How to compute Wasserstein distance?

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Arvind Ganesh
Arvind Ganesh 2019-5-23
编辑： Georgios Pyrgiotakis 2020-5-14
I have two probability distributions in arrays P and Q (normalized by area, of same length, and over same sample space). I want to find Wasserstein distance between them.
I tried to use the Earth Mover Distance from here:
https://www.mathworks.com/matlabcentral/fileexchange/22962-the-earth-mover-s-distance
My input was [Y, fval] = emd(X, X, P, Q, @gdf)
where X is the sample space. But it is giving output:
No feasible solution found.
Linprog stopped because no point satisfies the constraints.
Is this the way to compute Wasserstein distance? How do I fix this?

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回答（1 个）

Koorosh Aslansefat
Koorosh Aslansefat 2020-4-29
编辑：Koorosh Aslansefat 2020-4-29
I have recently added new set of functions for ECDF-based distance measure to MATLAB Exchange.
I would suggest to have a look.
https://uk.mathworks.com/matlabcentral/fileexchange/75282-ecdf-based-distance-measure-algorithms
  3 个评论
显示 1更早的评论
Koorosh Aslansefat
Koorosh Aslansefat 2020-5-13
If P and Q can be considered as empirical distribution function (ECDF), then you can use those functions with a bit of modification.
Georgios Pyrgiotakis
Georgios Pyrgiotakis 2020-5-14
编辑：Georgios Pyrgiotakis 2020-5-14
Yes P and Q are emprical CDF. How can I use these functions? I tried but I get lost. It seems that you start with the data set convert it to CDF and then calculate the area between the two curves?

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