Maximal Margin Estimation with Perceptron-Like Algorithm

Abstract

In this paper we propose and analyse a γ-margin generalisation of the perceptron learning algorithm of Rosenblatt. The difference between the original approach and the γ-margin approach is only in the update step. We consider the behaviour of such a modified algorithm in both separable and non-separable case and also when the γ-margin is negative. We give the convergence proof of such a modified algorithm, similar to the classical proof by Novikoff. Moreover we show how to change the margin of the update step in the progress of the algorithm to obtain the maximal possible margin of separation. In application part, we show the connection of the maximal margin of separation with SVM methods. © 2008 Springer-Verlag Berlin Heidelberg.