Skip to main content
SpringerLink
Log in

Fisher discrimination-based \(l_{2,1} \)-norm sparse representation for face recognition

  • Original Article
  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

In recent years, sparse representation-based classification (SRC) has made great progress in face recognition (FR). However, SRC emphasizes noise sparsity too much and it is not suitable for the real world. In this paper, we propose a robust \(l_{2,1}\)-norm Sparse Representation framework that constrains the noise penalty by the \(l_{2,1}\)-norm. The \(l_{2,1} \)-norm takes advantage of both the discriminative nature of the \(l_1 \)-norm and the systemic representation of the \(l_2 \)-norm. In addition, we use the nuclear norm to constrain the coefficient matrix. Motivated by the Fisher criterion, we propose the Fisher discriminant-based \(l_{2,1} \)-norm sparse representation method for FR which utilizes a supervised approach. Thus, we consider the within-class scatter and between-class scatter when all of the label information is available. The paper shows that the model can provide stronger discriminant power than the classical sparse representation models and can be solved by the alternating direction method of multiplier. Additionally, it is robust to the contiguous occlusion noise. Extensive experiments demonstrate that our method achieves significantly better results than SRC and some other sparse representation methods for FR when addressing large regions with contiguous occlusion.

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
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Zhao, W., Chellappa, R., Phillips, P., Rosenfeld, A.: Face recognition: a literature survey. ACM Comput. Surv. 35(4), 399–458 (2003)

    Article  Google Scholar 

  2. Bartlett, M., Movellan, J., Sejnowski, T.: Face recognition by independent component analysis. IEEE Trans. Neural Netw. 13(6), 1450–1464 (2002)

    Article  Google Scholar 

  3. Belhumeur, P., Hespanha, J., Kriegman, D.: Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans. Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)

    Article  Google Scholar 

  4. Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cognit. Neurosci. 3(1), 71–86 (1991)

    Article  Google Scholar 

  5. Zhang, B., Gao, Y., Zhao, S., Liu, J.: Local derivative pattern versus local binary pattern: face recognition with high-order local pattern descriptor. IEEE Trans. Image Process. 19(2), 533–544 (2010)

    Article  MathSciNet  Google Scholar 

  6. Tan, X., Triggs, B.: Enhanced local texture feature sets for face recognition under difficult lighting conditions. IEEE Trans. Image Process. 19(6), 1635–1650 (2010)

    Article  MathSciNet  Google Scholar 

  7. Ahonen, T., Hadid, A., Pietikainen, M.: Face description with local binary patterns: application to face recognition. IEEE Trans. Pattern Anal. Mach. Intell. 28(12), 2037–2041 (2006)

    Article  MATH  Google Scholar 

  8. Ortiz, E.G., Wright, A., Shah, M.: Face recognition in movie trailers via mean sequence sparse representation-based classification. In: Proceedings of the IEEE Conference CVPR, pp. 3531–3538 (2013)

  9. Ocegueda, O., Fang, T., Shah, S., Kakadiaris, I.: 3D-face discriminant analysis using Gauss–Markov posterior marginals. IEEE Trans. Pattern Anal. Mach. Intell. 35(3), 728–739 (2013)

    Article  Google Scholar 

  10. Quan, W., Jiang, Y., Zhang, J., Chen, J.X.: Robust object tracking with active context learning. Vis. Comput. 31(10), 1307–1318 (2015)

    Article  Google Scholar 

  11. Dawn, D.D., Shaikh, S.H.: A comprehensive survey of human action recognition with spatio-temporal interest point (STIP) detector. Vis. Comput. 1–18 (2015). doi:10.1007/s00371-015-1066-2

  12. Wu, J.Z., Hu, D., Chen, F.L.: Action recognition by hidden temporal models. Vis. Comput. 30(12), 1395–1404 (2013)

    Article  Google Scholar 

  13. Hong, J., Aleix, M.: Support vector machines in face recognition with occlusions. In: Conference on Computer Vision and Pattern Recognition, IEEE, pp. 136–141 (2009)

