# Difference between the Wasserstein metric, mallows metric and Earth mover's distance

I'm really confused, is there a difference between the Wasserstein metric, mallows metric and Earth mover's distance? If yes What is it?

Thank you

• Wasserstein's metric and earth mover's distance are two names for the same concept. – Dilip Sarwate May 28 '18 at 16:59
• Thank you. I heard that the wasserstein metric is "a natural extension of the euclidean metric" ? I don't really get why? – learneRS May 28 '18 at 17:21
• @learneRS This video helped me understand the general idea behind it. youtube.com/watch?v=ymWDGzpQdls – Jaden Travnik Sep 14 '18 at 15:15