Rhomboid Tiling for Geometric Graph Deep Learning

TL;DR

This paper introduces Rhomboid Tiling clustering and RTPool, a novel hierarchical pooling method for GNNs that captures complex geometric features, significantly improving graph classification performance.

Contribution

It proposes Rhomboid Tiling clustering to incorporate geometric information into GNNs and develops RTPool, a hierarchical pooling model leveraging this clustering for enhanced graph classification.

Findings

Outperforms 21 state-of-the-art methods on benchmark datasets

Effectively captures higher-order geometric structures in graphs

Demonstrates superior accuracy in graph classification tasks

Abstract

Graph Neural Networks (GNNs) have proven effective for learning from graph-structured data through their neighborhood-based message passing framework. Many hierarchical graph clustering pooling methods modify this framework by introducing clustering-based strategies, enabling the construction of more expressive and powerful models. However, all of these message passing framework heavily rely on the connectivity structure of graphs, limiting their ability to capture the rich geometric features inherent in geometric graphs. To address this, we propose Rhomboid Tiling (RT) clustering, a novel clustering method based on the rhomboid tiling structure, which performs clustering by leveraging the complex geometric information of the data and effectively extracts its higher-order geometric structures. Moreover, we design RTPool, a hierarchical graph clustering pooling model based on RT clustering for graph classification tasks. The proposed model demonstrates superior performance, outperforming 21 state-of-the-art competitors on all the 7 benchmark datasets.