  14. Tan, X., Chen, S., Zhou, Z.H., Liu, J.: Face recognition under occlusions and variant expressions with partial similarity. IEEE Trans. Inf. Forens. Secur. 4(2), 217–230 (2009)

    Article  Google Scholar 

  15. Lee, D., Seung, H., et al.: Learning the parts of objects by non-negative matrix factorization. Nature 401(6755), 788–791 (1999)

    Article  Google Scholar 

  16. Yuen, P., Lai, J.: Face representation using independent component analysis. Pattern Recognit. 35(6), 1247–1257 (2002)

    Article  MATH  Google Scholar 

  17. Liu, C., Wechsler, H.: Gabor feature based classification using the enhanced fisher linear discriminant model for face recognition. IEEE Trans. Image Process. 11(4), 467–476 (2002)

    Article  Google Scholar 

  18. Zhou, Z., Wagner, A., Mobahi, H., Wright, J., Ma, Y.: Face recognition with contiguous occlusion using Markov random fields. In: International Conference on Computer Vision, IEEE, pp. 1050–1057 (2009)

  19. Olshausen, B.A., Field, D.J.: Sparse coding with an over-complete basis set: a strategy employed by v1? Vis. Res. 37(23), 3311–3325 (1997)

    Article  Google Scholar 

  20. Vinje, W.E., Gallant, J.L.: Sparse coding and decorrelation in primary visual cortex during natural vision. Science 287(5456), 1273–1276 (2000)

    Article  Google Scholar 

  21. Yuan, X., Yan, S.: Visual classification with multi-task joint sparse representation. In: 2010 IEEE conference on computer vision and pattern recognition (CVPR), vol. 21, pp. 3493–3500. IEEE, San Francisco, CA (2010)

  22. Jenatton, R., Mairal, J., Obozinski, G., Bach, F.: Proximal methods for hierarchical sparse coding. J. Mach. Learn. Res. 12, 2297–2334 (2011)

    MathSciNet  MATH  Google Scholar 

  23. Chao, Y.W., Yeh, Y.R., Chen, Y.W., Lee, Y.J., Wang, Y.C.F.: Locality-constrained group sparse representation for robust face recognition. In: 18th IEEE international conference on image processing (ICIP), vol. 263, pp. 761–764. IEEE, Brussels (2011)

  24. Wright, J., Yang, A., Ganesh, A., Sastry, S., Ma, Y.: Robust face recognition via sparse representation. IEEE Trans. Pattern Anal. Mach. Intell. 31(2), 210–227 (2009)

    Article  Google Scholar 

  25. Wright, J., Ma, Y., Mairal, J., Ssairo, G., Huang, T., Yan, S.C.: Sparse representation for computer vision and pattern recognition. Proc. IEEE 98(6), 1031–1044 (2010)

    Article  Google Scholar 

  26. Yang, M., Zhang, L., Yang, J., Zhang, D.: Robust sparse coding for face recognition. In: 2011 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 47, pp. 625–632. IEEE, Providence, RI (2011)

  27. Huang, K., Aviyente, S.: Sparse representation for signal classification. Adv. Neural Inf. Process. Syst. 19, 609–616 (2007)

    Google Scholar 

  28. Wagner, A., Wright, J., Ganesh, A., Zhou, Z.H., Ma, Y.: Towards a practical face recognition system: robust registration and illumination by sparse representation. In: 2009 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 34, pp. 597–604. IEEE, Miami, FL (2009)

  29. Candes, E.J., Li, X.D., Ma, Y., Wright, J.: Robust principal component analysis? J. ACM 58(1), 1–37 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  30. Wanger, A., Wright, J., Ganesh, A., Zhou, Z.H., Ma, Y.: Towards a practical face recognition system: robust registration and illumination by sparse representation. IEEE Pattern Anal. Mach. Intell. 34(2), 372–386 (2012)

