Geometrical Properties of Nu Support Vector Machines with Different Norms

By employing the L₁ or L_∞ norms in maximizing margins, support vector machines (SVMs) result in a linear programming problem that requires a lower computational load compared to SVMs with the L₂ norm. However, how the change of norm affects the generalization ability of SVMs has not been clarified so far except for numerical experiments. In this letter, the geometrical meaning of SVMs with the L_p norm is investigated, and the SVM solutions are shown to have rather little dependency on p.