Rhomboid Tiling for Geometric Graph Deep Learning

2025-05-14

AI Summary

Existing graph neural networks (GNNs) heavily rely on topological connectivity and struggle to effectively capture higher-order geometric structures inherent in geometric graphs. To address this, we propose RTPool—a geometric-aware, hierarchical graph pooling method grounded in rhomboid tiling—marking the first integration of discrete geometric tiling structures into graph representation learning. RTPool enables interpretable and differentiable clustering of node neighborhoods into geometric substructures. By unifying computational geometry constructions, GNN-based modeling, and end-to-end optimization, it significantly enhances geometric feature extraction. Evaluated on seven standard graph classification benchmarks, RTPool consistently outperforms 21 state-of-the-art models, achieving substantial average accuracy gains. These results demonstrate its superior effectiveness, generalizability, and structural advantage in modeling geometric information.

Technology Category

• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• GNNs limited by graph connectivity for geometric features
• Proposes Rhomboid Tiling to capture geometric structures
• RTPool model outperforms 21 competitors on benchmarks

Innovation

• Rhomboid Tiling clustering leverages geometric data information
• RTPool model enhances hierarchical graph clustering
• Method outperforms 21 competitors on benchmarks