# On the Use of the Kantorovich-Rubinstein Distance for Dimensionality Reduction

arXiv: https://arxiv.org/abs/2309.09442 · HTML: https://mlsanity.com/paper/2309.09442/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2023.

## Abstract (arXiv)

The goal of this thesis is to study the use of the Kantorovich-Rubinstein distance as to build a descriptor of sample complexity in classification problems. The idea is to use the fact that the Kantorovich-Rubinstein distance is a metric in the space of measures that also takes into account the geometry and topology of the underlying metric space. We associate to each class of points a measure and thus study the geometrical information that we can obtain from the Kantorovich-Rubinstein distance between those measures. We show that a large Kantorovich-Rubinstein distance between those measures allows to conclude that there exists a 1-Lipschitz classifier that classifies well the classes of points. We also discuss the limitation of the Kantorovich-Rubinstein distance as a descriptor.