Reconstruct a weighted adjacent matrix

[yjgeno]

VGAE by default will reconstruct an adjacent matrix and the entries of which are simply the inner products of node latent embeddings.

I was wondering if there are already some efforts that allow the model to input and reconstruct a weighted adjacent matrix (which may contain pos/neg values)?
Any resources are appreciated.

[rusty1s]

How about you use an MLP on top of concatenated source and destination node embeddings to learn the weight between these nodes?

x = GNN(x, edge_index)
x_src, x_dst = x[edge_index[0]], x[edge_index[1]]
edge_weight = MLP(torch.cat([x_src, x_dst], dim=-1))

For undirected (but weighted graphs), you may want to apply the Hadamard product (x_src * x_dst) instead of concatenation.

[yjgeno]

Hi @rusty1s thanks

If I understand correctly, you are suggesting replacing the default inner-product decoder of VGAE with an MLP (concat or get Hadamard product of embeddings of a pair of nodes and reconstruct their edge)?

[rusty1s]

Yes, indeed.

[yjgeno]

@rusty1s Thanks a lot
and looks like no papers discussing this
Please let me know if you know any resources already achieved weighted graph reconstruction

[yikang7720]

Hi @rusty1s, it is an extraordinary idea. Could you please tell me what is the source of the newly VGAE architecture? Like which paper indicated this idea?

[rusty1s]

I don't have a specific paper in mind for this. The closest to my mind would be the Node2Vec paper as they are discussing different ways to combine node-level representations.