A Novel Robust Smooth Support Vector Machine

Abstract:

In this paper, we propose a new type of ε-insensitive loss function, called as ε-insensitive Fair estimator. With this loss function we can obtain better robustness and sparseness. To enhance the learning speed ,we apply the smoothing techniques that have been used for solving the support vector machine for classification, to replace the ε-insensitive Fair estimator by an accurate smooth approximation. This will allow us to solve ε-SFSVR as an unconstrained minimization problem directly. Based on the simulation results, the proposed approach has fast learning speed and better generalization performance whether outliers exist or not.

• Periodical: Applied Mechanics and Materials (Volumes 148-149)
• Pages: 1438-1441
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.148-149.1438
• Online since: December 2011
• Authors: Shao Chao Sun, Dao Huang
• Keywords: Outlier, Robust Estimators, Sparseness, Support Vector Regression (SVR)

References

[1] V.N. Vapnik, , 1995. The Nature of Statistical Learning Theory, Springer.

[2] J.A.K. Suykens, J. De Brabanter, L. Lukas, J. Vandewalle, Weighted least squares support vector machines: robustness and sparse approximation, Neurocomputing 48 (1–4), 85–105 (2002. ).

DOI: 10.1016/s0925-2312(01)00644-0

[3] Wentong Cui, Xuefeng Yan. 2009. Adaptive weighted least square support vector machine regression integrated withoutlier detection and its application in QSAR, Chemometrics and Intelligent Laboratory Systems 98 : 130-135.

DOI: 10.1016/j.chemolab.2009.05.008

[4] Jin-Tsong Jeng , Chen-ChiaChuang, Chin-WangTao. 2010. Hybrid SVMR-GPR for modeling of chaotic time series systems with noise and outliers, Neurocomputing 73: 1686-1693.

DOI: 10.1016/j.neucom.2009.12.028

[5] Diego Martinez Prata, Marcio Schwaab, Enrique Luis Lima, 2010. Simultaneous robust data reconciliation and gross error detection through particle swarm optimization for an industrial polypropylene reactor, Chemical Engineering Science, 65(17): 4943-4954.

DOI: 10.1016/j.ces.2010.05.017

[6] Prata, D. M., Pinto, J.C., Lima, E.L., 2008. Comparative analysis of robust estimators on nonlinear dynamic data reconciliation,. Computer-Aided Chemical Engineering. 25: 501- 506.

DOI: 10.1016/s1570-7946(08)80088-0

[7] Özyurt, D.B., Pike, R.W., 2004. Theory and practice of simultaneous data reconciliation and gross error detection for chemical process,. Computers and Chemical Engineering . 28: 381- 402.

DOI: 10.1016/j.compchemeng.2003.07.001

[8] Suykens, J. A. K., & Vandewalle, J. 1999. Least squares support vector machine classifiers,. Neural Process Letter, 9(3), 293-300.

[9] Suykens, J. A. K., Lukas, L., & Van Dooren, P. et al. 1999. Least squares support vector machine classifiers: A large scale algorithm,. In Proceedings of European conference of circuit theory design . pp.839-842.

[10] Wen Wen, Zhifeng Hao , Xiaowei Yang. 2008. A heuristic weight-setting strategy and iteratively updating algorithm forweighted least-squares support vector regression,. Neurocomputing 71: 3096-3103.

DOI: 10.1016/j.neucom.2008.04.022

[11] Yuh-Jye Lee, Wen-Feng Hsieh, and Chien-Ming Huang, 2005. ε-SSVR: A Smooth Support Vector Machine forε-Insensitive Regression,. IEEE Transactions on knowledge and data Engineering, 17(5) : 678-684.

DOI: 10.1109/tkde.2005.77

[12] Chen-Chia Chuang, Zne-Jung Lee, 2011. Hybrid robust support vector machines for regression with outliers,. Applied Soft Computing 11: 64-72.

DOI: 10.1016/j.asoc.2009.10.017