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Diffstat (limited to 'examples/gromov/plot_gromov_barycenter.py')
| -rwxr-xr-x | examples/gromov/plot_gromov_barycenter.py | 247 |
1 files changed, 247 insertions, 0 deletions
diff --git a/examples/gromov/plot_gromov_barycenter.py b/examples/gromov/plot_gromov_barycenter.py new file mode 100755 index 0000000..f6f031a --- /dev/null +++ b/examples/gromov/plot_gromov_barycenter.py @@ -0,0 +1,247 @@ +# -*- 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 <erwan.vautier@gmail.com>
+# Nicolas Courty <ncourty@irisa.fr>
+#
+# 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')
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