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Research Article
A comparative study of multi-class support vector machines in the unifying framework of large margin classifiers
Article first published online: 23 MAR 2005
DOI: 10.1002/asmb.534
Copyright © 2005 John Wiley & Sons, Ltd.
Issue
1526-4025/asset/cover.gif?v=1&s=01fa5528d2d885741f372bd93fe6cf4423e1bfda "Applied Stochastic Models in Business and Industry")
Applied Stochastic Models in Business and Industry
Special Issue: Statistical Learning
Volume 21, Issue 2, pages 199–214, March/April 2005
Additional Information
How to Cite
Guermeur, Y., Elisseeff, A. and Zelus, D. (2005), A comparative study of multi-class support vector machines in the unifying framework of large margin classifiers. Appl. Stochastic Models Bus. Ind., 21: 199–214. doi: 10.1002/asmb.534
Publication History
- Issue published online: 23 MAR 2005
- Article first published online: 23 MAR 2005
- Abstract
- References
- Cited By
Keywords:
- multi-class support vector machines (M-SVMs);
- generalization error bounds;
- large margin classifiers;
- extended VC dimensions
Abstract
Vapnik's statistical learning theory has mainly been developed for two types of problems: pattern recognition (computation of dichotomies) and regression (estimation of real-valued functions). Only in recent years has multi-class discriminant analysis been studied independently. Extending several standard results, among which a famous theorem by Bartlett, we have derived distribution-free uniform strong laws of large numbers devoted to multi-class large margin discriminant models. The capacity measure appearing in the confidence interval, a covering number, has been bounded from above in terms of a new generalized VC dimension. In this paper, the aforementioned theorems are applied to the architecture shared by all the multi-class SVMs proposed so far, which provides us with a simple theoretical framework to study them, compare their performance and design new machines. Copyright © 2005 John Wiley & Sons, Ltd.