Wasserstein Metric

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Wasserstein (or Vasershtein) metric is a distance function defined between probability distributions on a given metric space M. Intuitively, if each distribution is viewed as a unit amount of "dirt" piled on M, the metric is the minimum "cost" of turning one pile into the other, which is assumed to be the amount of dirt that needs to be moved times the distance it has to be moved. Because of this analogy, the metric is known in computer science as the earth mover's distance. The name "Wasserstein/Vasershtein distance" was coined by R.L. Dobrushin in 1970, after the Russian mathematician Leonid Nasonovich Vasershtein who introduced the concept in 1969. Most English-language publications use the German spelling "Wasserstein" (attributed to the name "Vasershtein" being of Germanic origin).

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