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author | Gard Spreemann <gspr@nonempty.org> | 2023-06-14 16:52:13 +0200 |
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committer | Gard Spreemann <gspr@nonempty.org> | 2023-06-14 16:52:13 +0200 |
commit | 2b51c7bfcf54d7e17ac7c2514f54408543cbe126 (patch) | |
tree | baf00cc603ceabad00626259eec898e6747d016c /examples/sliced-wasserstein/plot_variance_ssw.py | |
parent | a49f648b0b07737f7ef315fb83d8f78871780281 (diff) | |
parent | 96788a3fe5601e4c3f49b592aa0d9c034247862e (diff) |
Merge branch 'dfsg/latest'
Diffstat (limited to 'examples/sliced-wasserstein/plot_variance_ssw.py')
-rw-r--r-- | examples/sliced-wasserstein/plot_variance_ssw.py | 111 |
1 files changed, 111 insertions, 0 deletions
diff --git a/examples/sliced-wasserstein/plot_variance_ssw.py b/examples/sliced-wasserstein/plot_variance_ssw.py new file mode 100644 index 0000000..83d458f --- /dev/null +++ b/examples/sliced-wasserstein/plot_variance_ssw.py @@ -0,0 +1,111 @@ +# -*- coding: utf-8 -*- +""" +==================================================== +Spherical Sliced Wasserstein on distributions in S^2 +==================================================== + +This example illustrates the computation of the spherical sliced Wasserstein discrepancy as +proposed in [46]. + +[46] Bonet, C., Berg, P., Courty, N., Septier, F., Drumetz, L., & Pham, M. T. (2023). 'Spherical Sliced-Wasserstein". International Conference on Learning Representations. + +""" + +# Author: Clément Bonet <clement.bonet@univ-ubs.fr> +# +# License: MIT License + +# sphinx_gallery_thumbnail_number = 2 + +import matplotlib.pylab as pl +import numpy as np + +import ot + +############################################################################## +# Generate data +# ------------- + +# %% parameters and data generation + +n = 500 # nb samples + +xs = np.random.randn(n, 3) +xt = np.random.randn(n, 3) + +xs = xs / np.sqrt(np.sum(xs**2, -1, keepdims=True)) +xt = xt / np.sqrt(np.sum(xt**2, -1, keepdims=True)) + +a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples + +############################################################################## +# Plot data +# --------- + +# %% plot samples + +fig = pl.figure(figsize=(10, 10)) +ax = pl.axes(projection='3d') +ax.grid(False) + +u, v = np.mgrid[0:2 * np.pi:30j, 0:np.pi:30j] +x = np.cos(u) * np.sin(v) +y = np.sin(u) * np.sin(v) +z = np.cos(v) +ax.plot_surface(x, y, z, color="gray", alpha=0.03) +ax.plot_wireframe(x, y, z, linewidth=1, alpha=0.25, color="gray") + +ax.scatter(xs[:, 0], xs[:, 1], xs[:, 2], label="Source") +ax.scatter(xt[:, 0], xt[:, 1], xt[:, 2], label="Target") + +fs = 10 +# Labels +ax.set_xlabel('x', fontsize=fs) +ax.set_ylabel('y', fontsize=fs) +ax.set_zlabel('z', fontsize=fs) + +ax.view_init(20, 120) +ax.set_xlim(-1.5, 1.5) +ax.set_ylim(-1.5, 1.5) +ax.set_zlim(-1.5, 1.5) + +# Ticks +ax.set_xticks([-1, 0, 1]) +ax.set_yticks([-1, 0, 1]) +ax.set_zticks([-1, 0, 1]) + +pl.legend(loc=0) +pl.title("Source and Target distribution") + +############################################################################### +# Spherical Sliced Wasserstein for different seeds and number of projections +# -------------------------------------------------------------------------- + +n_seed = 50 +n_projections_arr = np.logspace(0, 3, 25, dtype=int) +res = np.empty((n_seed, 25)) + +# %% Compute statistics +for seed in range(n_seed): + for i, n_projections in enumerate(n_projections_arr): + res[seed, i] = ot.sliced_wasserstein_sphere(xs, xt, a, b, n_projections, seed=seed, p=1) + +res_mean = np.mean(res, axis=0) +res_std = np.std(res, axis=0) + +############################################################################### +# Plot Spherical Sliced Wasserstein +# --------------------------------- + +pl.figure(2) +pl.plot(n_projections_arr, res_mean, label=r"$SSW_1$") +pl.fill_between(n_projections_arr, res_mean - 2 * res_std, res_mean + 2 * res_std, alpha=0.5) + +pl.legend() +pl.xscale('log') + +pl.xlabel("Number of projections") +pl.ylabel("Distance") +pl.title('Spherical Sliced Wasserstein Distance with 95% confidence inverval') + +pl.show() |