Wasserstein metric

The Wasserstein metric, also known as the Wasserstein distance or Earth Mover's Distance (EMD), is a measure of the distance between two probability distributions on a given metric space. It originates from the field of optimal transport and has applications in various areas, including statistics, machine learning, and image processing. ### Key Concepts: 1. **Probability Distributions**: The Wasserstein metric is defined for two probability distributions \( P \) and \( Q \) on a metric space.