On the VC Dimension of Bounded Margin Classifiers

In this paper we prove a result that is fundamental to the generalization properties of Vapnik's support vector machines and other large margin classifiers. In particular, we prove that the minimum margin over all dichotomies of k ≤ n + 1 points inside a unit ball in R^sup n^ is maximized when the points form a regular simplex on the unit sphere. We also provide an alternative proof directly in the framework of level fat shattering.[PUBLICATION ABSTRACT]