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 language | English |
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Journal | Aequationes mathematicae |
Early online date | 6 Apr 2024 |
DOIs | |
Publication status | Published - 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
- General Mathematics
- Discrete Mathematics and Combinatorics