Provable cluster-preserving visualizations with curvature-based stochastic neighbor embeddings.

Authors

Tristan Luca Saidi, Abigail Hickok, Bastian Rieck, Andrew J Blumberg

Published in

Proceedings of the National Academy of Sciences of the United States of America. Volume 123. Issue 28. Pages e2509171123. Jul 14, 2026. Epub Jul 10, 2026.

Abstract

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.

PMID:
42430356
Bibliographic data and abstract were imported from PubMed on 11 Jul 2026.

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