Comparing Spatial and Spectral Graph Filtering for Preprocessing Neurophysiological Signals

Signals measured with multiple sensors simultaneously in time form multivariate signals and are commonly acquired in biomedical imaging. These temporal signals are generally not independent of each other, but exhibit a rich spatial structure. Graph filtering, either spatial or spectral, is a method that can leverage this spatial structure for various preprocessing tasks, such as graph denoising. Previous studies have focused on learning the parameters of spatial graph impulse response (GIR) filters, while neglecting spectral graph frequency response (GFR) filters, even though GFR filters offer unique advantages in terms of regularisation and interpretation. In this study, we therefore compare learning GIR filters and GFR filters as a trainable preprocessing step for two different neural networks on an Alzheimer’s classification task. We tested both a functional connectivity graph as well as a geometric graph as the base of each filter type, and varied the localisation of the spatial filter. As expected, the retrieved shapes of the trained filters suggest that GFR filters can be interpreted in terms of their graph structure, while the same does not hold for GIR filters. Contrarily, however, we found that only the geometric, highly localised GIR filter outperforms the baseline significantly, surpassing it by 3.8 percentage points. These findings suggest that the observed performance boost of a trained localised GIR filter may in fact not be due to the graph structure. Instead, we hypothesise that this boost is caused by favourable algebraic properties of the filter matrix.