Gromov Wasserstein solver + barycenter

README.md

@@ -200,3 +200,5 @@ You can also post bug reports and feature requests in Github issues. Make sure t
 [11] Flamary, R., Cuturi, M., Courty, N., & Rakotomamonjy, A. (2016). [Wasserstein Discriminant Analysis](https://arxiv.org/pdf/1608.08063.pdf). arXiv preprint arXiv:1608.08063.
 
 [12] Gabriel Peyré, Marco Cuturi, and Justin Solomon, [Gromov-Wasserstein averaging of kernel and distance matrices](http://proceedings.mlr.press/v48/peyre16.html)  International Conference on Machine Learning (ICML). 2016.
+
+[13] Mémoli, Facundo. [Gromov–Wasserstein distances and the metric approach to object matching](https://media.adelaide.edu.au/acvt/Publications/2011/2011-Gromov%E2%80%93Wasserstein%20Distances%20and%20the%20Metric%20Approach%20to%20Object%20Matching.pdf). Foundations of computational mathematics 11.4 (2011): 417-487.

docs/cache_nbrun

@@ -1 +1 @@
-{"plot_otda_mapping_colors_images.ipynb": "4f0587a00a3c082799a75a0ed36e9ce1", "plot_optim_OTreg.ipynb": "71d3c106b3f395a6b1001078a6ca6f8d", "plot_otda_color_images.ipynb": "d047d635f4987c81072383241590e21f", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_OT_L1_vs_L2.ipynb": "e15219bf651a7e39e7c5c3934069894c", "plot_barycenter_1D.ipynb": "6fd8167f98816dc832fe0c58b1d5527b", "plot_otda_classes.ipynb": "44bb8cd93317b5d342cd62e26d9bbe60", "plot_otda_d2.ipynb": "8ac4fd2ff899df0858ce1e5fead37f33", "plot_otda_mapping.ipynb": "d335a15af828aaa3439a1c67570d79d6", "plot_gromov.ipynb": "9d0893ec68851f200d0ca806bcbe847f", "plot_compute_emd.ipynb": "bd95981189df6adcb113d9b360ead734", "plot_OT_1D.ipynb": "e44c83f6112388ae18657cb0ad76d0e9", "plot_gromov_barycenter.ipynb": "a4d9636685394ceb13f26cdc613b9b5b", "plot_otda_semi_supervised.ipynb": "0261d339a692e339e15d3634488905cc", "plot_OT_2D_samples.ipynb": "3f125714daa35ff3cfe5dae1f71265c4"}
+{"plot_otda_mapping_colors_images.ipynb": "4f0587a00a3c082799a75a0ed36e9ce1", "plot_optim_OTreg.ipynb": "2ec33a099bb67120a134332a20f29313", "plot_otda_color_images.ipynb": "d047d635f4987c81072383241590e21f", "plot_WDA.ipynb": "27f8de4c6d7db46497076523673eedfb", "plot_OT_L1_vs_L2.ipynb": "871d60931f5118c085342e11cb638336", "plot_barycenter_1D.ipynb": "95708b025b6d96d97f579d30d268cbff", "plot_otda_classes.ipynb": "44bb8cd93317b5d342cd62e26d9bbe60", "plot_otda_d2.ipynb": "1a9547f07317612e1a161b7d9f07a5a8", "plot_otda_mapping.ipynb": "d335a15af828aaa3439a1c67570d79d6", "plot_gromov.ipynb": "825d79eba255314fe11469c64d38fc3d", "plot_compute_emd.ipynb": "bd95981189df6adcb113d9b360ead734", "plot_OT_1D.ipynb": "54dfea8ccb61f30729519275785c494c", "plot_gromov_barycenter.ipynb": "953e5047b886ec69ec621ec52f5e21d1", "plot_otda_semi_supervised.ipynb": "0261d339a692e339e15d3634488905cc", "plot_OT_2D_samples.ipynb": "3f125714daa35ff3cfe5dae1f71265c4"}

docs/source/all.rst

@@ -20,6 +20,13 @@ ot.bregman
 .. automodule:: ot.bregman
    :members:
 
+ot.gromov
+----------
+
+.. automodule:: ot.gromov
+   :members:
+
+
 ot.optim
 --------
 

docs/source/auto_examples/index.rst

@@ -1,8 +1,12 @@
+:orphan:
+
 POT Examples
 ============
 
 This is a gallery of all the POT example files.
 
+
+
 .. raw:: html
 
     <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of EMD and Sinkhorn transport plans and their visualiz...">
@@ -145,13 +149,13 @@ This is a gallery of all the POT example files.
 
