Skip to main content
SpringerLink
Log in

An effective two-dimensional linear discriminant analysis with locality preserving approach for image recognition

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

Abstract

Linear discriminant analysis (LDA) is one of the most popular feature extraction methods in image recognition. Nevertheless, LDA always suffers from some undesired behaviors caused by globality, namely ignoring local geometric structure of images. To fully capture the geometric information, we propose a novel two-dimensional linear discriminant analysis with locality preserving (2DLP-LDA) approach, which can cover both within-class and between-class local geometric information. 2DLP-LDA re-characterizes the within-class scatter matrix by employing locality preserving projection technique and re-characterizes the between-class scatter matrix by introducing a Gaussian weighting function, making the samples from the same class moderately cluster, while the samples from different classes properly distribute in the reduced subspace. Encouraging experimental results on FERET face database as well as SEU bovine iris database show the effectiveness of the proposed approach.

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

Similar content being viewed by others

References

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

    Article  Google Scholar 

  2. Belhumeur, P.N., Hespanha, J.P., 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 

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

    Article  Google Scholar 

  4. Dalal, N., Triggs, B.: Histograms of oriented gradients for human detection. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR’05). IEEE 1, 886–893 (2005)

  5. Ojala, T., Pietikäinen, M., Harwood, D.: A comparative study of texture measures with classification based on featured distributions. Pattern Recogn. 29(1), 51–59 (1996)

    Article  Google Scholar 

  6. Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vision 60(2), 91–110 (2004)

    Article  Google Scholar 

  7. Krizhevsky, A, Sutskever, I, Hinton, G E.: Imagenet classification with deep convolutional neural networks. In: Advances in neural information processing systems. pp. 1097–1105 (2012)

  8. de Alcantara, M. F., et al.: Action identification using a descriptor with autonomous fragments in a multilevel prediction scheme. In: Signal, Image and Video Processing, pp. 1–8 (2016)

  9. Jia, B., Feng, W., Zhu, M.: Obstacle detection in single images with deep neural networks. SIViP 10(6), 1033–1040 (2016)

  10. Li, J., Zou, L., Yan, J., et al.: No-reference image quality assessment using Prewitt magnitude based on convolutional neural networks. SIViP 10(4), 609–616 (2016)

    Article  Google Scholar 

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

    Article  Google Scholar 

  12. Zhi, R., Ruan, Q.: Two-dimensional direct and weighted linear discriminant analysis for face recognition. Neurocomputing 71(16), 3607–3611 (2008)

    Article  Google Scholar 

  13. Chen, F., An, S., Liu, W.: A new face recognition approach to boosting the worst-case performance. Advances in Multimedia Information Processing-PCM 2008. Springer, Berlin (2008)

    Google Scholar 

  14. Lu, C., An, S., Liu, W., et al.: An innovative weighted 2DLDA approach for face recognition. J. Signal Process. Syst. 65(1), 81–87 (2011)

    Article  Google Scholar 

  15. Gao, Q.X., Xu, H., Li, Y.Y., et al.: Two-dimensional supervised local similarity and diversity projection. Pattern Recogn. 43(10), 3359–3363 (2010)

    Article  MATH  Google Scholar 

  16. Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500), 2323–2326 (2000)

    Article  Google Scholar 

  17. Tenenbaum, J.B., De Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)

    Article  Google Scholar 

  18. Niyogi, X.: Locality preserving projections. Neural Information Processing Systems, p. 153. MIT, Cambridge (2004)

    Google Scholar 

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

    Article  Google Scholar 

  20. Sugiyama, M.: Dimensionality reduction of multimodal labeled data by local fisher discriminant analysis[J]. J. Mach. Learn. Res. 8, 1027–1061 (2007)

    MATH  Google Scholar 

  21. Zhang, D., Yang, J., Yang, J., et al.: Globally maximizing, locally minimizing: unsupervised discriminant projection with applications to face and palm biometrics[J]. IEEE Trans. Pattern Anal. Mach. Intell. 29(4), 650–664 (2007)

    Article  MathSciNet  Google Scholar 

  22. Shu, X., Gao, Y., Lu, H.: Efficient linear discriminant analysis with locality preserving for face recognition. Pattern Recogn. 45(5), 1892–1898 (2012)

    Article  MATH  Google Scholar 

  23. Gao, Q., Liu, J., Zhang, H., et al.: Enhanced fisher discriminant criterion for image recognition. Pattern Recogn. 45(10), 3717–3724 (2012)

    Article  Google Scholar 

  24. Zhang, D., He, J., Zhao, Y., et al.: Global plus local: a complete framework for feature extraction and recognition. Pattern Recogn. 47(3), 1433–1442 (2014)

    Article  MATH  Google Scholar 

  25. Fukunaga, K.: Introduction to Statistical Pattern Recognition, vol. 9, pp. 401–405. Academic Press, Cambridge (1990)

    MATH  Google Scholar 

  26. Belhumeur, P.N., Hespanha, J.P., 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 

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

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

    Article  MATH  Google Scholar 

  29. Song, F., Zhang, D., Wang, J., et al.: A parameterized direct LDA and its application to face recognition. Neurocomputing 71(1), 191–196 (2007)

