The Effect of Graph Frequencies on Dynamic Structures in Graph Signal Processing

Multivariate signals are signals consisting of multiple signals measured simultaneously over time and are most commonly acquired by sensor networks. The emerging field of graph signal processing (GSP) promises to analyse dynamic characteristics of multivariate signals, while at the same time taking the network, or spatial structure between the signals into account. To do so, GSP decomposes the multivariate signals into graph frequency signals, which are ordered by their magnitude. However, the meaning of the graph frequencies in terms of this ordering remains poorly understood. Here, we investigate the role the ordering plays in preserving valuable dynamic structures in the signals, with neuroimaging applications in mind. In order to overcome the limitations in sample size common to neurophysiological data sets, we introduce a minimalist simulation framework to generate arbitrary amounts of data. Using this artificial data, we find that lower graph frequency signals are less suitable for classifying neurophysiological data than higher graph frequency signals. We further introduce a baseline testing framework for GSP. Using this framework, we conclude that dynamic, or spectral structures are poorly preserved in GSP, high-lighting current limitations of GSP for neuroimaging.