A quadratic loss multi-class SVM for which a radius-margin bound applies

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.