Related papers: Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning

Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning

URL: http://arxiv.org/abs/2305.18962v1
Date: Tue, 30 May 2023 11:49:39 GMT
Title: Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning
Authors: Ya-Wei Eileen Lin, Ronald R. Coifman, Gal Mishne, Ronen Talmon
Abstract summary: 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. We show theoretically that our embedding and distance recover the underlying hierarchical structure.
Score: 13.976918651426205
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
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.

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