混沌时间序列的支持向量机预测

根据混沌动力系统的相空间延迟坐标重构理论,基于支持向量机的强大的非线性映射能力, 建立了混沌时间序列的支持向量机预测模型,并在统计学习理论的基础上采用最小二乘方法来训练预测模型,利用该模型对嵌入维数与模型的均方根误差的关系进行了探讨.最后利用Mackey-Glass时间序列和变参数的Ikeda 时间序列对该模型进行了验证,结果表明,该预测模型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最小二乘法

Prediction of the chaotic time series using support vector machines

Based on the powerful nonlinear mapping ability of support vector machines, the forecasting model of support vector machines in combination with Takens' delay coordinate phase reconstruction of chaotic time series has been established, and from the statistical learning theory, the least squares method is used to train this model. Moreover, using this model, relationships between the embedding dimension and mean-square-error of this model are discussed. Finally, the Mackey-Glass equation and the Ikeda map whose parameter values changing with time are,respectively, applied to test this model, and the results show that the support vector machine can predict chaotic time series accurately, even if the embedding dimension is unknown, and the predicted results are satisfied. This result implies that the support vector machine is a good tool to study chaotic time series.