---
abstract: |
    Detecting communities on graphs has received significant interest in recent literature. Current state-of-the-art community embedding approach called *ComE* tackles this problem by coupling graph embedding with community detection. Considering the success of hyperbolic representations of graph-structured data in last years, an ongoing challenge is to set up a hyperbolic approach for the community detection problem.

    The present paper meets this challenge by introducing a Riemannian equivalent of *ComE*. Our proposed approach combines hyperbolic embeddings with Riemannian K-means or Riemannian mixture models to perform community detection. We illustrate the usefulness of this framework through several experiments on real-world social networks and comparisons with *ComE* and recent hyperbolic-based classification approaches.
author:
- |
    Thomas Gerald[^1]\
    Science Sorbonne Université, Lip6\
    Paris, France\
    `thomas.gerald@lip6.fr`\
    Hadi Zaatiti$^*$\
    IRT SystemX\
    Palaiseau, France\
    `hadi.zaatiti@irt-systemx.fr`\
    Hatem Hajri$^*$\
    IRT SystemX\
    Palaiseau, France\
    `hatem.hajri@irt-systemx.fr`\
    Nicolas Baskiotis\
    Science Sorbonne Université, Lip6\
    Paris, France\
    `nicolas.baskiotis@lip6.fr`\
    Olivier Schwander\
    Science Sorbonne Université, Lip6\
    Paris, France\
    `olivier.schwander@lip6.fr`\
bibliography:
- 'biblio.bib'
title: 'From Node Embedding To Community Embedding : A Hyperbolic Approach'
---

Introduction
============

The Poincaré Ball model: Geometry and tools \[section\_ball\]
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Learning hyperbolic community embeddings\[section\_approach\]
=============================================================

Experiments \[section\_experiments\]
====================================

Conclusion
==========

[^1]: Equal contributions.
