tkipf
commented
5 years ago Great question, thanks for your comment!
I think there are a few overlapping problems which you bring up here: 1) Generalization to unseen nodes: this is usually not an issue if node features come from the same distribution. Just set up a new (possibly larger) graph at test time with these added nodes and run the model. 2) Prediction on single nodes: to make a prediction for a single node given a two-layer GCN model, you only need access to its first- and second-order neighborhoods. So you do not need to run the forward pass on the full graph if you only want a prediction for a subset of the nodes. 3) How to handle large graphs: One can do trivial mini-batching that follows from (2): sample a set of nodes and take their full second-order neighborhood into account. This is usually too expensive, and one can do some further subsampling to alleviate this. See, e.g. FastGCN https://arxiv.org/abs/1801.10247
pavlin-policar
I'm sorry if this has been answered before - I looked through several issues but found no mention of this.
Consider a graph where nodes and edges are constantly being added e.g. in a social network users register and form connections, existing users form new connections between each other. Could I use GCNs or somehow adapt them so as to handle this case? My current understanding is that we train the GCN using the adjacency matrix of the original graph, which is NxN. And if I add nodes, the Laplacian matrix used to train the graph changes entirely (because the node degrees change), and increases in size. So not only will the weight matrices W be the wrong size, but also the domain will change because the degree matrix will change. Any suggestions?
The first thing that pops to mind would be to train the GCN using smaller subnetworks i.e. sample the original network then train the GCN in "mini-batches". Of course, the issue here is that the "mini-batches" could have wildly different numbers of nodes (if we sample somewhere from the core or periphery of the network), but maybe filling the adjacency matrix with zeros to match the largest subnetwork might work. You've probably thought of this and I was wondering about your thoughts on this.
Another question that I had was what would happen if we permute the adjacency matrix or use an isomorphic graph after training the original model. The adjacency matrix would look quite different but the graph structure should be the same. I suspect that the trained model wouldn't do well on the permuted graph. Any thoughts?
Thanks!