Skip to main content
SpringerLink
Log in

Improved SDA based on mixed weighted Mahalanobis distance

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

We propose an improved subclass discriminant analysis based on the mixed weighted Mahalanobis distance, with the aim of resolving the classification problem that samples are multi-subclass distributed and the computed vectors are sub-optimal. There are three contributions in this paper. First, we used some theoretical support to improve the traditional discriminant criterion function in subclass discriminant analysis. Second, we propose a new distance measure called the mixed weighted Mahalanobis distance (MWMD), which considers the influence of the sample size and sample scatter. Finally, inspired by approximate weighted linear discriminant analysis, we applied MWMD to the improved criterion function. Our experimental results confirmed that the proposed method has a better classification performance than other discriminant analysis methods, using an artificial dataset and some benchmark databases.

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.

Fig. 1
Fig. 2

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Lu, J., Plataniotis, K.N., Venetsanopoulos, A.N.: Face recognition using LDA-based algorithms. IEEE Trans. Neural Netw. 14(1), 195–200 (2003)

    Article  Google Scholar 

  3. Wang, X., Tang, X.: Dual-space linear discriminant analysis for face recognition. In: Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR’04). IEEE Society Press, Washington, DC, USA (2004)

  4. Huang, J., Yuen, P.-C., Chen, W.-S., Lai, J.-H.: Choosing parameters of kernel subspace LDA for recognition of face images under pose and illumination variations. IEEE Trans. Syst. Man Cybern. B Cybern. 37(4), 847–862 (2007)

    Article  Google Scholar 

  5. Gui-Fu, L., Jian, Z., Yong, W.: Incremental complete LDA for face recognition. Pattern Recognit. 45(7), 2510–2521 (2012)

    Article  MATH  Google Scholar 

  6. Lee, K.C., Ou, J.S.: Radar target recognition by using linear discriminant algorithm on angular-diversity RCS. J. Electromagn. Waves Appl. 21(14), 2033–2048 (2007)

    Article  Google Scholar 

  7. Liu, J., Zhang, J., Zhao, F.: High resolution radar automatic target recognition based on an improved LDA method. FSDK (2008)

  8. AlSumait, L., Barbara, D., Domeniconi, C.: On-line LDA: adaptive topic models for mining text streams with applications to topic detection and tracking. In: Proceedings of the Conference on the 8th IEEE International Conference on Data Mining (ICDM2008). IEEE Society Press, Pisa, Italy, pp. 3–12 (2008)

  9. Liao, S., Chung, A.C.S.: A new subspace learning method in Fourier domain for texture classification. In: Proceedings of the Conference on Image Processing (ICIP 2010). IEEE Society Press, Hong Kong, China, pp. 4589–4592 (2010)

  10. Rao, C.R.: Linear Statistical Inference and Its Application, 2nd edn. Wiley-Interscience Press, London (2002)

    Google Scholar 

  11. Fukunaga, K.: Introduction to Statistical Pattern Recognition, 2nd edn. Academic Press, New York (1990)

    MATH  Google Scholar 

  12. Loog, M., Duin, R.P.W., Haed-Umbach, R.: Multiclass linear dimension reduction by weighted pairwise fisher criteria. IEEE Trans. Pattern Anal. Mach. Intell. 23(7), 762–766 (2001)

    Article  Google Scholar 

  13. Hastie, T., Buja, A., Tibshirani, R.: Penalized discriminant analysis. Ann. Stat. 23, 73–102 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  14. Zhu, M., Martinez, A.M.: Subclass discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1274–1286 (2006)

    Google Scholar 

  15. McLachlan, G.J., Krishnan, T.: The EM Algorithm and Extensions. Wiley Press, NY (2008)

    Book  MATH  Google Scholar 

  16. Jing, Z., Zhiyong, Y., Guohong, W., Xiaohui, S., Hongyun, Y.: An efficient fusion approach based on two dimensional subspace feature for SAR images recognition. In: Proceedings of 2011 IEEE Radar Conference (RADAR). IEEE Society Press, Kansas City, MO, USA, pp. 662–666 (2011)

  17. Chen, B., Yuan, L., Liu, H., Bao, Z.: Kernel subclass discriminant Analysis. Neurocomputing 71(1), 455–458 (2007)

    Article  Google Scholar 

  18. You, D., Hamsici, O.C., Martinez, A.M.: Kernel optimization in discriminant analysis. IEEE Trans. Pattern Anal. Mach. Intell. 33(3), 631–638 (2011)

