Graph Neural Networks for Community Detection in Graph Signal Analysis

TL;DR

This paper explores combining Graph Neural Networks with a Partition of Unity Method for improved community detection and signal interpolation in graph analysis, demonstrating accurate results on benchmark datasets.

Contribution

It introduces a novel integration of GNN-based community detection with GBF-PUM interpolation for scalable graph signal analysis.

Findings

GNN-derived communities improve local interpolation accuracy.

The combined method outperforms traditional approaches on benchmark datasets.

Deep learning-based clustering supports scalable graph signal processing.

Abstract

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.