Aligning Persistent Homology with Graph Pooling
Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning
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Keywords: graph pooling, persistent homology, graph neural networks
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TL;DR: We investigate the intrinsic similarity between persistent homology and graph pooling, and further develop a mechanism integrating both, consistently achieving substantial improvement on top of several 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 is performed along persistent sub-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. Code is open-sourced at https://anonymous.4open.science/r/TIP.
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Submission Number: 963
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