From ee19d423adc85a960c9a46e4f81c370196805dbf Mon Sep 17 00:00:00 2001 From: Rémi Flamary Date: Fri, 16 Feb 2018 15:04:04 +0100 Subject: update notebooks --- .../auto_examples/plot_gromov_barycenter.rst | 507 +++++++++++---------- 1 file changed, 256 insertions(+), 251 deletions(-) (limited to 'docs/source/auto_examples/plot_gromov_barycenter.rst') diff --git a/docs/source/auto_examples/plot_gromov_barycenter.rst b/docs/source/auto_examples/plot_gromov_barycenter.rst index ca2d4e9..531ee22 100644 --- a/docs/source/auto_examples/plot_gromov_barycenter.rst +++ b/docs/source/auto_examples/plot_gromov_barycenter.rst @@ -14,285 +14,285 @@ computation in POT. .. code-block:: python - - # 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 - + # 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 + + + + + + +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 .. code-block:: python - - - 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 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 .. code-block:: python - - - 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])]) - + 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 ----------------------- + + + + + +Barycenter computation +---------------------- .. code-block:: python - - - 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 + + + 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 .. code-block:: python - - - 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') + + + 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') @@ -302,11 +302,13 @@ Visualization -**Total running time of the script:** ( 8 minutes 43.875 seconds) +**Total running time of the script:** ( 0 minutes 5.906 seconds) + +.. only :: html -.. container:: sphx-glr-footer + .. container:: sphx-glr-footer .. container:: sphx-glr-download @@ -319,6 +321,9 @@ Visualization :download:`Download Jupyter notebook: plot_gromov_barycenter.ipynb ` -.. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery `_ +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ -- cgit v1.2.3