# Visualizing Riemannian data with Rie-SNE

arXiv: https://arxiv.org/abs/2203.09253 · HTML: https://mlsanity.com/paper/2203.09253/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 52 references that are in the map.
- First posted on arXiv 17 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [Continuous Hierarchical Representations with Poincar'e Variational Auto-Encoders](https://mlsanity.com/paper/1901.06033/) (2019)
- [Variational Autoencoders with Riemannian Brownian Motion Priors](https://mlsanity.com/paper/2002.05227/) (2020)
- [Geometry-aware Bayesian Optimization in Robotics using Riemannian Mat'ern Kernels](https://mlsanity.com/paper/2111.01460/) (2021)
- [Doubly Stochastic Neighbor Embedding on Spheres](https://mlsanity.com/paper/1609.01977/) (2016)
- [Unscented Orientation Estimation Based on the Bingham Distribution](https://mlsanity.com/paper/1311.5796/) (2013)
- [Probabilistic Riemannian submanifold learning with wrapped Gaussian process latent variable models](https://mlsanity.com/paper/1805.09122/) (2018)

## Built on by (most cited first, 1 of 1)

- [Beyond Euclid: An Illustrated Guide to Modern Machine Learning with Geometric, Topological, and Algebraic Structures](https://mlsanity.com/paper/2407.09468/) (2024)

## Abstract (arXiv)

Faithful visualizations of data residing on manifolds must take the underlying geometry into account when producing a flat planar view of the data. In this paper, we extend the classic stochastic neighbor embedding (SNE) algorithm to data on general Riemannian manifolds. We replace standard Gaussian assumptions with Riemannian diffusion counterparts and propose an efficient approximation that only requires access to calculations of Riemannian distances and volumes. We demonstrate that the approach also allows for mapping data from one manifold to another, e.g. from a high-dimensional sphere to a low-dimensional one.