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(Neural Computation. 2003;15:1667-1689.)
© 2003 The MIT Press

Letter

Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel

S. Sathiya Keerthi

mpessk{at}guppy.mpe.nus.edu.sg Department of Mechanical Engineering, National University of Singapore, Singapore 119260, Republic of Singapore

Chih-Jen Lin

cjlin{at}csie.ntu.edu.tw Department of Computer Science and Information Engineering, National Taiwan University, Taipei 106, Taiwan

Support vector machines (SVMs) with the gaussian (RBF) kernel have been popular for practical use. Model selection in this class of SVMs involves two hyperparameters: the penalty parameter C and the kernel width {sigma}. This letter analyzes the behavior of the SVM classifier when these hyperparameters take very small or very large values. Our results help in understanding the hyperparameter space that leads to an efficient heuristic method of searching for hyperparameter values with small generalization errors. The analysis also indicates that if complete model selection using the gaussian kernel has been conducted, there is no need to consider linear SVM.




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