Signal, Image and Video Processing

, Volume 11, Issue 1, pp 73–80 | Cite as

Semi-supervised low-rank representation for image classification

  • Chenxue Yang
  • Mao YeEmail author
  • Song Tang
  • Tao Xiang
  • Zijian Liu
Original Paper


Low-rank representation (LRR) is a useful tool for seeking the lowest rank representation among all the coefficient matrices that represent the images as linear combinations of the basis in the given dictionary. However, it is an unsupervised method and has poor applicability and performance in real scenarios because of the lack of image information. In this paper, based on LRR, we propose a novel semi-supervised approach, called label constrained sparse low-rank representation (LCSLRR), which incorporates the label information as an additional hard constraint. Specifically, this paper develops an optimization process in which the improvement of the discriminating power of the low-rank decomposition is presented explicitly by adding the label information constraint. We construct LCSLRR-graph to represent data structures for semi-supervised learning and provide the weights of edges in the graph by seeking a low-rank and sparse matrix. We conduct extensive experiments on publicly available databases to verify the effectiveness of our novel algorithm in comparison to the state-of-the-art approaches through a set of evaluations.


Low-rank representation Image classification Semi-supervised learning Label constraint 



This work was supported in part by the National Natural Science Foundation of China (61375038), Applied Basic Research Programs of Sichuan Science and Technology Department (2016JY0088), National Natural Science Foundation of China (11401060), Zhejiang Provincial Natural Science Foundation of China (LQ13 A010023).


