big update examples

1 files changed, 53 insertions, 6 deletions

diff --git a/docs/source/auto_examples/plot_barycenter_fgw.ipynb b/docs/source/auto_examples/plot_barycenter_fgw.ipynb
index 28229b2..4e4704c 100644
--- a/docs/source/auto_examples/plot_barycenter_fgw.ipynb
+++ b/docs/source/auto_examples/plot_barycenter_fgw.ipynb
@@ -26,7 +26,29 @@
       },
       "outputs": [],
       "source": [
-        "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License\n\n#%% load libraries\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport networkx as nx\nimport math\nfrom scipy.sparse.csgraph import shortest_path\nimport matplotlib.colors as mcol\nfrom matplotlib import cm\nfrom ot.gromov import fgw_barycenters\n#%% Graph functions\n\n\ndef find_thresh(C, inf=0.5, sup=3, step=10):\n    \"\"\" Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected\n        Tthe threshold is found by a linesearch between values \"inf\" and \"sup\" with \"step\" thresholds tested.\n        The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix\n        and the original matrix.\n    Parameters\n    ----------\n    C : ndarray, shape (n_nodes,n_nodes)\n            The structure matrix to threshold\n    inf : float\n          The beginning of the linesearch\n    sup : float\n          The end of the linesearch\n    step : integer\n            Number of thresholds tested\n    \"\"\"\n    dist = []\n    search = np.linspace(inf, sup, step)\n    for thresh in search:\n        Cprime = sp_to_adjency(C, 0, thresh)\n        SC = shortest_path(Cprime, method='D')\n        SC[SC == float('inf')] = 100\n        dist.append(np.linalg.norm(SC - C))\n    return search[np.argmin(dist)], dist\n\n\ndef sp_to_adjency(C, threshinf=0.2, threshsup=1.8):\n    \"\"\" Thresholds the structure matrix in order to compute an adjency matrix.\n    All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0\n    Parameters\n    ----------\n    C : ndarray, shape (n_nodes,n_nodes)\n        The structure matrix to threshold\n    threshinf : float\n        The minimum value of distance from which the new value is set to 1\n    threshsup : float\n        The maximum value of distance from which the new value is set to 1\n    Returns\n    -------\n    C : ndarray, shape (n_nodes,n_nodes)\n        The threshold matrix. Each element is in {0,1}\n    \"\"\"\n    H = np.zeros_like(C)\n    np.fill_diagonal(H, np.diagonal(C))\n    C = C - H\n    C = np.minimum(np.maximum(C, threshinf), threshsup)\n    C[C == threshsup] = 0\n    C[C != 0] = 1\n\n    return C\n\n\ndef build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):\n    \"\"\" Create a noisy circular graph\n    \"\"\"\n    g = nx.Graph()\n    g.add_nodes_from(list(range(N)))\n    for i in range(N):\n        noise = float(np.random.normal(mu, sigma, 1))\n        if with_noise:\n            g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)\n        else:\n            g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))\n        g.add_edge(i, i + 1)\n        if structure_noise:\n            randomint = np.random.randint(0, p)\n            if randomint == 0:\n                if i <= N - 3:\n                    g.add_edge(i, i + 2)\n                if i == N - 2:\n                    g.add_edge(i, 0)\n                if i == N - 1:\n                    g.add_edge(i, 1)\n    g.add_edge(N, 0)\n    noise = float(np.random.normal(mu, sigma, 1))\n    if with_noise:\n        g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)\n    else:\n        g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))\n    return g\n\n\ndef graph_colors(nx_graph, vmin=0, vmax=7):\n    cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)\n    cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')\n    cpick.set_array([])\n    val_map = {}\n    for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():\n        val_map[k] = cpick.to_rgba(v)\n    colors = []\n    for node in nx_graph.nodes():\n        colors.append(val_map[node])\n    return colors"
