Boosting Graph Pooling with Persistent Homology
Chaolong Ying Xinjian Zhao Tianshu Yu
Recently, there has been an emerging trend to integrate persistent homology
(PH) into graph neural networks (GNNs) to enrich expressive power. However,
naively plugging PH features into GNN layers always results in marginal
improvement with low interpretability. In this paper, we investigate a novel
mechanism for injecting global topological invariance into pooling layers using
PH, motivated by the observation that filtration operation in PH naturally
aligns graph pooling in a cut-off manner. In this fashion, message passing in
the coarsened graph acts along persistent pooled topology, leading to improved
performance. Experimentally, we apply our mechanism to a collection of graph
pooling methods and observe consistent and substantial performance gain over
several popular datasets, demonstrating its wide applicability and flexibility.