Partition of Unity Methods for Signal Processing on Graphs

TL;DR

This paper introduces an efficient partition of unity method for graph signal processing, combining clustering and basis functions to enable low-cost interpolation and classification with proven error bounds.

Contribution

It presents a novel greedy clustering scheme for generating partitions of unity on graphs and analyzes their theoretical and numerical properties.

Findings

Efficient partition of unity generation on graphs

Improved global approximation via local basis functions

Numerical validation of cost-efficiency and accuracy

Abstract

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.