A comparative study of multi‐class support vector machines in the unifying framework of large margin classifiers
Identifieur interne : 006315 ( Main/Exploration ); précédent : 006314; suivant : 006316A comparative study of multi‐class support vector machines in the unifying framework of large margin classifiers
Auteurs : Yann Guermeur [France] ; André Elisseeff [Allemagne] ; Dominique Zelus [Argentine]Source :
- Applied Stochastic Models in Business and Industry [ 1524-1904 ] ; 2005-03.
English descriptors
- Teeft :
- Appl, Binary vector, Capacity measure, Cardinality, Comparative study, Computer science, Convergence, Copyright, Corresponding dimension, Decision rule, Dimension, Discriminant, Discriminant analysis, Discriminant models, Elisseeff, Empirical margin risk, Empirical risk, Entropy numbers, Error expectation, Error rate, Feature space, Generalization capabilities, Generalization performance, Generalized lemma, Graph dimension, Growth function, Guermeur, Hilbert space, Ieee transactions, Indicator functions, Inductive principle, Information theory, Jjwk, John wiley sons, Kernel, Kernel methods, Kernel trick, Maximal cardinality, Maximal margin hyperplane, Model selection, Multicategory support vector machines, Multivariate case, Multivariate model, Neural networks, Nite, Objective function, Objective functions, Particular case, Pattern recognition, Penalty term, Pigeonhole principle, Probabilistic concepts, Regional conference series, Sample complexities, Sample complexity, Stochastic, Stochastic models, Straightforward extension, Structural risk minimization, Subset, Support vector, Support vector machines, Svms, System sciences, Technical report, Technical report neurocolt2, Training algorithm, Training algorithms, Uniform convergence, Uniform convergence result, Uniform dimension, Vapnik, Zelus.
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.
Url:
DOI: 10.1002/asmb.534
Affiliations:
- Allemagne, Argentine, France
- Bade-Wurtemberg, District de Tübingen, Grand Est, Lorraine (région)
- Tübingen
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