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Diagonalizable Shift and Filters for Directed Graphs Based on the Jordan-Chevalley Decomposition

Citation Author(s):
Chris Wendler, Markus Püschel
Submitted by:
Panagiotis Misiakos
Last updated:
14 May 2020 - 2:21am
Document Type:
Poster
Document Year:
2020
Event:
Presenters:
Panagiotis Misiakos
Paper Code:
1937
 

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.

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