Skip to main content
SpringerLink
Log in

Nonnegative representation based discriminant projection for face recognition

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

Dimensionality reduction (DR) has been widely used to deal with high-dimensional data, and plays an important role in alleviating the so-called “curse of dimensionality”. In this paper, we propose a novel unsupervised DR method with applications to face recognition, i.e., Nonnegative Representation based Discriminant Projection (NRDP). Different with other locality or globality preserving DR methods, NRDP focuses on both locality and nonlocality of data points and learns a discriminant projection by maximizing the nonlocal scatter and minimizing the local scatter simultaneously. A nonnegative representation model is designed in NRDP to discover the local structure and nonlocal structure of data. The \(\ell _1\)-norm is used as metric in nonnegative representation to enhance the robustness against noises, and an iterative algorithm is presented to solve the optimization model. NRDP is able to learn features with large inter-class or subspace scatter and small intra-class scatter in the case that label information is unavailable, which significantly improves the representation power and discrimination. Experimental results on several popular face datasets demonstrate the effectiveness of our proposed method.

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

Similar content being viewed by others

Notes

  1. http://www.briancbecker.com/blog/research/pubfig83-lfw-dataset/

References

  1. Li Z, Liu J, Tang J, Lu H (2015) Robust structured subspace learning for data representation. IEEE Trans Pattern Anal Mach Intell 37(10):2085–2098

    Google Scholar 

  2. Zhang X, Mei C, Chen D, Li J (2016) Feature selection in mixed data: a method using a novel fuzzy rough set-based information entropy. Pattern Recognit 56:1–15

    MATH  Google Scholar 

  3. Zhang W, Kang P, Fang X, Teng L, Han N (2019) Joint sparse representation and locality preserving projection for feature extraction. Int J Mach Learn Cybern 10(7):1731–1745

    Google Scholar 

  4. Wang H, Lu X, Hu Z, Zheng W (2013) Fisher discriminant analysis with l1-norm. IEEE Trans Cybern 44(6):828–842

    Google Scholar 

  5. Li H, Zhang L, Huang B, Zhou X (2020) Cost-sensitive dual-bidirectional linear discriminant analysis. Inf Sci 510:283–303

    MathSciNet  Google Scholar 

  6. Huang Z, Zhu H, Zhou JT, Peng X (2019) Multiple marginal fisher analysis. IEEE Trans Industrial Electron 66(12):9798–9807

    Google Scholar 

  7. Sun W, Xie S, Han N (2019) Robust discriminant analysis with adaptive locality preserving. Int J Mach Learn Cybern 10(10):2791–2804

    Google Scholar 

  8. Peng X, Yuan M, Yu Z, Yau WY, Zhang L (2016) Semi-supervised subspace learning with l2graph. Neurocomputing 208:143–152

    Google Scholar 

  9. Liu Z, Wang X, Pu J, Wang L, Zhang L (2017) Nonnegative low-rank representation based manifold embedding for semi-supervised learning. Knowl Based Syst 136:121–129

    Google Scholar 

  10. Yang J, Zhang D, Frangi AF, Yang JY (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans Pattern Anal Mach Intell 26(1):131–137

    Google Scholar 

  11. Lai Z, Wong WK, Xu Y, Yang J, Zhang D (2015) Approximate orthogonal sparse embedding for dimensionality reduction. IEEE Trans Neural Netw Learn Syst 27(4):723–735

    MathSciNet  Google Scholar 

  12. Liu G, Yan S (2011) Latent low-rank representation for subspace segmentation and feature extraction. In: ICCV, IEEE, pp 1615–1622

  13. Peng X, Lu J, Yi Z, Yan R (2016) Automatic subspace learning via principal coefficients embedding. IEEE Trans Cybern 47(11):3583–3596

    Google Scholar 

  14. Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 7:711–720

    Google Scholar 

  15. Yan S, Xu D, Zhang B, Zhang HJ, Yang Q, Lin S (2006) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40–51

    Google Scholar 

  16. Wen J, Fang X, Cui J, Fei L, Yan K, Chen Y, Xu Y (2018) Robust sparse linear discriminant analysis. IEEE Trans Circuits Syst Video Technol 29(2):390–403

