论文标题
通过双变量翻译不变性在图上的平稳性
Stationarity of Time-Series on Graph via Bivariate Translation Invariance
论文作者
论文摘要
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进行随后的分析。但是，在许多复杂的现实世界情景中，随机过程位于不规则的图结构上，CSP丢弃了分析此类结构化数据的基础结构。然后，必须建立一个新的框架来通过考虑基础结构来分析高维图结构的随机信号。为此，借着操作器理论的镜头，我们首先提出了一个新的双变量连接转换操作员（JTO），符合其他信号域中翻译运算符的结构特征。此外，我们根据提出的JTO表征了时间vertex过滤。于是，我们使用所提出的等距JTO及其频谱表征提出了时间vertex域中关节宽宽固定（JWSS）信号的新定义。然后提出了一个新的关节功率频谱密度（JPSD）估计器，称为广义Welch方法（GWM）。提供了仿真结果以显示此JPSD估计器的功效。此外，为了显示JWSS建模的有用性，我们专注于图表上的时间序列的分类。为此，通过将脑脑电图（EEG）信号建模为JWSS过程，我们将JPSD用作情感和阿尔茨海默氏病（AD）识别的特征。实验结果表明，与经典的功率谱密度（PSD）和Graph PSD（GPSD）相比，JPSD作为两种应用程序设置的特征相比，产生了卓越的情绪和AD识别精度。最终，我们提供了一些结论性的评论。
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.
