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authorRémi Flamary <remi.flamary@gmail.com>2020-04-24 17:32:57 +0200
committerRémi Flamary <remi.flamary@gmail.com>2020-04-24 17:32:57 +0200
commita54775103541ea37f54269de1ba1e1396a6d7b30 (patch)
tree376e23ba65b169b0493df445fcee7b17bfd26318 /examples/plot_free_support_barycenter.py
parente18e18f8453263fa95c61e666f14c89a1df5efb4 (diff)
exmaples in sections
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-# -*- coding: utf-8 -*-
-"""
-====================================================
-2D free support Wasserstein barycenters of distributions
-====================================================
-
-Illustration of 2D Wasserstein barycenters if discributions that are weighted
-sum of diracs.
-
-"""
-
-# Author: Vivien Seguy <vivien.seguy@iip.ist.i.kyoto-u.ac.jp>
-#
-# License: MIT License
-
-import numpy as np
-import matplotlib.pylab as pl
-import ot
-
-
-##############################################################################
-# Generate data
-# -------------
-#%% parameters and data generation
-N = 3
-d = 2
-measures_locations = []
-measures_weights = []
-
-for i in range(N):
-
- n_i = np.random.randint(low=1, high=20) # nb samples
-
- mu_i = np.random.normal(0., 4., (d,)) # Gaussian mean
-
- A_i = np.random.rand(d, d)
- cov_i = np.dot(A_i, A_i.transpose()) # Gaussian covariance matrix
-
- x_i = ot.datasets.make_2D_samples_gauss(n_i, mu_i, cov_i) # Dirac locations
- b_i = np.random.uniform(0., 1., (n_i,))
- b_i = b_i / np.sum(b_i) # Dirac weights
-
- measures_locations.append(x_i)
- measures_weights.append(b_i)
-
-
-##############################################################################
-# Compute free support barycenter
-# -------------
-
-k = 10 # number of Diracs of the barycenter
-X_init = np.random.normal(0., 1., (k, d)) # initial Dirac locations
-b = np.ones((k,)) / k # weights of the barycenter (it will not be optimized, only the locations are optimized)
-
-X = ot.lp.free_support_barycenter(measures_locations, measures_weights, X_init, b)
-
-
-##############################################################################
-# Plot data
-# ---------
-
-pl.figure(1)
-for (x_i, b_i) in zip(measures_locations, measures_weights):
- color = np.random.randint(low=1, high=10 * N)
- pl.scatter(x_i[:, 0], x_i[:, 1], s=b_i * 1000, label='input measure')
-pl.scatter(X[:, 0], X[:, 1], s=b * 1000, c='black', marker='^', label='2-Wasserstein barycenter')
-pl.title('Data measures and their barycenter')
-pl.legend(loc=0)
-pl.show()