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 --- examples/plot_gromov_barycenter.py | 247 ------------------------------------- 1 file changed, 247 deletions(-) delete mode 100755 examples/plot_gromov_barycenter.py (limited to 'examples/plot_gromov_barycenter.py') diff --git a/examples/plot_gromov_barycenter.py b/examples/plot_gromov_barycenter.py deleted file mode 100755 index 6b29687..0000000 --- a/examples/plot_gromov_barycenter.py +++ /dev/null @@ -1,247 +0,0 @@ -# -*- coding: utf-8 -*- -""" -===================================== -Gromov-Wasserstein Barycenter example -===================================== - -This example is designed to show how to use the Gromov-Wasserstein distance -computation in POT. -""" - -# Author: Erwan Vautier -# Nicolas Courty -# -# License: MIT License - - -import numpy as np -import scipy as sp - -import matplotlib.pylab as pl -from sklearn import manifold -from sklearn.decomposition import PCA - -import ot - -############################################################################## -# Smacof MDS -# ---------- -# -# This function allows to find an embedding of points given a dissimilarity matrix -# that will be given by the output of the algorithm - - -def smacof_mds(C, dim, max_iter=3000, eps=1e-9): - """ - Returns an interpolated point cloud following the dissimilarity matrix C - using SMACOF multidimensional scaling (MDS) in specific dimensionned - target space - - Parameters - ---------- - C : ndarray, shape (ns, ns) - dissimilarity matrix - dim : int - dimension of the targeted space - max_iter : int - Maximum number of iterations of the SMACOF algorithm for a single run - eps : float - relative tolerance w.r.t stress to declare converge - - Returns - ------- - npos : ndarray, shape (R, dim) - Embedded coordinates of the interpolated point cloud (defined with - one isometry) - """ - - rng = np.random.RandomState(seed=3) - - mds = manifold.MDS( - dim, - max_iter=max_iter, - eps=1e-9, - dissimilarity='precomputed', - n_init=1) - pos = mds.fit(C).embedding_ - - nmds = manifold.MDS( - 2, - max_iter=max_iter, - eps=1e-9, - dissimilarity="precomputed", - random_state=rng, - n_init=1) - npos = nmds.fit_transform(C, init=pos) - - return npos - - -############################################################################## -# Data preparation -# ---------------- -# -# The four distributions are constructed from 4 simple images - - -def im2mat(I): - """Converts and image to matrix (one pixel per line)""" - return I.reshape((I.shape[0] * I.shape[1], I.shape[2])) - - -square = pl.imread('../data/square.png').astype(np.float64)[:, :, 2] -cross = pl.imread('../data/cross.png').astype(np.float64)[:, :, 2] -triangle = pl.imread('../data/triangle.png').astype(np.float64)[:, :, 2] -star = pl.imread('../data/star.png').astype(np.float64)[:, :, 2] - -shapes = [square, cross, triangle, star] - -S = 4 -xs = [[] for i in range(S)] - - -for nb in range(4): - for i in range(8): - for j in range(8): - if shapes[nb][i, j] < 0.95: - xs[nb].append([j, 8 - i]) - -xs = np.array([np.array(xs[0]), np.array(xs[1]), - np.array(xs[2]), np.array(xs[3])]) - -############################################################################## -# Barycenter computation -# ---------------------- - - -ns = [len(xs[s]) for s in range(S)] -n_samples = 30 - -"""Compute all distances matrices for the four shapes""" -Cs = [sp.spatial.distance.cdist(xs[s], xs[s]) for s in range(S)] -Cs = [cs / cs.max() for cs in Cs] - -ps = [ot.unif(ns[s]) for s in range(S)] -p = ot.unif(n_samples) - - -lambdast = [[float(i) / 3, float(3 - i) / 3] for i in [1, 2]] - -Ct01 = [0 for i in range(2)] -for i in range(2): - Ct01[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[1]], - [ps[0], ps[1] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - -Ct02 = [0 for i in range(2)] -for i in range(2): - Ct02[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[2]], - [ps[0], ps[2] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - -Ct13 = [0 for i in range(2)] -for i in range(2): - Ct13[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[1], Cs[3]], - [ps[1], ps[3] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - -Ct23 = [0 for i in range(2)] -for i in range(2): - Ct23[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[2], Cs[3]], - [ps[2], ps[3] - ], p, lambdast[i], 'square_loss', # 5e-4, - max_iter=100, tol=1e-3) - - -############################################################################## -# Visualization -# ------------- -# -# The PCA helps in getting consistency between the rotations - - -clf = PCA(n_components=2) -npos = [0, 0, 0, 0] -npos = [smacof_mds(Cs[s], 2) for s in range(S)] - -npost01 = [0, 0] -npost01 = [smacof_mds(Ct01[s], 2) for s in range(2)] -npost01 = [clf.fit_transform(npost01[s]) for s in range(2)] - -npost02 = [0, 0] -npost02 = [smacof_mds(Ct02[s], 2) for s in range(2)] -npost02 = [clf.fit_transform(npost02[s]) for s in range(2)] - -npost13 = [0, 0] -npost13 = [smacof_mds(Ct13[s], 2) for s in range(2)] -npost13 = [clf.fit_transform(npost13[s]) for s in range(2)] - -npost23 = [0, 0] -npost23 = [smacof_mds(Ct23[s], 2) for s in range(2)] -npost23 = [clf.fit_transform(npost23[s]) for s in range(2)] - - -fig = pl.figure(figsize=(10, 10)) - -ax1 = pl.subplot2grid((4, 4), (0, 0)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax1.scatter(npos[0][:, 0], npos[0][:, 1], color='r') - -ax2 = pl.subplot2grid((4, 4), (0, 1)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax2.scatter(npost01[1][:, 0], npost01[1][:, 1], color='b') - -ax3 = pl.subplot2grid((4, 4), (0, 2)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax3.scatter(npost01[0][:, 0], npost01[0][:, 1], color='b') - -ax4 = pl.subplot2grid((4, 4), (0, 3)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax4.scatter(npos[1][:, 0], npos[1][:, 1], color='r') - -ax5 = pl.subplot2grid((4, 4), (1, 0)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax5.scatter(npost02[1][:, 0], npost02[1][:, 1], color='b') - -ax6 = pl.subplot2grid((4, 4), (1, 3)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax6.scatter(npost13[1][:, 0], npost13[1][:, 1], color='b') - -ax7 = pl.subplot2grid((4, 4), (2, 0)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax7.scatter(npost02[0][:, 0], npost02[0][:, 1], color='b') - -ax8 = pl.subplot2grid((4, 4), (2, 3)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax8.scatter(npost13[0][:, 0], npost13[0][:, 1], color='b') - -ax9 = pl.subplot2grid((4, 4), (3, 0)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax9.scatter(npos[2][:, 0], npos[2][:, 1], color='r') - -ax10 = pl.subplot2grid((4, 4), (3, 1)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax10.scatter(npost23[1][:, 0], npost23[1][:, 1], color='b') - -ax11 = pl.subplot2grid((4, 4), (3, 2)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax11.scatter(npost23[0][:, 0], npost23[0][:, 1], color='b') - -ax12 = pl.subplot2grid((4, 4), (3, 3)) -pl.xlim((-1, 1)) -pl.ylim((-1, 1)) -ax12.scatter(npos[3][:, 0], npos[3][:, 1], color='r') -- cgit v1.2.3