A Quadratic Loss Multi-Class SVM

Emmanuel Monfrini 1 Yann Guermeur 1
1 ABC - Machine Learning and Computational Biology
LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : Using a support vector machine requires to set two types of hyperparameters: the soft margin parameter C and the parameters of the kernel. To perform this model selection task, the method of choice is cross-validation. Its leave-one-out variant is known to produce an estimator of the generalization error which is almost unbiased. Its major drawback rests in its time requirement. To overcome this difficulty, several upper bounds on the leave-one-out error of the pattern recognition SVM have been derived. Among those bounds, the most popular one is probably the radius-margin bound. It applies to the hard margin pattern recognition SVM, and by extension to the 2-norm SVM. In this report, we introduce a quadratic loss M-SVM, the M-SVM^2, as a direct extension of the 2-norm SVM to the multi-class case. For this machine, a generalized radius-margin bound is then established.
Type de document :
Pré-publication, Document de travail
27 pages. 2008
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https://hal.archives-ouvertes.fr/hal-00276700
Contributeur : Yann Guermeur <>
Soumis le : mercredi 30 avril 2008 - 18:04:44
Dernière modification le : mardi 24 avril 2018 - 13:36:01
Document(s) archivé(s) le : vendredi 28 mai 2010 - 18:06:47

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  • HAL Id : hal-00276700, version 1
  • ARXIV : 0804.4898

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Emmanuel Monfrini, Yann Guermeur. A Quadratic Loss Multi-Class SVM. 27 pages. 2008. 〈hal-00276700〉

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