Constructing Large Margin Polytope Classifiers with a Multiclass Classification Algorithm

In this paper we present two new algorithms to solve non-linearly separable classification problems. First we propose a modification of a multiclass support vector machine, which for binary classification tasks can always find a convex polytope that includes the points of one class and excludes the others, if possible. Next we present a generalization of this approach for multiclass problems, where a non-convex polytope can be found for each class, so that each polytope contains the points of its corresponding class, and excludes other points. Some promising preliminary results are presented for two dimensional artificial datasets.