diff options
author | Rémi Flamary <remi.flamary@gmail.com> | 2019-06-25 14:36:23 +0200 |
---|---|---|
committer | Rémi Flamary <remi.flamary@gmail.com> | 2019-06-25 14:36:23 +0200 |
commit | c9775bde23527f8b55db53020352969405f8b6b5 (patch) | |
tree | 4195d28c2c144f66d758b20baf862e9f32111cd9 /examples | |
parent | 830d4ebd2e2c85b4f3503f358bb31a07918a27c5 (diff) | |
parent | 2364d56aad650d501753cc93a69ea1b8ddf28b0a (diff) |
Merge branch 'master' into doc_modules
Diffstat (limited to 'examples')
-rw-r--r-- | examples/plot_UOT_1D.py | 76 | ||||
-rw-r--r-- | examples/plot_UOT_barycenter_1D.py | 164 |
2 files changed, 240 insertions, 0 deletions
diff --git a/examples/plot_UOT_1D.py b/examples/plot_UOT_1D.py new file mode 100644 index 0000000..2ea8b05 --- /dev/null +++ b/examples/plot_UOT_1D.py @@ -0,0 +1,76 @@ +# -*- coding: utf-8 -*- +""" +=============================== +1D Unbalanced optimal transport +=============================== + +This example illustrates the computation of Unbalanced Optimal transport +using a Kullback-Leibler relaxation. +""" + +# Author: Hicham Janati <hicham.janati@inria.fr> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot +import ot.plot +from ot.datasets import make_1D_gauss as gauss + +############################################################################## +# Generate data +# ------------- + + +#%% parameters + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +a = gauss(n, m=20, s=5) # m= mean, s= std +b = gauss(n, m=60, s=10) + +# make distributions unbalanced +b *= 5. + +# loss matrix +M = ot.dist(x.reshape((n, 1)), x.reshape((n, 1))) +M /= M.max() + + +############################################################################## +# Plot distributions and loss matrix +# ---------------------------------- + +#%% plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +pl.plot(x, a, 'b', label='Source distribution') +pl.plot(x, b, 'r', label='Target distribution') +pl.legend() + +# plot distributions and loss matrix + +pl.figure(2, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, M, 'Cost matrix M') + + +############################################################################## +# Solve Unbalanced Sinkhorn +# -------------- + + +# Sinkhorn + +epsilon = 0.1 # entropy parameter +alpha = 1. # Unbalanced KL relaxation parameter +Gs = ot.unbalanced.sinkhorn_unbalanced(a, b, M, epsilon, alpha, verbose=True) + +pl.figure(4, figsize=(5, 5)) +ot.plot.plot1D_mat(a, b, Gs, 'UOT matrix Sinkhorn') + +pl.show() diff --git a/examples/plot_UOT_barycenter_1D.py b/examples/plot_UOT_barycenter_1D.py new file mode 100644 index 0000000..c8d9d3b --- /dev/null +++ b/examples/plot_UOT_barycenter_1D.py @@ -0,0 +1,164 @@ +# -*- coding: utf-8 -*- +""" +=========================================================== +1D Wasserstein barycenter demo for Unbalanced distributions +=========================================================== + +This example illustrates the computation of regularized Wassersyein Barycenter +as proposed in [10] for Unbalanced inputs. + + +[10] Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F. X. (2016). Scaling algorithms for unbalanced transport problems. arXiv preprint arXiv:1607.05816. + +""" + +# Author: Hicham Janati <hicham.janati@inria.fr> +# +# License: MIT License + +import numpy as np +import matplotlib.pylab as pl +import ot +# necessary for 3d plot even if not used +from mpl_toolkits.mplot3d import Axes3D # noqa +from matplotlib.collections import PolyCollection + +############################################################################## +# Generate data +# ------------- + +# parameters + +n = 100 # nb bins + +# bin positions +x = np.arange(n, dtype=np.float64) + +# Gaussian distributions +a1 = ot.datasets.make_1D_gauss(n, m=20, s=5) # m= mean, s= std +a2 = ot.datasets.make_1D_gauss(n, m=60, s=8) + +# make unbalanced dists +a2 *= 3. + +# creating matrix A containing all distributions +A = np.vstack((a1, a2)).T +n_distributions = A.shape[1] + +# loss matrix + normalization +M = ot.utils.dist0(n) +M /= M.max() + +############################################################################## +# Plot data +# --------- + +# plot the distributions + +pl.figure(1, figsize=(6.4, 3)) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') +pl.tight_layout() + +############################################################################## +# Barycenter computation +# ---------------------- + +# non weighted barycenter computation + +weight = 0.5 # 0<=weight<=1 +weights = np.array([1 - weight, weight]) + +# l2bary +bary_l2 = A.dot(weights) + +# wasserstein +reg = 1e-3 +alpha = 1. + +bary_wass = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + +pl.figure(2) +pl.clf() +pl.subplot(2, 1, 1) +for i in range(n_distributions): + pl.plot(x, A[:, i]) +pl.title('Distributions') + +pl.subplot(2, 1, 2) +pl.plot(x, bary_l2, 'r', label='l2') +pl.plot(x, bary_wass, 'g', label='Wasserstein') +pl.legend() +pl.title('Barycenters') +pl.tight_layout() + +############################################################################## +# Barycentric interpolation +# ------------------------- + +# barycenter interpolation + +n_weight = 11 +weight_list = np.linspace(0, 1, n_weight) + + +B_l2 = np.zeros((n, n_weight)) + +B_wass = np.copy(B_l2) + +for i in range(0, n_weight): + weight = weight_list[i] + weights = np.array([1 - weight, weight]) + B_l2[:, i] = A.dot(weights) + B_wass[:, i] = ot.unbalanced.barycenter_unbalanced(A, M, reg, alpha, weights) + + +# plot interpolation + +pl.figure(3) + +cmap = pl.cm.get_cmap('viridis') +verts = [] +zs = weight_list +for i, z in enumerate(zs): + ys = B_l2[:, i] + verts.append(list(zip(x, ys))) + +ax = pl.gcf().gca(projection='3d') + +poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) +poly.set_alpha(0.7) +ax.add_collection3d(poly, zs=zs, zdir='y') +ax.set_xlabel('x') +ax.set_xlim3d(0, n) +ax.set_ylabel(r'$\alpha$') +ax.set_ylim3d(0, 1) +ax.set_zlabel('') +ax.set_zlim3d(0, B_l2.max() * 1.01) +pl.title('Barycenter interpolation with l2') +pl.tight_layout() + +pl.figure(4) +cmap = pl.cm.get_cmap('viridis') +verts = [] +zs = weight_list +for i, z in enumerate(zs): + ys = B_wass[:, i] + verts.append(list(zip(x, ys))) + +ax = pl.gcf().gca(projection='3d') + +poly = PolyCollection(verts, facecolors=[cmap(a) for a in weight_list]) +poly.set_alpha(0.7) +ax.add_collection3d(poly, zs=zs, zdir='y') +ax.set_xlabel('x') +ax.set_xlim3d(0, n) +ax.set_ylabel(r'$\alpha$') +ax.set_ylim3d(0, 1) +ax.set_zlabel('') +ax.set_zlim3d(0, B_l2.max() * 1.01) +pl.title('Barycenter interpolation with Wasserstein') +pl.tight_layout() + +pl.show() |