# The Gene Mover's Distance: Single-cell similarity via Optimal Transport

arXiv: https://arxiv.org/abs/2102.01218 · HTML: https://mlsanity.com/paper/2102.01218/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 48 references that are in the map.
- First posted on arXiv 1 Feb 2021.

## Builds on (most cited first, 4 of 4)

- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [Inference for Empirical Wasserstein Distances on Finite Spaces](https://mlsanity.com/paper/1610.03287/) (2016)

## Built on by (most cited first, 8 of 8)

- [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)
- [Embedding Signals on Knowledge Graphs with Unbalanced Diffusion Earth Mover's Distance](https://mlsanity.com/paper/2107.12334/) (2021)
- [Leveraging Optimal Transport via Projections on Subspaces for Machine Learning Applications](https://mlsanity.com/paper/2311.13883/) (2023)
- [Low dimensional representation of multi-patient flow cytometry datasets using optimal transport for minimal residual disease detection in leukemia](https://mlsanity.com/paper/2407.17329/) (2024)
- [Fast unsupervised ground metric learning with tree-Wasserstein distance](https://mlsanity.com/paper/2411.07432/) (2024)
- [Unsupervised Ground Metric Learning](https://mlsanity.com/paper/2507.13094/) (2025)
- [Busemann Functions in the Wasserstein Space: Existence, Closed-Forms, and Applications to Slicing](https://mlsanity.com/paper/2510.04579/) (2025)

## Abstract (arXiv)

This paper introduces the Gene Mover's Distance, a measure of similarity between a pair of cells based on their gene expression profiles obtained via single-cell RNA sequencing. The underlying idea of the proposed distance is to interpret the gene expression array of a single cell as a discrete probability measure. The distance between two cells is hence computed by solving an Optimal Transport problem between the two corresponding discrete measures. In the Optimal Transport model, we use two types of cost function for measuring the distance between a pair of genes. The first cost function exploits a gene embedding, called gene2vec, which is used to map each gene to a high dimensional vector: the cost of moving a unit of mass of gene expression from a gene to another is set to the Euclidean distance between the corresponding embedded vectors. The second cost function is based on a Pearson distance among pairs of genes. In both cost functions, the more two genes are correlated, the lower is their distance. We exploit the Gene Mover's Distance to solve two classification problems: the classification of cells according to their condition and according to their type. To assess the impact of our new metric, we compare the performances of a k-Nearest Neighbor classifier using different distances. The computational results show that the Gene Mover's Distance is competitive with the state-of-the-art distances used in the literature.