Earth Mover's Distance

Earth Mover's Distance (EMD) measures how similar two distributions are by calculating the minimum effort needed to transform one into the other. Imagine piles of dirt shaped like the distributions’ data points; EMD finds the least total cost to move this dirt to match the other shape, considering both the amount of dirt and the distance it needs to be moved. It's a way to quantify differences between patterns, images, or data sets in a manner that reflects the true "work" involved in transforming one into the other.