Fβ support vector machines

We introduce in this paper F_β SVMs, a new parametrization of support vector machines. It allows to optimize a SVM in terms of F_β, a classical information retrieval criterion, instead of the usual classification rate. Experiments illustrate the advantages of this approach with respect to the traditional 2-norm soft-margin SVM when precision and recall are of unequal importance. An automatic model selection procedure based on the generalization F_β score is introduced. It relies on the results of Chapelle, Vapnjk et al. (2002) about the use of gradient-based techniques in SVM model selection. The derivatives of a F_β loss function with respect to the hyperparameters C and the width σ of a gaussian kernel are formally defined. The model is then selected by performing a gradient descent of the F_β loss function over the set of hyperparameters. Experiments on artificial and real-life data show the benefits of this method when the F_β score is considered.