On a New Class of Framelet Kernels for Support Vector Regression and Regularization Networks

  • Wei-Feng Zhang
  • Dao-Qing Dai
  • Hong Yan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4426)

Abstract

Kernel-based machine learning techniques, such as support vector machines, regularization networks, have been widely used in pattern analysis. Kernel function plays an important role in the design of such learning machines. The choice of an appropriate kernel is critical in order to obtain good performance. This paper presents a new class of kernel functions derived from framelet. Framelet is a wavelet frame constructed via multiresolution analysis, and has both the merit of frame and wavelet. The usefulness of the new kernels is demonstrated through simulation experiments.

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References

  1. 1.
    Poggio, T., Girosi, F.: Networks for approximation and learning. Proc. IEEE 78(9), 1481–1497 (1990)CrossRefGoogle Scholar
  2. 2.
    Bertero, M., Poggio, T., Torre, V.: Ill-posed problems in early vision. Proc. IEEE 76, 869–889 (1988)CrossRefGoogle Scholar
  3. 3.
    Chapelle, O., et al.: Choosing multiple parameters for support vector machines. Machine Learning 46, 131–159 (2002)CrossRefMATHGoogle Scholar
  4. 4.
    Cortes, C., Vapnik, V.N.: Support vector networks. Machine Learning 20, 1–25 (1995)Google Scholar
  5. 5.
    Cuker, F., Smale, S.: Best choices for regularization parameters in learning theory: on the bias-variance problem. Found. Comput. Math. 2, 413–428 (2002)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Daubechies, I., et al.: Framelets: MRA-based constructions of wavelet frames. Appl. Comput. Harmon. Anal. 124, 44–88 (2003)MathSciNetGoogle Scholar
  7. 7.
    Evgeniou, T., Pontil, M., Poggio, T.: Regularization networks and support vector machines. Advances in Computational Mathematics 13, 1–50 (2000)CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    Gao, J.B., Harris, C.J., Gunn, S.R.: On a class of support vector kernels based on frames in function hilbert spaces. Neural Computation 13(9), 1975–1994 (2001)CrossRefMATHGoogle Scholar
  9. 9.
    Girosi, F., Jones, M., Poggio, T.: Regularization theory and neural networks architectures. Neural Comput. 7, 219–269 (1995)CrossRefGoogle Scholar
  10. 10.
    Müller, K.R., et al.: An introduction to kernel-based learning algorithms. IEEE Transactions on Neural Networks 12(2), 181–201 (2001)CrossRefGoogle Scholar
  11. 11.
    Rakotomamonjy, A., Mary, X., Canu, S.: Non-parametric regression with wavelet kernels. Appl. Stochastic Models Bus. Ind. 21, 153–163 (2005)CrossRefMathSciNetMATHGoogle Scholar
  12. 12.
    Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge Univ. Press, Cambridge (2004)Google Scholar
  13. 13.
    Smola, A.J., Schölkopf, B., Müller, K.R.: The connection between regularization operators and support vector kernels. Neural Networks 11, 637–649 (1998)CrossRefGoogle Scholar
  14. 14.
    Tikhonov, A.N., Arsenin, V.Y.: Solutions of Ill-posed Problems. W.H. Winston, Washington (1977)MATHGoogle Scholar
  15. 15.
    Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, New York (1995)MATHGoogle Scholar
  16. 16.
    Vapnik, V.N.: Statistical Learning Theory. Wiley, New York (1998)MATHGoogle Scholar
  17. 17.
    Zhang, L., Zhou, W., Jiao, L.: Wavelet support vector machine. IEEE T. on System, Man and Cybernetics-Part B: Cybernetics 34(1), 34–39 (2004)CrossRefGoogle Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Wei-Feng Zhang
    • 1
  • Dao-Qing Dai
    • 1
  • Hong Yan
    • 2
  1. 1.Center for Computer Vision and Department of Mathematics, Sun Yat-Sen (Zhongshan) University, Guangzhou 510275China
  2. 2.Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, KowloonHong Kong

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