Multi-relational Poincar\'e Graph Embeddings

TL;DR

This paper introduces MuRP, a hyperbolic embedding model for multi-relational knowledge graphs that captures multiple hierarchies more effectively than Euclidean models, improving link prediction especially at lower dimensions.

Contribution

The paper presents MuRP, a novel hyperbolic embedding method that incorporates relation-specific transformations for multi-relational graphs, addressing limitations of previous hyperbolic models.

Findings

MuRP outperforms Euclidean embeddings on WN18RR.

MuRP achieves better link prediction at lower dimensions.

Hyperbolic embeddings better capture hierarchical structures.

Abstract

Hyperbolic embeddings have recently gained attention in machine learning due to their ability to represent hierarchical data more accurately and succinctly than their Euclidean analogues. However, multi-relational knowledge graphs often exhibit multiple simultaneous hierarchies, which current hyperbolic models do not capture. To address this, we propose a model that embeds multi-relational graph data in the Poincar\'e ball model of hyperbolic space. Our Multi-Relational Poincar\'e model (MuRP) learns relation-specific parameters to transform entity embeddings by M\"obius matrix-vector multiplication and M\"obius addition. Experiments on the hierarchical WN18RR knowledge graph show that our Poincar\'e embeddings outperform their Euclidean counterpart and existing embedding methods on the link prediction task, particularly at lower dimensionality.