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.
| Subjects: | Numerical Analysis (math.NA); Machine Learning (cs.LG) |
| Cite as: | arXiv:2605.19733 [math.NA] |
| (or arXiv:2605.19733v1 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2605.19733 arXiv-issued DOI via DataCite (pending registration) |
From: Roberto Cavoretto [view email]
[v1]
Tue, 19 May 2026 12:07:51 UTC (11 KB)
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