A Quadratic Loss Multi-Class SVM for which a Radius-Margin Bound Applies

  • Authors:
  • Yann Guermeur;Emmanuel Monfrini

  • Affiliations:
  • LORIA-CNRS, Campus Scientifique, BP 239, 54506 Vandœuvre-lès-Nancy cedex, France, E-mail: yann.guermeur@loria.fr;TELECOM SudParis, 9 rue Charles Fourier, 91011 EVRY cedex, France, E-mail: emmanuel.monfrini@it-sudparis.eu

  • Venue:
  • Informatica
  • Year:
  • 2011

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Abstract

To set the values of the hyperparameters of a support vector machine (SVM), the method of choice is cross-validation. Several upper bounds on the leave-one-out error of the pattern recognition SVM have been derived. One of the most popular is the radius-margin bound. It applies to the hard margin machine, and, by extension, to the 2-norm SVM. In this article, we introduce the first quadratic loss multi-class SVM: the M-SVM2. It can be seen as a direct extension of the 2-norm SVM to the multi-class case, which we establish by deriving the corresponding generalized radius-margin bound.