A note on the Radiant formula and its relations to the sliced Wasserstein distance

Gennaro Auricchio

Research output: Contribution to journalArticlepeer-review

Abstract

In this note, we show that the squared Wasserstein distance can be expressed as the average over the sphere of one dimensional Wasserstein distances. We name this new expression for the Wasserstein Distance Radiant Formula. Using this formula, we are able to highlight new connections between the Wasserstein distances and the Sliced Wasserstein distance, an alternative Wasserstein-like distance that is cheaper to compute.

Original languageEnglish
JournalAequationes mathematicae
Early online date6 Apr 2024
DOIs
Publication statusPublished - 6 Apr 2024

Data Availability Statement

Data availability is not applicable to this article as no new data were created or analysed in this study.

Keywords

  • 30L15
  • 49Q22
  • Optimal transport
  • Radiant formula
  • Sliced Wasserstein distance

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

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