Boosting Graph Pooling with Persistent Homology

TL;DR

This paper introduces a novel graph pooling mechanism that leverages persistent homology to incorporate global topological invariance, resulting in improved performance and interpretability in graph neural networks.

Contribution

It proposes a new method for integrating persistent homology into graph pooling layers, enhancing topological invariance and model performance.

Findings

Consistent performance improvements across multiple datasets.

Enhanced interpretability of graph pooling through topological features.

Wide applicability to various graph pooling methods.

Abstract

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.