Graph Inference Representation: Learning Graph Positional Embeddings with Anchor Path Encoding

Abstract: Learning node representations that incorporate information from graph structure benefits wide range of tasks on graph. The majority of existing graph neural networks (GNNs) have limited power in capturing position information for a given node. The idea of positioning nodes with selected anchors has been exploited, yet mainly relying on explicit labeling of distance information. Here we propose Graph Inference Representation (GIR), an anchor based GNN model encoding path information related to pre-selected anchors for each node. Abilities to get position-aware embeddings are theoretically and experimentally investigated on GIR and its core variants. Further, the complementarity between GIRs and typical GNNs is demonstrated. We show that GIRs get outperformed results in position-aware scenarios, and performances on typical GNNs could be improved by fusing GIR embeddings.