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A class of semi-supervised support vector machines by DC programming

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  • Liming Yang
  • Laisheng Wang

Abstract

This paper investigate a class of semi-supervised support vector machines ( $$\text{ S }^3\mathrm{VMs}$$ S 3 VMs ) with arbitrary norm. A general framework for the $$\text{ S }^3\mathrm{VMs}$$ S 3 VMs was first constructed based on a robust DC (Difference of Convex functions) program. With different DC decompositions, DC optimization formulations for the linear and nonlinear $$\text{ S }^3\mathrm{VMs}$$ S 3 VMs are investigated. The resulting DC optimization algorithms (DCA) only require solving simple linear program or convex quadratic program at each iteration, and converge to a critical point after a finite number of iterations. The effectiveness of proposed algorithms are demonstrated on some UCI databases and licorice seed near-infrared spectroscopy data. Moreover, numerical results show that the proposed algorithms offer competitive performances to the existing $$\text{ S }^3\mathrm{VM}$$ S 3 VM methods. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Liming Yang & Laisheng Wang, 2013. "A class of semi-supervised support vector machines by DC programming," 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. 7(4), pages 417-433, December.
    • Handle: RePEc:spr:advdac:v:7:y:2013:i:4:p:417-433
    DOI: 10.1007/s11634-013-0141-7
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    References listed on IDEAS

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    1. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    2. Hoai Le Thi & Tao Pham Dinh, 2011. "On solving Linear Complementarity Problems by DC programming and DCA," Computational Optimization and Applications, Springer, vol. 50(3), pages 507-524, December.
    3. 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.
    4. A. Astorino & A. Fuduli & M. Gaudioso, 2010. "DC models for spherical separation," Journal of Global Optimization, Springer, vol. 48(4), pages 657-669, December.
    5. Hoai Le Thi & Hoai Le & Van Nguyen & Tao Pham Dinh, 2008. "A DC programming approach for feature selection in support vector machines learning," 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. 2(3), pages 259-278, December.
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