Enhancing Graph Representation Learning with Localized Topological Features

2025-01-15

AI Summary

Graph neural networks (GNNs) suffer from limited expressive power on complex graph structures and struggle to capture higher-order connectivity. To address this, we propose a differentiable topological enhancement framework grounded in local persistent homology. Our approach introduces the first node-level localized modeling of persistent homology features and designs an end-to-end differentiable topological operator that seamlessly integrates explicit topological signatures—such as cycles and voids—into the GNN message-passing mechanism. Theoretical analysis demonstrates the complementarity between topological features and the local aggregation capacity of GNNs. Extensive experiments on multiple node classification and link prediction benchmarks show substantial performance gains, achieving state-of-the-art results. Notably, our method significantly improves generalization and robustness on structurally complex and noisy graphs.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be beneficial to explicitly extract and incorporate high-order topological and geometric information into these models. In this paper, we propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks and achieve state-of-the-art performance on various node classification and link prediction benchmarks. We also explore the option of end-to-end learning of the topological features, i.e., treating topological computation as a differentiable operator during learning. Our theoretical analysis and empirical study provide insights and potential guidelines for employing topological features in graph learning tasks.

Problem

• Graph Neural Networks
• Node Classification
• Link Prediction

Innovation

• Graph Neural Networks
• Structural Information Integration
• Enhanced Learning Capabilities