Classifier selection in a family of polyhedron classifiers

Abstract

We consider an algorithm to approximate each class region by a small number of convex hulls and to apply them to classification. The convex hull of a finite set of points is computationally hard to be constructed in high dimensionality. Therefore, instead of the exact convex hull, we find an approximate convex hull (a polyhedron) in a time complexity that is linear in dimension. On the other hand, the set of such convex hulls is often too much complicated for classification. Thus we control the complexity by adjusting the number of faces of convex hulls. For reducing the computational time, we use an upper bound of the leave-one-out estimated error to evaluate the classifiers. © 2009 Springer-Verlag Berlin Heidelberg.