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For multivariate chaotic time series prediction problem, a prediction based on input variable selection and extreme learning machine is proposed in this paper. The multivariate chaotic time series is reconstructed in phase space, and a mutual information based method is used to select the input variables, which have high statistics information with the output variables. The extreme learning machine is conducted to model the multivariate chaotic time series in the phase space by utilizing its approximation capability. In order to improve the prediction accuracy, a model selection algorithm is conducted for extreme learning machine to choose an expected minimum risk prediction model. Simulation results based on Lorenz, Rssler multivariate chaotic time series and Rssler hyperchaotic time series show the effectiveness of the proposed method.
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Keywords:
- chaotic time series prediction /
- input variables selection /
- extreme learning machine /
- model selection
[1] Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys. Sin. 59 1576 (in Chinese) [张淑清, 贾健, 高敏, 韩叙 2010 物理学报 59 1576]
[2] Cao L, Mees A, Judd K 1998 Physica D 121 75
[3] Chakraborty K, Mehrotra K, Mohan C K, Ranka S 1992 Neural Networks 5 961
[4] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 2708]
[5] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 5057 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 5057]
[6] Han M, Shi Z W, Guo W 2007 Acta Phys. Sin. 56 43 (in Chinese) [韩敏, 史志伟, 郭伟 2007 物理学报 56 43]
[7] Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[8] Chapelle O, Vapnik V, Bengio Y 2002 Mach. Learn. 48 9
[9] Takens F 1981 Dynam. Syst. Turbul. 898 366
[10] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 物理学报 59 7623]
[11] Kohavi R, John G H 1997 Artif. Intell. 97 273
[12] Peng H, Long F, Ding C 2005 IEEE Trans. Pattern Anal. Mach. Intell. 27 1226
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[1] Zhang S Q, Jia J, Gao M, Han X 2010 Acta Phys. Sin. 59 1576 (in Chinese) [张淑清, 贾健, 高敏, 韩叙 2010 物理学报 59 1576]
[2] Cao L, Mees A, Judd K 1998 Physica D 121 75
[3] Chakraborty K, Mehrotra K, Mohan C K, Ranka S 1992 Neural Networks 5 961
[4] Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 物理学报 57 2708]
[5] Song Q S, Feng Z R, Li R H 2009 Acta Phys. Sin. 58 5057 (in Chinese) [宋青松, 冯祖仁, 李人厚 2009 物理学报 58 5057]
[6] Han M, Shi Z W, Guo W 2007 Acta Phys. Sin. 56 43 (in Chinese) [韩敏, 史志伟, 郭伟 2007 物理学报 56 43]
[7] Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[8] Chapelle O, Vapnik V, Bengio Y 2002 Mach. Learn. 48 9
[9] Takens F 1981 Dynam. Syst. Turbul. 898 366
[10] Zhang C T, Ma Q L, Peng H 2010 Acta Phys. Sin. 59 7623 (in Chinese) [张春涛, 马千里, 彭宏 2010 物理学报 59 7623]
[11] Kohavi R, John G H 1997 Artif. Intell. 97 273
[12] Peng H, Long F, Ding C 2005 IEEE Trans. Pattern Anal. Mach. Intell. 27 1226
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