Graph Pooling via Ricci Flow
Abstract: Graph Machine Learning often involves the clustering of nodes based on similarity structure encoded in the graph’s topology and the nodes’ attributes. On homophilous graphs, the integration of pooling layers has been shown to enhance the performance of Graph Neural Networks by accounting for inherent multi-scale structure. Here, similar nodes are grouped together to coarsen the graph and reduce the input size in subsequent layers in deeper architectures. In both settings, the underlying clustering approach can be implemented via graph pooling operators, which often rely on classical tools from Graph Theory. In this work, we introduce a graph pooling operator (ORC-Pool), which utilizes a characterization of the graph’s geometry via Ollivier’s discrete Ricci curvature and an associated geometric flow. Previous Ricci flow based clustering approaches have shown great promise across several domains, but are by construction unable to account for similarity structure encoded in the node attributes. However, in many ML applications, such information is vital for downstream tasks. ORC-Pool extends such clustering approaches to attributed graphs, allowing for the integration of geometric coarsening into Graph Neural Networks as a pooling layer.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: In response to the reviewer's comments, we have made the following main changes to the manuscript:
1. We have added results for GCN without pooling layers (“No Pool”) for the node- and graph-level tasks. We observe that pooling layers, including ORC-Pool, improve performance across data sets.
2. We have added Graclus as an additional baseline. We observe that ORC-Pool achieves a larger performance boost than Graclus on almost all data sets, confirming the previously observed competitive performance of our proposed ORC-Pool approach.
3. We have incorporated the reviewers' feedback on improving the structure and clarity of writing. This includes an overview of the SRC component of the main pooling baselines in this study.
We have addressed further comments by the reviewers in a second revision.
Assigned Action Editor: ~Mark_Coates1
Submission Number: 3474
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