Coutino, M and Chepuri, SP and Maehara, T and Leus, G (2020) Fast spectral approximation of structured graphs with applications to graph filtering. In: Algorithms, 13 (9).
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Abstract
To analyze and synthesize signals on networks or graphs, Fourier theory has been extended to irregular domains, leading to a so-called graph Fourier transform. Unfortunately, different from the traditional Fourier transform, each graph exhibits a different graph Fourier transform. Therefore to analyze the graph-frequency domain properties of a graph signal, the graph Fourier modes and graph frequencies must be computed for the graph under study. Although to find these graph frequencies and modes, a computationally expensive, or even prohibitive, eigendecomposition of the graph is required, there exist families of graphs that have properties that could be exploited for an approximate fast graph spectrum computation. In this work, we aim to identify these families and to provide a divide-and-conquer approach for computing an approximate spectral decomposition of the graph. Using the same decomposition, results on reducing the complexity of graph filtering are derived. These results provide an attempt to leverage the underlying topological properties of graphs in order to devise general computational models for graph signal processing. © 2020 by the authors.
| Item Type: | Journal Article |
|---|---|
| Publication: | Algorithms |
| Publisher: | MDPI AG |
| Additional Information: | Copyright to this article belongs to MDPI AG |
| Keywords: | Fourier series; Frequency domain analysis; Graphic methods; Signal processing, Computational model; Divide-and-conquer approach; Eigen decomposition; Graph Fourier transforms; Spectral approximations; Spectral decomposition; Structured graphs; Topological properties, Topology |
| Department/Centre: | Division of Electrical Sciences > Electrical Communication Engineering |
| Date Deposited: | 27 Nov 2020 06:12 |
| Last Modified: | 27 Nov 2020 06:12 |
| URI: | http://eprints.iisc.ac.in/id/eprint/66829 |
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