Supervised Community Detection with Line Graph Neural Networks
This addresses the problem of community detection for researchers and practitioners in network analysis, offering a data-driven method that is incremental by building on existing GNN approaches.
The paper tackles community detection in graphs by proposing a novel family of Graph Neural Networks (GNNs) that recast it as a supervised node classification problem, showing they can match or surpass belief propagation performance on stochastic block models and achieve good results on real-world datasets.
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.