# An Analysis of the t-SNE Algorithm for Data Visualization

arXiv: https://arxiv.org/abs/1803.01768 · HTML: https://mlsanity.com/paper/1803.01768/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2018.

## Built on by (most cited first, 30 of 49)

- [Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data](https://mlsanity.com/paper/2105.07536/) (2021)
- [RouteFinder: Towards Foundation Models for Vehicle Routing Problems](https://mlsanity.com/paper/2406.15007/) (2024)
- [Can We Leave Deepfake Data Behind in Training Deepfake Detector?](https://mlsanity.com/paper/2408.17052/) (2024)
- [CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Data](https://mlsanity.com/paper/2111.15037/) (2021)
- [Your Contrastive Learning Is Secretly Doing Stochastic Neighbor Embedding](https://mlsanity.com/paper/2205.14814/) (2022)
- [A Probabilistic Graph Coupling View of Dimension Reduction](https://mlsanity.com/paper/2201.13053/) (2022)
- [t-SNE, Forceful Colorings and Mean Field Limits](https://mlsanity.com/paper/2102.13009/) (2021)
- [Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approach](https://mlsanity.com/paper/2203.00126/) (2022)
- [Stop Misusing t-SNE and UMAP for Visual Analytics](https://mlsanity.com/paper/2506.08725/) (2025)
- [Multidimensional Scaling: Approximation and Complexity](https://mlsanity.com/paper/2109.11505/) (2021)
- [An Empirical Evaluation of the t-SNE Algorithm for Data Visualization in Structural Engineering](https://mlsanity.com/paper/2109.08795/) (2021)
- [A Spectral Method for Assessing and Combining Multiple Data Visualizations](https://mlsanity.com/paper/2210.13711/) (2022)
- [GraphPrompter: Multi-stage Adaptive Prompt Optimization for Graph In-Context Learning](https://mlsanity.com/paper/2505.02027/) (2025)
- [Fake-Mamba: Real-Time Speech Deepfake Detection Using Bidirectional Mamba as Self-Attention's Alternative](https://mlsanity.com/paper/2508.09294/) (2025)
- [Empirical Evaluation and Theoretical Analysis for Representation Learning: A Survey](https://mlsanity.com/paper/2204.08226/) (2022)
- [ProcTag: Process Tagging for Assessing the Efficacy of Document Instruction Data](https://mlsanity.com/paper/2407.12358/) (2024)
- [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)
- [IAN: Iterated Adaptive Neighborhoods for manifold learning and dimensionality estimation](https://mlsanity.com/paper/2208.09123/) (2022)
- [Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold](https://mlsanity.com/paper/2401.17675/) (2024)
- [Large data limits and scaling laws for tSNE](https://mlsanity.com/paper/2410.13063/) (2024)
- [T-SNE Is Not Optimized to Reveal Clusters in Data](https://mlsanity.com/paper/2110.02573/) (2021)
- [Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data Visualization](https://mlsanity.com/paper/2207.12214/) (2022)
- [Are We Closing the Loop Yet? Gaps in the Generalizability of VIS4ML Research](https://mlsanity.com/paper/2308.06290/) (2023)
- [Task2Box: Box Embeddings for Modeling Asymmetric Task Relationships](https://mlsanity.com/paper/2403.17173/) (2024)
- [t-SNE Exaggerates Clusters, Provably](https://mlsanity.com/paper/2510.07746/) (2025)
- [Semantic properties of English nominal pluralization: Insights from word embeddings](https://mlsanity.com/paper/2203.15424/) (2022)
- [SSAS: Cross-subject EEG-based Emotion Recognition through Source Selection with Adversarial Strategy](https://mlsanity.com/paper/2512.13458/) (2025)
- [Indoor Smartphone SLAM with Learned Echoic Location Features](https://mlsanity.com/paper/2210.08493/) (2022)
- [Preserving local densities in low-dimensional embeddings](https://mlsanity.com/paper/2301.13732/) (2023)

## Abstract (arXiv)

A first line of attack in exploratory data analysis is data visualization, i.e., generating a 2-dimensional representation of data that makes clusters of similar points visually identifiable. Standard Johnson-Lindenstrauss dimensionality reduction does not produce data visualizations. The t-SNE heuristic of van der Maaten and Hinton, which is based on non-convex optimization, has become the de facto standard for visualization in a wide range of applications. This work gives a formal framework for the problem of data visualization - finding a 2-dimensional embedding of clusterable data that correctly separates individual clusters to make them visually identifiable. We then give a rigorous analysis of the performance of t-SNE under a natural, deterministic condition on the "ground-truth" clusters (similar to conditions assumed in earlier analyses of clustering) in the underlying data. These are the first provable guarantees on t-SNE for constructing good data visualizations. We show that our deterministic condition is satisfied by considerably general probabilistic generative models for clusterable data such as mixtures of well-separated log-concave distributions. Finally, we give theoretical evidence that t-SNE provably succeeds in partially recovering cluster structure even when the above deterministic condition is not met.