论文标题
在图上进行信号处理的统一方法的分区
Partition of Unity Methods for Signal Processing on Graphs
论文作者
论文摘要
图形上的统一方法（PUM）的分区是用于图形信号处理的简单且高度自适应的辅助工具。基于贪婪型公制聚类和增强方案，我们展示了如何在图形上以有效的方式生成统一分区。我们研究了如何与局部图基函数（GBF）近似方法结合使用PUM，以获得低成本的全局插值或分类方案。从理论的角度来看，我们研究了统一分配的必要先决条件，使得对相应的局部误差估计的全局误差估计值来自相应的局部误差。最后，对PUM的性质作为成本效益和近似精度进行数值研究。
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.
