Local Linear Approximation for Kernel Methods: The Railway Kernel

  • Alberto Muñoz
  • Javier González
  • Isaac Martín de Diego
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4225)


In this paper we present a new kernel, the Railway Kernel, that works properly for general (nonlinear) classification problems, with the interesting property that acts locally as a linear kernel. In this way, we avoid potential problems due to the use of a general purpose kernel, like the RBF kernel, as the high dimension of the induced feature space. As a consequence, following our methodology the number of support vectors is much lower and, therefore, the generalizacion capability of the proposed kernel is higher than the obtained using RBF kernels. Experimental work is shown to support the theoretical issues.


Support Vector Machine Kernel Method Linear Kernel Linear Support Vector Machine Local Linear Approximation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Cortes, C., Vapnik, V.: Support Vector Networks. Machine Learning 20, 273–297 (1995)MATHGoogle Scholar
  2. 2.
    Cristianini, N., Shawe-Taylor, J.: An introduction to Support Vector Machine. Cambridge University Press, Cambridge (2000)Google Scholar
  3. 3.
    Keerthi, S.S., Lin, C.: Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel. Neural Computation 15, 1667–1689 (2003)MATHCrossRefGoogle Scholar
  4. 4.
    Lin., Y., Wahba, G., Zhang, H., Lee, Y.: Statistical Properties and Adaptive Tuning of Support Vector Machines. Machine Learning 48, 115–136 (2002)CrossRefGoogle Scholar
  5. 5.
    Mangasarian, O.L., Wolberg, W.H.: Cancer diagnosis via linear programming. SIAM News 23(5), 1–18 (1990)Google Scholar
  6. 6.
    Moguerza, J., Muñoz, A.: SVM with aplications. In: Statistical Science ( in press, 2006)Google Scholar
  7. 7.
    Muñoz, A., Moguerza, J.M.: Estimation of High-Density Regions Using One Class Neighbor Machines. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(3), 476–480 (2006)CrossRefGoogle Scholar
  8. 8.
    Schölkopf, B., Platt, J.C., Shawe-Taylor, J., Smola, A.J., Williamson, R.C.: Estimating the Support of a High Dimensional Distribution. Neural Computation 13(7), 1443–1471 (2001)MATHCrossRefGoogle Scholar
  9. 9.
    Schölkopf, B., Herbrich, R., Smola, A., Williamson, R.: A Generalized Representer Theorem. NeuroCOLT2 TR Series, NC2-TR2000-81 (2000)Google Scholar
  10. 10.
    Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Alberto Muñoz
    • 1
  • Javier González
    • 1
  • Isaac Martín de Diego
    • 2
  1. 1.University Carlos III de MadridGetafeSpain
  2. 2.University Rey Juan CarlosMóstolesSpain

Personalised recommendations