GraphReach: Position-Aware Graph Neural Network using Reachability Estimations
This addresses a limitation in GNNs for predictive tasks that rely on node positions, offering a novel method with significant performance gains.
The paper tackles the problem of graph neural networks (GNNs) failing to encode node positions, which limits performance in tasks requiring such information, by developing GraphReach, a position-aware inductive GNN that uses reachability estimations with anchor nodes, resulting in up to 40% relative accuracy improvement and increased robustness to adversarial attacks.
Majority of the existing graph neural networks (GNN) learn node embeddings that encode their local neighborhoods but not their positions. Consequently, two nodes that are vastly distant but located in similar local neighborhoods map to similar embeddings in those networks. This limitation prevents accurate performance in predictive tasks that rely on position information. In this paper, we develop GraphReach, a position-aware inductive GNN that captures the global positions of nodes through reachability estimations with respect to a set of anchor nodes. The anchors are strategically selected so that reachability estimations across all the nodes are maximized. We show that this combinatorial anchor selection problem is NP-hard and, consequently, develop a greedy (1-1/e) approximation heuristic. Empirical evaluation against state-of-the-art GNN architectures reveal that GraphReach provides up to 40% relative improvement in accuracy. In addition, it is more robust to adversarial attacks.