Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning

Ya Wei Eileen Lin, Ronald R. Coifman, Gal Mishne, Ronen Talmon

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations

Abstract

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Original languageEnglish
Pages (from-to)21003-21025
Number of pages23
JournalProceedings of Machine Learning Research
Volume202
StatePublished - 2023
Event40th International Conference on Machine Learning, ICML 2023 - Honolulu, United States
Duration: 23 Jul 202329 Jul 2023

ASJC Scopus subject areas

  • Artificial Intelligence
  • Software
  • Control and Systems Engineering
  • Statistics and Probability

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