Generalized Discriminant Local Median Preserving Projections (GDLMPP) for Face Recognition

  • Ming-Hua Wan
  • Zhi-Hui Lai


To solve the problem of the singularity of the within-class scatter matrix in discriminant local median preserving projections (DLMPP) in the case of small sample size problem, an algorithm named generalized local median preserving projection (GDLMPP) is proposed. To solve the small size problem, GDLMPP firstly transforms the samples into a lower dimensional space equivalently, and then the optimal projection matrix can be solved. The theoretical analysis shows that GDLMPP is equivalent to DLMPP when the within-class scatter matrix is non-singular. Finally, we conduct extensive experiments to prove that the proposed algorithm can provide a better representation and achieve higher face recognition rates than previous approaches such as LPP, LDA and DLMPP on the ORL, Yale and AR face databases.


Face recognition Feature extraction Small sample size problem Discriminant local median preserving projections 



This work is partially supported by National Key R&D Program Grant No. 2017YFC0804002, the National Science Foundation of China under Grant Nos. 61462064, 6177227, 61362031, 61463008, 61403188, 61503195, 61603192, and the China Postdoctoral Science Foundation under Grant No. 2016M600674, the Natural Science Fund of Jiangsu Province under Grant BK20161580, BK20171494 and China’s Aviation Science (No. 20145556011).


  1. 1.
    Yang W, Sun C, Zhang L (2011) A multi-manifold discriminant analysis method for image feature extraction. Pattern Recogn 44(8):1649–1657CrossRefzbMATHGoogle Scholar
  2. 2.
    Yang W, Wang J, Ren M et al (2009) Feature extraction based on Laplacian bidirectional maximum margin criterion. Pattern Recogn 42(11):2327–2334CrossRefzbMATHGoogle Scholar
  3. 3.
    Yang W, Wang Z, Sun C (2015) A collaborative representation based projections method for feature extraction. Pattern Recogn 48(1):20–27CrossRefGoogle Scholar
  4. 4.
    Turk M, Pentland A (1991) Eigenfaces for recognition. J Cogn Neurosci 3(1):71–86CrossRefGoogle Scholar
  5. 5.
    Vidal R, Ma Y, Sastry SS (2016) Robust principal component analysis. Generalized principal component analysis. Springer, New York, pp 63–122zbMATHGoogle Scholar
  6. 6.
    Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711–720CrossRefGoogle Scholar
  7. 7.
    Wang S, Lu J, Gu X et al (2016) Semi-supervised linear discriminant analysis for dimension reduction and classification. Pattern Recogn 57:179–189CrossRefGoogle Scholar
  8. 8.
    He XF, Yan SC, Hu YX et al (2005) Face recognition using Laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):328–340CrossRefGoogle Scholar
  9. 9.
    Wen Y, Yang S, Hou L, et al (2016) Face recognition using locality sparsity preserving projections. In: 2016 international joint conference on neural networks (IJCNN), IEEE, pp 3600–3607Google Scholar
  10. 10.
    Yu WW, Teng XL, Liu CQ (2006) Face recognition using discriminant locality preserving projections. Image Vis Comput 24(3):239–248CrossRefGoogle Scholar
  11. 11.
    Huang P, Tang Z (2012) Discriminant of local median preserving projection with its application to face recognition. J Comput Aided Des Comput Graph 24(11):1420–1425Google Scholar
  12. 12.
    Wan M, Li M, Yang G, Gai S, Jin Z (2014) Feature extraction using two-dimensional maximum embedding difference. Inf Sci 274:55–69CrossRefGoogle Scholar
  13. 13.
    Lai Z, Wong W, Xu Y, Yang J, Tang J, Zhang D (2016) Approximate orthogonal sparse embedding for dimensionality reduction. IEEE Trans Neural Netw Learn Syst 27(4):723–735MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ning X, Li W, LI H et al (2016) Uncorrelated local preserving discriminant analysis based on bionics. J Comput Res Dev 53(11):2623–2629Google Scholar
  15. 15.
    Ma X, Tan Y (2014) Face recognition based on discriminant sparse preserving embedding. Acta Automatica Sinica 40(1):73–82zbMATHGoogle Scholar
  16. 16.
    Zhao Z, Hao X (2013) Linear locality preserving and discriminating projection for face recognition. J Electron Inf Technol 35(2):463–467CrossRefGoogle Scholar
  17. 17.
    Yin J, Zeng W, Wei L (2016) Optimal feature extraction methods for classification methods and their applications to biometric recognition. Knowl Based Syst 99:112–122CrossRefGoogle Scholar
  18. 18.
    Yin J, Wei L, Song M, Zeng W (2016) Optimized projection for collaborative representation based classification and its applications to face recognition. Pattern Recogn Lett 73:83–90CrossRefGoogle Scholar
  19. 19.
    Wan M, Lai Z, Yang G et al (2017) Local graph embedding based on maximum margin criterion via fuzzy set. Fuzzy Sets Syst 318:120–131MathSciNetCrossRefGoogle Scholar
  20. 20.
    Yang J, Zhang D, Yang J et al (2007) Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics. IEEE Trans Pattern Anal Mach Intell 29(4):650–664MathSciNetCrossRefGoogle Scholar

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

Authors and Affiliations

  1. 1.College of Computer Science and Software EngineeringShenzhen UniversityShenzhenChina
  2. 2.School of TechnologyNanjing Audit UniversityNanjingChina

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