    Article  Google Scholar 

  30. Kong, H., Teoh, E.K., Wang J.G., et al.: Two dimensional fisher discriminant analysis: Forget about small sample size problem. In: Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005 (ICASSP’05). IEEE. 2: 761–764 (2005)

  31. Noushath, S., Kumar, G.H., Shivakumara, P.: (2D) 2 LDA: An efficient approach for face recognition. Pattern Recogn. 39(7), 1396–1400 (2006)

    Article  MATH  Google Scholar 

  32. Kong, H., Wang, L., Teoh, E.K.: A framework of 2D Fisher discriminant analysis: application to face recognition with small number of training samples. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition 2005, CVPR 2005. IEEE 2, 1083–1088 (2005)

  33. Zheng, W.S., Lai, J.H., Li, S.Z.: 1D-LDA vs. 2D-LDA: When is vector-based linear discriminant analysis better than matrix-based? Pattern Recogn. 41(7), 2156–2172 (2008)

    Article  MATH  Google Scholar 

  34. Hu, D., Feng, G., Zhou, Z.: Two-dimensional locality preserving projections (2DLPP) with its application to palmprint recognition. Pattern Recogn. 40(1), 339–342 (2007)

    Article  MATH  Google Scholar 

  35. Weiwei, Y.: Two-dimensional discriminant locality preserving projections for face recognition. Pattern Recogn. Lett. 30(15), 1378–1383 (2009)

    Article  Google Scholar 

  36. Wong, W.K., Zhao, H.T.: Supervised optimal locality preserving projection. Pattern Recogn. 45(1), 186–197 (2012)

    Article  MATH  Google Scholar 

  37. Li, M., Yuan, B.: 2D-LDA: a statistical linear discriminant analysis for image matrix. Pattern Recogn. Lett. 26(5), 527–532 (2005)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (No. 71390333), the National Key Technology R&D Program of China during the 12th Five-Year Plan Period (No. 2013BAD19B05) and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (KYZZ15_0072).

Author information

Authors and Affiliations

  1. Institute of Systems Engineering, Southeast University, 2#Si Pai Lou, Nanjing, 210096, People’s Republic of China

    Zheng Wei, Yongjie Chu & Lindu Zhao

Authors
  1. Zheng Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongjie Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lindu Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lindu Zhao.

Appendix: Proof of rewriting \(S_{B}\)

Appendix: Proof of rewriting \(S_{B}\)

It follows from \(S_B =\sum _i^C {M_i (\bar{{A}}^{i}-\bar{{A}})^{T}(\bar{{A}}^{i}-\bar{{A}})} \) that

$$\begin{aligned}&S_B=\sum \nolimits _i^C {M_i \left( \bar{{A}}^{i}-\bar{{A}}\right) ^{T}\left( \bar{{A}}^{i}-\bar{{A}}\right) } \\&\quad =\sum \nolimits _{i=1}^C {M_i \left[ \left( \bar{{A}}^{i}\right) ^{T}\bar{{A}}^{i}-\bar{{A}}^{T}\bar{{A}}^{i}-(\bar{{A}}^{i})^{T}\bar{{A}}+\bar{{A}}^{T}\bar{{A}}\right] } \\&\quad =\sum \nolimits _{i=1}^C M \left( \bar{{A}}^{i}\right) ^{T}\bar{{A}}^{i}-M\bar{{A}}^{T}\bar{{A}} \\&\frac{1}{2}\sum _{i=1}^C {\sum _{j=1}^C {\frac{M_i M_j }{M}\left( \bar{{A}}^{i}-\bar{{A}}^{j}\right) ^{T}} } \left( \bar{{A}}^{i}-\bar{{A}}^{j}\right) \\&\quad =\frac{1}{2}\sum _{i=1}^C {\sum _{j=1}^C} \frac{M_i M_j }{M}\left[ \left( \bar{{A}}^{i}\right) ^{T}\bar{{A}}^{i}-\left( \bar{{A}}^{j}\right) ^{T}\bar{{A}}^{i}\right. \\&\qquad \left. -\left( \bar{{A}}^{i}\right) ^{T}\bar{{A}}^{j}+\left( \bar{{A}}^{j}\right) ^{T}\bar{{A}}^{j}\right] \\&\quad =\frac{1}{2}\left[ \sum _{i=1}^C {M_i } \left( \bar{{A}}^{i}\right) ^{T}\bar{{A}}^{i}-M\bar{{A}}^{T}\bar{{A}}-M\bar{{A}}^{T}\bar{{A}}\right. \\&\qquad \left. +\sum _{j=1}^C {M_j } \left( \bar{{A}}^{j}\right) ^{T}\bar{{A}}^{j}\right] \\&\quad =\sum _{i=1}^C {M_i } \left( \bar{{A}}^{i}\right) ^{T}\bar{{A}}^{i}-M\bar{{A}}^{T}\bar{{A}} \\ \end{aligned}$$

which yields Eq. (5).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, Z., Chu, Y. & Zhao, L. An effective two-dimensional linear discriminant analysis with locality preserving approach for image recognition. SIViP 11, 1577–1584 (2017). https://doi.org/10.1007/s11760-017-1122-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-017-1122-7

Keywords

Search

Navigation