Unified Kernel Function and Its Training Method for SVM

  • Ha-Nam Nguyen
  • Syng-Yup Ohn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4232)


This paper proposes a unified kernel function for support vector machine and its learning method with a fast convergence and a good classification performance. We defined the unified kernel function as the weighted sum of a set of different types of basis kernel functions such as neural, radial, and polynomial kernels, which are trained by a new learning method based on genetic algorithm. The weights of basis kernel functions in the unified kernel are determined in learning phase and used as the parameters in the decision model in the classification phase. The unified kernel and the learning method were applied to obtain the optimal decision model for the classification of two public data sets for diagnosis of cancer diseases. The experiment showed fast convergence in learning phase and resulted in the optimal decision model with the better performance than other kernels. Therefore, the proposed kernel function has the greater flexibility in representing a problem space than other kernel functions.


Support Vector Machine Kernel Function Learning Method Learning Phase High Dimensional Feature Space 
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.


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  1. 1.
    Cristianini, N., Shawe-Taylor, J.: An introduction to Support Vector Machines and other kernel-based learning methods, Cambridge (2000)Google Scholar
  2. 2.
    Vapnik, V.N., et al.: Theory of Support Vector Machines, Technical Report CSD TR-96- 17, Univ. of London (1996)Google Scholar
  3. 3.
    Kecman, V.: Learning and Soft Computing: Support Vector Machines, Neural Networks, and Fuzzy Logic Models (Complex Adaptive Systems). The MIT press, Cambridge (2001)Google Scholar
  4. 4.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. John Wiley & Sons Inc., Chichester (2001)MATHGoogle Scholar
  5. 5.
    Joachims, T.: Making large-Scale SVM Learning Practical. In: Advances in Kernel Methods - Support Vector Learning, ch. 11. MIT Press, Cambridge (1999)Google Scholar
  6. 6.
    Schökopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (Adaptive Computation and Machine Learning). MIT Press, Cambridge (2002)Google Scholar
  7. 7.
    Minsky, M.L., Papert, S.A.: Perceptrons. MIT Press, Cambridge (1969)MATHGoogle Scholar
  8. 8.
    Michalewicz, Z.: Genetic Algorithms + Data structures = Evolution Programs, 3rd rev. and extended edn. Springer, Heidelberg (1996)MATHGoogle Scholar
  9. 9.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization & Machine Learning. Addison Wesley, Reading (1989)MATHGoogle Scholar
  10. 10.
    Mitchell, M.: Introduction to genetic Algorithms, 5th printing. MIT Press, Cambridge (1999)Google Scholar
  11. 11.
    Alon, U., Barkai, N., Notterman, D., Gish, K., Ybarra, S., Mack, D., Levine, A.: Broad Patterns of Gene Expression Revealed by Clustering Analysis of Tumor and Normal Colon Tissues Probed by Oligonucleotide Arrays. Proceedings of National Academy of Sciences of the United States of American 96, 6745–6750 (1999)CrossRefGoogle Scholar
  12. 12.
    Golub, T.R., Slonim, D.K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J.P., Coller, H., Loh, M.L., Downing, J.R., Caligiuri, M.A., Bloomfield, C.D., Lander, E.S.: Molecular Classification of Cancer: Class Discovery and Class Prediction by Gene Expression Monitoring. Science 286, 531–537 (1999)CrossRefGoogle Scholar
  13. 13.
    Fröhlich, H., Chapelle, O., Scholkopf, B.: Feature selection for support vector machines by means of genetic algorithm, Tools with Artificial Intelligence. In: Proceedings of 15th IEEE International Conference on Tools with Artificial Intelligence, pp. 142–148 (2003)Google Scholar
  14. 14.
    Chen, X.-w.: Gene selection for cancer classification using bootstrapped genetic algorithms and support vector machines. In: Proceedings IEEE International Conference on the Computational Systems, Bioinformatics Conference, pp. 504–505 (2003)Google Scholar
  15. 15.
    Park, C., Cho, S.-B.: Genetic search for optimal ensemble of featureclassifier pairs in DNA gene expression profiles. In: Proceedings of the International Joint Conference Neural Networks, vol. 3, pp. 1702–1707 (2003)Google Scholar
  16. 16.
    Rüping, S.: mySVM-Manual, University of Dortmund, Lehrstuhl Informatik (2000) (online), Available http://www-ai.cs.uni-dortmund.de/SOFTWARE/MYSVM
  17. 17.
    Kohavi, R., John, G.H.: Wrappers for Feature Subset Selection. Artificial Intelligence, 273–324 (1997)Google Scholar
  18. 18.
    Blum, A.L., Langley, P.: Selection of Relevant Features and Examples in Machine Learning. Artificial Intelligence, 245–271 (1997)Google Scholar
  19. 19.
    Tom, M.: Michell: Machine Learning. McGraw Hill, New York (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ha-Nam Nguyen
    • 1
  • Syng-Yup Ohn
    • 1
  1. 1.Department of Computer EngineeringHankuk Aviation UniversitySeoulKorea

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