Graph-Variate Signal Analysis

Incorporating graph-based techniques in the analysis of multivariate signals is becoming a standard method to understand the interdependency of activity recorded at different sites. The new research frontier in this field includes the important problem of how to assess dynamic changes of signal activity. We present a unified framework of multivariate signals and network science through the graph-variate signal which opens up new ways to analyse such dynamics at high temporal resolution. This analysis branches off from graph signal processing by considering functions on the graph signal. We illustrate how the appropriate consideration of such functions allow for novel temporal probing of the connectivity information of multivariate signals, here referred to as temporal connectivity. Particularly, we present appropriate functions for three pertinent connectivity metricscorrelation, coherence and the phase-lag index. We also show how the framework allows the computation of classical network measures at the temporal resolution of the signal and can combine dependency and spatial information for analysis. This approach opens up promising new ways to analyse temporal information of networks which is conducive to probing research hypotheses and gathering novel insights based both on the connectivity and transient temporal dynamics of the data.