Unsupervised Hyperbolic Representation Learning via Message Passing Auto-Encoders

TL;DR

This paper introduces a novel unsupervised hyperbolic auto-encoder that leverages hyperbolic geometry for effective hierarchical data representation through message passing.

Contribution

It presents the first hyperbolic message passing auto-encoder designed for unsupervised learning, fully utilizing hyperbolic geometry in the encoding process.

Findings

Effective hierarchical representations in hyperbolic space

Enhanced unsupervised learning performance

Validation through extensive experiments

Abstract

Most of the existing literature regarding hyperbolic embedding concentrate upon supervised learning, whereas the use of unsupervised hyperbolic embedding is less well explored. In this paper, we analyze how unsupervised tasks can benefit from learned representations in hyperbolic space. To explore how well the hierarchical structure of unlabeled data can be represented in hyperbolic spaces, we design a novel hyperbolic message passing auto-encoder whose overall auto-encoding is performed in hyperbolic space. The proposed model conducts auto-encoding the networks via fully utilizing hyperbolic geometry in message passing. Through extensive quantitative and qualitative analyses, we validate the properties and benefits of the unsupervised hyperbolic representations. Codes are available at https://github.com/junhocho/HGCAE.