The soft-margin Support Vector Machine with ordered weighted average

This paper deals with a cost sensitive extension of the standard Support Vector Machine (SVM) using an ordered weighted sum of the deviations of misclassified individuals with respect to their corresponding supporting hyperplanes. In contrast with previous heuristic approaches, an exact method that applies the ordered weighted average operator in the classical SVM model is proposed. Specifically, when weights are sorted in non-decreasing order, a quadratic continuous formulation is developed. For general weights, a mixed integer quadratic formulation is proposed. In addition, our results prove that nonlinear kernel functions can be also applied to these new models extending its applicability beyond the linear case. Extensive computational results reported in the paper show that the predictive performance provided by the proposed exact solution approaches are better than the ones provided by the classical models (linear and nonlinear kernel) and similar or better than the previous ones provided by the heuristic solution by Maldonado et al. (2018). (c) 2021 The Authors. Published by Elsevier B.V.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by- nc- nd/4.0/).

Automated summary

This paper introduces an exact method for a cost sensitive extension of the standard SVM, which outperforms classical models and previous heuristic solutions, especially when utilizing nonlinear kernel functions.