arXiv:2605.19733math.NAcs.LG2026-05

用图神经网络划分社区,提升信号插值精度。

Graph Neural Networks for Community Detection in Graph Signal Analysis

  • 用GNN生成社区划分,构建局部子域进行信号插值。
  • 在多个基准图数据集上实现高精度信号重建。
  • 适合需要高效图信号分析的工程与城市网络场景。

社区检测是图分析的核心问题,广泛应用于网络科学和图信号处理。近年来,图神经网络(GNN)已成为学习图结构数据低维表示的有效工具,在大规模高维图的聚类任务中表现优异。本文研究在图信号插值框架下基于GNN的社区检测方法。根据标准分类体系回顾了主流GNN架构后,将所得图社区整合至分域统一法(PUM)中,结合图基函数(GBFs)进行插值。该方法利用GNN生成的社区构建局部子域,计算局部GBF插值器,并合成全局近似解。在包含几何与城市网络在内的多个基准图数据集上的数值实验表明,GNN聚类与GBF-PUM插值相结合,能实现精准的信号重构。结果表明,深度学习驱动的社区检测可为局部化插值方案提供有效图划分,支持其在可扩展图信号分析中的应用。

原文摘要 · Abstract (English)

Community detection is a central problem in graph analysis, with applications ranging from network science to graph signal processing. In recent years, Graph Neural Networks (GNNs) have emerged as effective tools for learning low-dimensional representations of graph-structured data and have shown strong performance in clustering tasks, particularly on large and high-dimensional graphs. This paper investigates the use of GNN-based community detection within a graph signal interpolation framework. After reviewing the main classes of GNN architectures for community detection according to a standard taxonomy, we integrate the resulting graph communities into a Partition of Unity Method (PUM) for interpolation with Graph Basis Functions (GBFs). In this approach, GNN-derived communities are used to construct local subdomains on which GBF interpolants are computed and subsequently combined into a global approximation. Numerical experiments on benchmark %graph datasets, including geometric and urban network examples demonstrate that the proposed combination of GNN-based clustering and GBF-PUM interpolation yields accurate signal reconstructions. The results indicate that deep learning-based community detection can provide effective graph partitions for localized interpolation schemes, supporting its use in scalable graph signal analysis.

图神经网络社区检测信号插值图基函数

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