Hyperbolic Node Embedding for Signed Networks

TL;DR

This paper introduces a hyperbolic embedding method for signed networks that captures hierarchical structures better than Euclidean methods, using Riemannian optimization to embed networks into a Poincaré ball.

Contribution

It proposes the first hyperbolic embedding approach for signed networks based on structural balance theory and Riemannian optimization, capturing hierarchical features effectively.

Findings

Outperforms six Euclidean-based baselines in three tasks

Effectively captures hierarchical structures in signed networks

Demonstrates superior performance on seven real-world datasets

Abstract

Signed network embedding methods aim to learn vector representations of nodes in signed networks. However, existing algorithms only managed to embed networks into low-dimensional Euclidean spaces whereas many intrinsic features of signed networks are reported more suitable for non-Euclidean spaces. For instance, previous works did not consider the hierarchical structures of networks, which is widely witnessed in real-world networks. In this work, we answer an open question that whether the hyperbolic space is a better choice to accommodate signed networks and learn embeddings that can preserve the corresponding special characteristics. We also propose a non-Euclidean signed network embedding method based on structural balance theory and Riemannian optimization, which embeds signed networks into a Poincar\'e ball in a hyperbolic space. This space enables our approach to capture underlying hierarchy of nodes in signed networks because it can be seen as a continuous tree. We empirically compare our method against six Euclidean-based baselines in three tasks on seven real-world datasets, and the results show the effectiveness of our method.