Skip to main content
Springer Nature Link
Log in

Face recognition using fuzzy maximum scatter discriminant analysis

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

As we know, classical Fisher discriminant analysis usually suffers from the small sample size problem due to the singularity problem of the within-class scatter matrix. In this paper, a novel fuzzy linear classifier, called fuzzy maximum scatter difference (FMSD) discriminant criterion, is proposed to extract features from samples, especially deals with outlier samples. FMSD takes the scatter difference between between-class and within-class as discriminant criterion, so it will not suffer from the small sample size problem. The conventional scatter difference discriminant criterion (SDDC) assumes the same level of relevance of each sample to the corresponding class. In this paper, the fuzzy set theory is introduced to the conventional SDDC algorithm, where the fuzzy k-nearest neighbor is adopted to achieve the distribution information of original samples. The distribution is utilized to redefine the scatter matrices that are different from the conventional SDDC and effective to extract discriminative features from outlier samples. Experiments conducted on FERET and ORL face databases demonstrate the effectiveness of the 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

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Chen LF, Liao HYM, Ko MT et al (2000) A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recogn 33(10):1713–1726

    Article  Google Scholar 

  2. Yu H, Yang J (2001) A direct LDA algorithm for high-dimensional data with application to face recognition. Pattern Recogn 34(10):2067–2070

    Article  MATH  Google Scholar 

  3. Zhao W, Chellappa R, Phillips J (1999) Subspace linear discriminant analysis for face recognition. Technical Report CS-TR4009, University of Maryland

  4. Yang J, Yang JY (2003) Why can LDA be performed in PCA transformed space? Pattern Recogn 36(2):563–566

    Article  Google Scholar 

  5. Zhuang XS, Dai DQ (2007) Improved discriminant analysis for high-dimensional data and its application to face recognition. Pattern Recogn 40(5):1570–1578

    Article  MATH  Google Scholar 

  6. Swets DL, Weng J (1996) Using discriminant eigenfeatures for image retrieval. IEEE Trans Pattern Anal Mach Intell 18(8):831–836

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Song FX, Cheng K, Yang JY et al (2004) Maximum scatter difference, large margin linear projection and support vector machines. Acta automatica sinica 30(6):890–896 (in Chinese)

    MathSciNet  Google Scholar 

  9. Zhang X-D (2004) Matrix analysis and application (in Chinese). Tsinghua University Press, Beijing

    Google Scholar 

  10. Heo G, Gader P (2011) Robust kernel discriminant analysis using fuzzy memberships. Pattern Recogn 44(3):716–723

    Article  MATH  Google Scholar 

  11. Jain AK, Duin RPW, Mao J (2000) Statistical pattern recognition: a review. IEEE Trans Pattern Anal Mach Intell 22(1):4–37

    Article  Google Scholar 

  12. Yang J, Zhang D, Yong X, Yang JY (2005) Two-dimensional discriminant transform for face recognition. Pattern Recogn 38(7):1125–1129

    Article  MATH  Google Scholar 

  13. Guru DS, Suraj MG, Manjunath S (2011) Fusion of covariance matrices of PCA and FLD. Pattern Recogn Lett 32(3):432–440

    Article  Google Scholar 

  14. Phillips PJ (2006) The facial recognition technology (FERET) database. http://www.itl.nist.gov/iad/humanid/feret/feret_master.html

  15. The ORL face database. http://www.cam_orl.co.uk/facedatabase.html

  16. Chen Z-P, Jiang J-H, Li Y et al (1999) Fuzzy linear discriminant analysis for chemical data sets. Chemometrics Intell Lab Syst 45(1–2):295–302

    Article  Google Scholar 

  17. Yang WK, Yan XY, Zhang L, Sun CY (2010) Feature extraction based on fuzzy 2DLDA. Neurocomputing 73:1556–1561

    Article  Google Scholar 

  18. Wang JG, Yang WK, Yang JY (2008) Fuzzy maximum scatter discriminant analysis and its application to face recognition. ICPR

  19. He XF, Yan SC, Hu YX, Zhang HJ (2005) Face recognition using laplacian faces. IEEE Trans Pattern Anal Mach Intell 27(3):328–340

    Article  Google Scholar 

  20. Zhi R, Ruan Q, Miao Z (2008) Fuzzy discriminant projections for facial expression recognition. ICPR

  21. Li X, Fei S, Zhang T (2009) Median MSD-based method for face recognition. Neurocomputing 72(16-18):3930–3934

    Article  Google Scholar 

  22. Kw KC, Pedry W (2005) Face recognition using a fuzzy fisher classifier. Pattern Recogn 38(10):1717–1732

    Article  Google Scholar 

  23. Zheng Y, Yang J et al (2006) Fuzzy Kernel Fisher Discriminant algorithm with application to face recognition. The 6th world Congress on Intelligent and Automation(WCICA06) 12(12): 9669–9672

  24. Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York

    Book  MATH  Google Scholar 

  25. Keller JM, Gray MR, Givens JR (1985) A fuzzy k-nearest neighbor algorithm. IEEE Trans Syst Man Cybern 15(4):580–585

    Article  Google Scholar 

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

    Article  Google Scholar 

  27. Tenenbaum JB, deSilva V, Langford JC (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290:2319–2323

    Article  Google Scholar 

  28. Belkin M, Niyogi P (2003) Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput 15(6):1373–1396

    Article  MATH  Google Scholar 

  29. Bengio Y, Paiement JF, Vincent P et al (2004) Out-of-sample extensions for LLE, isomap, MDS, eigenmaps, and spectral clustering. Neural Comput 16(10):2197–2219

    Article  MATH  Google Scholar 

  30. Yu W, Teng X, Liu C (2006) Face recognition using discriminant locality preserving projections. Image Vis Comput 24(3):239–248

    Article  Google Scholar 

  31. Hu H (2008) Orthogonal neighborhood preserving discriminant analysis for face recognition. Pattern Recogn 41(6):2045–2054

    Article  MATH  Google Scholar 

  32. Xu Y, Feng G, Zhao Y (2009) One improvement to two-dimensional locality preserving projection method for use with face recognition. Neurocomputing 73(1–3):245–249

    Article  Google Scholar 

  33. Xu Y, Song F, Feng G, Zhao Y (2010) A novel local preserving projection scheme for use with face recognition. Expert Syst Appl 37:6718–6721

    Article  Google Scholar 

  34. Xu Y, Zhong A, Yang J, Zhang D (2010) LPP solution schemes for use with face recognition. Pattern Recogn 43(12):4165–4176

    Article  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation P.R. China under Grant No. 60632050; the Research Program of Hebei Education Department under Grant Nos. Z2009141 and Z2010174; and the Research Program of Hebei Municipal Science & Technology Department under Grant No. 10213551.

Author information

Authors and Affiliations

  1. Department of Computer Science and Technology, Tangshan College, Tangshan, 063000, China

    Jianguo Wang

  2. School of Automation, Southeast University, Nanjing, 210096, China

    Wankou Yang

  3. School of Computer Science & Technology, Nanjing University of Science and Technology, Nanjing, 210094, China

    Jingyu Yang

Authors
  1. Jianguo Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Wankou Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Jingyu Yang
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Jianguo Wang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, J., Yang, W. & Yang, J. Face recognition using fuzzy maximum scatter discriminant analysis. Neural Comput & Applic 23, 957–964 (2013). https://doi.org/10.1007/s00521-012-1020-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-1020-4

Keywords