# Low-dimensional statistical manifold embedding of directed graphs

## TL;DR

This paper introduces a novel node embedding method for directed graphs using statistical manifolds, optimizing pairwise relative entropy and graph geodesics, which better preserves global structure and outperforms existing models.

## Contribution

It presents a new embedding approach that encodes nodes as probability densities on statistical manifolds, capturing directed graph geometry more effectively.

## Key findings

- Outperforms existing models on directed graph tasks
- Better preserves global geodesic information
- Effective in unsupervised learning settings

## Abstract

We propose a novel node embedding of directed graphs to statistical manifolds, which is based on a global minimization of pairwise relative entropy and graph geodesics in a non-linear way. Each node is encoded with a probability density function over a measurable space. Furthermore, we analyze the connection between the geometrical properties of such embedding and their efficient learning procedure. Extensive experiments show that our proposed embedding is better in preserving the global geodesic information of graphs, as well as outperforming existing embedding models on directed graphs in a variety of evaluation metrics, in an unsupervised setting.