Stationary subspace analysis of nonstationary processes
提出一种新的平稳子空间分析方法，通过最小化离散傅里叶变换的渐近不相关性来找到非平稳数据的平稳投影，适用于脑电图等信号分析。
Stationary subspace analysis (SSA) is a recent technique for finding linear transformations of nonstationary processes that are stationary in the limited sense that the first two moments or means and lag‐0 covariances are time‐invariant. It finds a matrix that projects the nonstationary data onto a stationary subspace by minimizing a Kullback–Leibler divergence between Gaussian distributions measuring the nonconstancy of the means and covariances across several segments. We propose an SSA procedure for general multivariate, second‐order nonstationary processes. It relies on the asymptotic uncorrelatedness of the discrete Fourier transform of a stationary time series to define a measure of departure from stationarity, which is then minimized to find the stationary subspace. The dimension of the subspace is estimated using a sequential testing procedure, and its asymptotic properties are discussed. We illustrate the broader applicability and better performance of our method in comparison to existing SSA methods through simulations and discuss an application in analyzing electroencephalogram (EEG) data from brain–computer interface (BCI) experiments.