What is the clustering used in Pooling?

[hkim716]

I'm trying to understand some pooling layers max_pool or mean_pool in PyG, but I'm stuck in the concept of clustering.
Why do we need the clustering when we coarsen the graphs?
Is it because we do not know node connections for the coarsened graphs?

[rusty1s]

The pooling strategy of using clusters of nodes was first introduced here, and it dictates how you want to coarsen the graph, i.e., nodes in the same cluster will form a super node in the coarsened graph. Supernodes are connected if there exists nodes in the underlying cluster which were connected in the original graph.

[hkim716]

Thanks for the information Matt.
I have another question that I got from someone. For 2d-convolution with image data, user can specify the numbers of channels and the size of the channels. However, in GCNConv, I only see the number of channels, which defines the number of node features at the next layer. Why I cannot see any size of channels in GCNConv layer? Is that because Message passing mechanism is totally different from image datasets?

[rusty1s]

You mean kernel size? The GCNConv transforms each neighbor equally, so there does not exist such an argument here. However, there exists some GNNs that try to simulate such behaviour, e.g., see our torch_geometric.nn.conv.SplineConv operator.