Understanding Concepts in Graph Signal Processing for Neurophysiological Signal Analysis

Multivariate signals measured simultaneously over time by sensor networks are becoming increasingly common. The emerging field of graph signal processing (GSP) promises to analyse spectral characteristics of these multivariate signals, while also taking the spatial structure between the time signals into account. A core idea in GSP is the graph Fourier transform, which projects a multivariate signal onto frequency-ordered graph Fourier modes and can be regarded as a spatial analogue of the classical Fourier transform. This chapter derives and discusses key concepts in GSP, with a specific focus on understanding the differences between parallel formulations and the interconnections between the various concepts. The experimental section focuses on the role of graph frequency in data classification, with applications to neuroimaging. To shed light on graph frequencies individually, sample sizes larger than those of relevant empirical data sets are needed. We therefore introduce a minimalist simulation to generate sufficiently many signals, which share key characteristics with neurophysiological signals. Using this artificial data, we find that higher graph frequency signals are more suitable for classification as compared to lower graph frequency signals and propose GSP mechanisms to explain our findings. Finally, we present a baseline testing framework for GSP. Using this framework, our results suggest that GSP may be applicable for dimensionality reduction in neurophysiological signals.