Partition of Unity Methods for Signal Processing on Graphs

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 co...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2021-08, Vol.27 (4), Article 66
Main Authors: Cavoretto, Roberto, De Rossi, Alessandra, Erb, Wolfgang
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximation
Approximations and Expansions
Basis functions
Clustering
Fourier Analysis
Graphs
Harmonic Analysis on Combinatorial Graphs
Interpolation
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Methods
Partial Differential Equations
Signal processing
Signal,Image and Speech Processing
Unity
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Summary: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.
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-021-09871-w