# Hierarchical Optimal Transport for Document Representation

arXiv: https://arxiv.org/abs/1906.10827 · HTML: https://mlsanity.com/paper/1906.10827/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Jun 2019.

## Built on by (most cited first, 30 of 53)

- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [Representing Mixtures of Word Embeddings with Mixtures of Topic Embeddings](https://mlsanity.com/paper/2203.01570/) (2022)
- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [Multi-Vector Models with Textual Guidance for Fine-Grained Scientific Document Similarity](https://mlsanity.com/paper/2111.08366/) (2021)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Wasserstein Task Embedding for Measuring Task Similarities](https://mlsanity.com/paper/2208.11726/) (2022)
- [On Transportation of Mini-batches: A Hierarchical Approach](https://mlsanity.com/paper/2102.05912/) (2021)
- [Adaptive Distribution Calibration for Few-Shot Learning with Hierarchical Optimal Transport](https://mlsanity.com/paper/2210.04144/) (2022)
- [Sentence Similarity Based on Contexts](https://mlsanity.com/paper/2105.07623/) (2021)
- [Supervised Tree-Wasserstein Distance](https://mlsanity.com/paper/2101.11520/) (2021)
- [Re-evaluating Word Mover's Distance](https://mlsanity.com/paper/2105.14403/) (2021)
- [Hierarchical Optimal Transport for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2112.02073/) (2021)
- [Lightspeed Geometric Dataset Distance via Sliced Optimal Transport](https://mlsanity.com/paper/2501.18901/) (2025)
- [Hilbert Curve Projection Distance for Distribution Comparison](https://mlsanity.com/paper/2205.15059/) (2022)
- [Hierarchical Refinement: Optimal Transport to Infinity and Beyond](https://mlsanity.com/paper/2503.03025/) (2025)
- [OTExtSum: Extractive Text Summarisation with Optimal Transport](https://mlsanity.com/paper/2204.10086/) (2022)
- [Riemannian block SPD coupling manifold and its application to optimal transport](https://mlsanity.com/paper/2201.12933/) (2022)
- [A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributions](https://mlsanity.com/paper/2405.03664/) (2024)
- [Hierarchical Optimal Transport for Comparing Histopathology Datasets](https://mlsanity.com/paper/2204.08324/) (2022)
- [Enhancing Unsupervised Graph Few-shot Learning via Set Functions and Optimal Transport](https://mlsanity.com/paper/2501.05635/) (2025)
- [Unsupervised Ground Metric Learning using Wasserstein Singular Vectors](https://mlsanity.com/paper/2102.06278/) (2021)
- [Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchy](https://mlsanity.com/paper/2410.21107/) (2024)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Order Constraints in Optimal Transport](https://mlsanity.com/paper/2110.07275/) (2021)
- [Explanatory Model Monitoring to Understand the Effects of Feature Shifts on Performance](https://mlsanity.com/paper/2408.13648/) (2024)
- [Efficient Transferable Optimal Transport via Min-Sliced Transport Plans](https://mlsanity.com/paper/2511.19741/) (2025)
- [Nested-Wasserstein Self-Imitation Learning for Sequence Generation](https://mlsanity.com/paper/2001.06944/) (2020)
- [Modeling Hierarchical Structural Distance for Unsupervised Domain Adaptation](https://mlsanity.com/paper/2211.11424/) (2022)
- [Few-Shot Object Detection via Synthetic Features with Optimal Transport](https://mlsanity.com/paper/2308.15005/) (2023)
- [Interpretable contrastive word mover's embedding](https://mlsanity.com/paper/2111.01023/) (2021)

## 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.