Kernel Optimization Using a Generalized Eigenvalue Approach

  • Jayadeva
  • Sameena Shah
  • Suresh Chandra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5909)


There is no single generic kernel that suits all estimation tasks. Kernels that are learnt from the data are known to yield better classification. The coefficients of the optimal kernel that maximizes the class separability in the empirical feature space had been previously obtained by a gradient-based procedure. In this paper, we show how these coefficients can be learnt from the data by simply solving a generalized eigenvalue problem. Our approach yields a significant reduction in classification errors on selected UCI benchmarks.


Data dependent kernel Fisher’s coefficient generalized eigenvalue kernel optimization Rayleigh quotient 


  1. 1.
    Aizerman, M.A., Braverman, E.M., Rozonoer, L.I.: Theoretical foundations of the potential function method in pattern recognition learning. Automation and Remote Control 25, 821–837 (1964)MathSciNetGoogle Scholar
  2. 2.
    Amari, S., Wu, S.: Improving support vector machine classifiers by modifying kernel functions. Neural Networks 12(6), 783–789 (1999)CrossRefGoogle Scholar
  3. 3.
    Xiong, H., Swamy, M.N.S., Ahmad, M.O.: Optimizing the Kernel in the Empirical Feature Space. IEEE Trans. Neural Networks 16(2), 460–474 (2005)CrossRefGoogle Scholar
  4. 4.
    Murphy, P.M., Aha, D.W.: UCI machine learning repository (1992),
  5. 5.
    Jaakkola, T.S., Haussler, D.: Exploiting generating models in discriminative classifiers. In: Proc. of Tenth Conference on Advances in Neural Information Processing Systems, Denver (December 1998)Google Scholar
  6. 6.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn., pp. 117–124. John Wiley and Sons, Inc., Chichester (2001)zbMATHGoogle Scholar
  7. 7.
    Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in System and Control Theory. Studies in Applied Mathematics, vol. 15. SIAM, Philadelphia (1994)zbMATHGoogle Scholar
  8. 8.

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jayadeva
    • 1
  • Sameena Shah
    • 1
  • Suresh Chandra
    • 1
  1. 1.Indian Institute of Technology DelhiNew DelhiIndia

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