Low-rank projections of GCNs Laplacian

Nathan Grinsztajn, Philippe Preux, Edouard Oyallon

Keywords: GCN, graph spectrum, stability, graph Laplacian

Abstract: In this work, we study the behavior of standard models for community detection under spectral manipulations. Through various ablation experiments, we evaluate the impact of bandpass filtering on the numerical performances of a GCN: we empirically show that most of the necessary and used information for nodes classification is contained in the low-frequency domain, and thus contrary to images, high-frequencies are less crucial to community detection. In particular, it is sometimes possible to obtain accuracies at a state-of-the-art level with simple classifiers that rely only on a few low frequencies.