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Incorporating graphs in the analysis of multivariate signals is becoming a standard way to understand the interdependency of activity recorded at different sites. The new research frontier in this direction includes the important problem of how to assess dynamic changes of signal activity. We address this problem in a novel way by defining the graph-variate signal alongside methods for its analysis. Essentially, graph-variate signal analysis leverages graphs of reliable connectivity information to filter instantaneous bivariate functions of the multivariate signal. This opens up a new and robust approach to analyze joint signal and network dynamics at sample resolution. When graph connectivity is estimated from the multivariate signal itself, the appropriate consideration of instantaneous graph signal functions allows for a novel dynamic connectivity measure— graph-variate dynamic (GVD) connectivity —which is robust to spurious short-term dependencies. For this, we present appropriate functions for correlation, coherence and the phase-lag index. We show that our approach can determine signals with a single correlated couple against wholly uncorrelated signals up to 128 nodes in size (1 out of 8128 weighted edges). GVD connectivity is also shown to be more robust than other GSP approaches at detecting a randomly traveling spheroid on a three-dimensional grid and standard dynamic connectivity in determining differences in EEG resting-state and task-related activity.
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