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

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.