 .. raw:: html
 
-    <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wassersyein Barycenter as proposed in [...">
+    <div class="sphx-glr-thumbcontainer" tooltip="OT for domain adaptation with image color adaptation [6] with mapping estimation [8].">
 
 .. only:: html
 
-    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_1D_thumb.png
+    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png
 
-        :ref:`sphx_glr_auto_examples_plot_barycenter_1D.py`
+        :ref:`sphx_glr_auto_examples_plot_otda_mapping_colors_images.py`
 
 .. raw:: html
 
@@ -161,17 +165,17 @@ This is a gallery of all the POT example files.
 .. toctree::
    :hidden:
 
-   /auto_examples/plot_barycenter_1D
+   /auto_examples/plot_otda_mapping_colors_images
 
 .. raw:: html
 
-    <div class="sphx-glr-thumbcontainer" tooltip="OT for domain adaptation with image color adaptation [6] with mapping estimation [8].">
+    <div class="sphx-glr-thumbcontainer" tooltip="This example illustrates the computation of regularized Wassersyein Barycenter as proposed in [...">
 
 .. only:: html
 
-    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_otda_mapping_colors_images_thumb.png
+    .. figure:: /auto_examples/images/thumb/sphx_glr_plot_barycenter_1D_thumb.png
 
-        :ref:`sphx_glr_auto_examples_plot_otda_mapping_colors_images.py`
+        :ref:`sphx_glr_auto_examples_plot_barycenter_1D.py`
 
 .. raw:: html
 
@@ -181,7 +185,7 @@ This is a gallery of all the POT example files.
 .. toctree::
    :hidden:
 
-   /auto_examples/plot_otda_mapping_colors_images
+   /auto_examples/plot_barycenter_1D
 
 .. raw:: html
 
@@ -308,19 +312,24 @@ This is a gallery of all the POT example files.
 
 
 
-.. container:: sphx-glr-footer
+.. only :: html
+
+ .. container:: sphx-glr-footer
 
 
   .. container:: sphx-glr-download
 
-    :download:`Download all examples in Python source code: auto_examples_python.zip </auto_examples/auto_examples_python.zip>`
+    :download:`Download all examples in Python source code: auto_examples_python.zip <//home/rflamary/PYTHON/POT/docs/source/auto_examples/auto_examples_python.zip>`
 
 
 
   .. container:: sphx-glr-download
 
-    :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip </auto_examples/auto_examples_jupyter.zip>`
+    :download:`Download all examples in Jupyter notebooks: auto_examples_jupyter.zip <//home/rflamary/PYTHON/POT/docs/source/auto_examples/auto_examples_jupyter.zip>`
+
+
+.. only:: html
 
-.. rst-class:: sphx-glr-signature
+ .. rst-class:: sphx-glr-signature
 
-    `Generated by Sphinx-Gallery <http://sphinx-gallery.readthedocs.io>`_
+    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_

