From 3007f1da1094f93fa4216386666085cf60316b04 Mon Sep 17 00:00:00 2001 From: Nicolas Courty Date: Thu, 31 Aug 2017 16:44:18 +0200 Subject: Minor corrections suggested by @agramfort + new barycenter example + test function --- examples/plot_gromov_barycenter.py | 240 +++++++++++++++++++++++++++++++++++++ 1 file changed, 240 insertions(+) create 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 new file mode 100755 index 0000000..6a72b3b --- /dev/null +++ b/examples/plot_gromov_barycenter.py @@ -0,0 +1,240 @@ +# -*- coding: utf-8 -*- +""" +===================================== +Gromov-Wasserstein Barycenter example +===================================== +This example is designed to show how to use the Gromov-Wassertsein distance +computation in POT. +""" + +# Author: Erwan Vautier +# Nicolas Courty +# +# License: MIT License + + +import numpy as np +import scipy as sp + +import scipy.ndimage as spi +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, maxIter=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 : np.ndarray(ns,ns) + dissimilarity matrix + dim : Integer + dimension of the targeted space + maxIter : Maximum number of iterations of the SMACOF algorithm for a single run + + eps : relative tolerance w.r.t stress to declare converge + + + Returns + ------- + npos : R**dim ndarray + Embedded coordinates of the interpolated point cloud (defined with one isometry) + + + """ + + seed = np.random.RandomState(seed=3) + + mds = manifold.MDS( + dim, + max_iter=3000, + eps=1e-9, + dissimilarity='precomputed', + n_init=1) + pos = mds.fit(C).embedding_ + + nmds = manifold.MDS( + 2, + max_iter=3000, + eps=1e-9, + dissimilarity="precomputed", + random_state=seed, + 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])) + + +carre = spi.imread('../data/carre.png').astype(np.float64) / 256 +rond = spi.imread('../data/rond.png').astype(np.float64) / 256 +triangle = spi.imread('../data/triangle.png').astype(np.float64) / 256 +fleche = spi.imread('../data/coeur.png').astype(np.float64) / 256 + +shapes = [carre, rond, triangle, fleche] + +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 +====================== +The four distributions are constructed from 4 simple images +""" +ns = [len(xs[s]) for s in range(S)] +N = 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) + + +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, [Cs[0], Cs[1]], [ + ps[0], ps[1]], p, lambdast[i], 'square_loss', 5e-4, numItermax=100, stopThr=1e-3) + +Ct02 = [0 for i in range(2)] +for i in range(2): + Ct02[i] = ot.gromov.gromov_barycenters(N, [Cs[0], Cs[2]], [ + ps[0], ps[2]], p, lambdast[i], 'square_loss', 5e-4, numItermax=100, stopThr=1e-3) + +Ct13 = [0 for i in range(2)] +for i in range(2): + Ct13[i] = ot.gromov.gromov_barycenters(N, [Cs[1], Cs[3]], [ + ps[1], ps[3]], p, lambdast[i], 'square_loss', 5e-4, numItermax=100, stopThr=1e-3) + +Ct23 = [0 for i in range(2)] +for i in range(2): + Ct23[i] = ot.gromov.gromov_barycenters(N, [Cs[2], Cs[3]], [ + ps[2], ps[3]], p, lambdast[i], 'square_loss', 5e-4, numItermax=100, stopThr=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 From bc68cc3e8b23ad7d542518ba8ffa665094d57663 Mon Sep 17 00:00:00 2001 From: Nicolas Courty Date: Thu, 31 Aug 2017 17:17:30 +0200 Subject: minor corrections --- examples/plot_gromov_barycenter.py | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) (limited to 'examples/plot_gromov_barycenter.py') diff --git a/examples/plot_gromov_barycenter.py b/examples/plot_gromov_barycenter.py index 6a72b3b..da52768 100755 --- a/examples/plot_gromov_barycenter.py +++ b/examples/plot_gromov_barycenter.py @@ -32,18 +32,19 @@ that will be given by the output of the algorithm """ -def smacof_mds(C, dim, maxIter=3000, eps=1e-9): +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 : np.ndarray(ns,ns) + C : ndarray, shape (ns, ns) dissimilarity matrix - dim : Integer + dim : int dimension of the targeted space - maxIter : Maximum number of iterations of the SMACOF algorithm for a single run + max_iter : int + Maximum number of iterations of the SMACOF algorithm for a single run eps : relative tolerance w.r.t stress to declare converge @@ -60,7 +61,7 @@ def smacof_mds(C, dim, maxIter=3000, eps=1e-9): mds = manifold.MDS( dim, - max_iter=3000, + max_iter=max_iter, eps=1e-9, dissimilarity='precomputed', n_init=1) @@ -68,7 +69,7 @@ def smacof_mds(C, dim, maxIter=3000, eps=1e-9): nmds = manifold.MDS( 2, - max_iter=3000, + max_iter=max_iter, eps=1e-9, dissimilarity="precomputed", random_state=seed, -- cgit v1.2.3