    Article  Google Scholar 

  19. Liang, Y., Li, C., Gong, W., Pan, Y.: Uncorrelated linear discriminant analysis based on weighted pairwise Fisher criterion. Pattern Recognit. 40, 3606–3615 (2007)

    Article  MATH  Google Scholar 

  20. Wang, H., Yan, S.C., Xu, D., Tang, X.O., Huang, T.: Trace ratio vs. ratio trace for dimensionality reduction. In: Proceedings of the Conference on Computer Vision and Pattern Recognition (CVPR’07). IEEE Society Press, Minneapolis, USA, pp. 1–8 (2007)

  21. Rao, C.R.: The utilization of multiple measurements in problems of biological classification. J. R. Stat. Soc. Ser B 10(2), 159–203 (1948)

    MATH  Google Scholar 

  22. Lu, J., Plataniotis, K.N., Venetsanopoulos, A.N.: Regularized discriminant analysis for the small sample size problem in face recognition. Pattern Recognit. Lett. 24(16), 3079–3087 (2003)

  23. Dai, D.-Q., Yuen, P.C.: Face recognition by regularized discriminant analysis. IEEE Trans. Syst. Man Cybern. B Cybern. 37(4), 1080–1085 (2007)

    Article  Google Scholar 

  24. Chen, L., Liao, H., Ko, M., et al.: A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recognit. 33(10), 1713–1726 (2000)

    Article  Google Scholar 

  25. Liu, W., Wang, Y., Li, S.Z., Tan, T.:: Null space-based kernel fisher discriminant analysis for face recognition, FG2004 (2004)

  26. Xiaoxun, Z., Yunde, J.: Symmetrical null space LDA for face and ear recognition. Neurocomputing 70(4–6), 842–848 (2007)

    Article  Google Scholar 

  27. Ye, J., Li, Q.: LDA/QR: an efficient and effective dimension reduction algorithm and its theoretical foundation. Pattern Recognit. 37(4), 851–854 (2004)

    Article  MathSciNet  Google Scholar 

  28. Ye, J.P., Li, Q.: A two-stage linear discriminant analysis via QR-decomposition. IEEE Trans. Pattern Anal. Mach. Intell. 27(6), 929–941 (2005)

    Article  Google Scholar 

  29. Gkalelis, N., Mezaris, V., Kompatsiaris, I.: Mixture subclass discriminant analysis. IEEE Signal Process. Lett. 18(5), 319–322 (2011)

  30. Lay, D.C.: Linear Algebra and Its Applications, 3rd edn. Addison Wesley, Reading, MA (2002)

    Google Scholar 

  31. Ji, Y., Lin, T., Zha, H.: Mahalanobis distance based non-negative sparse representation for face recognition. In: International Conference on Machine Learning and Applications (ICMLA 2009). IEEE Society Press, USA, pp. 41–46 (2009)

  32. Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley-Interscience press, New York (2000)

    Google Scholar 

  33. Tan, P.-N., Steinbach, M., Kumar, V.: Introduction to Data Mining, 1st edn. Addison Wesley Press, Reading, MA (2005)

    Google Scholar 

  34. Wang, D., Yeung, D.S., Tsang, E.C.C.: Weighted Mahalanobis distance kernels for support vector machines. IEEE Trans. Neural Netw. 18(5), 1453–1462 (2007)

    Article  MATH  Google Scholar 

  35. Bache, K., Lichman, M.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine, CA (2013). http://archive.ics.uci.edu/ml

  36. Yale face database: http://vision.ucsd.edu/content/yale-face-database

Download references

Acknowledgments

This work was supported by grants from Jilin Planned Projects for Science Technology Development (Grant Nos. 20120305 and 20130522119JH).

Conflict of interest

The authors declare that there are no conflicts of interest regarding the publication of this article.

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Jilin University, Changchun, 130012, China

    Ying Wang, Hongyin Ni, Peixun Liu & Wenhui Li

  2. State Key Laboratory of Automotive Simulation and Control, Changchun, 130012, China

    Ying Wang & Wenhui Li

Authors
  1. Ying Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hongyin Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peixun Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wenhui Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying Wang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, Y., Ni, H., Liu, P. et al. Improved SDA based on mixed weighted Mahalanobis distance. SIViP 10, 65–74 (2016). https://doi.org/10.1007/s11760-014-0703-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-014-0703-y

Keywords

Search

Navigation