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Diffstat (limited to 'examples')
-rw-r--r-- | examples/sliced-wasserstein/README.txt | 4 | ||||
-rw-r--r-- | examples/sliced-wasserstein/plot_variance.py | 84 |
2 files changed, 88 insertions, 0 deletions
diff --git a/examples/sliced-wasserstein/README.txt b/examples/sliced-wasserstein/README.txt new file mode 100644 index 0000000..a575345 --- /dev/null +++ b/examples/sliced-wasserstein/README.txt @@ -0,0 +1,4 @@ + + +Sliced Wasserstein Distance +---------------------------
\ No newline at end of file diff --git a/examples/sliced-wasserstein/plot_variance.py b/examples/sliced-wasserstein/plot_variance.py new file mode 100644 index 0000000..f3deeff --- /dev/null +++ b/examples/sliced-wasserstein/plot_variance.py @@ -0,0 +1,84 @@ +# -*- coding: utf-8 -*- +""" +============================== +2D Sliced Wasserstein Distance +============================== + +This example illustrates the computation of the sliced Wasserstein Distance as proposed in [31]. + +[31] Bonneel, Nicolas, et al. "Sliced and radon wasserstein barycenters of measures." Journal of Mathematical Imaging and Vision 51.1 (2015): 22-45 + +""" + +# Author: Adrien Corenflos <adrien.corenflos@aalto.fi> +# +# License: MIT License + +import matplotlib.pylab as pl +import numpy as np + +import ot + +############################################################################## +# Generate data +# ------------- + +# %% parameters and data generation + +n = 500 # nb samples + +mu_s = np.array([0, 0]) +cov_s = np.array([[1, 0], [0, 1]]) + +mu_t = np.array([4, 4]) +cov_t = np.array([[1, -.8], [-.8, 1]]) + +xs = ot.datasets.make_2D_samples_gauss(n, mu_s, cov_s) +xt = ot.datasets.make_2D_samples_gauss(n, mu_t, cov_t) + +a, b = np.ones((n,)) / n, np.ones((n,)) / n # uniform distribution on samples + +############################################################################## +# Plot data +# --------- + +# %% plot samples + +pl.figure(1) +pl.plot(xs[:, 0], xs[:, 1], '+b', label='Source samples') +pl.plot(xt[:, 0], xt[:, 1], 'xr', label='Target samples') +pl.legend(loc=0) +pl.title('Source and target distributions') + +################################################################################### +# Compute Sliced Wasserstein distance 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_distance(xs, xt, a, b, n_projections, seed) + +res_mean = np.mean(res, axis=0) +res_std = np.std(res, axis=0) + +################################################################################### +# Plot Sliced Wasserstein Distance +# ----------- + +pl.figure(2) +pl.plot(n_projections_arr, res_mean, label="SWD") +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('Sliced Wasserstein Distance with 95% confidence inverval') + +pl.show() |