Learning properties of support vector machines with p-norm

Support vector machines (SVMs) are a new classification technique, which has a high generalization ability, yet a heavy computational load since margin maximization results in a quadratic programming problem. It is known that this maximization task results in a pth-order programming problem if we employ the p-norm instead of the Euclidean norm, that is, when p=1, for example, it is a linear programming problem with a much lower computational load. In this article, we theoretically show that p has very little affect on the generalization performance of SVMs in practice by considering its geometrical meaning.