iglesias
commented
2 years ago Numerical instabilities, well-known problem in GSP graph frequencies (see [1] and references therein*)
[1] Graph Fourier Transform: A Stable Approximation https://arxiv.org/pdf/2001.05042.pdf
- From [1]'s introduction, "Authors have taken different approaches to avoid these issues and preserve F to be unitary. For example, 1) [17, 18] redefine the shift matrix to make it a norm preserving operator; 2) [19, 20] consider the case of a normal shift AAH = AHA and A is unitarily diagonalizable, but with eigenvalues not necessarily real valued ; 3) more often, the literature considers the graph to be undirected, so, the shift is symmetric, or take the shift to be the graph Laplacian L [12], either of which is diagonalizable by a unitary operator3 ; and 4) [21] considers directed graphs but redefines the GFT to keep it orthogonal and avoid Jordan decompositions. However, it may be hard to develop a graph filtering theory for [21]"
Finish answering the part of the question about high-order, with L=10, L=20, and how performance drops-off with it.
Nice-to-have: example plots to illustrate that "visual" demixing is not possible with lower N (e.g. N=34 as in karate instead of 70 or so in current figures in the response).