# Intrinsic Sliced Wasserstein Distances for Comparing Collections of Probability Distributions on Manifolds and Graphs

arXiv: https://arxiv.org/abs/2010.15285 · HTML: https://mlsanity.com/paper/2010.15285/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [Sliced-Wasserstein on Symmetric Positive Definite Matrices for M/EEG Signals](https://mlsanity.com/paper/2303.05798/) (2023)
- [Hyperbolic Sliced-Wasserstein via Geodesic and Horospherical Projections](https://mlsanity.com/paper/2211.10066/) (2022)
- [Hierarchical Hybrid Sliced Wasserstein: A Scalable Metric for Heterogeneous Joint Distributions](https://mlsanity.com/paper/2404.15378/) (2024)
- [Wasserstein-Aligned Hyperbolic Multi-View Clustering](https://mlsanity.com/paper/2512.09402/) (2025)
- [Generalized Multivariate Signs for Nonparametric Hypothesis Testing in High Dimensions](https://mlsanity.com/paper/2107.01103/) (2021)
- [Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition](https://mlsanity.com/paper/2512.08099/) (2025)

## Abstract (arXiv)

Collections of probability distributions arise in a variety of applications ranging from user activity pattern analysis to brain connectomics. In practice these distributions can be defined over diverse domain types including finite intervals, circles, cylinders, spheres, other manifolds, and graphs. This paper introduces an approach for detecting differences between two collections of distributions over such general domains. To this end, we propose the intrinsic slicing construction that yields a novel class of Wasserstein distances on manifolds and graphs. These distances are Hilbert embeddable, allowing us to reduce the distribution collection comparison problem to a more familiar mean testing problem in a Hilbert space. We provide two testing procedures one based on resampling and another on combining p-values from coordinate-wise tests. Our experiments in various synthetic and real data settings show that the resulting tests are powerful and the p-values are well-calibrated.