How to compute Wasserstein distance?

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?

Answer 1

[Koorosh Aslansefat]

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

[Georgios Pyrgiotakis]

I have been looking for something like this! thank you. So if I understood correctly, you can use these functions to find the various distances between two normalized distributions. I have an instrument that is directly exports percentage distribution and not number so I have hard time finding a way to compare the various distributions because I have no n (number of samples).

[Koorosh Aslansefat]

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]

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?