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Article

Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering

1
Department of Microelectronics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, 2628 CD Delft, The Netherlands
2
Department of Electrical and Communication Engineering, Indian Institute of Science, Bangalore 560 012, India
3
RIKEN Center for Advanced Intelligence Project, Tokyo 103-0027, Japan
*
Author to whom correspondence should be addressed.
Algorithms 2020, 13(9), 214; https://doi.org/10.3390/a13090214
Received: 5 July 2020 / Revised: 27 August 2020 / Accepted: 27 August 2020 / Published: 31 August 2020
(This article belongs to the Special Issue Efficient Graph Algorithms in Machine Learning)
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. View Full-Text
Keywords: graph signal processing; graph Fourier transform; approximate graph Fourier transform; divide-and-conquer graph signal processing; graph Fourier transform; approximate graph Fourier transform; divide-and-conquer
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MDPI and ACS Style

Coutino, M.; Chepuri, S.P.; Maehara, T.; Leus, G. Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering. Algorithms 2020, 13, 214. https://doi.org/10.3390/a13090214

AMA Style

Coutino M, Chepuri SP, Maehara T, Leus G. Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering. Algorithms. 2020; 13(9):214. https://doi.org/10.3390/a13090214

Chicago/Turabian Style

Coutino, Mario, Sundeep Prabhakar Chepuri, Takanori Maehara, and Geert Leus. 2020. "Fast Spectral Approximation of Structured Graphs with Applications to Graph Filtering" Algorithms 13, no. 9: 214. https://doi.org/10.3390/a13090214

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