# Low-dimensional statistical manifold embedding of directed graphs

arXiv: https://arxiv.org/abs/1905.10227 · HTML: https://mlsanity.com/paper/1905.10227/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2019.

## Built on by (most cited first, 4 of 4)

- [Zorro: Valid, Sparse, and Stable Explanations in Graph Neural Networks](https://mlsanity.com/paper/2105.08621/) (2021)
- [Finsler Multi-Dimensional Scaling: Manifold Learning for Asymmetric Dimensionality Reduction and Embedding](https://mlsanity.com/paper/2503.18010/) (2025)
- [Harnessing Data Asymmetry: Manifold Learning in the Finsler World](https://mlsanity.com/paper/2603.11396/) (2026)
- [Learning Eigenstructures of Unstructured Data Manifolds](https://mlsanity.com/paper/2512.01103/) (2025)

## Abstract (arXiv)

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.