# Stochastic Neighbor Embedding separates well-separated clusters

arXiv: https://arxiv.org/abs/1702.02670 · HTML: https://mlsanity.com/paper/1702.02670/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Feb 2017.

## Built on by (most cited first, 7 of 7)

- [Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data](https://mlsanity.com/paper/2105.07536/) (2021)
- [Informative Initialization and Kernel Selection Improves t-SNE for Biological Sequences](https://mlsanity.com/paper/2211.09263/) (2022)
- [Assessing and improving reliability of neighbor embedding methods: a map-continuity perspective](https://mlsanity.com/paper/2410.16608/) (2024)
- [The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reduction](https://mlsanity.com/paper/2503.09101/) (2025)
- [Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold](https://mlsanity.com/paper/2401.17675/) (2024)
- [t-SNE Exaggerates Clusters, Provably](https://mlsanity.com/paper/2510.07746/) (2025)
- [Stochastic neighborhood embedding and the gradient flow of relative entropy](https://mlsanity.com/paper/2409.16963/) (2024)

## Abstract (arXiv)

Stochastic Neighbor Embedding and its variants are widely used dimensionality reduction techniques -- despite their popularity, no theoretical results are known. We prove that the optimal SNE embedding of well-separated clusters from high dimensions to any Euclidean space R^d manages to successfully separate the clusters in a quantitative way. The result also applies to a larger family of methods including a variant of t-SNE.