关于辐射公式及其与瓦瑟斯坦切分距离关系的说明

Pub Date : 2024-04-06 DOI:10.1007/s00010-024-01049-1

Gennaro Auricchio

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引用次数: 0

摘要

摘要在本说明中，我们证明了瓦瑟斯坦距离的平方可以表示为一维瓦瑟斯坦距离在球面上的平均值。我们将这一新表达式命名为瓦瑟施泰因距离辐射公式。利用这个公式，我们能够突出瓦瑟施泰因距离和切片瓦瑟施泰因距离之间的新联系，切片瓦瑟施泰因距离是另一种类似瓦瑟施泰因的距离，计算起来更便宜。

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

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.

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