Networked scatter plot bidirectional coupling detection and its application in the diagnosis of depression

Abstract

Identifying the bidirectional coupling of bivariate time series is a basic problem in the analysis of complex systems in contemporary science. As an intuitive statistical graphical analysis tool, scatter plot allows direct analysis of the correlation between two bivariate time series. However, the scatter plot itself have the problems of not being able to conduct bidirectional coupling analysis and data points overlap. In this work, by introducing inner composition alignment (IOTA) and ordinal pattern transition network (OPTN) into scatter plot, the limitations of scatter plot are alleviated and a new approach for measuring bivariate time series bidirectional coupling is proposed. To facilitate the integration of the three methods, the IOTA scatter plot proposed and the new scatter plot been partitioned and coded. The coded partitions are defined as network nodes and a directed weighted network is constructed based on the temporal adjacency of the nodes. For the constructed OPTN, the mean output degree that commonly used in OPTN is used as a quantitative indicator of coupling strength. To test the characteristics and performance of the new method, it is used to analyse the unidirectional coupled Lorentz model and to compare it with existing methods. The results showed the new method had the advantages of easy parameter setting, efficiency, and suitable for short time series. Finally, the real EEG dataset from depressed patients at rest are analysed and some useful and interesting results are obtained by treating the relevant brain areas as routers.