Pytorch_geometric: How to train the adjacency (weight) matrix of the graph as a parameter？

[WeiyiLee6666]

❓ Questions & Help

The previous papers, including implementation, have already established graph structures. But suppose we have n sets of data {𝑥_𝑖,𝑦_𝑖 }_(𝑖=1)^𝑛, where 𝑦_𝑖∈{0,1}, 𝑥_𝑖∈R^(n×F), n is the number of points and F is the feature Number. My idea is to build a graph structure for each 𝑦_𝑖, in which the parameters of the adjacency matrix are randomly initialized and then GCN is performed. How should this be achieved?
Thanks

[rusty1s]

That's an interesting idea. To achieve that, you wan to make edge_weight explicitly learnable and adjust it after each optimizer step. A starting point could be the following:

adj = torch.rand((num_nodes, num_nodes)
edge_index = (adj > 0).nonzero().t()
edge_weight = adj[edge_index[0], edge_index[1]]
edge_weight.requires_grad = True

self.gcn_conv(x, edge_index, edge_weight)
...
loss.backward()

[WeiyiLee6666]

That's an interesting idea. To achieve that, you wan to make edge_weight explicitly learnable and adjust it after each optimizer step. A starting point could be the following:

adj = torch.rand((num_nodes, num_nodes)
edge_index = (adj > 0).nonzero().t()
edge_weight = adj[edge_index[0], edge_index[1]]
edge_weight.requires_grad = True

self.gcn_conv(x, edge_index, edge_weight)
...
loss.backward()

Thanks for your answer

[WeiyiLee6666]

There are a few papers learning the graph structure along with node features.

For example:
[1] Kazi, A., Cosmo, L., Navab, N. and Bronstein, M., 2020. Differentiable Graph Module (DGM) Graph Convolutional Networks. arXiv preprint arXiv:2002.04999.
https://arxiv.org/pdf/1801.07829.pdf

[2] ~Wang, Y., Sun, Y., Liu, Z., Sarma, S.E., Bronstein, M.M. and Solomon, J.M., 2019. Dynamic graph cnn for learning on point clouds. Acm Transactions On Graphics (tog), 38(5), pp.1-12. https://arxiv.org/pdf/2002.04999.pdf~
[Edit]: the above is already implemented, apologies.

@rusty1s any chance ~any of these methods~ of [1] being implemented in the future?

Thanks for you reply