Asymptotic Behaviors of Support Vector Machines with Gaussian Kernel

Support vector machines (SVMs) with the gaussian (RBF) kernel have been popular for practical use. Model selection in this class of SVMs involves two hyper parameters: the penalty parameter and the kernel width σ. This letter analyzes the behavior of the SVM classifier when these hyper parameters ta...

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Bibliographic Details
Published in:Neural computation 2003-07, Vol.15 (7), p.1667-1689
Main Authors: Keerthi, S. Sathiya, Lin, Chih-Jen
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
Calculus of variations and optimal control
Computer science
control theory
systems
Exact sciences and technology
Learning and adaptive systems
Markov processes
Mathematical analysis
Mathematics
Models, Theoretical
Normal Distribution
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
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Summary:Support vector machines (SVMs) with the gaussian (RBF) kernel have been popular for practical use. Model selection in this class of SVMs involves two hyper parameters: the penalty parameter and the kernel width σ. This letter analyzes the behavior of the SVM classifier when these hyper parameters 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.
ISSN:0899-7667
1530-888X
DOI:10.1162/089976603321891855