Including node coordinates as node feature

[chinmay5]

Thank you for the wonderful and inspiring work. I have a question regarding generating graphs with 3D node coordinate locations. If I want to generate graphs that should also learn orientation information (in 3D space) of the underlying distribution (by means of generating raw coordinates for the nodes along with other node features), should I

1. Use the node coordinates as additional node features (these would be continuous and would be concatenated with one-hot node degree features. I imagine this might be sub-optimal, but I am not exactly sure).
2. Have it as a third component in the SDE, i.e. imagine it as the third component in a graph structure and have the SDE working with three terms.

Your insights would be extremely helpful.

Thanks,
Chinmay

[harryjo97]

Hi Chinmay,

If you are trying to generate adjacency matrices, node features, and 3D coordinates all at once, I think the second method would be optimal (in the sense that each SDE can be optimally designed with respect to the objects to be generated). The extension of GDSS by adding the third component would be fairly trivial in the context of modeling the systems of SDEs.

Note that your first method may work fairly well when assuming that the node features and the 3D coordinates share similar properties (that can be modeled by the same diffusion process).

Best,
Jaehyeong