Graph signal processing benefits significantly from the direct and highly adaptable supplementary techniques offered by partition of unity methods (PUMs) on graphs. In our approach, we demonstrate the generation of a partition of unity solely based on the underlying graph structure, employing an algorithm that relies exclusively on centrality measures and modularity, without requiring the input of the number of subdomains. Subsequently, we integrate PUMs with a local graph basis function (GBF) approximation method to develop cost-effective global interpolation schemes. We also discuss numerical experiments conducted on both synthetic and real datasets to assess the performance of this presented technique.

翻译：图信号处理得益于图形上单位划分方法（PUMs）提供的直接且高度自适应的辅助技术。在我们的方法中，我们展示了一种仅基于底层图结构生成单位划分的方式，采用了一种仅依赖中心性度量和模块度、无需输入子区域数量的算法。随后，我们将PUMs与局部图基函数（GBF）近似方法相结合，以开发成本效益高的全局插值方案。我们还讨论了在合成数据集和真实数据集上进行的数值实验，以评估所提出技术的性能。