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A Maximal Margin Hypersphere SVM

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Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12953))

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Abstract

In this work we propose a generalization of the Support Vector Machine (SVM) method in which the separator is a curve, but the concept of margin and maximization of the margin is still present. The idea of using different functions for the separation has been explored in particular in the scope of hyperspheres. However, most of these proposals use two spheres, using concepts different from maximal margin or one sphere but with a poor performance when data from the classes have a linear shape. In this paper we present a formulation of the linear SVM that generalizes it to a spherical separation shape, but still maximizing the margin. A linear relaxation of this quadratic formulation is also presented. The performance of these two formulations for classification purpose is tested and the results are encouraging.

This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P., under the scope of the project UIDB/00297/2020 (Center for Mathematics and Applications).

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Acknowledgments

We would like to thank the reviewers for their valuable comments and suggestions that helped to improve our manuscript.

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Authors and Affiliations

  1. Nova SST—FCT Nova, Campus de Caparica, 2829-516, Caparica, Portugal

    Rui Malha & Paula Amaral

  2. NovaMaths CMA Nova, Campus de Caparica, 2829-516, Caparica, Portugal

    Paula Amaral

Authors
  1. Rui Malha
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  2. Paula Amaral
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Corresponding author

Correspondence to Paula Amaral .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

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Malha, R., Amaral, P. (2021). A Maximal Margin Hypersphere SVM. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12953. Springer, Cham. https://doi.org/10.1007/978-3-030-86976-2_21

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  • DOI: https://doi.org/10.1007/978-3-030-86976-2_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86975-5

  • Online ISBN: 978-3-030-86976-2

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