Abstract
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.
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References
Alamoa T, Bravob JM et al (2008) A set-membership state estimation algorithm based on DC programming. Automatica 44:216–224
Astorino A, Fuduli A (2007) Nonsmooth optimization techniques for semi-supervised classification. IEEE Trans Pattern Anal Machine Intell 9(12):2135–2142
Astorino A, Fuduli A, Gaudioso M (2010) DC models for spherical separation. J Global Optim 48(4): 657–669
Bennett K, Demiriz A (1998) Semi-supervised support vector machines. In: Advances in neural information processing systems, vol 12. MIT Press, Cambridge, pp 368–374
Chapelle O, Sindhwani V, Keerthi S (2006) Branch and bound for semi-supervised support vector machines. In: Advances in neural information processing systems, vol 17. MIT Press, Cambridge pp 217–224
Chapelle O, Sindhwani V, Keerthi S (2008) Optimization techniques for semi-supervised support vector machines. J Mach Learn 9:203–233
Chapelle O, Zien A (2005) Semi-supervised classification by low density separation. In: Proceedings of 10th International Workshop on artificial intelligence and statistics, Barbados, pp 57–64
Collobert R, Sinz F et al (2006) Large scale transductive SVMs. J Mach Learn 7:1687–1712
Fawcett T (2005) An introduction to ROC analysis. Pattern Recogn Lett 27:861–874
Fung G, Mangasarian O (2001) Semi-supervised support vector machines for unlabeled data classification. Optim Methods Softw 15:29–44
Horst R, Thoai N (1999) DC programming: overview. J Optim Theory Appl 103(1):1–43
Joachims T (1999) Transductive inference for text classification using support vector machines. In: 16th International Conference on machine learning, San Francisco, USA, pp 200–209
Kimeldorf G, Wahba G (1971) Some results on Tchebycheffian spline functions. J Math Anal 33:82–95
Le Thi HA, Pham Dinh T (2005) The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann Oper Res 133:23–46
Le Thi HA et al (2008) A DC programming approach for feature selection in support vector machines learning. Adv Data Anal Classif 2:259–278
Le Thi HA, Pham Dinh T (2011) On solving linear complementarity problems by DC programming and DCA. Comput Optim Appl 50(3):507–524
Le Thi HA et al (2012) Binary classification via spherical separator by DC programming and DCA. J Global Optim. doi:10.1007/s10898-012-9859-6
Reddy IS, Shevade S, Murty MN (2011) A fast quasi-Newton method for semi-supervised SVM. Pattern Recogn 44:2305–2313
Toland J (1978) Duality in nonconvex optimization. J Math Anal Appl 66:399–415
Vapnik VN (1998) Statistical learning theory. Wiley, New York
Wang L, Shen X, Pan W (2007) On transductive support vector machines. In: Verducci J, Shen X, Lafferty J (eds) Prediction and Discovery. American Mathematical Society. http://www.stat.umn.edu/xshen/paper/tsvm.pdf
Wang G et al (2013) A novel DPSO-SVM system for variable interval selection of endometrial tissue sections by near infrared spectroscopy. Talanta 112(15):136–142
Acknowledgments
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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Yang, L., Wang, L. A class of semi-supervised support vector machines by DC programming. Adv Data Anal Classif 7, 417–433 (2013). https://doi.org/10.1007/s11634-013-0141-7
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DOI: https://doi.org/10.1007/s11634-013-0141-7