  1. 1.
    Liu, G., Lin, Z., Yu, Y.: Robust subspace segmentation by low-rank representation. Mach. Learn. pp. 663–670 (2010)Google Scholar
  2. 2.
    Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Trans. Pattern Anal. Mach. Intell. 35(1), 171–184 (2013)CrossRefGoogle Scholar
  3. 3.
    Du, H., Hu, Q., Qiao, D., et al.: Robust face recognition via low-rank sparse representation-based classification. Int. J. Autom. Comput. 12(6), 579–587 (2015)CrossRefGoogle Scholar
  4. 4.
    Shen, X., Wu, Y.: A unified approach to salient object detection via low rank matrix recovery. IEEE Conference on Computer Vision and Pattern Recognition pp. 853–860 (2012)Google Scholar
  5. 5.
    Cui, X., Huang, J., Zhang, S., Metaxas, D.: Background Subtraction Using Low Rank and Group Sparsity Constraints. Springer, Berlin (2012)CrossRefGoogle Scholar
  6. 6.
    Zhang, T., Ghanem, B., Ahuja, N.: Low-rank Sparse Learning for Robust Visual Tracking. Springer, Berlin (2012)CrossRefGoogle Scholar
  7. 7.
    Lee, J., Shi, B. ,Matsushita, Y., Kweon, I., Ikeuchi, K.: Radiometric calibration by transform invariant low-rank structure. IEEE Conference on Computer Vision and Pattern Recognition, pp. 2337–2344 (2011)Google Scholar
  8. 8.
    He, R., Zheng, W.S., Hu, B.G., Kong, X.W.: Nonnegative sparse coding for discriminative semi-supervised learning. IEEE Conference on Computer Vision and Pattern Recognition, pp. 792–801 (2011)Google Scholar
  9. 9.
    Fumin, S., Chunhua, S., Anton, H., Zhenmin, T.: Approximate least trimmed sum of squares fitting and applications in image analysis. IEEE Trans. Image Process. 22(5), 1836–1847 (2013)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Fumin, S., Chunhua, S., Rhys, H., Anton, H., Zhenmin, T.: Fast approximate \(L_\infty \) minimization: speeding up robust regression. Comput. Stat. Data Anal. 77, 25–37 (2014)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Fumin, S., Wankou, Y., et al.: Robust regression based face recognition with fast outlier removal. Multimed. Tools Appl. 1–12 (2014)Google Scholar
  12. 12.
    Zhuang, L., Gao, H., Lin, Z., Ma, Y., Zhang, X., Yu, N.: Non-negative low rank and sparse graph for semi-supervised learning. IEEE Conference on Computer Vision and Pattern Recognition pp. 2328–2335 (2012)Google Scholar
  13. 13.
    Ma, L., Wang, C., Xiao, B., Zhou, W.: Sparse representation for face recognition based on discriminative low-rank dictionary learning. IEEE Conference on Computer Vision and Pattern Recognition, pp. 2586–2593 (2012)Google Scholar
  14. 14.
    Zhang, Y., Jiang, Z., Davis, L.S.: Learning structured low-rank representations for image classification. IEEE Conference on Computer Vision and Pattern Recognition, pp. 676–683 (2013)Google Scholar
  15. 15.
    Candés, E.J., Li, X., Ma, Y., Wright, J.: Robust principal component analysis? JACM 58(3) (2011)Google Scholar
  16. 16.
    Cai, J.F., Candés, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 4, 1956–1982 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Computer Science and Applied Mathematics, vol. 1, pp. 234–243. Academic Press, Boston (1982)Google Scholar
  18. 18.
    Lin, Z., Liu, R., Su, Z.: Linearized alternating direction method with adaptive penalty for low rank representation. In NIPS (2011)Google Scholar
  19. 19.
  20. 20.
  21. 21.
  22. 22.
  23. 23.
  24. 24.
  25. 25.
    Zhu, X., Ghahramani, Z., Lafferty, J.: Semi-supervised learning using Gaussian fields and harmonic functions. ICML 20, 912–919 (2003)Google Scholar
  26. 26.
    Zhou, D., Bousquet, O., Lal, T., Weston, J., Schölkopf, B.: Learning with local and global consistency. In NIPS, pp. 595–602 (2004)Google Scholar
  27. 27.
    Yan, S., Wang, H.: Semi-supervised learning by sparse representation, pp. 792–801. In SIAM International Conference on Data Mining, SDM (2009)Google Scholar
  28. 28.
    Wright, J., Ma, Y., Mairal, J., Sapiro, G., Huang, T.S., Yan, S.: Sparse representation for computer vision and pattern recognition. Proc. IEEE 98(6), 1031–1044 (2010)CrossRefGoogle Scholar
  29. 29.
    Cai, D., He, X., Han, J.: Semi-supervised discriminant analysis. IEEE 11th International Conference on Computer Vision, pp. 1–7 (2007)Google Scholar
  30. 30.
    Li, Y., Liu, J., Lu, H., et al.: Learning robust face representation with classwise block-diagonal structure. IEEE Trans. Inf. Forensics Secur. 9(12), 2051–2062 (2014)CrossRefGoogle Scholar
  31. 31.
    Yang, S., Feng, Z., Ren, Y., et al.: Semi-supervised classification via kernel low-rank representation graph. Knowledge-Based Syst. 69, 150–158 (2014)CrossRefGoogle Scholar
  32. 32.
    Yang, S., Wang, X., Wang, M., et al.: Semi-supervised low-rank representation graph for pattern recognition. IET Image Process. 7(2), 131–136 (2013)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Chen, C. F., Wei, C. P., Wang, Y. C. F.: Low-rank matrix recovery with structural incoherence for robust face recognition. Computer Vision and Pattern Recognition (CVPR), 2012 IEEE Conference on IEEE, pp. 2618–2625 (2012)Google Scholar
  34. 34.
    Wright, J., Ganesh, A., Rao, S., et al.: Robust principal component analysis: exact recovery of corrupted low-rank matrices via convex optimization. Advances in neural information processing systems, pp. 2080–2088 (2009)Google Scholar
  35. 35.
    Wright, J., Yang, A.Y., Ganesh, A., et al.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 210–227 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  • Chenxue Yang
    • 1
  • Mao Ye
    • 1
    Email author
  • Song Tang
    • 1
  • Tao Xiang
    • 1
  • Zijian Liu
    • 2
  1. 1.School of Computer Science and Engineering, Center for Robotics, Key Laboratory for NeuroInformation of Ministry of EducationUniversity of Electronic Science and Technology of ChinaChengduPeople’s Republic of China
  2. 2.School of ScienceChongqingjiaotong UniversityChongqingPeople’s Republic of China

Personalised recommendations