Optimal arrangements of hyperplanes for multiclass classification

TL;DR

This paper introduces a new method for multiclass classification using arrangements of hyperplanes, employing mixed integer programming and kernel trick adaptations, with demonstrated superior performance over existing methods.

Contribution

It presents novel mixed integer programming formulations for hyperplane arrangements in multiclass classification, including dimensionality reduction and variable fixing strategies.

Findings

Outperforms previous methodologies in experiments

Effective use of kernel trick in hyperplane arrangements

Demonstrates computational efficiency with reduction strategies

Abstract

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.