Stationary subspace analysis of nonstationary processes
Stationary subspace analysis of nonstationary processes
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DOI：
10.1111/jtsa.12274
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发表时间：
2018-05-01
影响因子：
0.9
通讯作者：
Pourahmadi, Mohsen
中科院分区：
文献类型：
--
作者：
Sundararajan, Raanju Ragavendar;Pourahmadi, Mohsen
平稳子空间分析（Stationary Subspace Analysis，SSA）是一种寻找非平稳过程的线性变换的新技术，它在有限意义下是平稳的，即前两阶矩或均值和滞后0协方差是时不变的。它找到一个矩阵，通过最小化高斯分布之间的Kullback-Leibler散度将非平稳数据投影到一个平稳子空间上，测量几个段之间的均值和协方差的不恒定性。我们提出了一般的多元，二阶非平稳过程的SSA程序。它依赖于平稳时间序列的离散傅立叶变换的渐近不相关性来定义偏离平稳性的度量，然后将其最小化以找到平稳子空间。子空间的维数估计使用序贯检验程序，并讨论其渐近性质。我们通过模拟说明了与现有的SSA方法相比，我们的方法具有更广泛的适用性和更好的性能，并讨论了在分析脑机接口（BCI）实验中的脑电（EEG）数据中的应用。
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.