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author | Rémi Flamary <remi.flamary@gmail.com> | 2018-02-16 15:04:04 +0100 |
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committer | Rémi Flamary <remi.flamary@gmail.com> | 2018-02-16 15:04:04 +0100 |
commit | ee19d423adc85a960c9a46e4f81c370196805dbf (patch) | |
tree | 1c0bc21a605d0097616c26cfdb846fc744ed43a0 /docs/source/auto_examples/plot_gromov_barycenter.rst | |
parent | efdbf9e4fe9295fb1bec893e8aaa9102537cb7f5 (diff) |
update notebooks
Diffstat (limited to 'docs/source/auto_examples/plot_gromov_barycenter.rst')
-rw-r--r-- | docs/source/auto_examples/plot_gromov_barycenter.rst | 507 |
1 files changed, 256 insertions, 251 deletions
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 <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
-
+ # 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
+ + + + + + +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 <plot_gromov_barycenter.ipynb>` -.. rst-class:: sphx-glr-signature - `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_ +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_ |