Abstract
This paper proposes robust version to unsupervised classification algorithm based on modified robust version of primal problem of standard SVMs, which directly relaxes it with label variables to a semi-definite programming. Numerical results confirm the robustness of the proposed method.
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References
J. A. Hartigan, Clustering Algorithms, John Wiley & Sons, New York, NY, 1975.
B. Schoelkopf and A. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, Massachusetts, Cambridge, 2002.
S. Melvyn, Robust optimization, PhD. Thesis, Massachusetts Institute of Technology, 2004.
B. Dimitris and S. Melvyn, The price of robustness, Opertions Research, 2004, 52(1): 35–53.
A. L. Souster, Convex programming with set-inclusive constraints and applications to inexact linear programming, Oper. Res., 1973, 21: 1154–1157.
A. Ben-Tal and A. Nemirovski, Robust convex optimization, Math. Oper. Res., 1998, 23: 769–805.
A. Ben-Tal and A. Nemirovski, Robust solutions to uncertain programs, Oper. Res. Letters, 1999, 25: 1–13.
A. Ben-Tal and A. Nemirovski, Robust solutions of linear programming problems constrained with uncertain data, Math. Program., 2000, 88: 411–424.
L. El-Ghaoui and H. Lebret, Robust solutions to least-square problems to uncertain data matrices, SIAM J. Matrix Anal. Appl., 1997, 18: 1035–1064.
L. El-Ghaoui, F. Oustry, and H. Lebret, Robust solutions to uncertain semidefinite programs, SIAM J. Optim., 1998, 9(1): 33–52.
N. Y. Deng and Y. J. Tian, A New Method of Data Mining: Support Vector Machines, Science Press, Beijing, 2004.
D. R. Chen, et al., Support vector machine soft margin classifiers: Error analysis, Machine Learning Research, 2004(5): 1143–1175.
S. Smale and D. X. Zhou, Learning theory estimates via integral operators and their approximations, Constr. Approx., 2007, 26: 153–172.
J. F. Sturm, Using SeDuMi1.02, A Matlab toolbox for optimization over symmetric cones, Optimization Methods and Software, 1999, (11–12): 625–653.
K. C. Toh, M. J. Todd, and R. H. Tütüncü, SDPT3 — A Matlab package for semidefinite programming, Technical Report, School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY, USA, 1996.
G. Lanckriet, et al., Learning the kernel matrix with semidefinite programming, Journal of Machine Learning Research, 2004, (5).
T. De Bie and N. Crisrianini, Convex methods for transduction, Advances in Neural Information Processing Systems, 16(NIPS-03), 2003.
L. Xu, et al., Maximum margin clustering, Advances in Neural Information Processing Systems, 17(NIPS-04), 2004.
K. Zhao, Y. J. Tian, and N. Y. Deng, Unsupervised and semi-supervised two-class support vector machines, Sixth IEEE Internaitonal Conference on Data Minging Workshops, 2006.
K. Zhao, Y. J. Tian, and N. Y. Deng, Unsupervised and semi-supervised lagrangian support vector machines, Internaitonal Conference on Computational Science Workshops, Lecture Notes in Computer Science, 2007, 4489(5): 882–889.
K. Zhao, Y. J. Tian, and N. Y. Deng, New unsupervised support vector machines, Proceeding of MCDM, CCIS, 2009, 35: 606–613.
K. Zhao, Y. J. Tian, and N. Y. Deng, Robust unsupervised and semi-supervised bounded C-support vector machines, Proceedings of the Seventh IEEE International Conference on Data Mining Workshops, Omaha NE, USA, October, 2007.
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This research is supported by the Key Project of the National Natural Science Foundation of China under Grant No. 10631070.
This paper was recommended for publication by Editor Xiaoguang YANG.
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Zhao, K., Zhang, M. & Deng, N. New robust unsupervised support vector machines. J Syst Sci Complex 24, 466–476 (2011). https://doi.org/10.1007/s11424-011-8102-8
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DOI: https://doi.org/10.1007/s11424-011-8102-8