 Wasserstein metric

In mathematics, the Wasserstein or Kantorovich–Rubinstein metric or distance is a distance function defined between probability distributions on a given metric space formula_1.Intuitively, if each distribution is viewed as a unit amount of "dirt" piled on "formula_1", 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 mean distance it has to be moved.