On the VC Dimension of Bounded Margin Classifiers

Authors:
Don Hush;Clint Scovel
Affiliations:
Los Alamos National Laboratory, Los Alamos, NM, 87545, USA. dhush@lanl.gov;Los Alamos National Laboratory, Los Alamos, NM, 87545, USA. jcs@lanl.gov
Venue:
Machine Learning
Year:
2001

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Abstract

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 Rn 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.