Scalable Topology-Preserving Graph Coarsening with Graph Collapse
This addresses the scalability issue in topology-preserving graph coarsening for GNN training, offering a more efficient method for researchers and practitioners in graph machine learning.
The paper tackles the problem of graph coarsening for graph neural networks (GNNs) by proposing Scalable Topology-Preserving Graph Coarsening (STPGC), which introduces algorithms based on graph collapse concepts to preserve topological features efficiently, reducing exponential time complexity and demonstrating effectiveness in node classification experiments.
Graph coarsening reduces the size of a graph while preserving certain properties. Most existing methods preserve either spectral or spatial characteristics. Recent research has shown that preserving topological features helps maintain the predictive performance of graph neural networks (GNNs) trained on the coarsened graph but suffers from exponential time complexity. To address these problems, we propose Scalable Topology-Preserving Graph Coarsening (STPGC) by introducing the concepts of graph strong collapse and graph edge collapse extended from algebraic topology. STPGC comprises three new algorithms, GStrongCollapse, GEdgeCollapse, and NeighborhoodConing based on these two concepts, which eliminate dominated nodes and edges while rigorously preserving topological features. We further prove that STPGC preserves the GNN receptive field and develop approximate algorithms to accelerate GNN training. Experiments on node classification with GNNs demonstrate the efficiency and effectiveness of STPGC.