Optimal Transport between empirical distributions

Illustration of optimal transport between distributions in 2D that are weighted sum of Diracs. The OT matrix is plotted with the samples.

# Author: Remi Flamary <remi.flamary@unice.fr>
#         Kilian Fatras <kilian.fatras@irisa.fr>
#
# License: MIT License

# sphinx_gallery_thumbnail_number = 4

import numpy as np
import matplotlib.pylab as pl
import ot
import ot.plot

Generate data

n = 50  # nb samples

mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])

mu_t = np.array([4, 4])
cov_t = np.array([[1, -0.8], [-0.8, 1]])

xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s)
xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t)

a, b = np.ones((n,)) / n, np.ones((n,)) / n  # uniform distribution on samples

# loss matrix
M = ot.dist(xs, xt)

Plot data

pl.figure(1)
pl.plot(xs[:, 0], xs[:, 1], "+b", label="Source samples")
pl.plot(xt[:, 0], xt[:, 1], "xr", label="Target samples")
pl.legend(loc=0)
pl.title("Source and target distributions")

pl.figure(2)
pl.imshow(M, interpolation="nearest", cmap="gray_r")
pl.title("Cost matrix M")