# Hybrid Wasserstein Distance and Fast Distribution Clustering

arXiv: https://arxiv.org/abs/1812.11026 · HTML: https://mlsanity.com/paper/1812.11026/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2018.

## Built on by (most cited first, 9 of 9)

- [Wasserstein K-means for clustering probability distributions](https://mlsanity.com/paper/2209.06975/) (2022)
- [Asymptotic Theory of Geometric and Adaptive k-Means Clustering](https://mlsanity.com/paper/2202.13423/) (2022)
- [Geometric Sparse Coding in Wasserstein Space](https://mlsanity.com/paper/2210.12135/) (2022)
- [Expectation Distance-based Distributional Clustering for Noise-Robustness](https://mlsanity.com/paper/2110.08871/) (2021)
- [The geometry of financial institutions -- Wasserstein clustering of financial data](https://mlsanity.com/paper/2305.03565/) (2023)
- [The Causal Impact of Credit Lines on Spending Distributions](https://mlsanity.com/paper/2312.10388/) (2023)
- [Kernel K-means clustering of distributional data](https://mlsanity.com/paper/2509.18037/) (2025)
- [Gamifying optimization: a Wasserstein distance-based analysis of human search](https://mlsanity.com/paper/2112.06292/) (2021)
- [Wasserstein-based Kernel Principal Component Analysis for Clustering Applications](https://mlsanity.com/paper/2503.14357/) (2025)

## Abstract (arXiv)

We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms. The first term --- which has a closed form --- measures the location-scale differences between the distributions. The second term is an approximation that measures the remaining distance after accounting for location-scale differences. We consider several forms of approximation with our main emphasis being a tangent space approximation that can be estimated using nonparametric regression. We evaluate the strengths and weaknesses of this approach on simulated and real examples.