# EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings

arXiv: https://arxiv.org/abs/2509.03703 · HTML: https://mlsanity.com/paper/2509.03703/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 30 references that are in the map.
- First posted on arXiv 3 Sep 2025.

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

- [Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding](https://mlsanity.com/paper/1712.09005/) (2017)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Attraction-Repulsion Spectrum in Neighbor Embeddings](https://mlsanity.com/paper/2007.08902/) (2020)
- [On UMAP's true loss function](https://mlsanity.com/paper/2103.14608/) (2021)
- [Path-Based Spectral Clustering: Guarantees, Robustness to Outliers, and Fast Algorithms](https://mlsanity.com/paper/1712.06206/) (2017)

## Built on by (most cited first, 2 of 2)

- [Discrete scalar curvature as a weighted sum of Ollivier-Ricci curvatures](https://mlsanity.com/paper/2510.04936/) (2025)
- [Understanding Differentiable Embeddings Through Differential and Integral Geometry](https://mlsanity.com/paper/2608.06809/) (2026)

## Abstract (arXiv)

Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often produce visualizations that do not preserve the geometry of noisy and high dimensional data. In particular, they can spuriously separate connected components of the underlying data submanifold and can fail to find clusters in well-clusterable data. To address these limitations, we propose EmbedOR, a SNE algorithm that incorporates discrete graph curvature. Our algorithm stochastically embeds the data using a curvature-enhanced distance metric that emphasizes underlying cluster structure. Critically, we prove that the EmbedOR distance metric extends consistency results for tSNE to a much broader class of datasets. We also describe extensive experiments on synthetic and real data that demonstrate the visualization and geometry-preservation capabilities of EmbedOR. We find that, unlike other SNE algorithms and UMAP, EmbedOR is much less likely to fragment continuous, high-density regions of the data. Finally, we demonstrate that the EmbedOR distance metric can be used as a tool to annotate existing visualizations to identify fragmentation and provide deeper insight into the underlying geometry of the data.