Optimal arrangements of hyperplanes for multiclass classification

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.

arXiv comment8 Figures, 2 Tables

References in corpus (5)

• Scikit-learn: Machine Learning in Python
• A general framework for locating hyperplanes to fitting set of points
• On support vector machines under a multiple-cost scenario
• On ${\ell }_p$-Support Vector Machines and Multidimensional Kernels
• Revisiting several problems and algorithms in continuous location with ${\ell }_p$ norms

Cited by in corpus (4)

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• Tightening big Ms in integer programming formulations for support vector machines with ramp loss
• On the multisource hyperplanes location problem to fitting set of points
• A Mathematical Programming approach to Binary Supervised Classification with Label Noise