Optimal arrangements of hyperplanes for multiclass classification
This work addresses multiclass classification problems for machine learning practitioners, but appears incremental as it builds on existing measures and methods.
The paper tackles multiclass classification by constructing classifiers through arrangements of hyperplanes, using mixed integer programming formulations with kernel adaptations and optimization strategies, and reports extensive experiments showing its powerfulness compared to prior methods.
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.