A comparative study of multi-class support vector machines in the unifying 
framework of large margin classifiers

Guermeur, J; Elisseeff, A; Zelus, D

doi:10.1002/asmb.534

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A comparative study of multi-class support vector machines in the unifying framework of large margin classifiers

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Elisseeff, A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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https://onlinelibrary.wiley.com/doi/epdf/10.1002/asmb.534
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Citation

Guermeur, J., Elisseeff, A., & Zelus, D. (2005). A comparative study of multi-class support vector machines in the unifying framework of large margin classifiers. Applied Stochastic Models in Business and Industry, 21(2), 199-214. doi:10.1002/asmb.534.

Cite as: https://hdl.handle.net/21.11116/0000-0004-DC40-C

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.