Bridging ML and algorithms: comparison of hyperbolic embeddings

Hyperbolic embeddings are well-studied both in the machine learning and algorithm community. However, as the research proceeds independently in those two communities, comparisons and even awareness seem to be currently lacking. We compare the performance (time needed to compute embeddings) and the quality of the embeddings obtained by the popular approaches, both on real-life hierarchies and networks and simulated networks. In particular, according to our results, the algorithm by Bläsius et al (ESA 2016) is about 100 times faster than the Poincaré embeddings (NIPS 2017) and Lorentz embeddings (ICML 2018) by Nickel and Kiela, while achieving results of similar (or, in some cases, even better) quality.