Multivariate chaotic time series prediction using multiple kernel extreme learning machine

Wang Xin-Ying; Han Min

doi:10.7498/aps.64.070504

Abstract

Multivariate chaotic time series is widely present in nature, such as in economy, society, industry and other fields. Modeling and predicting multivariate time series will help human to better manage, control, and make decision. A prediction method based on multiple kernel extreme learning machine is proposed in this paper to model the complex dynamics of multivariate chaotic time series. First, the multivariate chaotic time series is reconstructed in phase space, transforming the temporal correlation into spatial correlation. Then, a prediction model-multiple kernel extreme learning machine, which combines the multiple kernel learning and extreme learning machine with kernels, is proposed to approximate the nonlinear function of the input - output data in phase space. The proposed multiple kernel extreme learning machine could effectively combine the simple training of extreme learning machine with kernels and the data fusion capabilities of multiple kernel learning. Simulation results based on Lorenz chaotic time series prediction and San Francisco monthly runoff prediction demonstrate that, compared with other state-of-art chaotic time series prediction methods, the proposed multiple kernel extreme learning machine could get a better prediction accuracy.

Keywords:

Authors and contacts

1.
Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116023, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 61374154), and the State Key Development Program for Basic Research of China (973 Program) (Grant No. 2013CB430403).

References

[1]	Deyle E, Sugihara G 2011 PLoS ONE 6 e18295
[2]	De Gooijer J G, Hyndman R J 2006 Int. J. Forecasting 22 443
[3]	Frenzel S, Pompe B 2007 Phys. Rev. Lett. 99 204101
[4]	Wang X Y, Han M 2012 Acta Phys. Sin. 61 80507 (in Chinese) [王新迎, 韩敏 2012 61 80507]
[5]	Grigorievskiy A, Miche Y, Ventela A M, Severin E, Lendasse A 2014 Neural Netw. 51 50
[6]	Butcher J B, Verstraeten D, Schrauwen B, Day C R, Haycock P W 2013 Neural Netw. 38 76
[7]	Tang Z J, Ren F, Peng T, Wang W B 2014 Acta Phys. Sin. 63 50505 (in Chinese) [唐舟进, 任峰, 彭涛, 王文博 2014 63 50505]
[8]	Sapankevych N, Sankar R 2009 IEEE Comput. Intell. M. 4 24
[9]	Huang G B, Zhou H M, Ding X J, Zhang R 2012 IEEE Trans. Syst. Man Cybern. B Cybern. 42 513
[10]	Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[11]	Wang H Q, Sun F C, Cai Y N, Chen N, Ding L G 2010 Acta Autom. Sin. 36 1037 (in Chinese) [汪洪桥, 孙富春, 蔡艳宁, 陈宁, 丁林阁 2010 自动化学报 36 1037]
[12]	Gönen M, Alpaydin E 2011 J. Mach. Learn. Res. 12 2211
[13]	Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 57 2708]
[14]	Rakotomamonjy A, Bach F, Canu S, Grandvalet Y 2008 J. Mach. Learn. Res. 9 2491
[15]	Takens F 1981 Dynam. Syst. Turbul. 898 366
[16]	Liang N Y, Huang G B, Saratchandran P, Sundararajan N 2006 IEEE Trans. Neurl Netw. 17 1411
[17]	Hipel K W, McLeod A I 1994 Time series modelling of water resources and environmental systems. (Amsterdam: Elsevier) p553

Cited By

[1]	Deyle E, Sugihara G 2011 PLoS ONE 6 e18295
[2]	De Gooijer J G, Hyndman R J 2006 Int. J. Forecasting 22 443
[3]	Frenzel S, Pompe B 2007 Phys. Rev. Lett. 99 204101
[4]	Wang X Y, Han M 2012 Acta Phys. Sin. 61 80507 (in Chinese) [王新迎, 韩敏 2012 61 80507]
[5]	Grigorievskiy A, Miche Y, Ventela A M, Severin E, Lendasse A 2014 Neural Netw. 51 50
[6]	Butcher J B, Verstraeten D, Schrauwen B, Day C R, Haycock P W 2013 Neural Netw. 38 76
[7]	Tang Z J, Ren F, Peng T, Wang W B 2014 Acta Phys. Sin. 63 50505 (in Chinese) [唐舟进, 任峰, 彭涛, 王文博 2014 63 50505]
[8]	Sapankevych N, Sankar R 2009 IEEE Comput. Intell. M. 4 24
[9]	Huang G B, Zhou H M, Ding X J, Zhang R 2012 IEEE Trans. Syst. Man Cybern. B Cybern. 42 513
[10]	Huang G B, Zhu Q Y, Siew C K 2006 Neurocomputing 70 489
[11]	Wang H Q, Sun F C, Cai Y N, Chen N, Ding L G 2010 Acta Autom. Sin. 36 1037 (in Chinese) [汪洪桥, 孙富春, 蔡艳宁, 陈宁, 丁林阁 2010 自动化学报 36 1037]
[12]	Gönen M, Alpaydin E 2011 J. Mach. Learn. Res. 12 2211
[13]	Zhang J F, Hu S S 2008 Acta Phys. Sin. 57 2708 (in Chinese) [张军峰, 胡寿松 2008 57 2708]
[14]	Rakotomamonjy A, Bach F, Canu S, Grandvalet Y 2008 J. Mach. Learn. Res. 9 2491
[15]	Takens F 1981 Dynam. Syst. Turbul. 898 366
[16]	Liang N Y, Huang G B, Saratchandran P, Sundararajan N 2006 IEEE Trans. Neurl Netw. 17 1411
[17]	Hipel K W, McLeod A I 1994 Time series modelling of water resources and environmental systems. (Amsterdam: Elsevier) p553

