Wasserstein distance, also known as Earth Mover’s Distance (EMD) is the distance between two probability distributions over a region D. The Wasserstein distance of order p is defined as the p-th root of the total cost incurred when transporting measure a to measure b in an optimal way, where the cost of transporting a unit of mass from
x to y is given as the p-th power of the Euclidean distance.
It is claimed to be useful for distributions that do not align well with traditional measures like Euclidean distance.