Partition of Unity Methods for Signal Processing on Graphs

被引：17
|
作者：
Cavoretto, Roberto [1 ]
De Rossi, Alessandra [1 ]
Erb, Wolfgang [2 ,3 ]
机构：
[1] Univ Torino, Turin, Italy
[2] Univ Padua, Padua, Italy
[3] Catholic Univ Eichstatt Ingolstadt, Eichstatt, Germany
来源：
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2021年 / 27卷 / 04期
关键词：
Partition of unity method (PUM); Graph signal processing; Graph basis functions (GBFs); Kernel-based approximation and interpolation; Spectral graph theory;
D O I：
10.1007/s00041-021-09871-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
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页数：29
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