Wasserstein distance (also called Earth Mover's Distance or EMD) is defined as follows:
Don't worry about the preceding equation if you find it hard to understand. It essentially describes the least distance between two variables sampled from all possible joint distributions. In plain words, it is the minimum cost of moving one pile of dirt (in a shape of certain distribution) to form a different pile (another distribution), as shown in the following screenshot:
The Wasserstein distance: optimal transportation ...
