Earth Mover’s Distance

Earth Mover’s Distance is used to compare two distributions in a highly intuitive and powerful way. As the name suggests, it imagines how much “earth” must be moved to transform one distribution into the other. This approach is important in image similarity, generative modeling, optimal transport, and distribution comparison problems. Unlike simple pointwise difference metrics, it accounts for structural transformation cost. That makes it a much more meaningful notion of similarity for certain classes of problems.