Premium
A comparative study of multi‐class support vector machines in the unifying framework of large margin classifiers
Author(s) -
Guermeur Yann,
Elisseeff André,
Zelus Dominique
Publication year - 2005
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.534
Subject(s) - margin (machine learning) , support vector machine , discriminant , class (philosophy) , statistical learning theory , linear discriminant analysis , computer science , dimension (graph theory) , artificial intelligence , bounded function , machine learning , mathematics , vc dimension , pure mathematics , mathematical analysis
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.