+        "# Author: Titouan Vayer <titouan.vayer@irisa.fr>\n#\n# License: MIT License"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "import numpy as np\nimport matplotlib.pyplot as plt\nimport networkx as nx\nimport math\nfrom scipy.sparse.csgraph import shortest_path\nimport matplotlib.colors as mcol\nfrom matplotlib import cm\nfrom ot.gromov import fgw_barycenters"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "def find_thresh(C, inf=0.5, sup=3, step=10):\n    \"\"\" Trick to find the adequate thresholds from where value of the C matrix are considered close enough to say that nodes are connected\n        Tthe threshold is found by a linesearch between values \"inf\" and \"sup\" with \"step\" thresholds tested.\n        The optimal threshold is the one which minimizes the reconstruction error between the shortest_path matrix coming from the thresholded adjency matrix\n        and the original matrix.\n    Parameters\n    ----------\n    C : ndarray, shape (n_nodes,n_nodes)\n            The structure matrix to threshold\n    inf : float\n          The beginning of the linesearch\n    sup : float\n          The end of the linesearch\n    step : integer\n            Number of thresholds tested\n    \"\"\"\n    dist = []\n    search = np.linspace(inf, sup, step)\n    for thresh in search:\n        Cprime = sp_to_adjency(C, 0, thresh)\n        SC = shortest_path(Cprime, method='D')\n        SC[SC == float('inf')] = 100\n        dist.append(np.linalg.norm(SC - C))\n    return search[np.argmin(dist)], dist\n\n\ndef sp_to_adjency(C, threshinf=0.2, threshsup=1.8):\n    \"\"\" Thresholds the structure matrix in order to compute an adjency matrix.\n    All values between threshinf and threshsup are considered representing connected nodes and set to 1. Else are set to 0\n    Parameters\n    ----------\n    C : ndarray, shape (n_nodes,n_nodes)\n        The structure matrix to threshold\n    threshinf : float\n        The minimum value of distance from which the new value is set to 1\n    threshsup : float\n        The maximum value of distance from which the new value is set to 1\n    Returns\n    -------\n    C : ndarray, shape (n_nodes,n_nodes)\n        The threshold matrix. Each element is in {0,1}\n    \"\"\"\n    H = np.zeros_like(C)\n    np.fill_diagonal(H, np.diagonal(C))\n    C = C - H\n    C = np.minimum(np.maximum(C, threshinf), threshsup)\n    C[C == threshsup] = 0\n    C[C != 0] = 1\n\n    return C\n\n\ndef build_noisy_circular_graph(N=20, mu=0, sigma=0.3, with_noise=False, structure_noise=False, p=None):\n    \"\"\" Create a noisy circular graph\n    \"\"\"\n    g = nx.Graph()\n    g.add_nodes_from(list(range(N)))\n    for i in range(N):\n        noise = float(np.random.normal(mu, sigma, 1))\n        if with_noise:\n            g.add_node(i, attr_name=math.sin((2 * i * math.pi / N)) + noise)\n        else:\n            g.add_node(i, attr_name=math.sin(2 * i * math.pi / N))\n        g.add_edge(i, i + 1)\n        if structure_noise:\n            randomint = np.random.randint(0, p)\n            if randomint == 0:\n                if i <= N - 3:\n                    g.add_edge(i, i + 2)\n                if i == N - 2:\n                    g.add_edge(i, 0)\n                if i == N - 1:\n                    g.add_edge(i, 1)\n    g.add_edge(N, 0)\n    noise = float(np.random.normal(mu, sigma, 1))\n    if with_noise:\n        g.add_node(N, attr_name=math.sin((2 * N * math.pi / N)) + noise)\n    else:\n        g.add_node(N, attr_name=math.sin(2 * N * math.pi / N))\n    return g\n\n\ndef graph_colors(nx_graph, vmin=0, vmax=7):\n    cnorm = mcol.Normalize(vmin=vmin, vmax=vmax)\n    cpick = cm.ScalarMappable(norm=cnorm, cmap='viridis')\n    cpick.set_array([])\n    val_map = {}\n    for k, v in nx.get_node_attributes(nx_graph, 'attr_name').items():\n        val_map[k] = cpick.to_rgba(v)\n    colors = []\n    for node in nx_graph.nodes():\n        colors.append(val_map[node])\n    return colors"
       ]
     },
     {
@@ -37,6 +59,13 @@
       ]
     },
