This paper proposes a kind of novel kernel functions obtained from the reproducing kernels of Hilbert spaces associated with special inner product. SVM with the proposed kernel functions only need less support vectors to construct two-class hyperplane than the SVM with Gaussian kernel functions, so the proposed kernel functions have the better generalization. Finally, SVM with reproducing and Gaussian kernels are respectively applied to two benchmark examples: the well-known Wisconsin breast cancer data and artificial dataset.


SVM Reproducing Kernel 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Zhang, Q.L., Wang, S.T.: A solution to the reproducing kernels space. In: 5th International DCABES Conference, pp. 42–46. Shanghai University Press, Shanghai (2006) Google Scholar
  2. 2.
    Qinli, Z., et al.: The numerical methods for solving Euler system of equations in reproducing kernel space H2 (R). Journal of Computational Mathematics 3, 327–336 (2001) Google Scholar
  3. 3.
    Xianggen, X., Nashed, M.Z.: The Backus-Gilbert methods for signals in reproducing kernel Hilbert spaces and wavelet subspaces. Inverse Problems 10, 785–804 (1994) Google Scholar
  4. 4.
    Sánchez, V.D.A.: Advanced support vector machines and kernel methods. Neurocomputing 2, 5–20 (2003) Google Scholar
  5. 5.
    Evgeniou, T., Pontil, M., Poggio, T.: Regrularization networks and support vector machines. Advance Computational Math. 1, 1–50 (2000) Google Scholar
  6. 6.
    Smola, A., Scholkopf, B., Muller, K.R.: The connection between regularization operators and support vector kernels. Neural Networks 11, 637–649 (1998) Google Scholar
  7. 7.
    Gunter, L., Zhu, J.: Efficient Computation and Model Selection for the Support Vector Regression. Neural Computation 19, 1633–1655 (2007) Google Scholar
  8. 8.
    Burges, C.J.C.: A tutorial on SVM for pattern recognition. Data mining and Knowledge Discovery 2, 955–974 (1998) Google Scholar
  9. 9.
    Chapelle, O., Vapnik, V., Bengio, Y.: Model Selection for Small Sample Regression. Machine Learning 48, 9–23 (2002) Google Scholar
  10. 10.
    Zhang, Q.L., Wang, S.T.: A Novel SVM and its application Breast Cancer. In: 1st IEEE ICBBE, pp. 633–636. IEEE Press, New York (2007) Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xinfei Liao
    • 1
  • Limin Tao
    • 2
  1. 1.Department of ComputerWenzhou Vocational and Technical CollegeWenzhouChina
  2. 2.School of Information Science and EngineeringHangzhou Normal UniversityHangzhouChina

Personalised recommendations