中国物理B ›› 2006, Vol. 15 ›› Issue (6): 1208-1215.doi: 10.1088/1009-1963/15/6/014

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Prediction of chaotic systems with multidimensional recurrent least squares support vector machines

孙建成1, 周亚同2, 罗建国2   

  1. (1)Department of Communication Engineering, University of Finance and Economics, Nanchang 330013, China ;Department of Information and Communication Engineering,Xi'an Jiaotong University, Xi'an 710049, China; (2)Department of Information and Communication Engineering,Xi'an Jiaotong University, Xi'an 710049, China
  • 收稿日期:2005-12-25 修回日期:2006-03-07 出版日期:2006-06-20 发布日期:2006-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 90207012).

Prediction of chaotic systems with multidimensional recurrent least squares support vector machines

Sun Jian-Cheng (孙建成)ab, Zhou Ya-Tong (周亚同)a, Luo Jian-Guo (罗建国)a   

  1. a Department of Communication Engineering, University of Finance and Economics, Nanchang 330013, China; b Department of Information and Communication Engineering, Xi'an Jiaotong University, Xi'an 710049, China
  • Received:2005-12-25 Revised:2006-03-07 Online:2006-06-20 Published:2006-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 90207012).

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摘要： In this paper, we propose a multidimensional version of recurrent least squares support vector machines (MDRLS-SVM) to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens's embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the high-dimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.

关键词: chaotic systems, support vector machines, least squares, noise

Abstract: In this paper, we propose a multidimensional version of recurrent least squares support vector machines (MDRLS-SVM) to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens's embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the high-dimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.

Key words: chaotic systems, support vector machines, least squares, noise

中图分类号:  (Time series analysis)

  • 05.45.Tp
05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)