Is GCN spectral or spatial?

Hi all,

I am slightly confused about GCN being called a spectral method in some overview papers. As far as I understand it, the implementation here, is rather a spatial method, right? Which we can write like this:
image
Is this exactly the same as the spectral version that is proposed in the original paper?

Or am I miss-understanding the entire difference in general? :wink:

Kind regards,
Erik

The differentiation between spectral GNNs and spatial GNNs lies more at the original motivation. If a GNN is motivated by spectral graph theory, people call it a spectral one. This does not mean that we cannot formulate a spectral GNN from the spatial perspective, vice versa.

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Thank you for that explanation! Just to be 100% sure, the implementation of GCN in DGL is exactly the same as the one from the paper right? Just explained from the different perspective.

Yes, same implementation.

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so when described as message, reduce, update, then its spatial, but when it is described as H^{i}= W^{i}D{-1}AH^{i-1} or similar then its spectral?

Iā€™m not sure if we can put it that way. The boundary is just not clear if we are not talking about motivations.