Topological Relational Learning on Graphs
This addresses robustness and performance issues in graph learning for applications like node classification, representing an incremental improvement by combining topological methods with existing GNNs.
The paper tackles the over-smoothing and vulnerability to perturbations in graph neural networks (GNNs) by proposing a topological relational inference (TRI) framework, which integrates higher-order graph information and rewires graphs using persistent homology, resulting in outperforming 14 state-of-the-art baselines on 6 out of 7 graphs and up to 10% better performance under noisy scenarios.
Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framework of topological relational inference (TRI) which allows for integrating higher-order graph information to GNNs and for systematically learning a local graph structure. The key idea is to rewire the original graph by using the persistent homology of the small neighborhoods of nodes and then to incorporate the extracted topological summaries as the side information into the local algorithm. As a result, the new framework enables us to harness both the conventional information on the graph structure and information on the graph higher order topological properties. We derive theoretical stability guarantees for the new local topological representation and discuss their implications on the graph algebraic connectivity. The experimental results on node classification tasks demonstrate that the new TRI-GNN outperforms all 14 state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to perturbations, yielding up to 10\% better performance under noisy scenarios.