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Margin maximization in spherical separation

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  • Annabella Astorino
  • Antonio Fuduli
  • Manlio Gaudioso

Abstract

We face the problem of strictly separating two sets of points by means of a sphere, considering the two cases where the center of the sphere is fixed or free, respectively. In particular, for the former we present a fast and simple solution algorithm, whereas for the latter one we use the DC-Algorithm based on a DC decomposition of the error function. Numerical results for both the cases are presented on several classical binary datasets drawn from the literature. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • Annabella Astorino & Antonio Fuduli & Manlio Gaudioso, 2012. "Margin maximization in spherical separation," Computational Optimization and Applications, Springer, vol. 53(2), pages 301-322, October.
    • Handle: RePEc:spr:coopap:v:53:y:2012:i:2:p:301-322
    DOI: 10.1007/s10589-012-9486-7
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    References listed on IDEAS

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    1. Le An & Pham Tao, 2005. "The DC (Difference of Convex Functions) Programming and DCA Revisited with DC Models of Real World Nonconvex Optimization Problems," Annals of Operations Research, Springer, vol. 133(1), pages 23-46, January.
    2. A. Astorino & M. Gaudioso, 2009. "A fixed-center spherical separation algorithm with kernel transformations for classification problems," Computational Management Science, Springer, vol. 6(3), pages 357-372, August.
    3. A. Astorino & M. Gaudioso, 2002. "Polyhedral Separability Through Successive LP," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 265-293, February.
    4. Lembke B., 1918. "√ a. p," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 111(1), pages 709-712, February.
    5. A. Astorino & A. Fuduli & M. Gaudioso, 2010. "DC models for spherical separation," Journal of Global Optimization, Springer, vol. 48(4), pages 657-669, December.
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    Cited by:

    1. F. Mashkoorzadeh & N. Movahedian & S. Nobakhtian, 2022. "The DTC (difference of tangentially convex functions) programming: optimality conditions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 270-295, July.
    2. Annabella Astorino & Manlio Gaudioso & Alberto Seeger, 2014. "An illumination problem: optimal apex and optimal orientation for a cone of light," Journal of Global Optimization, Springer, vol. 58(4), pages 729-750, April.
    3. Abbaszadehpeivasti, Hadi, 2024. "Performance analysis of optimization methods for machine learning," Other publications TiSEM 3050a62d-1a1f-494e-99ef-7, Tilburg University, School of Economics and Management.
    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2015. "Optimal Replenishment Order Placement in a Finite Time Horizon," Journal of Optimization Theory and Applications, Springer, vol. 164(3), pages 1078-1089, March.
    5. 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.
    6. Hadi Abbaszadehpeivasti & Etienne Klerk & Moslem Zamani, 2024. "On the Rate of Convergence of the Difference-of-Convex Algorithm (DCA)," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 475-496, July.
    7. Astorino, Annabella & Avolio, Matteo & Fuduli, Antonio, 2022. "A maximum-margin multisphere approach for binary Multiple Instance Learning," European Journal of Operational Research, Elsevier, vol. 299(2), pages 642-652.
    8. A. Astorino & M. Gaudioso & W. Khalaf, 2014. "Edge detection by spherical separation," Computational Management Science, Springer, vol. 11(4), pages 517-530, October.
    9. Kaisa Joki & Adil M. Bagirov & Napsu Karmitsa & Marko M. Mäkelä, 2017. "A proximal bundle method for nonsmooth DC optimization utilizing nonconvex cutting planes," Journal of Global Optimization, Springer, vol. 68(3), pages 501-535, July.

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