Abstract
Radial basis function (RBF) neural network has very good performance on prediction of chaotic time series, but the precision of prediction is great affected by embedding dimension and delay time of phase-space reconstruction in the process of predicting. Based on hereinbefore problems, we comprehensive optimize embedding dimension and delay time by particle swarm optimization, to get the optimal values of embedding dimension and delay time in RBF single-step and multi-step prediction models. In addition, we made single step and multi-step prediction to the Lorenz system by this method, the results show that the prediction accuracy of optimized prediction model is obvious improved.
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References
Zhao, Y.P., Zhang, L.Y., Li, D.C., Wang, L.F., Jiang, H.Z.: Chaotic Time Series Prediction Using Filtering Window Based Least Squares Support Vector Regression. Acta. Phys. Sin. 62, 120511-1–120511-9 (2013)
Han, M., Xu, M.L.: A Hybrid Prediction Model of Multivariate Chaotic Time Series Based on Error Correction. Acta. Phys. Sin. 62, 120510-1–120510-7 (2013)
Yu, Y.H., Song, J.D.: Redundancy-Test-Based Hyper-Parameters Selection Approach for Support Vector Machines to Predict Time Series. Acta. Phys. Sin. 61, 170516-1–170516-13 (2012)
Zhang, C.T., Liu, X.F., Xiang, R.Y., Liu, J.K., Guo, J.: Multi-Step-Prediction of Chaotic Time Series Based on Maximized Mutual Information. Control and Decision 27, 941–944 (2012)
Arash, M., Majid, A.: Developing a Local Least-Squares Support Vector Machines-Based Neuro-Fuzzy Model for Nonlinear and Chaotic Time Series Prediction. IEEE Transactions on Neural Networks and Learning Systems 24, 207–218 (2013)
Takens, F.: Dynamical Systems and Turbulence. Springer, Berlin (1981)
Fraser, A.M.: Information and Entropy in Strange Attractors. IEEE Transactions on Information Theory 35, 245–262 (1989)
Kugiumtzis, D.: State Space Reconstruction Parameters in the Analysis of Chaotic Time Series-The Role of the Ttime Window Length. Physica D 95, 13–28 (1996)
Kim, H.S., Eykholt, R., Salas, J.D.: Nonlinear Dynamics Delay Times and Embedding Windows. Physica D 127, 48–60 (1999)
Packard, N.H.: Geom Etry From a Time Series. Phys. Rev. Lett. 45, 712–718 (1980)
Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE Int. Conf. on Neural Networks (1995)
Shi, Y.H., Eberhart, R.: A Modified Particle Swarm Optimizer. In: Proc. of IEEE Int. Conf. on Evolutionary Computation (1998)
Parsopoulos, K.E., Vrahatis, M.N.: On the Computation of All Global Minimizers through Particle swarm Optimization. IEEE Trans. on Evolutionary Computation 8, 211–224 (2004)
Trelea, I.C.: The Particle Swarm Optimization Algorithm: Convergence Analysis and Parameter Selection. Information Processing Letters 85, 317–325 (2003)
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Du, B., Xu, W., Song, B., Ding, Q., Chu, SC. (2014). Prediction of Chaotic Time Series of RBF Neural Network Based on Particle Swarm Optimization. In: Pan, JS., Snasel, V., Corchado, E., Abraham, A., Wang, SL. (eds) Intelligent Data analysis and its Applications, Volume II. Advances in Intelligent Systems and Computing, vol 298. Springer, Cham. https://doi.org/10.1007/978-3-319-07773-4_48
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DOI: https://doi.org/10.1007/978-3-319-07773-4_48
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07772-7
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