# Hydra: A method for strain-minimizing hyperbolic embedding of network- and distance-based data

arXiv: https://arxiv.org/abs/1903.08977 · HTML: https://mlsanity.com/paper/1903.08977/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2019.

## Built on by (most cited first, 11 of 11)

- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [Pulling back symmetric Riemannian geometry for data analysis](https://mlsanity.com/paper/2403.06612/) (2024)
- [Capacity Bounds for Hyperbolic Neural Network Representations of Latent Tree Structures](https://mlsanity.com/paper/2308.09250/) (2023)
- [Accelerating hyperbolic t-SNE](https://mlsanity.com/paper/2401.13708/) (2024)
- [Bayesian Hyperbolic Multidimensional Scaling](https://mlsanity.com/paper/2210.15081/) (2022)
- [Curvature Corrected Nonnegative Manifold Data Factorization](https://mlsanity.com/paper/2502.15124/) (2025)
- [Strain-Minimizing Hyperbolic Network Embeddings with Landmarks](https://mlsanity.com/paper/2207.06775/) (2022)
- [Symmetry-driven embedding of networks in hyperbolic space](https://mlsanity.com/paper/2406.10711/) (2024)
- [Geometric organization of olfactory descriptor data in the Poincar'e disk](https://mlsanity.com/paper/2609.09573/) (2026)
- [Hyperbolic Graph Embeddings: a Survey and an Evaluation on Anomaly Detection](https://mlsanity.com/paper/2512.18826/) (2025)
- [Bayesian Latent Space Models for Graphs Are Misspecified: Toward Robust Inference via Generalized Posteriors](https://mlsanity.com/paper/2605.18927/) (2026)

## Abstract (arXiv)

We introduce hydra (hyperbolic distance recovery and approximation), a new method for embedding network- or distance-based data into hyperbolic space. We show mathematically that hydra satisfies a certain optimality guarantee: It minimizes the `hyperbolic strain' between original and embedded data points. Moreover, it recovers points exactly, when they are located on a hyperbolic submanifold of the feature space. Testing on real network data we show that the embedding quality of hydra is competitive with existing hyperbolic embedding methods, but achieved at substantially shorter computation time. An extended method, termed hydra+, outperforms existing methods in both computation time and embedding quality.