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基于平均场支持向量机的混沌时间序列预测
引用本文:崔万照,朱长纯,保文星,刘君华.基于平均场支持向量机的混沌时间序列预测[J].中国物理 B,2005,14(5):922-929.
作者姓名:崔万照  朱长纯  保文星  刘君华
作者单位:School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China;School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China;School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China;School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
基金项目:国家自然科学基金资助(60476037 和 60276037)
摘    要:提出了一种新的基于支持向量机的混沌时间序列预测方法,该方法利用平均场理论使支持向量机的学习过程变得简单高效。同时由于该方法将支持向量机的参数近似为高斯分布的,因此采用平均场理论能够容易的求解这些参数,这样获得的支持向量机的参数比传统的基于二次规划的算法更加精确,而且学习速度更快。最后利用该方法对嵌入维数与模型的泛化能力关系进行了探讨,并利用Mackey-Glass时间序列对该方法进行了验证,结果表明:该预测方法能精确地预测混沌时间序列,而且在混沌时间序列的嵌入维数未知时也能取得比较好的预测效果.这一结论预示着平均场支持向量机是一种研究混沌时间序列的有效方法.

关 键 词:混沌时间序列  支持向量机  平均场理论
收稿时间:2004-11-11

Chaotic time series prediction using mean-field theory for support vector machine
Cui Wan-Zhao,Zhu Chang-Chun,Bao Wen-Xing and Liu Jun-Hua.Chaotic time series prediction using mean-field theory for support vector machine[J].Chinese Physics B,2005,14(5):922-929.
Authors:Cui Wan-Zhao  Zhu Chang-Chun  Bao Wen-Xing and Liu Jun-Hua
Institution:School of Electronics and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China
Abstract:This paper presents a novel method for predicting chaotic time series which is based on the support vector machines approach and it uses the mean-field theory for developing an easy and efficient learning procedure for the support vector machine. The proposed method approximates the distribution of the support vector machine parameters to a Gaussian process and uses the mean-field theory to estimate these parameters easily, and select the weights of the mixture of kernels used in the support vector machine estimation more accurately and faster than traditional quadratic programming-based algorithms. Finally, relationships between the embedding dimension and the predicting performance of this method are discussed, and the Mackey-Glass equation is applied to test this method. The stimulations show that the mean-field theory for support vector machine can predict chaotic time series accurately, and even if the embedding dimension is unknown, the predicted results are still satisfactory. This result implies that the mean-field theory for support vector machine is a good tool for studying chaotic time series.
Keywords:chaotic time series  support vector machine  mean-field theory
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