-
多元混沌时间序列广泛存在于自然、经济、社会、工业等领域. 对多元混沌时间序列进行建模预测有助于人类更好地管理, 控制与决策. 针对多元混沌时间序列的建模预测问题, 本文提出一种基于多核极端学习机的预测方法. 首先对多元混沌时间序列进行相空间重构, 将多元混沌时间序列序列的时间相关性转化为空间相关性. 提出一种结合多核学习算法与核极端学习机模型的多核极端学习机建立相空间中输入输出数据的非线性映射. 多核极端学习机模型结合了多核学习算法的数据融合能力以及核极端学习机的训练简便优势. 基于Lorenz混沌时间序列预测和San Francisco河流月径流量预测的仿真实验表明, 与其他常见混沌时间序列预测方法相比, 本文提出的基于多核极端学习机的多元混沌时间序列预测方法具有更小的预测误差.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:
- chaotic time series /
- neural networks /
- kernel methods /
- prediction
[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] 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
计量
- 文章访问数: 7308
- PDF下载量: 603
- 被引次数: 0
下载:
