Advances in Data Analysis and Classification

, Volume 7, Issue 4, pp 417–433 | Cite as

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

  • Liming YangEmail author
  • Laisheng Wang
Regular Article


This paper investigate a class of semi-supervised support vector machines (\(\text{ S }^3\mathrm{VMs}\)) with arbitrary norm. A general framework for the \(\text{ S }^3\mathrm{VMs}\) 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 \(\text{ S }^3\mathrm{VMs}\) 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 \(\text{ S }^3\mathrm{VM}\) methods.


Nonconvex optimization DC programming Semi-supervised support vector machine 

Mathematics Subject Classification (2000)

90C26 90C90 



This work is supported by National Nature Science Foundation of China (11271367) and Research Projects of Teachers (2010JS052). Moreover, the authors thank the referees and the editors for their constructive comments. Their suggestions improved the paper significantly.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.College of ScienceChina Agricultural UniversityBeijingChina

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