A Spectral Perspective on Deep Supervised Community Detection

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 Euclidean graph (e.g., images), high-frequencies are less crucial to community detection. In particular, it is possible to obtain accuracies at a state-of-the-art level with simple classifiers that rely only on a few low frequencies: this is surprising because contrary to GCNs, no cascade of filtering along the graph structure is involved and it indicates that the important spectral components for the supervised community detection task are essentially in the low-frequency domain.

One-sentence Summary: We study the numerical performances of GCNs in the spectral domain and show that only a few low frequencies allow MLPs to become competitive.

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