RegD: Hierarchical Embeddings via Dissimilarity between Arbitrary Euclidean Regions

TL;DR

RegD introduces a flexible Euclidean-based framework for hierarchical data embeddings using arbitrary geometric regions, achieving hyperbolic-like expressiveness and outperforming existing methods in real-world tasks.

Contribution

It proposes a novel Euclidean region-based embedding method that emulates hyperbolic properties, enhancing flexibility and applicability in hierarchical and ontology embedding tasks.

Findings

RegD outperforms state-of-the-art methods on multiple datasets.

It effectively models exponential growth similar to hyperbolic geometry.

RegD demonstrates versatility in applications beyond pure hierarchies.

Abstract

Hierarchical data is common in many domains like life sciences and e-commerce, and its embeddings often play a critical role. While hyperbolic embeddings offer a theoretically grounded approach to representing hierarchies in low-dimensional spaces, current methods often rely on specific geometric constructs as embedding candidates. This reliance limits their generalizability and makes it difficult to integrate with techniques that model semantic relationships beyond pure hierarchies, such as ontology embeddings. In this paper, we present RegD, a flexible Euclidean framework that supports the use of arbitrary geometric regions -- such as boxes and balls -- as embedding representations. Although RegD operates entirely in Euclidean space, we formally prove that it achieves hyperbolic-like expressiveness by incorporating a depth-based dissimilarity between regions, enabling it to emulate key properties of hyperbolic geometry, including exponential growth. Our empirical evaluation on diverse real-world datasets shows consistent performance gains over state-of-the-art methods and demonstrates RegD's potential for broader applications such as the ontology embedding task that goes beyond hierarchy.