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Optimal arrangements of hyperplanes for SVM-based multiclass classification

Author

Listed:
  • Víctor Blanco

    (Universidad de Granada)

  • Alberto Japón

    (Universidad de Sevilla)

  • Justo Puerto

    (Universidad de Sevilla)

Abstract

In this paper, we present a novel SVM-based 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 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.

Suggested Citation

  • Víctor Blanco & Alberto Japón & Justo Puerto, 2020. "Optimal arrangements of hyperplanes for SVM-based multiclass classification," 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. 14(1), pages 175-199, March.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:1:d:10.1007_s11634-019-00367-6
    DOI: 10.1007/s11634-019-00367-6
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    References listed on IDEAS

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    1. Ghaddar, Bissan & Naoum-Sawaya, Joe, 2018. "High dimensional data classification and feature selection using support vector machines," European Journal of Operational Research, Elsevier, vol. 265(3), pages 993-1004.
    2. Adil Bagirov & Julien Ugon & Dean Webb & Gurkan Ozturk & Refail Kasimbeyli, 2013. "A novel piecewise linear classifier based on polyhedral conic and max–min separabilities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 3-24, April.
    3. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "Revisiting several problems and algorithms in continuous location with $$\ell _\tau $$ ℓ τ norms," Computational Optimization and Applications, Springer, vol. 58(3), pages 563-595, July.
    4. Lee, Yoonkyung & Lin, Yi & Wahba, Grace, 2004. "Multicategory Support Vector Machines: Theory and Application to the Classification of Microarray Data and Satellite Radiance Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 67-81, January.
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    Cited by:

    1. Baldomero-Naranjo, Marta & Martínez-Merino, Luisa I. & Rodríguez-Chía, Antonio M., 2020. "Tightening big Ms in integer programming formulations for support vector machines with ramp loss," European Journal of Operational Research, Elsevier, vol. 286(1), pages 84-100.

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