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Multilevel Clustering via Wasserstein Means

arXiv 1706.03883 ↗First posted 13 Jun 2017stat.ML stat.CO stat.MEcited by 49

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Abstract (arXiv)

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

Key facts. Cited by 49 papers in the map (data through 14 Oct 2026). First posted on arXiv 13 Jun 2017.

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Citing papers per year: 2021: 18; 2022: 8; 2023: 11; 2024: 4; 2025: 4; 2026: 4.

49 papers.

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  1. 2021Point-set Distances for Learning Representations of 3D Point Cloudscited by 48
  2. 2021Improving Mini-batch Optimal Transport via Partial Transportationcited by 41
  3. 2021Automatic Text Evaluation through the Lens of Wasserstein Barycenterscited by 38
  4. 2021Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descentcited by 32
  5. 2021Unbalanced Optimal Transport through Non-negative Penalized Linear Regressioncited by 31
  6. 2021Wasserstein barycenters are NP-hard to computecited by 28
  7. 2021On Robust Optimal Transport: Computational Complexity and Barycenter Computationcited by 27
  8. 2022Revisiting Sliced Wasserstein on Images: From Vectorization to Convolutioncited by 25
  9. 2022Hierarchical Sliced Wasserstein Distancecited by 23
  10. 2023Quasi-Monte Carlo for 3D Sliced Wassersteincited by 22
  11. 2025On the Relation between Rectified Flows and Optimal Transportcited by 18
  12. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 16
37 more
  1. 2022On Unbalanced Optimal Transport: Gradient Methods, Sparsity and Approximation Errorcited by 16
  2. 2023Sliced Wasserstein Estimation with Control Variatescited by 16
  3. 2022Wasserstein Barycenter-based Model Fusion and Linear Mode Connectivity of Neural Networkscited by 15
  4. 2021Semi-Discrete Optimal Transport: Hardness, Regularization and Numerical Solutioncited by 13
  5. 2021Dimensionality Reduction for Wasserstein Barycentercited by 13
  6. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  7. 2022Small Transformers Compute Universal Metric Embeddingscited by 12
  8. 2023Lower Complexity Adaptation for Empirical Entropic Optimal Transportcited by 12
  9. 2021Hierarchical Optimal Transport for Unsupervised Domain Adaptationcited by 10
  10. 2024Interaction-Force Transport Gradient Flowscited by 9
  11. 2021Projection Robust Wasserstein Barycenterscited by 8
  12. 2021On Multimarginal Partial Optimal Transport: Equivalent Forms and Computational Complexitycited by 8
  13. 2021Functional optimal transport: map estimation and domain adaptation for functional datacited by 7
  14. 2023Self-Attention Amortized Distributional Projection Optimization for Sliced Wasserstein Point-Cloud Reconstructioncited by 7
  15. 2024Tree-Sliced Wasserstein Distance: A Geometric Perspectivecited by 7
  16. 2024Prototypical Partial Optimal Transport for Universal Domain Adaptationcited by 7
  17. 2023LCOT: Linear circular optimal transportcited by 4
  18. 2023Fast Dual Subgradient Optimization of the Integrated Transportation Distance Between Stochastic Kernelscited by 4
  19. 2022Improving Generative Flow Networks with Path Regularizationcited by 3
  20. 2024Approximate Algorithms For k-Sparse Wasserstein Barycenter With Outlierscited by 3
  21. 2025Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysiscited by 2
  22. 2026An Efficient and Effective Evaluator for Text2SQL Models on Unseen and Unlabeled Datacited by 2
  23. 2026UniPROT: Uniform Prototype Selection via Partial Optimal Transport with Submodular Guaranteescited by 2
  24. 2021Limit Distribution Theory for the Smooth 1-Wasserstein Distance with Applicationscited by 1
  25. 2022Stability of Entropic Wasserstein Barycenters and application to random geometric graphscited by 1
  26. 2023Keypoint-Guided Optimal Transport: Models, Algorithms, and Applicationscited by 1
  27. 2023The geometry of financial institutions -- Wasserstein clustering of financial datacited by 1
  28. 2023Parameter Estimation in DAGs from Incomplete Data via Optimal Transportcited by 1
  29. 2023A Specialized Semismooth Newton Method for Kernel-Based Optimal Transportcited by 1
  30. 2025Federated Calculation of the Free-Support Transportation Barycenter by Single-Loop Dual Decompositioncited by 1
  31. 2021Selective information exchange in collaborative clustering using regularized Optimal Transportcited by 0
  32. 2021Estimation of Stationary Optimal Transport Planscited by 0
  33. 2022Efficient Forecasting of Large Scale Hierarchical Time Series via Multilevel Clusteringcited by 0
  34. 2023Learning to Quantize Vulnerability Patterns and Match to Locate Statement-Level Vulnerabilitiescited by 0
  35. 2025Partial Distribution Alignment via Adaptive Optimal Transportcited by 0
  36. 2026Multi-Domain Clustering via Measure Quantizationcited by 0
  37. 2026Robust blind unmixing: A geometric approach to overcoming basis variationcited by 0