This is really cool. The underlying graph optimization algorithm seems similar to how graphical models are trained. Is that correct? Can someone please help me understand the difference?
Yes, label propagation is very similar to belief propagation on a Gaussian Markov random field (a particularly simple type of graphical model). To be precise this is 'inference' on the graphical model, rather than 'training' or 'learning'. See the author's 2016 JMLR paper for more details: http://www.jmlr.org/proceedings/papers/v51/ravi16.pdf
I mean, it should be.. you are learning a probability distribution over the nodes and then performing some kind of inference at eval time.