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

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  • Behzad Pirouz

    (Department of Computer Engineering, Modelling, Electronics and Systems Engineering, University of Calabria, 87036 Rende, Italy)

  • Behrouz Pirouz

    (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.

Suggested Citation

  • Behzad Pirouz & Behrouz Pirouz, 2023. "Multi-Objective Models for Sparse Optimization in Linear Support Vector Machine Classification," Mathematics, MDPI, vol. 11(17), pages 1-18, August.
  • Handle: RePEc:gam:jmathe:v:11:y:2023:i:17:p:3721-:d:1228333
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    References listed on IDEAS

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    1. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico & Adil M. Bagirov, 2018. "Minimizing nonsmooth DC functions via successive DC piecewise-affine approximations," Journal of Global Optimization, Springer, vol. 71(1), pages 37-55, May.
    2. Daniel Horn & Aydın Demircioğlu & Bernd Bischl & Tobias Glasmachers & Claus Weihs, 2018. "A comparative study on large scale kernelized support vector machines," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(4), pages 867-883, December.
    3. F. Rinaldi & F. Schoen & M. Sciandrone, 2010. "Concave programming for minimizing the zero-norm over polyhedral sets," Computational Optimization and Applications, Springer, vol. 46(3), pages 467-486, July.
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