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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

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

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