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# -*- 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 <erwan.vautier@gmail.com>
# Nicolas Courty <ncourty@irisa.fr>
#
# 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, 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 : 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=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=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]))
<<<<<<< HEAD
square = spi.imread('../data/carre.png').astype(np.float64) / 256
circle = spi.imread('../data/rond.png').astype(np.float64) / 256
triangle = spi.imread('../data/triangle.png').astype(np.float64) / 256
arrow = spi.imread('../data/coeur.png').astype(np.float64) / 256
shapes = [square, circle, triangle, arrow]
=======
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]
>>>>>>> 986f46ddde3ce2f550cb56f66620df377326423d
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)]
<<<<<<< HEAD
n_samples = 30
=======
N = 30
>>>>>>> 986f46ddde3ce2f550cb56f66620df377326423d
"""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)]
<<<<<<< HEAD
p = ot.unif(n_samples)
=======
p = ot.unif(N)
>>>>>>> 986f46ddde3ce2f550cb56f66620df377326423d
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):
<<<<<<< HEAD
Ct01[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[1]], [
=======
Ct01[i] = ot.gromov.gromov_barycenters(N, [Cs[0], Cs[1]], [
>>>>>>> 986f46ddde3ce2f550cb56f66620df377326423d
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):
<<<<<<< HEAD
Ct02[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[0], Cs[2]], [
=======
Ct02[i] = ot.gromov.gromov_barycenters(N, [Cs[0], Cs[2]], [
>>>>>>> 986f46ddde3ce2f550cb56f66620df377326423d
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):
<<<<<<< HEAD
Ct13[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[1], Cs[3]], [
=======
Ct13[i] = ot.gromov.gromov_barycenters(N, [Cs[1], Cs[3]], [
>>>>>>> 986f46ddde3ce2f550cb56f66620df377326423d
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):
<<<<<<< HEAD
Ct23[i] = ot.gromov.gromov_barycenters(n_samples, [Cs[2], Cs[3]], [
=======
Ct23[i] = ot.gromov.gromov_barycenters(N, [Cs[2], Cs[3]], [
>>>>>>> 986f46ddde3ce2f550cb56f66620df377326423d
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')
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