docs/source/auto_examples/plot_OT_1D.ipynb

@@ -1,126 +1,126 @@
 {
-  "nbformat_minor": 0, 
-  "nbformat": 4, 
   "cells": [
     {
-      "execution_count": null, 
-      "cell_type": "code", 
-      "source": [
-        "%matplotlib inline"
-      ], 
-      "outputs": [], 
+      "execution_count": null,
       "metadata": {
         "collapsed": false
-      }
-    }, 
+      },
+      "outputs": [],
+      "source": [
+        "%matplotlib inline"
+      ],
+      "cell_type": "code"
+    },
     {
+      "metadata": {},
       "source": [
         "\n# 1D optimal transport\n\n\nThis example illustrates the computation of EMD and Sinkhorn transport plans\nand their visualization.\n\n\n"
-      ], 
-      "cell_type": "markdown", 
-      "metadata": {}
-    }, 
+      ],
+      "cell_type": "markdown"
+    },
     {
-      "execution_count": null, 
-      "cell_type": "code", 
-      "source": [
-        "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nfrom ot.datasets import get_1D_gauss as gauss"
-      ], 
-      "outputs": [], 
+      "execution_count": null,
       "metadata": {
         "collapsed": false
-      }
-    }, 
+      },
+      "outputs": [],
+      "source": [
+        "# Author: Remi Flamary <remi.flamary@unice.fr>\n#\n# License: MIT License\n\nimport numpy as np\nimport matplotlib.pylab as pl\nimport ot\nimport ot.plot\nfrom ot.datasets import get_1D_gauss as gauss"
+      ],
+      "cell_type": "code"
+    },
     {
+      "metadata": {},
       "source": [
         "Generate data\n-------------\n\n"
-      ], 
-      "cell_type": "markdown", 
-      "metadata": {}
-    }, 
+      ],
+      "cell_type": "markdown"
+    },
     {
-      "execution_count": null, 
-      "cell_type": "code", 
-      "source": [
-        "#%% parameters\n\nn = 100  # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5)  # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()"
-      ], 
-      "outputs": [], 
+      "execution_count": null,
       "metadata": {
         "collapsed": false
-      }
-    }, 
+      },
+      "outputs": [],
+      "source": [
+        "#%% parameters\n\nn = 100  # nb bins\n\n# bin positions\nx = np.arange(n, dtype=np.float64)\n\n# Gaussian distributions\na = gauss(n, m=20, s=5)  # m= mean, s= std\nb = gauss(n, m=60, s=10)\n\n# loss matrix\nM = ot.dist(x.reshape((n, 1)), x.reshape((n, 1)))\nM /= M.max()"
+      ],
+      "cell_type": "code"
+    },
     {
+      "metadata": {},
       "source": [
         "Plot distributions and loss matrix\n----------------------------------\n\n"
-      ], 
-      "cell_type": "markdown", 
-      "metadata": {}
-    }, 
+      ],
+      "cell_type": "markdown"
+    },
     {
-      "execution_count": null, 
-      "cell_type": "code", 
-      "source": [
-        "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')"
-      ], 
-      "outputs": [], 
+      "execution_count": null,
       "metadata": {
         "collapsed": false
-      }
-    }, 
+      },
+      "outputs": [],
+      "source": [
+        "#%% plot the distributions\n\npl.figure(1, figsize=(6.4, 3))\npl.plot(x, a, 'b', label='Source distribution')\npl.plot(x, b, 'r', label='Target distribution')\npl.legend()\n\n#%% plot distributions and loss matrix\n\npl.figure(2, figsize=(5, 5))\not.plot.plot1D_mat(a, b, M, 'Cost matrix M')"
+      ],
+      "cell_type": "code"
+    },
     {
+      "metadata": {},
       "source": [
         "Solve EMD\n---------\n\n"
-      ], 
-      "cell_type": "markdown", 
-      "metadata": {}
-    }, 
+      ],
+      "cell_type": "markdown"
+    },
     {
-      "execution_count": null, 
-      "cell_type": "code", 
-      "source": [
-        "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')"
-      ], 
-      "outputs": [], 
+      "execution_count": null,
       "metadata": {
         "collapsed": false
-      }
-    }, 
+      },
+      "outputs": [],
+      "source": [
+        "#%% EMD\n\nG0 = ot.emd(a, b, M)\n\npl.figure(3, figsize=(5, 5))\not.plot.plot1D_mat(a, b, G0, 'OT matrix G0')"
+      ],
+      "cell_type": "code"
+    },
     {
+      "metadata": {},
       "source": [
         "Solve Sinkhorn\n--------------\n\n"
-      ], 
-      "cell_type": "markdown", 
-      "metadata": {}
-    }, 
+      ],
+      "cell_type": "markdown"
+    },
     {
-      "execution_count": null, 
-      "cell_type": "code", 
-      "source": [
-        "#%% Sinkhorn\n\nlambd = 1e-3\nGs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n\npl.show()"
-      ], 
-      "outputs": [], 
+      "execution_count": null,
       "metadata": {
         "collapsed": false
-      }
+      },
+      "outputs": [],
+      "source": [
+        "#%% Sinkhorn\n\nlambd = 1e-3\nGs = ot.sinkhorn(a, b, M, lambd, verbose=True)\n\npl.figure(4, figsize=(5, 5))\not.plot.plot1D_mat(a, b, Gs, 'OT matrix Sinkhorn')\n\npl.show()"
+      ],
+      "cell_type": "code"
     }
-  ], 
+  ],
   "metadata": {
-    "kernelspec": {
-      "display_name": "Python 2", 
-      "name": "python2", 
-      "language": "python"
-    }, 
     "language_info": {
-      "mimetype": "text/x-python", 
-      "nbconvert_exporter": "python", 
-      "name": "python", 
-      "file_extension": ".py", 
-      "version": "2.7.12", 
-      "pygments_lexer": "ipython2", 
+      "name": "python",
       "codemirror_mode": {
-        "version": 2, 
-        "name": "ipython"
-      }
+        "name": "ipython",
+        "version": 3
+      },
+      "nbconvert_exporter": "python",
+      "version": "3.5.2",
+      "pygments_lexer": "ipython3",
+      "file_extension": ".py",
+      "mimetype": "text/x-python"
+    },
+    "kernelspec": {
+      "display_name": "Python 3",
+      "name": "python3",
+      "language": "python"
     }
-  }
+  },
+  "nbformat_minor": 0,
+  "nbformat": 4
 }

docs/source/auto_examples/plot_OT_1D.py

@@ -16,6 +16,7 @@
 import numpy as np
 import matplotlib.pylab as pl
 import ot
+import ot.plot
 from ot.datasets import get_1D_gauss as gauss
 
 ##############################################################################

docs/source/auto_examples/plot_OT_1D.rst

@@ -23,6 +23,7 @@ and their visualization.
     import numpy as np
     import matplotlib.pylab as pl
     import ot
+    import ot.plot
     from ot.datasets import get_1D_gauss as gauss
 
 
@@ -171,11 +172,13 @@ Solve Sinkhorn
       110|1.527180e-10|
 
 
-**Total running time of the script:** ( 0 minutes  1.198 seconds)
+**Total running time of the script:** ( 0 minutes  1.061 seconds)
 
 
 
-.. container:: sphx-glr-footer
+.. only :: html
+
+ .. container:: sphx-glr-footer
 
 
   .. container:: sphx-glr-download
@@ -188,6 +191,9 @@ Solve Sinkhorn
 
      :download:`Download Jupyter notebook: plot_OT_1D.ipynb <plot_OT_1D.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>`_