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authorRĂ©mi Flamary <remi.flamary@gmail.com>2020-04-21 17:48:37 +0200
committerGitHub <noreply@github.com>2020-04-21 17:48:37 +0200
commita303cc6b483d3cd958c399621e22e40574bcbbc8 (patch)
treedea049cb692020462da8f00d9e117f93b839bb55 /docs/source/auto_examples/plot_barycenter_fgw.rst
parent0b2d808aaebb1cab60a272ea7901d5f77df43a9f (diff)
[MRG] Actually run sphinx-gallery (#146)
* generate gallery * remove mock * add sklearn to requirermnt?txt for example * remove latex from fgw example * add networks for graph example * remove all * add requirement.txt rtd * rtd debug * update readme * eradthedoc with redirection * add conf rtd
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-.. only:: html
-
- .. note::
- :class: sphx-glr-download-link-note
-
- Click :ref:`here <sphx_glr_download_auto_examples_plot_barycenter_fgw.py>` to download the full example code
- .. rst-class:: sphx-glr-example-title
-
- .. _sphx_glr_auto_examples_plot_barycenter_fgw.py:
-
-
-=================================
-Plot graphs' barycenter using FGW
-=================================
-
-This example illustrates the computation barycenter of labeled graphs using FGW
-
-Requires networkx >=2
-
-.. [18] Vayer Titouan, Chapel Laetitia, Flamary R{'e}mi, Tavenard Romain
- and Courty Nicolas
- "Optimal Transport for structured data with application on graphs"
- International Conference on Machine Learning (ICML). 2019.
-
-
-
-.. code-block:: default
-
-
- # Author: Titouan Vayer <titouan.vayer@irisa.fr>
- #
- # License: MIT License
-
-
-
-
-
-
-
-
-
-.. code-block:: default
-
- import numpy as np
- import matplotlib.pyplot as plt
- import networkx as nx
- import math
- from scipy.sparse.csgraph import shortest_path
- import matplotlib.colors as mcol
- from matplotlib import cm
- from ot.gromov import fgw_barycenters
-
-
-
-
-
-
-
-
-.. code-block:: default
-
-
-
- def find_thresh(C, inf=0.5, sup=3, step=10):
- """ Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected
- Tthe threshold is found by a linesearch between values "inf" and "sup" with "step" thresholds tested.
- The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix
- and the original matrix.
- Parameters
- ----------
- C : ndarray, shape (n_nodes,n_nodes)
- The structure matrix to threshold
- inf : float
- The beginning of the linesearch
- sup : float
- The end of the linesearch
- step : integer
- Number of thresholds tested
- """
- dist = []
- search = np.linspace(inf, sup, step)
- for thresh in search:
- Cprime = sp_to_adjency(C, 0, thresh)
- SC = shortest_path(Cprime, method='D')
- SC[SC == float('inf')] = 100
- dist.append(np.linalg.norm(SC - C))
- return search[np.argmin(dist)], dist
-
-
- def sp_to_adjency(C, threshinf=0.2, threshsup=1.8):
- """ Thresholds the structure matrix in order to compute an adjency matrix.
- All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0
- Parameters
- ----------
- C : ndarray, shape (n_nodes,n_nodes)
- The structure matrix to threshold
- threshinf : float
- The minimum value of distance from which the new value is set to 1
- threshsup : float
- The maximum value of distance from which the new value is set to 1
- Returns
- -------
- C : ndarray, shape (n_nodes,n_nodes)
- The threshold matrix. Each element is in {0,1}
- """
- H = np.zeros_like(C)
- np.fill_diagonal(H, np.diagonal(C))
- C = C - H
- C = np.minimum(np.maximum(C, threshinf), threshsup)
- C[C == threshsup] = 0
- C[C != 0] = 1
-
- return C
-
-
- def build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):
- """ Create a noisy circular graph
- """
- g = nx.Graph()
- g.add_nodes_from(list(range(N)))
- for i in range(N):
- noise = float(np.random.normal(mu, sigma, 1))
- if with_noise:
- g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)
- else:
- g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))
- g.add_edge(i, i + 1)
- if structure_noise:
- randomint = np.random.randint(0, p)
- if randomint == 0:
- if i <= N - 3:
- g.add_edge(i, i + 2)
- if i == N - 2:
- g.add_edge(i, 0)
- if i == N - 1:
- g.add_edge(i, 1)
- g.add_edge(N, 0)
- noise = float(np.random.normal(mu, sigma, 1))
- if with_noise:
- g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)
- else:
- g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))
- return g
-
-
- def graph_colors(nx_graph, vmin=0, vmax=7):
- cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)
- cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')
- cpick.set_array([])
- val_map = {}
- for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():
- val_map[k] = cpick.to_rgba(v)
- colors = []
- for node in nx_graph.nodes():
- colors.append(val_map[node])
- return colors
-
-
-
-
-
-
-
-
-Generate data
--------------
-
-We build a dataset of noisy circular graphs.
-Noise is added on the structures by random connections and on the features by gaussian noise.
-
-
-.. code-block:: default
-
-
-
- np.random.seed(30)
- X0 = []
- for k in range(9):
- X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))
-
-
-
-
-
-
-
-
-Plot data
----------
-
-
-.. code-block:: default
-
-
- plt.figure(figsize=(8, 10))
- for i in range(len(X0)):
- plt.subplot(3, 3, i + 1)
- g = X0[i]
- pos = nx.kamada_kawai_layout(g)
- nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)
- plt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)
- plt.show()
-
-
-
-
-.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_001.png
- :class: sphx-glr-single-img
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- /home/rflamary/PYTHON/POT/examples/plot_barycenter_fgw.py:155: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
- plt.show()
-
-
-
-
-Barycenter computation
-----------------------
-
-Features distances are the euclidean distances
-
-
-.. code-block:: default
-
- Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]
- ps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]
- Ys = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]
- lambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()
- sizebary = 15 # we choose a barycenter with 15 nodes
-
- A, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True)
-
-
-
-
-
-
-
-
-Plot Barycenter
--------------------------
-
-
-.. code-block:: default
-
- bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))
- for i, v in enumerate(A.ravel()):
- bary.add_node(i, attr_name=v)
-
-
-
-
-
-
-
-
-
-.. code-block:: default
-
- pos = nx.kamada_kawai_layout(bary)
- nx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)
- plt.suptitle('Barycenter', fontsize=20)
- plt.show()
-
-
-
-.. image:: /auto_examples/images/sphx_glr_plot_barycenter_fgw_002.png
- :class: sphx-glr-single-img
-
-
-.. rst-class:: sphx-glr-script-out
-
- Out:
-
- .. code-block:: none
-
- /home/rflamary/PYTHON/POT/examples/plot_barycenter_fgw.py:184: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
- plt.show()
-
-
-
-
-
-.. rst-class:: sphx-glr-timing
-
- **Total running time of the script:** ( 0 minutes 1.949 seconds)
-
-
-.. _sphx_glr_download_auto_examples_plot_barycenter_fgw.py:
-
-
-.. only :: html
-
- .. container:: sphx-glr-footer
- :class: sphx-glr-footer-example
-
-
-
- .. container:: sphx-glr-download sphx-glr-download-python
-
- :download:`Download Python source code: plot_barycenter_fgw.py <plot_barycenter_fgw.py>`
-
-
-
- .. container:: sphx-glr-download sphx-glr-download-jupyter
-
- :download:`Download Jupyter notebook: plot_barycenter_fgw.ipynb <plot_barycenter_fgw.ipynb>`
-
-
-.. only:: html
-
- .. rst-class:: sphx-glr-signature
-
- `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_