    Article  Google Scholar 

  31. Wang, J., Lu, C.Y., Wang, M., Li, P.P.: Robust face recognition via adaptive sparse representation. IEEE Trans. Cybern. 44(12), 2368–2378 (2014)

  32. Edouard, G., Guillaume, O., Francis, B.: Trace lasso: a trace norm regularization for correlated designs. In: Proceedings of the Advances in Neural Information Processing Systems, pp. 2187–2195 (2011)

  33. Ou, W.H., You, X.G., Tao, D.C., Zhang, P.Y., et al.: Robust face recognition via occlusion dictionary learning. Pattern Recognit. 47, 1559–1572 (2014)

    Article  Google Scholar 

  34. Lee, H., Battle, A., Raina, R., Ng, A.Y.: Efficient sparse coding algorithms. Adv. Neural Inf. Process. Syst. 19, 801–808 (2007)

    Google Scholar 

  35. Zhang, Z.L., Yu, M., Jia, J., Liu, H., et al.: Fisher discriminant based low rank matrix recovery for face recognition. Pattern Recognit. 47, 3502–3511 (2014)

    Article  Google Scholar 

  36. Liu, G., Lin, Z., Yu, Y.: Robust subspace segmentation by low-rank representation. In: Proceedings of the ICML, pp. 663–670 (2010)

  37. Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs fisherface: recognition using class specific linear projection. IEEE Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)

    Article  Google Scholar 

  38. Li, Z., Lin, D., Tang, X.: Nonparametric discriminant analysis for face recognition. IEEE Pattern Anal. Mach. Intell. 31(4), 755–761 (2009)

    Article  Google Scholar 

  39. Lu, J., Tan, Y., Wang, G.: Discriminative multi-manifold analysis for face recognition from a single training sample per person. IEEE Pattern Anal. Mach. Intell. 35(1), 39–51 (2013)

  40. Hua, G., Viola, P., Drucker, S.: Face recognition using discriminatively trained orthogonal rank one tensor projections. In: IEEE Conference on Computer Vision and Pattern Recognition, 2007, CVPR ’07, vol. 7, pp. 1–8. IEEE, Minneapolis, MN (2007)

  41. Gao, Q., Liu, J., Zhang, H., Hou, J., Yang, X.: Enhanced fisher discriminant criterion for image classification. Pattern Recognit. 45(10), 3717–3724 (2012)

    Article  Google Scholar 

  42. Gao, Q., Ma, J., Zhang, H., Gao, X., Liu, Y.: Stable orthogonal discriminant embedding for linear dimensionality reduction. IEEE Trans. Image Process. 22(7), 2521–2531 (2013)

    Article  Google Scholar 

  43. Yang, J., Chu, D., Zhang, L.: Sparse representation classifier steered discriminative projection with applications to face recognition. IEEE Trans. Neural Netw. Learn. Syst. 24(7), 1023–1035 (2013)

    Article  Google Scholar 

  44. Zhang, N., Yang, J.: Low-rank representation based discriminative projection for robust feature extraction. Neurocomputing 111(2), 13–20 (2013)

    Article  Google Scholar 

  45. Ding, C., Zhou, D., He, X.F., Zha, H.Y.: R1-PCA: rotational invariant L1-norm principal component analysis for robust subspace factorization. In: Proceeding of the 23th International Conference on Machine Learning, pp. 281–288 (2006)

  46. Liu, G., Lin, Z., Yan, S., Sun, J., Yu, Y., Ma, Y.: Robust recovery of subspace structures by low-rank representation. IEEE Pattern Anal. Mach. Intell. 35(1), 171–184 (2013)

    Article  Google Scholar 

  47. Belhumeur, P.N., Hespanha, J.P., Kriegman, D.J.: Eigenfaces vs fisherfaces: recognition using class specific linear projection. IEEE Pattern Anal. Mach. Intell. 19(7), 711–720 (1997)

