pygsp icon indicating copy to clipboard operation
pygsp copied to clipboard

Add support for the magnetic laplacian

Open pulquero opened this issue 3 years ago • 6 comments

The magnetic laplacian provides an alternative to symmetrizing the adjacency matrix for directed graphs. See e.g. "Graph Signal Processing for Directed Graphs based on the Hermitian Laplacian".

pulquero avatar Jun 27 '21 21:06 pulquero

Could you maybe point us to a reference paper?

nperraud avatar Jun 28 '21 07:06 nperraud

The magnetic Laplacian is widely mentioned, my fav is https://ecmlpkdd2019.org/downloads/paper/499.pdf. Note for q=0, the magnetic Laplacian is the same as the symmetrised one, so you could just introduce q as a kwarg and default it to 0 to be backwards compatible.

pulquero avatar Jun 28 '21 19:06 pulquero

Btw, I'm not sure if it is intentional or not, but the directed symmetrised laplacian as it is currently in the code isnt using dw from the symmetrised W but self.dw.

pulquero avatar Jun 28 '21 21:06 pulquero

I've put together a nice demo here: https://github.com/pulquero/sgw/blob/main/examples/graphwave.py

pulquero avatar Jun 29 '21 08:06 pulquero

Thanks a lot.

I need to have a look at what you did, but I am really overworked. I will try to do it asap.

nperraud avatar Jun 29 '21 13:06 nperraud

Came across another useful hermitian Laplacian for directed graphs: https://core.ac.uk/download/pdf/206608976.pdf (Laplacians and the Cheeger inequality for directed graphs, Fan Chung).

pulquero avatar Oct 01 '21 09:10 pulquero