[1]	Huang Wei-Jian, Li Yong-Tao, Huang Yuan. Prediction of chaotic time series using hybrid neural network and attention mechanism. Acta Physica Sinica, 2021, 70(1): 010501. doi: 10.7498/aps.70.20200899
[2]	Mei Ying, Tan Guan-Zheng, Liu Zhen-Tao, Wu He. Chaotic time series prediction based on brain emotional learning model and self-adaptive genetic algorithm. Acta Physica Sinica, 2018, 67(8): 080502. doi: 10.7498/aps.67.20172104
[3]	Shen Li-Hua, Chen Ji-Hong, Zeng Zhi-Gang, Jin Jian. Chaotic time series prediction based on robust extreme learning machine. Acta Physica Sinica, 2018, 67(3): 030501. doi: 10.7498/aps.67.20171887
[4]	Wei De-Zhi, Chen Fu-Ji, Zheng Xiao-Xue. Internet public opinion chaotic prediction based on chaos theory and the improved radial basis function in neural networks. Acta Physica Sinica, 2015, 64(11): 110503. doi: 10.7498/aps.64.110503
[5]	Li Rui-Guo, Zhang Hong-Li, Fan Wen-Hui, Wang Ya. Hermite orthogonal basis neural network based on improved teaching-learning-based optimization algorithm for chaotic time series prediction. Acta Physica Sinica, 2015, 64(20): 200506. doi: 10.7498/aps.64.200506
[6]	Zhang Wen-Zhuan, Long Wen, Jiao Jian-Jun. Parameter determination based on composite evolutionary algorithm for reconstructing phase-space in chaos time series. Acta Physica Sinica, 2012, 61(22): 220506. doi: 10.7498/aps.61.220506
[7]	Mao Yuan, Guo Li-Xin, Din Hui-Fen, Liu Wei. A new method to predict the wind direction from HF radar Doppler spectrum. Acta Physica Sinica, 2012, 61(4): 044201. doi: 10.7498/aps.61.044201
[8]	Li Jun, Zhang You-Peng. Single-step and multiple-step prediction of chaotic time series using Gaussian process model. Acta Physica Sinica, 2011, 60(7): 070513. doi: 10.7498/aps.60.070513
[9]	Zhang Xian, Wang Hong-Li. Selective forgetting extreme learning machine and its application to time series prediction. Acta Physica Sinica, 2011, 60(8): 080504. doi: 10.7498/aps.60.080504
[10]	Zhang Xian, Wang Hong-Li. Incremental regularized extreme learning machine based on Cholesky factorization and its application to time series prediction. Acta Physica Sinica, 2011, 60(11): 110201. doi: 10.7498/aps.60.110201
[11]	Li He, Yang Zhou, Zhang Yi-Min, Wen Bang-Chun. Methodology of estimating the embedding dimension in chaos time series based on the prediction performance of radial basis function neural networks. Acta Physica Sinica, 2011, 60(7): 070512. doi: 10.7498/aps.60.070512
[12]	Zhang Chun-Tao, Ma Qian-Li, Peng Hong. Chaotic time series prediction based on information entropy optimized parameters of phase space reconstruction. Acta Physica Sinica, 2010, 59(11): 7623-7629. doi: 10.7498/aps.59.7623
[13]	Mao Jian-Qin, Ding Hai-Shan, Yao Jian. Chaotic time series prediction based on fuzzy tree. Acta Physica Sinica, 2009, 58(4): 2220-2230. doi: 10.7498/aps.58.2220
[14]	Ma Qian-Li, Zheng Qi-Lun, Peng Hong, Qin Jiang-Wei. Chaotic time series prediction based on fuzzy boundary modular neural networks. Acta Physica Sinica, 2009, 58(3): 1410-1419. doi: 10.7498/aps.58.1410
[15]	Wang Yong-Sheng, Sun Jin, Wang Chang-Jin, Fan Hong-Da. Prediction of the chaotic time series from parameter-varying systems using artificial neural networks. Acta Physica Sinica, 2008, 57(10): 6120-6131. doi: 10.7498/aps.57.6120
[16]	He Tao, Zhou Zheng-Ou. Prediction of chaotic time series based on fractal self-affinity. Acta Physica Sinica, 2007, 56(2): 693-700. doi: 10.7498/aps.56.693
[17]	Zhang Jun-Feng, Hu Shou-Song. Chaotic time series prediction based on RBF neural networks with a new clustering algorithm. Acta Physica Sinica, 2007, 56(2): 713-719. doi: 10.7498/aps.56.713
[18]	Ye Mei-Ying, Wang Xiao-Dong, Zhang Hao-Ran. Chaotic time series forecasting using online least squares support vector machine regression. Acta Physica Sinica, 2005, 54(6): 2568-2573. doi: 10.7498/aps.54.2568
[19]	Li Jun, Liu Jun-Hua. On the prediction of chaotic time series using a new generalized radial basis function neural networks. Acta Physica Sinica, 2005, 54(10): 4569-4577. doi: 10.7498/aps.54.4569
[20]	Tan Wen, Wang Yao-Nan, Zhou　Shao-Wu, Liu　Zu-Run. Prediction of the chaotic time series using neuro-fuzzy networks. Acta Physica Sinica, 2003, 52(4): 795-801. doi: 10.7498/aps.52.795

Catalog

Vol. 64, Issue 7 - 2015-04-05

Metrics

Abstract views: 7309
PDF Downloads: 603
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板