    Google Scholar 

  17. Li X, Chen M, Nie F, Wang Q (2017) Locality adaptive discriminant analysis. In: IJCAI, pp 2201–2207

  18. Kang Z, Pan H, Hoi SCH, Xu Z (2020) Robust graph learning from noisy data. IEEE Trans Cybern 50(5):1833–1843

    Google Scholar 

  19. Lu Y, Lai Z, Xu Y, Li X, Zhang D, Yuan C (2016) Low-rank preserving projections. IEEE Trans Cybern 46(8):1900–1913

    Google Scholar 

  20. Liu G, Lin Z, Yan S, Sun J, Yu Y, Ma Y (2012) Robust recovery of subspace structures by low-rank representation. IEEE Trans Pattern Anal Mach Intell 35(1):171–184

    Google Scholar 

  21. Yin M, Gao J, Lin Z (2016) Laplacian regularized low-rank representation and its applications. IEEE Trans Pattern Anal Mach Intell 38(3):504–517

    Google Scholar 

  22. He X, Niyogi P (2004) Locality preserving projections. In: NeurIPS, pp 153–160

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

    Google Scholar 

  24. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323–2326

    Google Scholar 

  25. He X, Cai D, Yan S, Zhang HJ (2005) Neighborhood preserving embedding. ICCV 2:1208–1213

    Google Scholar 

  26. Lu GF, Lin Z, Jin Z (2010) Face recognition using discriminant locality preserving projections based on maximum margin criterion. Pattern Recognit 43(10):3572–3579

    MATH  Google Scholar 

  27. Chen S, Ding CHQ, Luo B (2018) Linear regression based projections for dimensionality reduction. Inf Sci 467:74–86

    MathSciNet  MATH  Google Scholar 

  28. Wang J, Zhao R, Wang Y, Zheng C, Kong J, Yi Y (2017) Locality constrained graph optimization for dimensionality reduction. Neurocomputing 245:55–67

    Google Scholar 

  29. Lu J, Tan YP (2009) Regularized locality preserving projections and its extensions for face recognition. IEEE Trans Syst Man, Cybern B, Cybern 40(3):958–963

    MathSciNet  Google Scholar 

  30. Wen J, Han N, Fang X, Fei L, Yan K, Zhan S (2019) Low-rank preserving projection via graph regularized reconstruction. IEEE Trans Cybern 49(4):1279–1291

    Google Scholar 

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

    Google Scholar 

  32. Wright J, Yang AY, Ganesh A, Sastry SS, Ma Y (2008) Robust face recognition via sparse representation. IEEE Trans Pattern Anal Mach Intell 31(2):210–227

    Google Scholar 

  33. Lai Z, Xu Y, Chen Q, Yang J, Zhang D (2014) Multilinear sparse principal component analysis. IEEE Trans Neural Netw Learn Syst 25(10):1942–1950

    Google Scholar 

  34. Cheng B, Yang J, Yan S, Fu Y, Huang TS (2010) Learning with \(\ell ^{1}\)-graph for image analysis. IEEE Trans Image Process 19(4):858–866

    MathSciNet  MATH  Google Scholar 

  35. Song Z, Cui K, Cheng G (2020) Image set face recognition based on extended low rank recovery and collaborative representation. Int J Mach Learn Cybern 11(1):71–80

    Google Scholar 

  36. Qiao L, Chen S, Tan X (2010) Sparsity preserving projections with applications to face recognition. Pattern Recognit 43(1):331–341

    MATH  Google Scholar 

  37. Yang W, Wang Z, Sun C (2015) A collaborative representation based projections method for feature extraction. Pattern Recognit 48(1):20–27

    Google Scholar 

  38. Peng X, Yu Z, Yi Z, Tang H (2017) Constructing the l2-graph for robust subspace learning and subspace clustering. IEEE Trans Cybern 47(4):1053–1066

    Google Scholar 

  39. Zhang L, Chen S, Qiao L (2012) Graph optimization for dimensionality reduction with sparsity constraints. Pattern Recognit 45(3):1205–1210

