# On a linear Gromov-Wasserstein distance

arXiv: https://arxiv.org/abs/2112.11964 · HTML: https://mlsanity.com/paper/2112.11964/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2021.

## Built on by (most cited first, 17 of 17)

- [On a linear fused Gromov-Wasserstein distance for graph structured data](https://mlsanity.com/paper/2203.04711/) (2022)
- [A Novel Sliced Fused Gromov-Wasserstein Distance](https://mlsanity.com/paper/2508.02364/) (2025)
- [Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spaces](https://mlsanity.com/paper/2307.09057/) (2023)
- [Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problem](https://mlsanity.com/paper/2303.05978/) (2023)
- [Slicing Wasserstein Over Wasserstein Via Functional Optimal Transport](https://mlsanity.com/paper/2509.22138/) (2025)
- [Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification](https://mlsanity.com/paper/2506.08761/) (2025)
- [Generalized Wasserstein Flow Matching: Transport Plans, Everywhere, All at Once](https://mlsanity.com/paper/2605.08424/) (2026)
- [Linear Partial Gromov-Wasserstein Embedding](https://mlsanity.com/paper/2410.16669/) (2024)
- [Approximative Algorithms for Multi-Marginal Optimal Transport and Free-Support Wasserstein Barycenters](https://mlsanity.com/paper/2202.00954/) (2022)
- [Structure-Sensitive Graph Dictionary Embedding for Graph Classification](https://mlsanity.com/paper/2306.10505/) (2023)
- [Gromov-Wasserstein and optimal transport: from assignment problems to probabilistic numeric](https://mlsanity.com/paper/2509.04089/) (2025)
- [Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition](https://mlsanity.com/paper/2512.08099/) (2025)
- [Well-Posed KL-Regularized Control via Wasserstein and Kalman-Wasserstein KL Divergences](https://mlsanity.com/paper/2602.02250/) (2026)
- [Beyond Rigid Alignment: Graph Federated Learning via Dual Manifold Calibration](https://mlsanity.com/paper/2605.06260/) (2026)
- [k-Nearest Neighbors in Gromov--Wasserstein Space](https://mlsanity.com/paper/2606.10295/) (2026)
- [Gromov-Wasserstein Quantization and Clustering: Structure, Rates, and Algorithms](https://mlsanity.com/paper/2608.11016/) (2026)
- [Gromov-Monge Flow Matching for Equivariant Graph Generation](https://mlsanity.com/paper/2608.26961/) (2026)

## Abstract (arXiv)

Gromov-Wasserstein distances are generalization of Wasserstein distances, which are invariant under distance preserving transformations. Although a simplified version of optimal transport in Wasserstein spaces, called linear optimal transport (LOT), was successfully used in practice, there does not exist a notion of linear Gromov-Wasserstein distances so far. In this paper, we propose a definition of linear Gromov-Wasserstein distances. We motivate our approach by a generalized LOT model, which is based on barycentric projection maps of transport plans. Numerical examples illustrate that the linear Gromov-Wasserstein distances, similarly as LOT, can replace the expensive computation of pairwise Gromov-Wasserstein distances in applications like shape classification.