mlsanityData to 7 Oct 2026

Clustering with t-SNE, provably

arXiv 1706.02582 ↗First posted 8 Jun 2017cs.LG stat.MLcited by 51

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Abstract (arXiv)

t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters; more precisely, we prove that t-SNE in the `early exaggeration' phase, an optimization technique proposed by van der Maaten & Hinton (2008) and van der Maaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests novel ways for setting the exaggeration parameter α and step size h. Numerical examples illustrate the effectiveness of these rules: in particular, the quality of embedding of topological structures (e.g. the swiss roll) improves. We also discuss a connection to spectral clustering methods.

Key facts. Cited by 51 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Jun 2017.

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Citing papers per year: 2021: 8; 2022: 7; 2023: 10; 2024: 15; 2025: 7; 2026: 4.

51 papers.

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  1. 2023Manifold learning: what, how, and whycited by 66
  2. 2021Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Datacited by 55
  3. 2021On UMAP's true loss functioncited by 32
  4. 2022Your Contrastive Learning Is Secretly Doing Stochastic Neighbor Embeddingcited by 28
  5. 2021Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolutioncited by 14
  6. 2022A Probabilistic Graph Coupling View of Dimension Reductioncited by 13
  7. 2023SNEkhorn: Dimension Reduction with Symmetric Entropic Affinitiescited by 12
  8. 2021t-SNE, Forceful Colorings and Mean Field Limitscited by 10
  9. 2022Learning Low-Dimensional Nonlinear Structures from High-Dimensional Noisy Data: An Integral Operator Approachcited by 8
  10. 2021Multidimensional Scaling: Approximation and Complexitycited by 7
  11. 2022Enhancing cluster analysis via topological manifold learningcited by 6
  12. 2023A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reductioncited by 6
38 more
  1. 2025DeepGB-TB: A Risk-Balanced Cross-Attention Gradient-Boosted Convolutional Network for Rapid, Interpretable Tuberculosis Screeningcited by 6
  2. 2025The Shape of Attraction in UMAP: Exploring the Embedding Forces in Dimensionality Reductioncited by 5
  3. 2024Quantum Architecture Search with Unsupervised Representation Learningcited by 4
  4. 2024Convergence analysis of t-SNE as a gradient flow for point cloud on a manifoldcited by 4
  5. 2024Large data limits and scaling laws for tSNEcited by 4
  6. 2024Assessing and improving reliability of neighbor embedding methods: a map-continuity perspectivecited by 4
  7. 2021T-SNE Is Not Optimized to Reveal Clusters in Datacited by 3
  8. 2024Outlier Detection in Large Radiological Datasets using UMAPcited by 3
  9. 2025t-SNE Exaggerates Clusters, Provablycited by 3
  10. 2022Semantic properties of English nominal pluralization: Insights from word embeddingscited by 2
  11. 2024Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservationcited by 2
  12. 2022AVIDA: Alternating method for Visualizing and Integrating Datacited by 1
  13. 2023MN-Pair Contrastive Damage Representation and Clustering for Prognostic Explanationcited by 1
  14. 2023Preserving local densities in low-dimensional embeddingscited by 1
  15. 2023From structure mining to unsupervised exploration of atomic octahedral networkscited by 1
  16. 2023Few-shot 1/a Anomalies Feedback : Damage Vision Mining Opportunity and Embedding Feature Imbalancecited by 1
  17. 2023DatasetEquity: Are All Samples Created Equal? In The Quest For Equity Within Datasetscited by 1
  18. 2023Universal Deoxidation of Semiconductor Substrates Assisted by Machine-Learning and Real-Time-Feedback-Controlcited by 1
  19. 2024Feature Clock: High-Dimensional Effects in Two-Dimensional Plotscited by 1
  20. 2024Stochastic neighborhood embedding and the gradient flow of relative entropycited by 1
  21. 2024MIK: Modified Isolation Kernel for Biological Sequence Visualization, Classification, and Clusteringcited by 1
  22. 2024In-situ Self-optimization of Quantum Dot Emission for Lasers by Machine-Learning Assisted Epitaxycited by 1
  23. 2024Intrinsic Dimensionality of Fermi-Pasta-Ulam-Tsingou High-Dimensional Trajectories Through Manifold Learning: A Linear Approachcited by 1
  24. 2024Attraction-Repulsion Swarming: A Generalized Framework of t-SNE via Force Normalization and Tunable Interactionscited by 1
  25. 2024Federated t-SNE and UMAP for Distributed Data Visualizationcited by 1
  26. 2025Node Embeddings via Neighbor Embeddingscited by 1
  27. 2026On the continuum limit of t-SNE for data visualizationcited by 1
  28. 2026Some Theoretical Limitations of t-SNEcited by 1
  29. 2021Advances in Electron Microscopy with Deep Learningcited by 0
  30. 2021Topological Indoor Mapping through WiFi Signalscited by 0
  31. 2022May the force be with youcited by 0
  32. 2023Materials Informatics: An Algorithmic Design Rulecited by 0
  33. 2024Cell Culture Assistive Application for Precipitation Image Diagnosiscited by 0
  34. 2024Convergence Guarantees for the DeepWalk Embedding on Block Modelscited by 0
  35. 2025HDTree: Generative Modeling of Cellular Hierarchies for Robust Lineage Inferencecited by 0
  36. 2025Cluster and then Embed: A Modular Approach for Visualizationcited by 0
  37. 2025The Tree-SNE Tree Existscited by 0
  38. 2026A Comparative Study of UMAP and Other Dimensionality Reduction Methodscited by 0

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