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Conic Relaxations for Semi-supervised Support Vector Machines

Author

Listed:
  • Yanqin Bai

    (Shanghai University)

  • Xin Yan

    (Shanghai University)

Abstract

Semi-supervised support vector machines arise in machine learning as a model of mixed integer programming problem for classification. In this paper, we propose two convex conic relaxations for the original mixed integer programming problem. The first one is a new semi-definite relaxation, and its possibly maximal ratio of the optimal value is estimated approximately. The second one is a doubly nonnegative relaxation, which is relaxed from a well-known conic programming problem called completely positive programming problem that is equivalent to the original problem. Furthermore, we prove that the doubly nonnegative relaxation is tighter than the semi-definite relaxation. Finally, the numerical results show that two proposed relaxations not only generate proper classifiers but also outperform some existing methods in classification accuracy.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:169:y:2016:i:1:d:10.1007_s10957-015-0843-4
    DOI: 10.1007/s10957-015-0843-4
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    References listed on IDEAS

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    1. 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.
    2. Tay, Francis E. H. & Cao, Lijuan, 2001. "Application of support vector machines in financial time series forecasting," Omega, Elsevier, vol. 29(4), pages 309-317, August.
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