Greetings,

I am very new to the area of machine learning, so excuse what may appear as a stupid question.

I am interested in using graph convolution networks for semi-supervised classification of nodes in a graph. I would like to impose a graph constraint on the network. I have included an image to illustrate

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Constraining node classification of a GCN with a graph constraint (connectivity of communities).

The graph constraint I want to impose is that there can only be one communities/region for each label (blue, green, red). In the above figure you can see a sample resulting GCN classification that produces two green communities/regions. I was thinking that perhaps there is a way to create a community/region graph from the resulting GCN algorithm then I compare that with the constraint graph. That comparison, or similarity measure, would be incorporated into some loss function and somehow back propagate that back into to GCN and finally arrive at a classification where there is only one community/region per label.

Is this possible? Is there a better way to approach this (perhaps using an doing some graph embedding or autoencoder/decorder technique)?

Thanks for any suggestions or comments 🙂