Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learning

TL;DR

This paper introduces a novel hierarchical data embedding method combining diffusion geometry and hyperbolic space, effectively capturing hierarchical structures and improving graph embedding performance.

Contribution

It proposes a new embedding technique that integrates diffusion geometry with hyperbolic spaces to better represent hierarchical data structures.

Findings

The method accurately recovers hierarchical structures.

It outperforms existing embedding methods on benchmarks.

Theoretical guarantees support the approach.

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.