基于相重构和主流形识别的非线性时间序列降噪方法

Nonlinear time series noise reduction method based on phase reconstruction and principal manifold learning

提出了一种基于相重构和主流形识别的非线性时间序列降噪方法.带噪的时间序列在高维的相空间中其本质特征隐含在一个低维的主流形中,利用局部切空间变换方法提取其主流形,再根据主流形对时间序列进行重构,就可以达到降噪的目的.与现有的非线性时间序列消噪算法不同,基于主流形的消噪算法更强调时间序列的整体结构.数值仿真分析的结果验证了该降噪方法能有效地消除非线性时间序列中的高斯白噪声.

A noise reduction method in nonlinear time series based on phase reconstruction and manifold learning was proposed. In a high dimensional phase space, the inherent features of time series were exhibited as a low dimensional nonlinear principal manifold. The noise was reduced by the reconstruction with the underlying manifold which was obtained through a local tangent space alignment algorithm. Different from the existent noise reduction methods in nonlinear time series, the method based on principal manifold learning emphasized more on the global structure of time series. The results of numerical simulation proved that the method could remove the Gaussian white noise in nonlinear time series effectively.