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Updated: Jul 12, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

Published on: October 27, 2016

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

Tristan Luca Saidi¹, Abigail Hickok², Bastian Rieck³

¹Department of Computer Science, Columbia University, New York, NY 10027.

Proceedings of the National Academy of Sciences of the United States of America

|July 10, 2026

Summary

EmbedOR, a new Stochastic Neighbor Embedding (SNE) algorithm, improves data visualization by incorporating discrete graph curvature. This method better preserves data geometry and cluster structures compared to UMAP and tSNE.

Keywords:

discrete graph curvature embeddings nonlinear dimensionality reduction single-cell biology

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Last Updated: Jul 12, 2026

Visualization Method for Proprioceptive Drift on a 2D Plane Using Support Vector Machine

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Published on: October 27, 2016

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Large-scale Reconstructions and Independent, Unbiased Clustering Based on Morphological Metrics to Classify Neurons in Selective Populations

Published on: February 15, 2017

Area of Science:

Data Visualization
Machine Learning
Computational Geometry

Background:

Stochastic Neighbor Embedding (SNE) algorithms like UMAP and tSNE often fail to preserve the geometry of high-dimensional data.
These methods can spuriously separate connected components and miss clusters in complex datasets.

Purpose of the Study:

To introduce EmbedOR, a novel SNE algorithm designed to overcome the limitations of existing methods.
To enhance data visualization by preserving geometric structures and improving cluster identification.

Main Methods:

EmbedOR utilizes a curvature-enhanced distance metric within its stochastic embedding process.
The algorithm incorporates discrete graph curvature to emphasize underlying cluster structures.
Theoretical consistency results for tSNE are extended to a broader class of datasets using the EmbedOR metric.

Main Results:

Extensive experiments on synthetic and real data demonstrate EmbedOR's superior visualization and geometry-preservation capabilities.
EmbedOR significantly reduces the fragmentation of continuous, high-density data regions compared to UMAP and tSNE.
The EmbedOR distance metric proves effective in annotating existing visualizations to identify fragmentation.

Conclusions:

EmbedOR offers a robust solution for visualizing high-dimensional data, addressing key limitations of current SNE techniques.
The incorporation of graph curvature enhances the preservation of underlying data geometry and cluster integrity.
EmbedOR provides a valuable tool for deeper insights into data structure and for annotating complex visualizations.