     {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "We build a dataset of noisy circular graphs.\nNoise is added on the structures by random connections and on the features by gaussian noise.\n\n"
+      ]
+    },
+    {
       "cell_type": "code",
       "execution_count": null,
       "metadata": {
@@ -44,7 +73,7 @@
       },
       "outputs": [],
       "source": [
-        "#%% circular dataset\n# We build a dataset of noisy circular graphs.\n# Noise is added on the structures by random connections and on the features by gaussian noise.\n\n\nnp.random.seed(30)\nX0 = []\nfor k in range(9):\n    X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))"
+        "np.random.seed(30)\nX0 = []\nfor k in range(9):\n    X0.append(build_noisy_circular_graph(np.random.randint(15, 25), with_noise=True, structure_noise=True, p=3))"
       ]
     },
     {
@@ -62,7 +91,7 @@
       },
       "outputs": [],
       "source": [
-        "#%% Plot graphs\n\nplt.figure(figsize=(8, 10))\nfor i in range(len(X0)):\n    plt.subplot(3, 3, i + 1)\n    g = X0[i]\n    pos = nx.kamada_kawai_layout(g)\n    nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)\nplt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)\nplt.show()"
+        "plt.figure(figsize=(8, 10))\nfor i in range(len(X0)):\n    plt.subplot(3, 3, i + 1)\n    g = X0[i]\n    pos = nx.kamada_kawai_layout(g)\n    nx.draw(g, pos=pos, node_color=graph_colors(g, vmin=-1, vmax=1), with_labels=False, node_size=100)\nplt.suptitle('Dataset of noisy graphs. Color indicates the label', fontsize=20)\nplt.show()"
       ]
     },
     {
@@ -73,6 +102,13 @@
       ]
     },
     {
+      "cell_type": "markdown",
+      "metadata": {},
+      "source": [
+        "Features distances are the euclidean distances\n\n"
+      ]
+    },
+    {
       "cell_type": "code",
       "execution_count": null,
       "metadata": {
@@ -80,7 +116,7 @@
       },
       "outputs": [],
       "source": [
-        "#%% We compute the barycenter using FGW. Structure matrices are computed using the shortest_path distance in the graph\n# Features distances are the euclidean distances\nCs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]\nps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]\nYs = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]\nlambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()\nsizebary = 15  # we choose a barycenter with 15 nodes\n\nA, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True)"
+        "Cs = [shortest_path(nx.adjacency_matrix(x)) for x in X0]\nps = [np.ones(len(x.nodes())) / len(x.nodes()) for x in X0]\nYs = [np.array([v for (k, v) in nx.get_node_attributes(x, 'attr_name').items()]).reshape(-1, 1) for x in X0]\nlambdas = np.array([np.ones(len(Ys)) / len(Ys)]).ravel()\nsizebary = 15  # we choose a barycenter with 15 nodes\n\nA, C, log = fgw_barycenters(sizebary, Ys, Cs, ps, lambdas, alpha=0.95, log=True)"
       ]
     },
     {
@@ -98,7 +134,18 @@
       },
       "outputs": [],
       "source": [
-        "#%% Create the barycenter\nbary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))\nfor i, v in enumerate(A.ravel()):\n    bary.add_node(i, attr_name=v)\n\n#%%\npos = nx.kamada_kawai_layout(bary)\nnx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)\nplt.suptitle('Barycenter', fontsize=20)\nplt.show()"
+        "bary = nx.from_numpy_matrix(sp_to_adjency(C, threshinf=0, threshsup=find_thresh(C, sup=100, step=100)[0]))\nfor i, v in enumerate(A.ravel()):\n    bary.add_node(i, attr_name=v)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "collapsed": false
+      },
+      "outputs": [],
+      "source": [
+        "pos = nx.kamada_kawai_layout(bary)\nnx.draw(bary, pos=pos, node_color=graph_colors(bary, vmin=-1, vmax=1), with_labels=False)\nplt.suptitle('Barycenter', fontsize=20)\nplt.show()"
       ]
     }
   ],
@@ -118,7 +165,7 @@
       "name": "python",
       "nbconvert_exporter": "python",
       "pygments_lexer": "ipython3",
-      "version": "3.6.8"
+      "version": "3.6.9"
     }
   },
   "nbformat": 4,