Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry
This work addresses the challenge of efficiently learning hierarchical structures for applications like organizational analysis and linguistics, though it is incremental as it builds on existing hyperbolic embedding methods.
The paper tackled the problem of discovering hierarchical relationships from large-scale unstructured similarity scores by learning embeddings in the Lorentz model of hyperbolic geometry, resulting in substantially more efficient and higher-quality embeddings than the Poincaré-ball model, especially in low dimensions.
We are concerned with the discovery of hierarchical relationships from large-scale unstructured similarity scores. For this purpose, we study different models of hyperbolic space and find that learning embeddings in the Lorentz model is substantially more efficient than in the Poincaré-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincaré embeddings, especially in low dimensions. Lastly, we apply our model to discover hierarchies in two real-world datasets: we show that an embedding in hyperbolic space can reveal important aspects of a company's organizational structure as well as reveal historical relationships between language families.