mlsanityData to 7 Oct 2026

A Probabilistic Graph Coupling View of Dimension Reduction

arXiv 2201.13053 ↗First posted 31 Jan 2022math.PR math.ST stat.MLcited by 13

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Abstract (arXiv)

Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full understanding of their properties and limitations. To that extent, we introduce a unifying statistical framework based on the coupling of hidden graphs using cross entropy. These graphs induce a Markov random field dependency structure among the observations in both input and latent spaces. We show that existing pairwise similarity DR methods can be retrieved from our framework with particular choices of priors for the graphs. Moreover this reveals that these methods suffer from a statistical deficiency that explains poor performances in conserving coarse-grain dependencies. Our model is leveraged and extended to address this issue while new links are drawn with Laplacian eigenmaps and PCA.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 10 of its 59 references that are in the map. First posted on arXiv 31 Jan 2022.

Builds on

10 of 59 references.

References · 10

  1. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  2. 2018UMAP: Uniform Manifold Approximation and Projection for Dimension Reductioncited by 2,841
  3. 2020Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualizationcited by 170
  4. 2016Visualizing Large-scale and High-dimensional Datacited by 79
  5. 2017Efficient Algorithms for t-distributed Stochastic Neighborhood Embeddingcited by 75
  6. 2017Clustering with t-SNE, provablycited by 51
  7. 2018An Analysis of the t-SNE Algorithm for Data Visualizationcited by 49
  8. 2019Heavy-tailed kernels reveal a finer cluster structure in t-SNE visualisationscited by 22
  9. 2018t-SNE-CUDA: GPU-Accelerated t-SNE and its Applications to Modern Datacited by 19
  10. 2019High-dimensional Gaussian graphical model for network-linked datacited by 5

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 5; 2025: 1; 2026: 2.

13 papers.

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  1. 2023Contrastive Learning Is Spectral Clustering On Similarity Graphcited by 24
  2. 2023Matrix Information Theory for Self-Supervised Learningcited by 21
  3. 2023SNEkhorn: Dimension Reduction with Symmetric Entropic Affinitiescited by 12
  4. 2024Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wassersteincited by 12
  5. 2024Dimension Reduction with Locally Adjusted Graphscited by 9
  6. 2024Assessing and improving reliability of neighbor embedding methods: a map-continuity perspectivecited by 4
  7. 2024Lambda: Learning Matchable Prior For Entity Alignment with Unlabeled Dangling Casescited by 3
  8. 2024Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNEcited by 3
  9. 2025A dimensionality reduction technique based on the Gromov-Wasserstein distancecited by 3
  10. 2023Kernel-Based Testing for Single-Cell Differential Analysiscited by 2
  11. 2023Interpolating between Clustering and Dimensionality Reduction with Gromov-Wassersteincited by 0
  12. 2026UMAP Is Spectral Clustering on the Fuzzy Nearest-Neighbor Graphcited by 0
1 more
  1. 2026The Rashomon Effect for Visualizing High-Dimensional Datacited by 0