# Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance

arXiv: https://arxiv.org/abs/2405.15959 · HTML: https://mlsanity.com/paper/2405.15959/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2024.

## Built on by (most cited first, 13 of 13)

- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [On Probabilistic Embeddings in Optimal Dimension Reduction](https://mlsanity.com/paper/2408.02433/) (2024)
- [A dimensionality reduction technique based on the Gromov-Wasserstein distance](https://mlsanity.com/paper/2501.13732/) (2025)
- [Metric properties of partial and robust Gromov-Wasserstein distances](https://mlsanity.com/paper/2411.02198/) (2024)
- [Joint Metric Space Embedding by Unbalanced OT with Gromov-Wasserstein Marginal Penalization](https://mlsanity.com/paper/2502.07510/) (2025)
- [Structure-Preserving Multi-View Embedding Using Gromov-Wasserstein Optimal Transport](https://mlsanity.com/paper/2604.02610/) (2026)
- [Gromov-Wasserstein Methods for Multi-View Relational Embedding and Clustering](https://mlsanity.com/paper/2604.23912/) (2026)
- [On Robust Cross Domain Alignment](https://mlsanity.com/paper/2412.15861/) (2024)
- [Feature-based morphological analysis of shape graph data](https://mlsanity.com/paper/2602.16120/) (2026)
- [Fused Gromov-Wasserstein Distance with Feature Selection](https://mlsanity.com/paper/2605.12161/) (2026)
- [Bridging Maximum Likelihood and Optimal Transport for Efficient Inference and Model Selection in Stochastic Block Models](https://mlsanity.com/paper/2605.28488/) (2026)
- [Network Learning with Semi-relaxed Gromov-Wasserstein](https://mlsanity.com/paper/2606.02223/) (2026)
- [Gromov-Wasserstein Distillation for Inductive Multi-View Embedding](https://mlsanity.com/paper/2609.40047/) (2026)

## Abstract (arXiv)

Dimension reduction techniques typically seek an embedding of a high-dimensional point cloud into a low-dimensional Euclidean space which optimally preserves the geometry of the input data. Based on expert knowledge, one may instead wish to embed the data into some other manifold or metric space in order to better reflect the geometry or topology of the point cloud. We propose a general method for manifold-valued multidimensional scaling based on concepts from optimal transport. In particular, we establish theoretical connections between the recently introduced semi-relaxed Gromov-Wasserstein (srGW) framework and multidimensional scaling by solving the Monge problem in this setting. We also derive novel connections between srGW distance and Gromov-Hausdorff distance. We apply our computational framework to analyze ensembles of political redistricting plans for states with two Congressional districts, achieving an effective visualization of the ensemble as a distribution on a circle which can be used to characterize typical neutral plans, and to flag outliers.