogle Scholar
  44. 44.
    Lee KC, Ho J, Driegman D (2005) Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans Pattern Anal Mach Intell 27(5):684–698CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer ScienceShanghai Maritime UniversityShanghaiChina

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