Beyond Node Classification: Group Detection through Learned Graph Coarsening

Money-laundering schemes, coordinated manipulation on social platforms, and fraud rings are inherently group-level: the object of interest is a coordinated set of nodes whose members may appear unremarkable in isolation. Yet graph-learning approaches often reduce such problems to node-level prediction. We address group detection directly, treating the group itself as the prediction unit. We formulate the task as learned graph coarsening: from training groups, we learn a target subspace under which unknown groups emerge as supernodes. We characterize the target-subspace properties required for coarsening to detect groups and translate them into a learning objective. We parameterize the target with a GNN, enabling sparse computation and inductive transfer to unseen graphs. We establish bounds on group-indicator distortion and supernode purity. To convert the learned target into group predictions, we adapt Ward clustering, introduce a merge score linked to coarsening error, and derive sufficient conditions for exact group recovery. Experiments demonstrate high-precision detection across synthetic, financial, and large community graphs, with transfer to unseen graphs.