  In this paper, we present a novel approach to construct multiclass
classifiers by means of arrangements of hyperplanes. We propose different mixed
integer (linear and non linear) programming formulations for the problem using
extensions of widely used measures for misclassifying observations where the
\textit{kernel trick} can be adapted to be applicable. Some dimensionality
reductions and variable fixing strategies are also developed for these models.
An extensive battery of experiments has been run which reveal the powerfulness
of our proposal as compared with other previously proposed methodologies.
