From a54775103541ea37f54269de1ba1e1396a6d7b30 Mon Sep 17 00:00:00 2001 From: Rémi Flamary Date: Fri, 24 Apr 2020 17:32:57 +0200 Subject: exmaples in sections --- .../plot_partial_wass_and_gromov.py | 165 +++++++++++++++++++++ 1 file changed, 165 insertions(+) create mode 100755 examples/unbalanced-partial/plot_partial_wass_and_gromov.py (limited to 'examples/unbalanced-partial/plot_partial_wass_and_gromov.py') diff --git a/examples/unbalanced-partial/plot_partial_wass_and_gromov.py b/examples/unbalanced-partial/plot_partial_wass_and_gromov.py new file mode 100755 index 0000000..0c5cbf9 --- /dev/null +++ b/examples/unbalanced-partial/plot_partial_wass_and_gromov.py @@ -0,0 +1,165 @@ +# -*- coding: utf-8 -*- +""" +================================================== +Partial Wasserstein and Gromov-Wasserstein example +================================================== + +This example is designed to show how to use the Partial (Gromov-)Wassertsein +distance computation in POT. +""" + +# Author: Laetitia Chapel +# License: MIT License + +# sphinx_gallery_thumbnail_number = 2 + +# necessary for 3d plot even if not used +from mpl_toolkits.mplot3d import Axes3D # noqa +import scipy as sp +import numpy as np +import matplotlib.pylab as pl +import ot + + +############################################################################# +# +# Sample two 2D Gaussian distributions and plot them +# -------------------------------------------------- +# +# For demonstration purpose, we sample two Gaussian distributions in 2-d +# spaces and add some random noise. + + +n_samples = 20 # nb samples (gaussian) +n_noise = 20 # nb of samples (noise) + +mu = np.array([0, 0]) +cov = np.array([[1, 0], [0, 2]]) + +xs = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov) +xs = np.append(xs, (np.random.rand(n_noise, 2) + 1) * 4).reshape((-1, 2)) +xt = ot.datasets.make_2D_samples_gauss(n_samples, mu, cov) +xt = np.append(xt, (np.random.rand(n_noise, 2) + 1) * -3).reshape((-1, 2)) + +M = sp.spatial.distance.cdist(xs, xt) + +fig = pl.figure() +ax1 = fig.add_subplot(131) +ax1.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +ax2 = fig.add_subplot(132) +ax2.scatter(xt[:, 0], xt[:, 1], color='r') +ax3 = fig.add_subplot(133) +ax3.imshow(M) +pl.show() + +############################################################################# +# +# Compute partial Wasserstein plans and distance +# ---------------------------------------------- + +p = ot.unif(n_samples + n_noise) +q = ot.unif(n_samples + n_noise) + +w0, log0 = ot.partial.partial_wasserstein(p, q, M, m=0.5, log=True) +w, log = ot.partial.entropic_partial_wasserstein(p, q, M, reg=0.1, m=0.5, + log=True) + +print('Partial Wasserstein distance (m = 0.5): ' + str(log0['partial_w_dist'])) +print('Entropic partial Wasserstein distance (m = 0.5): ' + + str(log['partial_w_dist'])) + +pl.figure(1, (10, 5)) +pl.subplot(1, 2, 1) +pl.imshow(w0, cmap='jet') +pl.title('Partial Wasserstein') +pl.subplot(1, 2, 2) +pl.imshow(w, cmap='jet') +pl.title('Entropic partial Wasserstein') +pl.show() + + +############################################################################# +# +# Sample one 2D and 3D Gaussian distributions and plot them +# --------------------------------------------------------- +# +# 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 = 20 # nb samples +n_noise = 10 # nb of samples (noise) + +p = ot.unif(n_samples + n_noise) +q = ot.unif(n_samples + n_noise) + +mu_s = np.array([0, 0]) +cov_s = np.array([[1, 0], [0, 1]]) + +mu_t = np.array([0, 0, 0]) +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) +xs = np.concatenate((xs, ((np.random.rand(n_noise, 2) + 1) * 4)), axis=0) +P = sp.linalg.sqrtm(cov_t) +xt = np.random.randn(n_samples, 3).dot(P) + mu_t +xt = np.concatenate((xt, ((np.random.rand(n_noise, 3) + 1) * 10)), axis=0) + +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 partial Gromov-Wasserstein plans and distance +# ----------------------------------------------------- + +C1 = sp.spatial.distance.cdist(xs, xs) +C2 = sp.spatial.distance.cdist(xt, xt) + +# transport 100% of the mass +print('-----m = 1') +m = 1 +res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True) +res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10, + m=m, log=True) + +print('Wasserstein distance (m = 1): ' + str(log0['partial_gw_dist'])) +print('Entropic Wasserstein distance (m = 1): ' + str(log['partial_gw_dist'])) + +pl.figure(1, (10, 5)) +pl.title("mass to be transported m = 1") +pl.subplot(1, 2, 1) +pl.imshow(res0, cmap='jet') +pl.title('Wasserstein') +pl.subplot(1, 2, 2) +pl.imshow(res, cmap='jet') +pl.title('Entropic Wasserstein') +pl.show() + +# transport 2/3 of the mass +print('-----m = 2/3') +m = 2 / 3 +res0, log0 = ot.partial.partial_gromov_wasserstein(C1, C2, p, q, m=m, log=True) +res, log = ot.partial.entropic_partial_gromov_wasserstein(C1, C2, p, q, 10, + m=m, log=True) + +print('Partial Wasserstein distance (m = 2/3): ' + + str(log0['partial_gw_dist'])) +print('Entropic partial Wasserstein distance (m = 2/3): ' + + str(log['partial_gw_dist'])) + +pl.figure(1, (10, 5)) +pl.title("mass to be transported m = 2/3") +pl.subplot(1, 2, 1) +pl.imshow(res0, cmap='jet') +pl.title('Partial Wasserstein') +pl.subplot(1, 2, 2) +pl.imshow(res, cmap='jet') +pl.title('Entropic partial Wasserstein') +pl.show() -- cgit v1.2.3