# Wasserstein Exponential Kernels

arXiv: https://arxiv.org/abs/2002.01878 · HTML: https://mlsanity.com/paper/2002.01878/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2020.

## Built on by (most cited first, 10 of 10)

- [On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry](https://mlsanity.com/paper/2106.00286/) (2021)
- [Unbalanced Optimal Transport: A Unified Framework for Object Detection](https://mlsanity.com/paper/2307.02402/) (2023)
- [Ollivier-Ricci Curvature for Hypergraphs: A Unified Framework](https://mlsanity.com/paper/2210.12048/) (2022)
- [Adversarially Robust Kernel Smoothing](https://mlsanity.com/paper/2102.08474/) (2021)
- [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)
- [Optimal Transport-inspired Deep Learning Framework for Slow-Decaying Kolmogorov n-width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernel](https://mlsanity.com/paper/2308.13840/) (2023)
- [Gamifying optimization: a Wasserstein distance-based analysis of human search](https://mlsanity.com/paper/2112.06292/) (2021)
- [Pseudo-Likelihood Inference](https://mlsanity.com/paper/2311.16656/) (2023)
- [Wasserstein-based Kernel Principal Component Analysis for Clustering Applications](https://mlsanity.com/paper/2503.14357/) (2025)
- [Families of Optimal Transport Kernels for Cell Complexes](https://mlsanity.com/paper/2507.16569/) (2025)

## Abstract (arXiv)

In the context of kernel methods, the similarity between data points is encoded by the kernel function which is often defined thanks to the Euclidean distance, a common example being the squared exponential kernel. Recently, other distances relying on optimal transport theory - such as the Wasserstein distance between probability distributions - have shown their practical relevance for different machine learning techniques. In this paper, we study the use of exponential kernels defined thanks to the regularized Wasserstein distance and discuss their positive definiteness. More specifically, we define Wasserstein feature maps and illustrate their interest for supervised learning problems involving shapes and images. Empirically, Wasserstein squared exponential kernels are shown to yield smaller classification errors on small training sets of shapes, compared to analogous classifiers using Euclidean distances.