I was reading the following article on Towards Data Science (here) and it says the following, regarding the calculation of convolutional layers:

So the overall steps are:

  1. Transform the graph into the spectral domain using eigendecomposition
  2. Apply eigendecomposition to the specified kernel
  3. Multiply the spectral graph and spectral kernel (like vanilla convolutions)
  4. Return results in the original spatial domain (analogous to inverse GFT)

Question: How can we visualize the convolutional layer working for a graph neural network?

For example, for a CNN we can imagine the following (source: Stanford CS231n YouTube lectures, Lecture 5: Convolutional Neural Networks (here)). What is the analogous image for a graph convolutional filter?

CNN filter sliding across image

  • $\begingroup$ Note that there are several graph neural networks and, from what I remember when I was studying them, they can be quite different, so it may not be possible to give an explanation that applies to all GNNs. Moreover, it seems to me that now you changed the question to ask for a diagram that illustrates how the convolutional layer for some specific GNN works. If that's the case, you may also want to change the title to reflect that. $\endgroup$
    – nbro
    Sep 18 at 14:15
  • $\begingroup$ Thanks @nbro, I'll make the updates in the morning. Do you have any links to resources you used when you were studying the topic? $\endgroup$ Sep 19 at 1:32
  • 1
    $\begingroup$ I didn't study geometric deep learning or graph neural networks thoroughly. I had read a few papers and articles online, so my knowledge of the topic is not very solid, so I don't really have one resource that I would recommend. Back then (i.e. about 2-3 years ago), there weren't many good resources on this topic. Maybe this answer is useful. Don't forget to upvote the question and answer there if you find them useful ;). In any case, it seems to me you're already aware of this book. $\endgroup$
    – nbro
    Sep 19 at 23:53
  • $\begingroup$ Many thanks @nbro! Appreciate the help $\endgroup$ Sep 20 at 2:48

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