mlsanityData to 7 Oct 2026

Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein

arXiv 2402.02239 ↗First posted 3 Feb 2024cs.LG stat.MLcited by 12

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Abstract (arXiv)

Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. Traditionally, this involves using dimensionality reduction (DR) methods to project data onto lower-dimensional spaces or organizing points into meaningful clusters (clustering). In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem. This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem. We empirically demonstrate its relevance to the identification of low-dimensional prototypes representing data at different scales, across multiple image and genomic datasets.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 29 of its 99 references that are in the map. First posted on arXiv 3 Feb 2024.

Builds on

29 of 99 references.

References · 29

  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. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,131
  4. 2018Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometrycited by 261
  5. 2018Riemannian Adaptive Optimization Methodscited by 187
  6. 2018Optimal Transport for structured data with application on graphscited by 170
  7. 2018Gromov-Wasserstein Alignment of Word Embedding Spacescited by 119
  8. 2020Geoopt: Riemannian Optimization in PyTorchcited by 109
  9. 2019Scalable Gromov-Wasserstein Learning for Graph Partitioning and Matchingcited by 102
  10. 2021Linear-Time Gromov Wasserstein Distances using Low Rank Couplings and Costscited by 61
  11. 2016Convergence Rate of Frank-Wolfe for Non-Convex Objectivescited by 59
  12. 2021HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projectionscited by 47
17 more
  1. 2020CO-Optimal Transportcited by 42
  2. 2020Generalized Spectral Clustering via Gromov-Wasserstein Learningcited by 37
  3. 2021Online Graph Dictionary Learningcited by 37
  4. 2021CO-SNE: Dimensionality Reduction and Visualization for Hyperbolic Datacited by 28
  5. 2021Minimum-Distortion Embeddingcited by 26
  6. 2019Gromov-Wasserstein Factorization Models for Graph Clusteringcited by 25
  7. 2022Aligning individual brains with Fused Unbalanced Gromov-Wassersteincited by 23
  8. 2022Template based Graph Neural Network with Optimal Transport Distancescited by 20
  9. 2023Hyperbolic Diffusion Embedding and Distance for Hierarchical Representation Learningcited by 18
  10. 2023A Gromov--Wasserstein Geometric View of Spectrum-Preserving Graph Coarseningcited by 15
  11. 2021Nested Hyperbolic Spaces for Dimensionality Reduction and Hyperbolic NN Designcited by 14
  12. 2022A Probabilistic Graph Coupling View of Dimension Reductioncited by 13
  13. 2023SNEkhorn: Dimension Reduction with Symmetric Entropic Affinitiescited by 12
  14. 2016Doubly Stochastic Neighbor Embedding on Spherescited by 9
  15. 2020Block majorization-minimization with diminishing radius for constrained nonsmooth nonconvex optimizationcited by 9
  16. 2018(Probably) Concave Graph Matchingcited by 7
  17. 2021Unified Framework for Spectral Dimensionality Reduction, Maximum Variance Unfolding, and Kernel Learning By Semidefinite Programming: Tutorial and Surveycited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 3; 2026: 7.

12 papers.

  1. 2024On Probabilistic Embeddings in Optimal Dimension Reductioncited by 5
  2. 2025A dimensionality reduction technique based on the Gromov-Wasserstein distancecited by 3
  3. 2025Constrained Sliced Wasserstein Embeddingcited by 2
  4. 2026Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transportcited by 2
  5. 2024Linear Partial Gromov-Wasserstein Embeddingcited by 1
  6. 2025Graph-based Clustering Revisited: A Relaxation of Kernel k-Means Perspectivecited by 1
  7. 2026Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clusteringcited by 1
  8. 2026Group Contrastive Learning for Weakly Paired Multimodal Datacited by 0
  9. 2026On sparsity, extremal structure, and monotonicity properties of Wasserstein and Gromov-Wasserstein optimal transport planscited by 0
  10. 2026Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Modelscited by 0
  11. 2026Network Learning with Semi-relaxed Gromov-Wassersteincited by 0
  12. 2026Gromov-Wasserstein Distillation for Inductive Multi-View Embeddingcited by 0