Feature selection in SVM via polyhedral k-norm

We treat the feature selection problem in the support vector machine (SVM) framework by adopting an optimization model based on use of the ℓ pseudo-norm. The objective is to control the number of non-zero components of the normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm ‖. ‖ [k], intermediate between ‖. ‖ 1 and ‖. ‖ ∞, plays a significant role, allowing us to come out with a DC (difference of convex) optimization problem that is tackled by means of DCA algorithm. The results of several numerical experiments on benchmark classification datasets are reported.