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Support Vector Machine Polyhedral Separability in Semisupervised Learning

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Listed:
  • Annabella Astorino

    (Università della Calabria)

  • Antonio Fuduli

    (Università della Calabria)

Abstract

We introduce separation margin maximization, a characteristic of the Support Vector Machine technique, into the approach to binary classification based on polyhedral separability and we adopt a semisupervised classification framework. In particular, our model aims at separating two finite and disjoint sets of points by means of a polyhedral surface in the semisupervised case, that is, by exploiting information coming from both labeled and unlabeled samples. Our formulation requires the minimization of a nonconvex nondifferentiable error function. Numerical results are presented on several data sets drawn from the literature.

Suggested Citation

  • Annabella Astorino & Antonio Fuduli, 2015. "Support Vector Machine Polyhedral Separability in Semisupervised Learning," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1039-1050, March.
    • Handle: RePEc:spr:joptap:v:164:y:2015:i:3:d:10.1007_s10957-013-0458-6
    DOI: 10.1007/s10957-013-0458-6
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    References listed on IDEAS

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    1. A. Astorino & M. Gaudioso, 2002. "Polyhedral Separability Through Successive LP," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 265-293, February.
    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. A. Astorino & A. Fuduli & M. Gaudioso, 2010. "DC models for spherical separation," Journal of Global Optimization, Springer, vol. 48(4), pages 657-669, December.
    4. Annabella Astorino & Antonio Fuduli & Manlio Gaudioso, 2012. "Margin maximization in spherical separation," Computational Optimization and Applications, Springer, vol. 53(2), pages 301-322, October.
    5. Hoai Le Thi & Hoai Le & Tao Pham Dinh & Ngai Van Huynh, 2013. "Binary classification via spherical separator by DC programming and DCA," Journal of Global Optimization, Springer, vol. 56(4), pages 1393-1407, August.
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    Cited by:

    1. Yanqin Bai & Xin Yan, 2016. "Conic Relaxations for Semi-supervised Support Vector Machines," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 299-313, April.
    2. Xeniya Vladimirovna Grigor’eva, 2016. "Approximate Functions in a Problem of Sets Separation," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 550-572, November.
    3. Veronica Piccialli & Marco Sciandrone, 2022. "Nonlinear optimization and support vector machines," Annals of Operations Research, Springer, vol. 314(1), pages 15-47, July.
    4. Veronica Piccialli & Marco Sciandrone, 2018. "Nonlinear optimization and support vector machines," 4OR, Springer, vol. 16(2), pages 111-149, June.

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