Multi-Objective Models for Sparse Optimization in Linear Support Vector Machine Classification

Author:

Pirouz Behzad1ORCID,Pirouz Behrouz2ORCID

Affiliation:

1. Department of Computer Engineering, Modelling, Electronics and Systems Engineering, University of Calabria, 87036 Rende, Italy

2. Department of Civil Engineering, University of Calabria, 87036 Rende, Italy

Abstract

The design of linear Support Vector Machine (SVM) classification techniques is generally a Multi-objective Optimization Problem (MOP). These classification techniques require finding appropriate trade-offs between two objectives, such as the amount of misclassified training data (classification error) and the number of non-zero elements of the separator hyperplane. In this article, we review several linear SVM classification models in the form of multi-objective optimization. We put particular emphasis on applying sparse optimization (in terms of minimization of the number of non-zero elements of the separator hyperplane) to Feature Selection (FS) for multi-objective optimization linear SVM. Our primary purpose is to demonstrate the advantages of considering linear SVM classification techniques as MOPs. In multi-objective cases, we can obtain a set of Pareto optimal solutions instead of one optimal solution in single-objective cases. The results of these linear SVMs are reported on some classification datasets. The test problems are specifically designed to challenge the number of non-zero components of the normal vector of the separator hyperplane. We used these datasets for multi-objective and single-objective models.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

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