Kantorovich distance

Kantorovich distance, also known as the Wasserstein distance, measures how much one probability distribution needs to be "moved" to transform into another. Imagine shifting a pile of dirt to match a different shape; the distance quantifies the total effort or cost involved in these moves, considering both the amount of dirt moved and the distance it travels. It's a way of understanding how similar or different two distributions are by evaluating the minimal total "work" required for their transformation.