# A dimensionality reduction technique based on the Gromov-Wasserstein distance

arXiv: https://arxiv.org/abs/2501.13732 · HTML: https://mlsanity.com/paper/2501.13732/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 15 references that are in the map.
- First posted on arXiv 23 Jan 2025.

## Builds on (most cited first, 7 of 7)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [A Probabilistic Graph Coupling View of Dimension Reduction](https://mlsanity.com/paper/2201.13053/) (2022)
- [Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance](https://mlsanity.com/paper/2405.15959/) (2024)
- [SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities](https://mlsanity.com/paper/2305.13797/) (2023)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [Entropic Wasserstein Component Analysis](https://mlsanity.com/paper/2303.05119/) (2023)

## Built on by (most cited first, 3 of 3)

- [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)
- [Gromov-Wasserstein Distillation for Inductive Multi-View Embedding](https://mlsanity.com/paper/2609.40047/) (2026)

## Abstract (arXiv)

Analyzing relationships between objects is a pivotal problem within data science. In this context, Dimensionality reduction (DR) techniques are employed to generate smaller and more manageable data representations. This paper proposes a new method for dimensionality reduction, based on optimal transportation theory and the Gromov-Wasserstein distance. We offer a new probabilistic view of the classical Multidimensional Scaling (MDS) algorithm and the nonlinear dimensionality reduction algorithm, Isomap (Isometric Mapping or Isometric Feature Mapping) that extends the classical MDS, in which we use the Gromov-Wasserstein distance between the probability measure of high-dimensional data, and its low-dimensional representation. Through gradient descent, our method embeds high-dimensional data into a lower-dimensional space, providing a robust and efficient solution for analyzing complex high-dimensional datasets.