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Orthogonal Quadratic Discriminant Functions for Face Recognition

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5553))

Abstract

Small sample size (SSS) problem is usually a limit to the robustness of learning methods in face recognition. Especially in the quadratic discriminant functions (QDF), too many parameters need to be estimated and covariance matrix of a class is usually singular. In order to overcome the SSS problems, we proposed a novel approach called orthogonal quadratic discriminant functions (OQDF). The OQDF assumes probability distribution functions of each two classes of face images have a uniform shape. Then, three OQDF models are developed. The Laplacian smoothing transform (LST) and Fisher’s linear discriminant (FLD) are employed to preprocess the face images for the OQDF classifier. Finally, we evaluate our proposed algorithms on two face databases, ORL and Yale.

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References

  1. Er, M.J., Chen, W., Wu, S.: High-Speed Face Recognition Based on Discrete Cosine Transform and RBF Neural Networks. IEEE Trans. Neural Networks 16(3) (2005)

    Google Scholar 

  2. Heisele, B., Ho, P., Poggio, T.: Face Recognition with Support Vector Machines: Global Versus Component-Based Approach. In: ICCV (2001)

    Google Scholar 

  3. Kimura, F., Wakabayashi, T., Tsuruoka, S., Miyake, Y.: Modified Quadratic Discriminant Functions and its Application to Chinese Character Recognition. IEEE Trans. Pattern Anal. Mach. Intell., 149–153 (1987)

    Google Scholar 

  4. Liu, C.L., Sako, H., Fujisawa, H.: Discriminative Learning Quadratic Discriminant Function for Handwriting Recognition. IEEE Trans. Neural Networks (2004)

    Google Scholar 

  5. Friedman, J.H.: Regularized Discriminant Analysis. J. Am. Statist. Ass. 84, 165–175 (1989)

    Article  MathSciNet  Google Scholar 

  6. Lu, J., Plataniotis, K., Venetsanopoulos, A.: Regularized Discriminant Analysis for the Small Sample Size Problem in Face Recognition. Patten Recognition Letters, 3079–3087 (2003)

    Google Scholar 

  7. Wang, J., Plataniotis, K., Lu, J., Venetsanopoulos, A.: Kernel Quadratic Discriminant Analysis for Small Sample Size Proble. Pattern Recognition, 1528–1538 (2008)

    Google Scholar 

  8. Yu, H., Yang, J.: A Direct lda Algorithm for High-Dimensional Datawith Application to Face Recognition. Pattern Recognit. 34, 2067–2070 (2001)

    Article  MATH  Google Scholar 

  9. Gu, S., Tan, Y., He, X.: Laplacian Smoothing Transfrorm for Face Recognition. TPAMI (submitted, 2008)

    Google Scholar 

  10. Duda, R., Hart, P.: Pattern Classification, 2nd edn. Wiley, New York (2001)

    MATH  Google Scholar 

  11. Moghaddam, B., Pentland, A.: Probabilistic Visual Learning for Object Representation. IEEE Trans. Pattern Anal. Mach. Intell. 696–710 (1997)

    Google Scholar 

  12. Long, T., Jin, L.: Building Compact mqdf Classifier for Large Character Set Recognition by Subspace Distribution Sharing. Pattern Recognition 41, 2916–2925 (2008)

    Article  MATH  Google Scholar 

  13. Juang, B.H., Katagiri, S.: Discriminative Learning for Minimum Error Classification. IEEE Trans. Signal Processing 40, 3043–3054 (1992)

    Article  MATH  Google Scholar 

  14. Turk, M., Pentland, A.: Eigenfaces for Recognition. J. Cognitive Neuroscience 3, 71–86 (1991)

    Article  Google Scholar 

  15. Cover, T., Hart., P.: Nearest Neighbor Pattern Classification. IEEE Trans. Info. Theo., 21–27 (1967)

    Google Scholar 

  16. Fan, R.E., Chen, P.H., Lin, C.J.: Working Set Selection Using Second Order Information for Training Support Vector Machines. Journal of Machine Learning Research 6, 1889–1918 (2005)

    MathSciNet  MATH  Google Scholar 

  17. Turk, M., Pentland, A.: Eigenfaces for recognition. J. Cognitive Neuroscience 3(1), 71–86 (1991)

    Article  Google Scholar 

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© 2009 Springer-Verlag Berlin Heidelberg

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Gu, S., Tan, Y., He, X. (2009). Orthogonal Quadratic Discriminant Functions for Face Recognition. In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5553. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01513-7_51

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  • DOI: https://doi.org/10.1007/978-3-642-01513-7_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-01512-0

  • Online ISBN: 978-3-642-01513-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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