# Speeding up Word Mover's Distance and its variants via properties of distances between embeddings

arXiv: https://arxiv.org/abs/1912.00509 · HTML: https://mlsanity.com/paper/1912.00509/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Dec 2019.

## Built on by (most cited first, 5 of 5)

- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Improving Neural Cross-Lingual Summarization via Employing Optimal Transport Distance for Knowledge Distillation](https://mlsanity.com/paper/2112.03473/) (2021)
- [Re-evaluating Word Mover's Distance](https://mlsanity.com/paper/2105.14403/) (2021)
- [Hawk: An Industrial-strength Multi-label Document Classifier](https://mlsanity.com/paper/2301.06057/) (2023)
- [WMDecompose: A Framework for Leveraging the Interpretable Properties of Word Mover's Distance in Sociocultural Analysis](https://mlsanity.com/paper/2110.07330/) (2021)

## Abstract (arXiv)

The Word Mover's Distance (WMD) proposed by Kusner et al. is a distance between documents that takes advantage of semantic relations among words that are captured by their embeddings. This distance proved to be quite effective, obtaining state-of-art error rates for classification tasks, but is also impracticable for large collections/documents due to its computational complexity. For circumventing this problem, variants of WMD have been proposed. Among them, Relaxed Word Mover's Distance (RWMD) is one of the most successful due to its simplicity, effectiveness, and also because of its fast implementations. Relying on assumptions that are supported by empirical properties of the distances between embeddings, we propose an approach to speed up both WMD and RWMD. Experiments over 10 datasets suggest that our approach leads to a significant speed-up in document classification tasks while maintaining the same error rates.