Abstract
Support Vector Machines (SVMs) have been dominant learning techniques for more than ten years, and mostly applied to supervised learning problems. These years two-class unsupervised and semi-supervised classification algorithms based on Bounded C-SVMs, Bounded ν-SVMs, Lagrangian SVMs (LSVMs) and robust version to Bounded C − SVMs respectively, which are relaxed to Semi-definite Programming (SDP), get good classification results. But the parameter C in Bounded C-SVMs has no specific in quantification. Therefore we proposed robust version to unsupervised and semi-supervised classification algorithms based on Bounded ν− Support Vector Machines (Bν−SVMs). Numerical results confirm the robustness of proposed methods and show that our new algorithms based on robust version to Bν−SVM often obtain more accurate results than other algorithms.
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References
Sim, M.: Robust Optimization, Phd.Thesis MIT (2004)
Bertsimas, D., Sim, M.: The price of robustness. Opertions Research 52, 35–53 (2004)
Soyster, A.L.: Convex programming with set-inclusive constraints and applications to inexact linear programming. Oper. Res. 21, 1154–1157 (1973)
Ben-Tal, A., Nemirovski, A.: Rubust convex optimization. Math. Oper. Res. 23, 769–805 (1998)
Ben-Tal, A., Nemirovski, A.: Rubust solutions to uncertain programs. Oper. Res. Letters 25, 1–13 (1999)
Ben-Tal, A., Nemirovski, A.: Rubust solutions of linear programming problems constrained with uncertain data. Math. Program. 88, 411–424 (2000)
El-Ghaoui, L., Lebret, H.: Rubust solutions to least-square problems to uncertain data matrices. SIAM J. Matrix Anal. Appl. 18, 1035–1064 (1997)
El-Ghaoui, L., Oustry, F., Lebret, H.: Rubust solutions to semidefinite programs. SIAM J. Optim. 9, 33–52 (1998)
Schoelkopf, B., Smola, A.: Learning with kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2002)
Lanckriet, G., Cristianini, N., Bartlett, P., Ghaoui, L., Jordan, M.: Learning the kernel matrix with semidefinite programming. Journal of Machine learning research 5 (2004)
De Bie, T., Crisrianini, N.: Convex methods for transduction. In: Advances in Neural Information Processing Systems (NIPS 2003), vol. 16 (2003)
Xu, L., Neufeld, J., Larson, B., Schuurmans, D.: Maximum margin clustering. In: Advances in Neural Information Processing Systems (NIPS 2004), vol. 17 (2004)
Kun, Z., Yingjie, T., Naiyang, D.: Unsupervised and Semi-Supervised Two-class Support Vector Machines. In: Proceedings of the Sixth IEEE International Conference on Data Mining Workshops, pp. 813–817 (2006)
Kun, Z., Yingjie, T., Naiyang, D.: Unsupervised and Semi-Supervised Lagrangian Support Vector Machines. In: Proceedings of the Seventh International Conference on Computational Science Workshops, pp. 882–889 (2007)
Kun, Z., Yingjie, T., Naiyang, D.: Robust Unsupervised and Semisupervised Bounded C − Support Vector Machines. In: Proceedings of the Seventh IEEE International Conference on Data Mining Workshops, pp. 331–336 (2007)
Friess, T., Christianini, C.N., Campbell, C.: The Kernel Adatron Algorithm: A Fast and Simple Learning Procedure for Support Vector Machines. In: Proceeding of 15th Intl. Con Machine Learning, Morgan Kaufman Publishers, San Francisco (1998)
Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge University Press, Cambridge (2000)
Jos, F.S.: Using SeDuMi1.02, A Matlab Toolbox for Optimization over Symmetric Cones. Optimization Methods and Software 11-12, 625–653 (1999)
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Zhao, K., Tian, Yj., Deng, Ny. (2009). Robust Unsupervised and Semi-supervised Bounded ν − Support Vector Machines . In: Yu, W., He, H., Zhang, N. (eds) Advances in Neural Networks – ISNN 2009. ISNN 2009. Lecture Notes in Computer Science, vol 5552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01510-6_36
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DOI: https://doi.org/10.1007/978-3-642-01510-6_36
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