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Multi-class support vector machine based on minimization of reciprocal-geometric-margin norms

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  • Kusunoki, Yoshifumi
  • Tatsumi, Keiji
Abstract
In this paper, we propose a Support Vector Machine (SVM) method for multi-class classification. It follows multi-objective multi-class SVM (MMSVM), which maximizes class-pair margins on a multi-class linear classifier. The proposed method, called reciprocal-geometric-margin-norm SVM (RGMNSVM) is derived by applying the ℓp-norm scalarization and convex approximation to MMSVM. Additionally, we develop the margin theory for multi-class linear classification, in order to justify minimization of reciprocal class-pair geometric margins. Experimental results on synthetic datasets explain situations where the proposed RGMNSVM successfully works, while conventional multi-class SVMs fail to fit underlying distributions. Results of classification performance evaluation using benchmark data sets show that RGMNSVM is generally comparable with conventional multi-class SVMs. However, we observe that the proposed approach to geometric margin maximization actually performs better classification accuracy for certain real-world data sets.

Suggested Citation

  • Kusunoki, Yoshifumi & Tatsumi, Keiji, 2025. "Multi-class support vector machine based on minimization of reciprocal-geometric-margin norms," European Journal of Operational Research, Elsevier, vol. 324(2), pages 580-589.
    • Handle: RePEc:eee:ejores:v:324:y:2025:i:2:p:580-589
    DOI: 10.1016/j.ejor.2025.03.028
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    References listed on IDEAS

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    1. Lee, In Gyu & Yoon, Sang Won & Won, Daehan, 2022. "A Mixed Integer Linear Programming Support Vector Machine for Cost-Effective Group Feature Selection: Branch-Cut-and-Price Approach," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1055-1068.
    2. Keiji Tatsumi & Tetsuzo Tanino, 2014. "Support vector machines maximizing geometric margins for multi-class classification," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 815-840, October.
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    5. Koen W. de Bock & Kristof Coussement & Arno De Caigny & Roman Slowiński & Bart Baesens & Robert N Boute & Tsan-Ming Choi & Dursun Delen & Mathias Kraus & Stefan Lessmann & Sebastián Maldonado & David , 2023. "Explainable AI for Operational Research: A Defining Framework, Methods, Applications, and a Research Agenda," Post-Print hal-04219546, HAL.
    6. Aytug, Haldun, 2015. "Feature selection for support vector machines using Generalized Benders Decomposition," European Journal of Operational Research, Elsevier, vol. 244(1), pages 210-218.
    7. Keiji Tatsumi & Tetsuzo Tanino, 2014. "Rejoinder on: Support Vector Machines Maximizing Geometric Margins for Multi-Class Classification," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 856-859, October.
    8. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, March.
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