I gave a talk last night at the Berlin machine learning meetup on learning graph embeddings in hyperbolic space, featuring the recent NIPS 2017 paper of Nickel & Kiela. Covered are:
- An illustration of why the Euclidean plane is not a good place to embed trees (since circle circumference grows only linearly in the radius);
- Extending this same argument to higher dimensional Euclidean space;
- An introduction to the hyperbolic plane and the Poincaré disc model;
- A discussion of Rik Sarkar’s result that trees embed with arbitrarily small error in the hyperbolic plane;
- A demonstration that, in the hyperbolic plane, circle circumference is exponential in the radius (better written here);
- A review of the results of Nickel & Kiela on the (transitive closure of the) WordNet hypernymy graph;
- Some thoughts on the gradient optimisation (perhaps better written here).
And here are the slides!
One Reply to “Graph embeddings in Hyperbolic Space”
Does anyone have hyperparameters to reproduce the results in Poincare Embeddings for Learning Hierarchical Representations ? It would be really helpful!