Topological Pooling on Graphs

Graph neural networks (GNNs) have demonstrated a significant success in various graph learning tasks, from classification to anomaly detection. There recently has emerged number of approaches adopting pooling operation within GNNs, with goal preserve attributive and structural features during the representation learning. However, most existing operations suffer limitations relying on node-wise neighbor weighting embedding, which leads insufficient encoding rich topological structures node attributes exhibited by real-world networks. By invoking machinery persistent homology concept landmarks, we propose novel layer witness complex-based embedding mechanism that allow us systematically integrate hidden information at both local global levels. Specifically, design new learnable representations Wit-TopoPool simultaneously extract discriminative graphs. Experiments 11 diverse benchmark datasets against 18 baseline models conjunction tasks indicate significantly outperforms all competitors across datasets.