An optimal training subset online fuzzy least squares support vector machine (OTSOF-LSSVM) is proposed for chaotic time series prediction. Samples nearest to the prediction sample in both time and space are chosen to form the optimal training subset. An "-insensitive function is introduced to formulate the fuzzy membership. Thus a prediction model is established by fuzzy LSSVM. The subset and model are updated with the moving time window. Computational complexity is reduced by matrix partitioning. Experiment of predicting the time-variant chaotic time series Ikeda shows that the proposed method has better accuracy and high training speed as compared to offline and online LSSVM.
WEN Xiang-xi, MENG Xiang-ru, LI Ming-xun
. Chaotic Time Series Prediction Based on Optimal Training Subset Online Fuzzy LSSVM[J]. Journal of Applied Sciences, 2013
, 31(4)
: 411
-417
.
DOI: 10.3969/j.issn.0255-8297.2013.04.012
[1] KHATIBI R, Bellie SIVAKUMAR B, Mohammad Ali GHORBANI M A, Ozgur KISI O, Kasim KOÇAK K, Davod Farsadi ZADEH D F. Investigating chaos in river stage and discharge time series [J]. Journal of Hydrology, 2012, 414-415: 108-117.
[2] LI Huaqing, LIAO Xiaofeng, LI Chuandong, LI Chaojie. Chaos control and synchronization via a novel chatter free sliding mode control strategy [J]. Neurocomputing, 2011, 74: 3212-3222.
[3] DU Jianguo, HUANG Tingwen, SHENG Zhaohan, ZHANG Haibin. A new method to control chaos in an economic system [J]. Applied Mathematics and Computation, 2010, 217: 2370-2380.
[4] De PAULA A S, SAVI M A. Comparative analysis of chaos control methods: a mechanical system case study [J]. International Journal of Non-Linear Mechanics 2011, 46(8): 1076-1089.
[5] SMITH R K, GRABOWSKI M, CAMLEY R E. Period doubling toward chaos in a driven magnetic macrospin [J]. Journal of Magnetism and Magnetic Materials, 2010, 322: 2127-2134.
[6] LI Hengchao, ZHANG Jiashu, XIAO Xianci. Neural Volterra(是人名吗？) filter for chaotic time series prediction [J]. Chinese physics, 2005, 14(11): 2181-2188.（是人名，滤波方法）
[7] Alan Wolf, Jack B Swift, Harry L Swinney, John A. Vastano. Determining Lyapunov exponents from a time series [J]. Physics D, 1985, 16(2): 285-317.
[8] 张勇，关伟. 基于最大李亚普诺夫指数的改进混沌时间序列预测 [J]. 信息与控制，2009, 38(3): 360-364.
Zhang Yong, Guan Wei. An improved method for forecasting chaotic time series based on maximum Lyapunov exponent [J]. Information and Control, 2009, 38(3): 360-364. (in Chinese)
[9] Han M, Xi J, Xu S, Yin F L. Prediction of chaotic time series based on the recurrent predictor neural network [J]. IEEE Transaction on Signal Processing, 2004, 52(12): 3409-3416.
[10] MA Qianli, ZHENG Qilun, PENG Hong, ZHONG Tanwei, QIN Jiangwei. Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network [J]. Chinese Physics B, 2008, 17(2): 536-542.
[11] DU H, ZHANG N. Time series prediction using evolving radial basis function networks with encoding scheme [J]. Neurocomputing, 2008, 71: 1388-1400.
[12] VAPNIK V. Statistical learning theory [M]. New York: Wiley, 1998.
[13] 崔万照，朱长纯，保文星. 混沌时间序列的支持向量机预测 [J]. 物理学报，2004, 53(10): 3303-3310.
CUI Wanzhao, ZHU Changchun, BAO Wenxing. Prediction of the chaotic time series using support vector machines [J]. Acta Physica Sinica, 2004, 53(10): 3303-3310. (in Chinese)
[14] CUI Wanzhao, ZHU Changchun, BAO Wenxing, LIU Junhua. Chaotic time series prediction using mean-field theory for support vector machine [J]. Chinese physics, 2005, 14(4): 922-927.
[15] MA J, THEILER J, PERKINS S. Accurate online support vector regression [J]. Neural Computation, 2003, 15(11): 2683-2703.
[16] SUYKENS J A K, VANDEWALLE J. Least squares support vector machine classifiers [J]. Neural Processing Letters, 1999, 9(3): 293-300.
[17] 叶美盈，汪晓东，张浩然. 基于在线最小二乘支持向量机回归的混沌时间序列预测 [J]. 物理学报，2005, 54(6): 2568-2573.
YE Meiying, WANG Xiaodong, ZHANG Haoran. Chaotic time series forecasting using online least squares support vector machine regression [J]. Acta Physica Sinica, 2005, 54(6): 2568-2573. (in Chinese)
[18] 肖支才，王杰，王永生. 基于在线LS-SVM算法的变参数混沌时间序列预测 [J]. 航空计算技术，2010, 40(3): 29-33.
XIAO Zhicai, WANG Jie, WANG Yongsheng. Predict the time series of the parameter-varying chaotic system based on recursive lease square support vector machine (RLS-SVM) [J]. Aeronautical Computing Technique, 2010, 40(3): 29-33. (in Chinese)
