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Hierarchical Optimal Transport for Document Representation

arXiv 1906.10827 ↗First posted 26 Jun 2019cs.LG cs.CL cs.IRcited by 53

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Abstract (arXiv)

The ability to measure similarity between documents enables intelligent summarization and analysis of large corpora. Past distances between documents suffer from either an inability to incorporate semantic similarities between words or from scalability issues. As an alternative, we introduce hierarchical optimal transport as a meta-distance between documents, where documents are modeled as distributions over topics, which themselves are modeled as distributions over words. We then solve an optimal transport problem on the smaller topic space to compute a similarity score. We give conditions on the topics under which this construction defines a distance, and we relate it to the word mover's distance. We evaluate our technique for k-NN classification and show better interpretability and scalability with comparable performance to current methods at a fraction of the cost.

Key facts. Cited by 53 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Jun 2019.

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Citing papers per year: 2020: 1; 2021: 13; 2022: 10; 2023: 7; 2024: 5; 2025: 8; 2026: 9.

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  1. 2023Recent Advances in Optimal Transport for Machine Learningcited by 66
  2. 2022Representing Mixtures of Word Embeddings with Mixtures of Topic Embeddingscited by 36
  3. 2021A Survey on Optimal Transport for Machine Learning: Theory and Applicationscited by 35
  4. 2021Multi-Vector Models with Textual Guidance for Fine-Grained Scientific Document Similaritycited by 35
  5. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  6. 2022Wasserstein Task Embedding for Measuring Task Similaritiescited by 24
  7. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  8. 2022Adaptive Distribution Calibration for Few-Shot Learning with Hierarchical Optimal Transportcited by 14
  9. 2021Sentence Similarity Based on Contextscited by 12
  10. 2021Supervised Tree-Wasserstein Distancecited by 10
  11. 2021Re-evaluating Word Mover's Distancecited by 10
  12. 2021Hierarchical Optimal Transport for Unsupervised Domain Adaptationcited by 10
38 more
  1. 2025Lightspeed Geometric Dataset Distance via Sliced Optimal Transportcited by 10
  2. 2022Hilbert Curve Projection Distance for Distribution Comparisoncited by 9
  3. 2022OTExtSum: Extractive Text Summarisation with Optimal Transportcited by 8
  4. 2025Hierarchical Refinement: Optimal Transport to Infinity and Beyondcited by 8
  5. 2022Riemannian block SPD coupling manifold and its application to optimal transportcited by 7
  6. 2024A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributionscited by 7
  7. 2022Hierarchical Optimal Transport for Comparing Histopathology Datasetscited by 6
  8. 2025Enhancing Unsupervised Graph Few-shot Learning via Set Functions and Optimal Transportcited by 6
  9. 2021Unsupervised Ground Metric Learning using Wasserstein Singular Vectorscited by 5
  10. 2024Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchycited by 5
  11. 2025Slicing Wasserstein Over Wasserstein Via Functional Optimal Transportcited by 5
  12. 2021Order Constraints in Optimal Transportcited by 4
  13. 2024Explanatory Model Monitoring to Understand the Effects of Feature Shifts on Performancecited by 4
  14. 2025Efficient Transferable Optimal Transport via Min-Sliced Transport Planscited by 4
  15. 2020Nested-Wasserstein Self-Imitation Learning for Sequence Generationcited by 3
  16. 2022Modeling Hierarchical Structural Distance for Unsupervised Domain Adaptationcited by 3
  17. 2023Few-Shot Object Detection via Synthetic Features with Optimal Transportcited by 3
  18. 2021Interpretable contrastive word mover's embeddingcited by 2
  19. 2024What is the Right Notion of Distance between Predict-then-Optimize Tasks?cited by 2
  20. 2026Robust Generalization with Adaptive Optimal Transport Priors for Decision-Focused Learningcited by 2
  21. 2021Limit Distribution Theory for the Smooth 1-Wasserstein Distance with Applicationscited by 1
  22. 2022Budget-Constrained Bounds for Mini-Batch Estimation of Optimal Transportcited by 1
  23. 2023Keypoint-Guided Optimal Transport: Models, Algorithms, and Applicationscited by 1
  24. 2023Towards Generalising Neural Topical Representationscited by 1
  25. 2023TaskDiff: A Similarity Metric for Task-Oriented Conversationscited by 1
  26. 2024SAVA: Scalable Learning-Agnostic Data Valuationcited by 1
  27. 2025Scalable Sobolev IPM for Probability Measures on a Graphcited by 1
  28. 2026OT on the Map: Quantifying Domain Shifts in Geographic Spacecited by 1
  29. 2021Hawkes Processes on Graphonscited by 0
  30. 2021Efficient Optimal Transport Algorithm by Accelerated Gradient descentcited by 0
  31. 2022Coherence-Based Distributed Document Representation Learning for Scientific Documentscited by 0
  32. 2023A Novel Dual of Shannon Information and Weighting Schemecited by 0
  33. 2025How Vital is the Jurisprudential Relevance: Law Article Intervened Legal Case Retrieval and Matchingcited by 0
  34. 2025Generalized Sobolev IPM for Graph-Based Measurescited by 0
  35. 2026HOT-POT: Optimal Transport for Sparse Stereo Matchingcited by 0
  36. 2026Grammatical Error Correction Evaluation by Optimally Transporting Edit Representationcited by 0
  37. 2026Calibrating Tabular Anomaly Detection via Optimal Transportcited by 0
  38. 2026Online Continual Learning with Dynamic Label Hierarchiescited by 0

50 most cited of 53 All 53 (JSON)