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Diffstat (limited to 'docs/source/auto_examples/plot_gromov_barycenter.py')
| -rw-r--r-- | docs/source/auto_examples/plot_gromov_barycenter.py | 248 |
1 files changed, 0 insertions, 248 deletions
diff --git a/docs/source/auto_examples/plot_gromov_barycenter.py b/docs/source/auto_examples/plot_gromov_barycenter.py deleted file mode 100644 index 58fc51a..0000000 --- a/docs/source/auto_examples/plot_gromov_barycenter.py +++ /dev/null @@ -1,248 +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 <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 : 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 = spi.imread('../data/square.png').astype(np.float64)[:, :, 2] / 256
-cross = spi.imread('../data/cross.png').astype(np.float64)[:, :, 2] / 256
-triangle = spi.imread('../data/triangle.png').astype(np.float64)[:, :, 2] / 256
-star = spi.imread('../data/star.png').astype(np.float64)[:, :, 2] / 256
-
-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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