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A short note about the application of polynomial kernels with fractional degree in Support Vector Learning

  • Rolf Rossius
  • Gérard Zenker
  • Andreas Ittner
  • Werner Dilger
Support Vector Learning
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1398)

Abstract

In the mid 90's a fundamental new Machine Learning approach was developed by V. N. Vapnik: The Support Vector Machine (SVM). This new method can be regarded as a very promising approach and is getting more and more attention in the fields where neural networks and decision tree methods are applied. Whilst neural networks may be considered (correctly or not) to be well understood and are in wide use, Support Vector Learning has some rough edges in theoretical details and its inherent numerical tasks prevent it from being easily applied in practice. This paper picks up a new aspect - the use of fractional degrees on polynomial kernels in the SVM - discovered in the course of an implementation of the algorithm. Fractional degrees on polynomial kernels broaden the capabilities of the SVM and offer the possibility to deal with feature spaces of infinite dimension. We introduce a method to simplify the quadratic programming problem, as the core of the SVM.

Keywords

Support Vector Machine Feature Space HESSE Matrix Image Space Polynomial Kernel 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. [CV95]
    C. Cortes and V. N. Vapnik. Support-vector networks. Machine Learning, 20:273–297, 1995.Google Scholar
  2. [Fri93]
    B. Fritzke. Growing cell structures — a self-organizing network for unsupervised and supervised learning. Technical Report 93-026, International Computer Science Institute, Berkeley, California, 1993.Google Scholar
  3. [IRZ98]
    A. Ittner, R. Rossius, and G. Zenker. Support Vector Learning. Technical Report CSR-98, Chemnitz University of Technology, Chemnitz, Germany, 1998.Google Scholar
  4. [Vap95]
    V. N. Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Rolf Rossius
    • 1
  • Gérard Zenker
    • 1
  • Andreas Ittner
    • 1
  • Werner Dilger
    • 1
  1. 1.Department of Computer Science Artificial Intelligence GroupChemnitz University of TechnologyChemnitz

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