Geometry of OT distances

Shows how to compute multiple Wasserstein and Sinkhorn with two different ground metrics and plot their values for different distributions.

# Author: Remi Flamary <remi.flamary@unice.fr>
#
# License: MIT License

# sphinx_gallery_thumbnail_number = 2

import numpy as np
import matplotlib.pylab as pl
import ot
from ot.datasets import make_1D_gauss as gauss

Generate data

n = 100  # nb bins
n_target = 20  # nb target distributions


# bin positions
x = np.arange(n, dtype=np.float64)

lst_m = np.linspace(20, 90, n_target)

# Gaussian distributions
a = gauss(n, m=20, s=5)  # m= mean, s= std

B = np.zeros((n, n_target))

for i, m in enumerate(lst_m):
    B[:, i] = gauss(n, m=m, s=5)

# loss matrix and normalization
M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), "euclidean")
M /= M.max() * 0.1
M2 = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)), "sqeuclidean")
M2 /= M2.max() * 0.1

Plot data

pl.figure(1)
pl.subplot(2, 1, 1)
pl.plot(x, a, "r", label="Source distribution")
pl.title("Source distribution")
pl.subplot(2, 1, 2)
for i in range(n_target):
    pl.plot(x, B[:, i], "b", alpha=i / n_target)
pl.plot(x, B[:, -1], "b", label="Target distributions")
pl.title("Target distributions")
pl.tight_layout()