Optimal Transport Distance value in domain adaptation

[XLoizeau]

Hello,
I am currently working on a software that relies on the computation of OT distance between colour palettes.

Basing myself on this example from the official gallery I was a bit surprised to see that the distance is not returned plainly.

After a bit of digging around, I saw that when using the Earth Movers distance as follows:

ot_emd = ot.da.EMDTransport()
ot_emd.fit(Xs = Xs, Xt = Xt)
transp_Xs_emd = ot_emd.transform(Xs = X1)

the distance seems to be stored in the log_ attribute of ot_emd in the cost key. Yet, I am not entirely sure as the documentation about those attributes is a bit sibylline.

When it comes to the other distances (sinkhorn and mapping transport) demonstrated in this example, I could not find the distance at all.

Would anyone be able to tell me if I am missing something and if there is a reason for those quantities not to be returned?

Thank you so much for your help.
Best,
Zhav

[rflamary]

The OT distance is returned by function ot.emd2 same with sinkhorn

# a,b are 1D histograms (sum to 1 and positive)
# M is the ground cost matrix
Wd = ot.emd2(a, b, M) # exact linear program
Wd_reg = ot.sinkhorn2(a, b, M, reg) # entropic regularized OT
# if b is a matrix compute all distances to a and return a vector

Or we have the more recent ot.solve function that returns a class containing the OT plan ot.solve(...).plan ad the value ot.solve(...).value

[XLoizeau]

Oh... I feel a bit stupid now... Thank you for taking the time to answer!
Best,
Zhav