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# -*- coding: utf-8 -*-
"""
==========================
Gromov-Wasserstein example
==========================
This example is designed to show how to use the Gromov-Wassertsein distance
computation in POT.
"""
# Author: Erwan Vautier <erwan.vautier@gmail.com>
# Nicolas Courty <ncourty@irisa.fr>
#
# License: MIT License
import scipy as sp
import numpy as np
import matplotlib.pylab as pl
from mpl_toolkits.mplot3d import Axes3D # noqa
import ot
#############################################################################
#
# Sample two Gaussian distributions (2D and 3D)
# ---------------------------------------------
#
# The Gromov-Wasserstein distance allows to compute distances with samples that
# do not belong to the same metric space. For demonstration purpose, we sample
# two Gaussian distributions in 2- and 3-dimensional spaces.
n_samples = 30 # nb samples
mu_s = np.array([0, 0])
cov_s = np.array([[1, 0], [0, 1]])
mu_t = np.array([4, 4, 4])
cov_t = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
xs = ot.datasets.make_2D_samples_gauss(n_samples, mu_s, cov_s)
P = sp.linalg.sqrtm(cov_t)
xt = np.random.randn(n_samples, 3).dot(P) + mu_t
#############################################################################
#
# Plotting the distributions
# --------------------------
fig = pl.figure()
ax1 = fig.add_subplot(121)
ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples')
ax2 = fig.add_subplot(122, projection='3d')
ax2.scatter(xt[:, 0], xt[:, 1], xt[:, 2], color='r')
pl.show()
#############################################################################
#
# Compute distance kernels, normalize them and then display
# ---------------------------------------------------------
C1 = sp.spatial.distance.cdist(xs, xs)
C2 = sp.spatial.distance.cdist(xt, xt)
C1 /= C1.max()
C2 /= C2.max()
pl.figure()
pl.subplot(121)
pl.imshow(C1)
pl.subplot(122)
pl.imshow(C2)
pl.show()
#############################################################################
#
# Compute Gromov-Wasserstein plans and distance
# ---------------------------------------------
p = ot.unif(n_samples)
q = ot.unif(n_samples)
gw0, log0 = ot.gromov.gromov_wasserstein(
C1, C2, p, q, 'square_loss', verbose=True, log=True)
gw, log = ot.gromov.entropic_gromov_wasserstein(
C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)
print('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))
print('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))
pl.figure(1, (10, 5))
pl.subplot(1, 2, 1)
pl.imshow(gw0, cmap='jet')
pl.title('Gromov Wasserstein')
pl.subplot(1, 2, 2)
pl.imshow(gw, cmap='jet')
pl.title('Entropic Gromov Wasserstein')
pl.show()
#############################################################################
#
# Compute GW with a scalable stochastic method with any loss function
# ----------------------------------------------------------------------
def loss(x, y):
return np.abs(x - y)
pgw, plog = ot.gromov.pointwise_gromov_wasserstein(C1, C2, p, q, loss, max_iter=100,
log=True)
sgw, slog = ot.gromov.sampled_gromov_wasserstein(C1, C2, p, q, loss, epsilon=0.1, max_iter=100,
log=True)
print('Pointwise Gromov-Wasserstein distance estimated: ' + str(plog['gw_dist_estimated']))
print('Variance estimated: ' + str(plog['gw_dist_std']))
print('Sampled Gromov-Wasserstein distance: ' + str(slog['gw_dist_estimated']))
print('Variance estimated: ' + str(slog['gw_dist_std']))
pl.figure(1, (10, 5))
pl.subplot(1, 2, 1)
pl.imshow(pgw.toarray(), cmap='jet')
pl.title('Pointwise Gromov Wasserstein')
pl.subplot(1, 2, 2)
pl.imshow(sgw, cmap='jet')
pl.title('Sampled Gromov Wasserstein')
pl.show()
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