    Article  Google Scholar 

  48. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  49. Qian, J.J., Yang, J., Zhang, F.L., Lin, Z.C.: Robust low-rank regularized regression for face recognition with occlusion. In: Computer Vision and Pattern Recognition Workshops, pp. 21–26 (2014)

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

    Article  MathSciNet  MATH  Google Scholar 

  51. Cai, J.F., Candes, E.J., Shen, Z.: A singular value thresholding algorithm for matrix completion. SIAM J. Optim. 20(4), 1956–1982 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  52. Yang, M., Zhang, L., Feng, X.C., Zhang, D.: Fisher discrimination dictionary learning for sparse representation. In: 2011 IEEE International Conference on Computer Vision (ICCV), pp. 543–550. IEEE, Barcelona (2011)

  53. Can, C.Y., Min, H., Gui, J., Zhu, L., Lei, Y.K.: Face recognition via weighted sparse representation. J. Vis. Commun. Image R 24, 111–116 (2013)

    Article  Google Scholar 

  54. Lee, K., Ho, J., Kriegman, D.: Acquiring linear subspaces for face recognition under variable lighting. IEEE Trans. Pattern Anal. Mach. Intell. 27(5), 684–698 (2005)

    Article  Google Scholar 

  55. Georghiades, A., Belhumeur, P., Kriegman, D.: From few to many: illumination cone models for face recognition under variable lighting and pose. IEEE Trans. Pattern Anal. Mach. Intell. 23(6), 643–660 (2001)

    Article  Google Scholar 

Download references

Acknowledgments

The research project was supported by the National Natural Foundation of China under Grant No. 61390510, 61300065, 61370119, 61171169 and Beijing Natural Science Foundation No. 4132013, 4142010 and supported by the Beijing science and technology project No. Z151100002115040, and also supported by PHR(IHLB).

Author information

Authors and Affiliations

  1. Beijing Key Laboratory of Multimedia and Intelligent Software Technology, College of Metropolitan Transportation, Beijing University of Technology, Beijing, 100124, China

    Lu Zhao, Yong Zhang, Baocai Yin, Yanfeng Sun, Yongli Hu, Xinglin Piao & Qianjun Wu

  2. School of Software Technology, Dalian University of Technology, Dalian, 116024, China

    Baocai Yin

  3. Collaborative Innovation Center of Electric Vehicles in Beijing, Beijing, China

    Baocai Yin

Authors
  1. Lu Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yong Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Baocai Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanfeng Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yongli Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Xinglin Piao
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Qianjun Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lu Zhao.

Appendix

Appendix

Definitions of \(R_1,R_2,Q,{\hat{Q}}\).

Let \(E_i =[1]_{n_i \times n_i } \) be a matrix of size \(n_i \times n_i \) with all entries being 1, and let \(R_1 =I_{n\times n} -\hbox {diag}(E_i)/n\), \(i=[1,2,\ldots ,c]\); \(R_2 =1/n\,\hbox {diag}(E_i )-1/{nc}\,I_{n\times n};\) \(R(A)=\sum \nolimits _{i=1}^c {\sum _{\begin{array}{c} j=1 \\ j\ne i \end{array}}^c {\Vert {D_j A_i^j}\Vert }_F^2 }, A_i^j\) is the coding coefficient of \(Y_i\) over the sub-dictionary \(D_j\), \(A_i^j\) should have nearly zero coefficients, and thus, we use a select matrix Q with a dot product for the constraint. To facilitate the calculation, we use each row vector of the matrix Q as a diagonal, expanding to a diagonal matrix \({\hat{Q}}\).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhao, L., Zhang, Y., Yin, B. et al. Fisher discrimination-based \(l_{2,1} \)-norm sparse representation for face recognition. Vis Comput 32, 1165–1178 (2016). https://doi.org/10.1007/s00371-015-1169-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00371-015-1169-9

Keywords

Search

Navigation