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).
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).