Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry

Maximillian Nickel, Douwe Kiela
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:3779-3788, 2018.

Abstract

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 Poincar{é}-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincar{é} 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.

Cite this Paper


BibTeX
@InProceedings{pmlr-v80-nickel18a, title = {Learning Continuous Hierarchies in the {L}orentz Model of Hyperbolic Geometry}, author = {Nickel, Maximillian and Kiela, Douwe}, booktitle = {Proceedings of the 35th International Conference on Machine Learning}, pages = {3779--3788}, year = {2018}, editor = {Dy, Jennifer and Krause, Andreas}, volume = {80}, series = {Proceedings of Machine Learning Research}, month = {10--15 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v80/nickel18a/nickel18a.pdf}, url = {http://proceedings.mlr.press/v80/nickel18a.html}, abstract = {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 Poincar{é}-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincar{é} 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.} }
Endnote
%0 Conference Paper %T Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry %A Maximillian Nickel %A Douwe Kiela %B Proceedings of the 35th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2018 %E Jennifer Dy %E Andreas Krause %F pmlr-v80-nickel18a %I PMLR %P 3779--3788 %U http://proceedings.mlr.press/v80/nickel18a.html %V 80 %X 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 Poincar{é}-ball model. We show that the proposed approach allows us to learn high-quality embeddings of large taxonomies which yield improvements over Poincar{é} 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.
APA
Nickel, M. & Kiela, D.. (2018). Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry. Proceedings of the 35th International Conference on Machine Learning, in Proceedings of Machine Learning Research 80:3779-3788 Available from http://proceedings.mlr.press/v80/nickel18a.html.

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