Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in an efficient way on graphs. We investigate how PUMs can be combined with a local graph basis function (GBF) approximation method in order to obtain low-cost global interpolation or classification schemes. From a theoretical point of view, we study necessary prerequisites for the partition of unity such that global error estimates of the PUM follow from corresponding local ones. Finally, properties of the PUM as cost-efficiency and approximation accuracy are investigated numerically.

图上的统一方法 (PUM) 划分是用于图信号处理的简单且高度自适应的辅助工具。基于贪婪型度量聚类和增强方案，我们展示了如何在图上以有效的方式生成统一分区。我们研究了 PUM 如何与局部图基函数 (GBF) 近似方法相结合，以获得低成本的全局插值或分类方案。从理论的角度来看，我们研究了统一划分的必要先决条件，以便 PUM 的全局误差估计遵循相应的局部误差估计。最后，数值研究了 PUM 作为成本效率和近似精度的特性。