A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space

TL;DR

This paper introduces a geometry-aware algorithm for learning hierarchical embeddings in hyperbolic space, addressing geometric mismatches and improving performance on synthetic and real-world datasets.

Contribution

It proposes a novel dilation and regularization technique to overcome geometric challenges in hyperbolic embedding learning, with theoretical and empirical validation.

Findings

Superior performance on synthetic datasets

Enhanced accuracy on real-world hierarchical data

Theoretical insights into dilation operation mechanism

Abstract

Hyperbolic embeddings are a class of representation learning methods that offer competitive performances when data can be abstracted as a tree-like graph. However, in practice, learning hyperbolic embeddings of hierarchical data is difficult due to the different geometry between hyperbolic space and the Euclidean space. To address such difficulties, we first categorize three kinds of illness that harm the performance of the embeddings. Then, we develop a geometry-aware algorithm using a dilation operation and a transitive closure regularization to tackle these illnesses. We empirically validate these techniques and present a theoretical analysis of the mechanism behind the dilation operation. Experiments on synthetic and real-world datasets reveal superior performances of our algorithm.