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Robust Prediction Model of Least Squares Support Vector Machine Based on Sliding Window |
ZHAO YongPing, SUN JianGuo |
College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016 |
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Abstract In this paper, the mathematical model of weighted least squares support vector machine (WLSSVM) is introduced. Based on the algorithms of heuristic learning and sliding window, a mathematical model of robust prediction of least squares support vector machine (LSSVM) using sliding window is proposed. with the modified heuristic learning algorithm, the strategy of iterative computing matrix inverse is employed to reduce the predicted time without loss of accuracy. Finally, two examples have proved that the proposed model can eliminate the outliers, realize robust prediction and achieve good results.
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Received: 05 March 2007
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[1] Vapnik V N. The Nature of Statistical Learning Theory. New York, USA: SpringerVerlag, 1995 [2] Nguyen H N, Ohn S Y. Unified Kernel Function and Its Training Method for SVM // Proc of the 13th International Conference on Neural Information Processing. Hongkong, China, 2006: 792800 [3] Vapnik V N, Golowich S E, Smola A. Support Vector Method for Function Approximation, Regression Estimation, and Signal Processing // Mozer M C, Jordan M I, Petsche T, eds. Advances in Neural Information Processing Systems. London, UK: MIT Press, 1997,9: 281287 [4] Li Qing, Jiao Licheng, Hao Yingjuan. Adaptive Simplification of Solution for Support Vector Machine. Pattern Recognition, 2007, 40(3): 972980 [5] Smola A J, Schlkopf B. A Tutorial on Support Vector Regression. Statics and Computing, 2004, 14(3): 199222 [6] Suykens J A K, Vandewalle J. Least Squares Support Vector Machines Classifiers. Neural Processing Letters, 1999, 9(3): 293300 [7] Suykens J A K, Gestel T V, Brabanter J D, et al. Least Squares Support Vector Machines. Singapore, Singapore: World Scientific, 2002 [8] An S J, Liu W Q, Venkatesh S. Fast CrossValidation Algorithms for Least Squares Support Vector Machine and Kernel Ridge Regression. Pattern Recognition, 2007, 40(8): 21542162 [9] Suykens J A K, de Brabanter J, Lukas L, et al. Weighted Least Squares Support Vector Machines: Robustness and Sparse Approximation. Neurocomputing, 2002, 48(1): 85105 [10] Wen Wen, Hao Zhifeng, Shao Zhuangfeng, et al. A Heuristic WeightSetting Algorithm for Robust Weighted Least Squares Support Vector Regression // Proc of the 13th International Conference on Neural Information Processing. Hongkong, China, 2006: 773781 [11] Yan Weiwu, Chang Junlin, Shao Huihe. Least Squares SVM Regression Method Based on Sliding Time Window and Its Simulation. Journal of Shanghai Jiaotong University, 2004, 38(4): 524526 (in Chinese) (阎威武,常俊林,邵惠鹤.基于滚动时间窗的最小二积支持向量机回归估计方法及传真.上海交通大学学报, 2004, 38(4): 524526) [12] Suykens J A K, Lukas L, Vandewalle J. Sparse Approximation Using Least Squares Support Vector // Proc of the IEEE International Symposium on Circuits and Systems. Geneva, Switzerland, 2000, Ⅱ: 757760 [13] Baudat G, Anouar F. KernelBased Methods and Function Approximation // Proc of the International Joint Conference on Neural Networks. Washington, USA, 2001, Ⅱ: 12441249 [14] Hang Hongxuan, Han Jiye. Mathematical Programming. Beijing, China: Tsinghua University Press, 2006 (in Chinese) (黄红选,韩继业. 数学规划. 北京:清华大学出版社, 2006) |
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