Department of Electrical and Computer Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece.
Department of Complex Systems, Institute of Computer Science of the Czech Academy of Sciences, Pod Vodárenskou věží 2, 182 07 Prague 8, Czech Republic.
Chaos. 2022 May;32(5):053111. doi: 10.1063/5.0087910.
Instantaneous phases extracted from multivariate time series can retain information about the relationships between the underlying mechanisms that generate the series. Although phases have been widely used in the study of nondirectional coupling and connectivity, they have not found similar appeal in the study of causality. Herein, we present a new method for phase-based causality analysis, which combines ideas from the mixed embedding technique and the information-theoretic approach to causality in coupled oscillatory systems. We then use the introduced method to investigate causality in simulated datasets of bivariate, unidirectionally paired systems from combinations of Rössler, Lorenz, van der Pol, and Mackey-Glass equations. We observe that causality analysis using the phases can capture the true causal relation for coupling strength smaller than the analysis based on the amplitudes can capture. On the other hand, the causality estimation based on the phases tends to have larger variability, which is attributed more to the phase extraction process than the actual phase-based causality method. In addition, an application on real electroencephalographic data from an experiment on elicited human emotional states reinforces the usefulness of phases in causality identification.
从多变量时间序列中提取的瞬时相位可以保留生成序列的潜在机制之间关系的信息。尽管相位已广泛用于非定向耦合和连接性的研究，但在因果关系的研究中，它们并没有找到类似的吸引力。在此，我们提出了一种基于相位的因果分析新方法，该方法结合了混合嵌入技术和耦合振荡系统中因果关系的信息论方法的思想。然后，我们使用介绍的方法研究了来自 Rössler、Lorenz、van der Pol 和 Mackey-Glass 方程组合的二元、单向配对系统的模拟数据集的因果关系。我们观察到，使用相位进行因果分析可以捕捉到小于基于幅度的分析可以捕捉到的耦合强度的真实因果关系。另一方面，基于相位的因果估计往往具有更大的可变性，这更多归因于相位提取过程，而不是实际的基于相位的因果方法。此外，在关于诱发人类情绪状态的实验的真实脑电图数据上的应用增强了相位在因果识别中的有用性。