    MATH  Google Scholar 

  40. Wang L, Wu HY, Pan C (2015) Manifold regularized local sparse representation for face recognition. IEEE Trans Circuits Syst Video Techn 25(4):651–659

    Google Scholar 

  41. Yang W, Li J, Zheng H, Xu RYD (2018) A nuclear norm based matrix regression based projections method for feature extraction. IEEE Access 6:7445–7451

    Google Scholar 

  42. Yang W, Sun C, Zheng W (2016) A regularized least square based discriminative projections for feature extraction. Neurocomputing 175:198–205

    Google Scholar 

  43. Gui J, Sun Z, Jia W, Hu R, Lei Y, Ji S (2012) Discriminant sparse neighborhood preserving embedding for face recognition. Pattern Recognit 45(8):2884–2893

    MATH  Google Scholar 

  44. Wen J, Zhang B, Xu Y, Yang J, Han N (2018) Adaptive weighted nonnegative low-rank representation. Pattern Recognit 81:326–340

    Google Scholar 

  45. Cai D, He X, Han J, Huang TS (2010) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33(8):1548–1560

    Google Scholar 

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

    MATH  Google Scholar 

  47. Chen C, Chan RH, Ma S, Yang J (2015) Inertial proximal admm for linearly constrained separable convex optimization. SIAM J Imaging Sci 8(4):2239–2267

    MathSciNet  MATH  Google Scholar 

  48. Yang J, Zhang Y (2011) Alternating direction algorithms for \(\ell _1\)-problems in compressive sensing. SIAM J Sci Comput 33(1):250–278

    MathSciNet  Google Scholar 

  49. Georghiades AS, Belhumeur PN, Kriegman DJ (2001) From few to many: Illumination cone models for face recognition under variable lighting and pose. IEEE Trans Pattern Anal Mach Intell 6:643–660

    Google Scholar 

  50. Martinez AM, Benavente R (1998) The AR face database. Tech. rep, CVC, Barcelona, Spain

  51. Sim T, Baker S, Bsat M (2003) The CMU Pose, Illumination, and expression database. IEEE Trans Pattern Anal Mach Intell 25(12):1615–1618

    Google Scholar 

  52. Pinto N, Stone Z, Zickler T, Cox D (2011) Scaling up biologically-inspired computer vision: a case study in unconstrained face recognition on facebook. In: CVPR Workshops, pp 35–42

  53. Zhu P, Zuo W, Zhang L, Hu Q, Shiu SCK (2015) Unsupervised feature selection by regularized self-representation. Pattern Recognit 48(2):438–446

    MATH  Google Scholar 

  54. Tang C, Zhu X, Chen J, Wang P, Liu X, Tian J (2018) Robust graph regularized unsupervised feature selection. Expert Syst Appl 96:64–76

    Google Scholar 

  55. Van der Maaten L, Hinton G (2008) Visualizing data using t-sne. J Mach Learn Res 9:2579–2605

    MATH  Google Scholar 

  56. Becker B, Ortiz E (2013) Evaluating open-universe face identification on the web. In: CVPR Workshops, pp 904–911

Download references

Acknowledgements

The authors would like to thank the editor and anonymous reviewers for their constructive comments. This work was partially supported by the National Key Research and Development Program of China (Nos. 2018YFB1402600, 2016YFD0702100), and the National Natural Science Foundation of China (Nos. 71671086, 61876079).

Author information

Authors and Affiliations

  1. Department of Control and Systems Engineering, Nanjing University, Nanjing, 210093, China

    Chao Zhang, Huaxiong Li, Chunlin Chen & Xianzhong Zhou

  2. Research Center for Novel Technology of Intelligent Equipment, Nanjing University, Nanjing, 210093, China

    Huaxiong Li, Chunlin Chen & Xianzhong Zhou

Authors
  1. Chao Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Huaxiong Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chunlin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xianzhong Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Huaxiong Li.

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

Zhang, C., Li, H., Chen, C. et al. Nonnegative representation based discriminant projection for face recognition. Int. J. Mach. Learn. & Cyber. 12, 733–745 (2021). https://doi.org/10.1007/s13042-020-01199-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-020-01199-z

Keywords

Search

Navigation