Low-Rank Projections of GCNs Laplacian

TL;DR

This paper investigates how spectral filtering affects GCNs in community detection, revealing that low-frequency components contain most of the classification information, enabling high accuracy with simple low-frequency classifiers.

Contribution

It demonstrates that low-frequency spectral components are sufficient for effective community detection in GCNs, challenging the emphasis on high-frequency information.

Findings

Low frequencies contain most information for node classification.

High frequencies are less crucial for community detection.

Simple classifiers using only low frequencies can achieve state-of-the-art accuracy.

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 performance 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.