- Abstract: We study data-driven methods for community detection on graphs, an inverse problem that is typically solved using the spectrum of certain operators or via posterior inference under certain 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. Community detection can be recast as a node-wise graph classification problem and therefore studied 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 multiclass stochastic block models, which is known to reach the computational threshold in these cases. In particular, we propose to augment GNNs with the non-backtracking operator defined on the line graph of edge adjacencies. The GNNs are also tested on real datasets, yielding better performance than other published models. In addition, we perform the first analysis of the optimization landscape of using GNNs to solve community detection problems, demonstrating that under certain simplifications and assumptions, the loss value at any local minimum is close to the loss value at the global minimum/minima.
- Keywords: community detection, graph neural networks, belief propagation, energy landscape, non-backtracking operator
- TL;DR: We propose a novel graph neural network architecture based on the non-backtracking operator defined over edge adjacencies and demonstrate its effectiveness on community detection tasks on graphs.