Supervised Community Detection with Line Graph Neural Networks

TL;DR

This paper introduces a novel supervised GNN approach augmented with non-backtracking operators for community detection, outperforming traditional algorithms and analyzing the optimization landscape.

Contribution

It presents a new GNN architecture using line graph non-backtracking operators for community detection, achieving competitive results without relying on generative models.

Findings

GNNs match or surpass belief propagation performance on stochastic block models

Models perform well on real-world datasets

Analysis shows local and global minima are close in loss landscape

Abstract

Traditionally, community detection in graphs can be solved using spectral methods or posterior inference under probabilistic graphical models. Focusing on random graph families such as the stochastic block model, recent research has unified both approaches and identified both statistical and computational detection thresholds in terms of the signal-to-noise ratio. By recasting community detection as a node-wise classification problem on graphs, we can also study it from a learning perspective. We present a novel family of Graph Neural Networks (GNNs) for solving community detection problems in a supervised learning setting. We show that, in a data-driven manner and without access to the underlying generative models, they can match or even surpass the performance of the belief propagation algorithm on binary and multi-class stochastic block models, which is believed to reach the computational threshold. In particular, we propose to augment GNNs with the non-backtracking operator defined on the line graph of edge adjacencies. Our models also achieve good performance on real-world datasets. In addition, we perform the first analysis of the optimization landscape of training linear GNNs for community detection problems, demonstrating that under certain simplifications and assumptions, the loss values at local and global minima are not far apart.