Diagonalizable Shift and Filters for Directed Graphs Based on the Jordan-Chevalley Decomposition
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Date
2020Type
- Conference Paper
Abstract
Graph signal processing on directed graphs poses theoretical challenges since an eigendecomposition of filters is in general not available. Instead, Fourier analysis requires a Jordan decomposition and the frequency response is given by the Jordan normal form, whose computation is numerically unstable for large sizes. In this paper, we propose to replace a given adjacency shift A by a diagonalizable shift A(D) obtained via the Jordan-Chevalley decomposition. This means, as we show, that A(D) generates the subalgebra of all diagonalizable filters and is itself a polynomial in A (i.e., a filter). For several synthetic and real-world graphs, we show how A(D) adds and removes edges compared to A. Show more
Publication status
publishedExternal links
Book title
2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)Pages / Article No.
Publisher
IEEEEvent
Subject
Graph signal processing; Digraphs; Jordan normal form; Algebraic signal processing; Diagonalizable filtersOrganisational unit
03893 - Püschel, Markus / Püschel, Markus
Notes
Due to the Corona virus (COVID-19) the conference was conducted virtually.More
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