The LCCP for Optimizing Kernel Parameters for SVM

  • Sabri Boughorbel
  • Jean Philippe Tarel
  • Nozha Boujemaa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3697)

Abstract

Tuning hyper-parameters is a necessary step to improve learning algorithm performances. For Support Vector Machine classifiers, adjusting kernel parameters increases drastically the recognition accuracy. Basically, cross-validation is performed by sweeping exhaustively the parameter space. The complexity of such grid search is exponential with respect to the number of optimized parameters. Recently, a gradient descent approach has been introduced in[1] which reduces drastically the search steps of the optimal parameters. In this paper, we define the LCCP (Log Convex Concave Procedure) optimization scheme derived from the CCCP (Convex ConCave Procedure) for optimizing kernel parameters by minimizing the radius-margin bound. To apply the LCCP, we prove, for a particular choice of kernel, that the radius is log convex and the margin is log concave. The LCCP is more efficient than gradient descent technique since it insures that the radius margin bound decreases monotonically and converges to a local minimum without searching the size step. Experimentations with standard data sets are provided and discussed.

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References

  1. 1.
    Chapelle, O., Vapnik, V., Bousquet, O., Mukherjee, S.: Choosing multiple parameters for support vector machines. Machine Learning 46(1-3), 131–159 (2002)CrossRefMATHGoogle Scholar
  2. 2.
    Vapnik, V.: The Nature of Statistical Learning Theory, 2nd edn. Springer, New York (1999)Google Scholar
  3. 3.
    Tsuda, K.: Optimal hyperplane classifier with adaptive norm. Technical report tr-99-9, ETL (1999)Google Scholar
  4. 4.
    Yuille, A.L., Rangarajan, A.: The concave-convex procedure. Neural Computation 15(4), 915–936 (2003)CrossRefMATHGoogle Scholar
  5. 5.
    Boughorbel, S.: Kernels for Image Classification with SVM, Ph.D. thesis, submited to University of Paris Sud, Orsay (2005)Google Scholar
  6. 6.
    Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)MATHGoogle Scholar
  7. 7.
    Ratsch, G., Onoda, T., Muller, K.R.: Soft margins for adaboost. Machine Learning 42(3), 287–320 (2001)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Sabri Boughorbel
    • 1
  • Jean Philippe Tarel
    • 2
  • Nozha Boujemaa
    • 1
  1. 1.IMEDIA Group, INRIA RocquencourtLe ChesnayFrance
  2. 2.DESE, LCPCParisFrance

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