# Kernel Wasserstein Distance

arXiv: https://arxiv.org/abs/1905.09314 · HTML: https://mlsanity.com/paper/1905.09314/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 May 2019.

## Built on by (most cited first, 4 of 4)

- [Squared Wasserstein-2 Distance for Efficient Reconstruction of Stochastic Differential Equations](https://mlsanity.com/paper/2401.11354/) (2024)
- [Gaussian Process regression over discrete probability measures: on the non-stationarity relation between Euclidean and Wasserstein Squared Exponential Kernels](https://mlsanity.com/paper/2212.01310/) (2022)
- [Achieving Counterfactual Fairness with Imperfect Structural Causal Model](https://mlsanity.com/paper/2303.14665/) (2023)
- [Optimal Transport for Kernel Gaussian Mixture Models](https://mlsanity.com/paper/2310.18586/) (2023)

## Abstract (arXiv)

The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common divergences on distributions such as Kullback-Leibler or Jensen-Shannon, it is (weakly) continuous, and thus ideal for analyzing corrupted data. To date, however, no kernel methods for dealing with nonlinear data have been proposed via the Wasserstein distance. In this work, we develop a novel method to compute the L2-Wasserstein distance in a kernel space implemented using the kernel trick. The latter is a general method in machine learning employed to handle data in a nonlinear manner. We evaluate the proposed approach in identifying computerized tomography (CT) slices with dental artifacts in head and neck cancer, performing unsupervised hierarchical clustering on the resulting Wasserstein distance matrix that is computed on imaging texture features extracted from each CT slice. Our experiments show that the kernel approach outperforms classical non-kernel approaches in identifying CT slices with artifacts.