# Families of Optimal Transport Kernels for Cell Complexes

arXiv: https://arxiv.org/abs/2507.16569 · HTML: https://mlsanity.com/paper/2507.16569/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 21 references that are in the map.
- First posted on arXiv 22 Jul 2025.

## Builds on (most cited first, 13 of 13)

- [Stochastic Optimization for Large-scale Optimal Transport](https://mlsanity.com/paper/1605.08527/) (2016)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [Fused Gromov-Wasserstein distance for structured objects: theoretical foundations and mathematical properties](https://mlsanity.com/paper/1811.02834/) (2018)
- [Mat'ern Gaussian Processes on Graphs](https://mlsanity.com/paper/2010.15538/) (2020)
- [GOT: An Optimal Transport framework for Graph comparison](https://mlsanity.com/paper/1906.02085/) (2019)
- [A Survey on Optimal Transport for Machine Learning: Theory and Applications](https://mlsanity.com/paper/2106.01963/) (2021)
- [Hodge-Compositional Edge Gaussian Processes](https://mlsanity.com/paper/2310.19450/) (2023)
- [Gaussian Processes on Cellular Complexes](https://mlsanity.com/paper/2311.01198/) (2023)
- [Wasserstein Exponential Kernels](https://mlsanity.com/paper/2002.01878/) (2020)
- [Gaussian process regression with Sliced Wasserstein Weisfeiler-Lehman graph kernels](https://mlsanity.com/paper/2402.03838/) (2024)
- [Gaussian Processes on Distributions based on Regularized Optimal Transport](https://mlsanity.com/paper/2210.06574/) (2022)
- [Graph Classification Gaussian Processes via Spectral Features](https://mlsanity.com/paper/2306.03770/) (2023)
- [Graph Classification Gaussian Processes via Hodgelet Spectral Features](https://mlsanity.com/paper/2410.10546/) (2024)

## Abstract (arXiv)

Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the Wasserstein distance between cell complex signal distributions in terms of a Hodge-Laplacian matrix. This leads to a structurally meaningful measure to compare CW complexes and define the optimal transportation map. In order to simultaneously include both feature and structure information, we extend the Fused Gromov-Wasserstein distance to CW complexes. Finally, we introduce novel kernels over the space of probability measures on CW complexes based on the dual formulation of optimal transport.