Support vector machines with different norms: motivation, formulations and results

Abstract We introduce two formulations for training support vector machines, based on considering the L 1 and L ∞ norms instead of the currently used L 2 norm, and maximising the margin between the separating hyperplane and each data sets using L 1 and L ∞ distances. We exploit the geometrical properties of these different norms, and propose what kind of results should be expected for them. Formulations in mathematical programming for linear problems corresponding to L 1 and L ∞ norms are also provided, for both the separable and non-separable cases. We report results obtained for some standard benchmark problems, which confirmed that the performance of all the formulations is similar. As expected, the CPU time required for machines solvable with linear programming is much shorter.