# On Procrustes Analysis in Hyperbolic Space

arXiv: https://arxiv.org/abs/2102.03723 · HTML: https://mlsanity.com/paper/2102.03723/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Feb 2021.

## Built on by (most cited first, 5 of 5)

- [Ultrahyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2206.00449/) (2022)
- [Small Transformers Compute Universal Metric Embeddings](https://mlsanity.com/paper/2209.06788/) (2022)
- [Generalizing Knowledge Graph Embedding with Universal Orthogonal Parameterization](https://mlsanity.com/paper/2405.08540/) (2024)
- [Structured Pruning for Efficient Visual Place Recognition](https://mlsanity.com/paper/2409.07834/) (2024)
- [Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hulls](https://mlsanity.com/paper/2308.06895/) (2023)

## Abstract (arXiv)

Congruent Procrustes analysis aims to find the best matching between two point sets through rotation, reflection and translation. We formulate the Procrustes problem for hyperbolic spaces, review the canonical definition of the center of point sets, and give a closed form solution for the optimal isometry for noise-free measurements. We also analyze the performance of the proposed method under measurement noise.