基于二元平移不变性的图上时间序列平稳性
Stationarity of Time-Series on Graph via Bivariate Translation Invariance
摘要：
平稳性是经典信号处理（CSP）的基石，用于建模和表征各种随机信号以用于随后的分析。然而，在许多复杂的现实世界中，随机过程位于不规则的图形结构上，CSP在分析这种结构化数据时丢弃了底层结构。因此，有必要建立一个新的分析框架来分析高维图结构的随机信号。为此，通过算子理论的视角，我们首先提出了一种新的二元等距联合平移算子（JTO），它与其他信号域中平移算子的结构特征相一致。此外，我们表征时间顶点滤波的基础上提出的JTO。在此基础上，我们提出了一个新的定义联合广义平稳（JWSS）信号的时间-顶点域的建议等距JTO及其频谱特征。在此基础上，提出了一种新的联合功率谱密度（JPSD）估计方法--广义Welch方法（GWM）.仿真结果显示了这种JPSD估计的有效性。此外，为了显示JWSS建模的有用性，我们专注于图上的时间序列的分类。为此，通过将脑电（EEG）信号建模为JWSS过程，我们使用JPSD作为情感和阿尔茨海默病（AD）识别的特征。实验结果表明，JPSD产生优越的情感和AD识别精度相比，经典的功率谱密度（PSD）和图形PSD（GPSD）作为这两个应用程序的特征集。最后，我们提出一些结论性意见。
英文摘要：
Stationarity is a cornerstone in classical signal processing (CSP) for modeling and characterizing various stochastic signals for the ensuing analysis. However, in many complex real world scenarios, where the stochastic process lies over an irregular graph structure, CSP discards the underlying structure in analyzing such structured data. Then it is essential to establish a new framework to analyze the high-dimensional graph structured stochastic signals by taking the underlying structure into account. To this end, looking through the lens of operator theory, we first propose a new bivariate isometric joint translation operator (JTO) consistent with the structural characteristic of translation operators in other signal domains. Moreover, we characterize time-vertex filtering based on the proposed JTO. Thereupon, we put forth a new definition of joint wide-sense stationary (JWSS) signals in time-vertex domain using the proposed isometric JTO together with its spectral characterization. Then a new joint power spectral density (JPSD) estimator, called generalized Welch method (GWM), is presented. Simulation results are provided to show the efficacy of this JPSD estimator. Furthermore, to show the usefulness of JWSS modeling, we focus on the classification of time-series on graph. To that end, by modeling the brain Electroencephalography (EEG) signals as JWSS processes, we use JPSD as the feature for the Emotion and Alzheimer's disease (AD) recognition. Experimental results demonstrate that JPSD yields superior Emotion and AD recognition accuracy in comparison with the classical power spectral density (PSD) and graph PSD (GPSD) as the feature set for both applications. Eventually, we provide some concluding remarks.
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