Community detection methods for GBF-PUM signal approximation on graphs

• Spectral methods for community detection are studied and tested. • Methods for graph division into two disjoint communities are presented. • Iterative algorithms are proposed by extending the two-community division methods to the case of more than two communities. • All the MATLAB routines implemented are available as open-access codes. • Community detection methods are applied in partition of unity interpolation on graphs. Graph signal approximation plays a key role in processing irregularly distributed data on graphs, where achieving smooth and computationally efficient interpolation is essential. In this work, we introduce a new approach that combines a spectral community detection technique with the partition of unity method (PUM) applied to signal approximation on graphs. The PUM provides an effective technique for handling irregularly distributed data by dividing the graph into smaller subgraphs, constructing local interpolants and combining them to produce a global approximation. Since the first step in the PUM consists in dividing the graph into disjoint communities, we focus in particular on exploring and testing some community detection algorithms based on the maximization of the modularity. Then, we integrate the PUM with a local graph basis function approximation scheme, resulting in an accurate and computationally efficient approach for graph signal approximation.