Optimal arrangements of hyperplanes for multiclass classification

In this paper, we present a novel approach to construct multiclass clasifiers by means of arrangements of hyperplanes. We propose different mixed integer non linear programming formulations for the problem by using extensions of widely used measures for misclassifying observations. We prove that kernel tools can be extended to these models. Some strategies are detailed that help solving the associated mathematical programming problems more efficiently. An extensive battery of experiments has been run which reveal the powerfulness of our proposal in contrast to other previously proposed methods.