mlsanityData to 7 Oct 2026

Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold

arXiv 2401.17675 ↗First posted 31 Jan 2024stat.ML cs.DS cs.LGcited by 4

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Abstract (arXiv)

We present a theoretical foundation regarding the boundedness of the t-SNE algorithm. t-SNE employs gradient descent iteration with Kullback-Leibler (KL) divergence as the objective function, aiming to identify a set of points that closely resemble the original data points in a high-dimensional space, minimizing KL divergence. Investigating t-SNE properties such as perplexity and affinity under a weak convergence assumption on the sampled dataset, we examine the behavior of points generated by t-SNE under continuous gradient flow. Demonstrating that points generated by t-SNE remain bounded, we leverage this insight to establish the existence of a minimizer for KL divergence.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 12 of its 28 references that are in the map. First posted on arXiv 31 Jan 2024.

Builds on

12 of 28 references.

References · 12

  1. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
  2. 2016Visualizing Large-scale and High-dimensional Datacited by 79
  3. 2017Efficient Algorithms for t-distributed Stochastic Neighborhood Embeddingcited by 75
  4. 2021Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Datacited by 55
  5. 2017Clustering with t-SNE, provablycited by 51
  6. 2018An Analysis of the t-SNE Algorithm for Data Visualizationcited by 49
  7. 2020Attraction-Repulsion Spectrum in Neighbor Embeddingscited by 41
  8. 2019Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisationscited by 22
  9. 2017Manifold learning with bi-stochastic kernelscited by 19
  10. 2021t-SNE, Forceful Colorings and Mean Field Limitscited by 10
  11. 2018Stochastic Neighbor Embedding under f-divergencescited by 9
  12. 2017Stochastic Neighbor Embedding separates well-separated clusterscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 2.

4 papers.

  1. 2025t-SNE Exaggerates Clusters, Provablycited by 3
  2. 2024Stochastic neighborhood embedding and the gradient flow of relative entropycited by 1
  3. 2026On the continuum limit of t-SNE for data visualizationcited by 1
  4. 2026On the Abundance of Critical Points of the t-SNE Energycited by 0