{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Node representations with GraphWave\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden",
    "tags": [
     "CloudRunner"
    ]
   },
   "source": [
    "<table><tr><td>Run the latest release of this notebook:</td><td><a href=\"https://mybinder.org/v2/gh/stellargraph/stellargraph/master?urlpath=lab/tree/demos/embeddings/graphwave-embeddings.ipynb\" alt=\"Open In Binder\" target=\"_parent\"><img src=\"https://mybinder.org/badge_logo.svg\"/></a></td><td><a href=\"https://colab.research.google.com/github/stellargraph/stellargraph/blob/master/demos/embeddings/graphwave-embeddings.ipynb\" alt=\"Open In Colab\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\"/></a></td></tr></table>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This demo features the algorithm GraphWave published in \"Learning Structural Node Embeddings via Diffusion Wavelets\" [https://arxiv.org/pdf/1710.10321.pdf]. GraphWave embeds the structural features of a node in a dense embeddings. We will demonstrate the use of GraphWave on a barbell graph demonstrating that structurally equivalent nodes have similar embeddings."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we load the required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "nbsphinx": "hidden",
    "tags": [
     "CloudRunner"
    ]
   },
   "outputs": [],
   "source": [
    "# install StellarGraph if running on Google Colab\n",
    "import sys\n",
    "if 'google.colab' in sys.modules:\n",
    "  %pip install -q stellargraph[demos]==1.2.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "nbsphinx": "hidden",
    "tags": [
     "VersionCheck"
    ]
   },
   "outputs": [],
   "source": [
    "# verify that we're using the correct version of StellarGraph for this notebook\n",
    "import stellargraph as sg\n",
    "\n",
    "try:\n",
    "    sg.utils.validate_notebook_version(\"1.2.1\")\n",
    "except AttributeError:\n",
    "    raise ValueError(\n",
    "        f\"This notebook requires StellarGraph version 1.2.1, but a different version {sg.__version__} is installed.  Please see <https://github.com/stellargraph/stellargraph/issues/1172>.\"\n",
    "    ) from None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import networkx as nx\n",
    "from stellargraph.mapper import GraphWaveGenerator\n",
    "from stellargraph import StellarGraph\n",
    "from sklearn.decomposition import PCA\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from scipy.sparse.linalg import eigs\n",
    "import tensorflow as tf\n",
    "from tensorflow.keras import backend as K"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Graph construction\n",
    "\n",
    "Next, we construct the barbell graph, shown below. It consists of 2 fully connected graphs (at the 'ends' of the graph) connected by a chain of nodes. All nodes in the fully connected ends are structurally equivalent, as are the opposite nodes in the chain. A good structural embedding algorithm should embed equivalent nodes close together in the embedding space."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "m1 = 9\n",
    "m2 = 11\n",
    "gnx = nx.barbell_graph(m1=m1, m2=m2)\n",
    "\n",
    "classes = [0,] * len(gnx.nodes)\n",
    "# number of nodes with a non-zero class (the path, plus the nodes it connects to on either end)\n",
    "nonzero = m2 + 2\n",
    "# count up to the halfway point (rounded up)\n",
    "first = range(1, (nonzero + 1) // 2 + 1)\n",
    "# and down for the rest\n",
    "second = reversed(range(1, nonzero - len(first) + 1))\n",
    "classes[m1 - 1 : (m1 + m2) + 1] = list(first) + list(second)\n",
    "\n",
    "nx.draw(gnx, node_color=classes, cmap=\"jet\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GraphWave embedding calculation\n",
    "\n",
    "Now, we're ready to calculate the GraphWave embeddings. We need to specify some information about the approximation to use: \n",
    "\n",
    "- an iterable of wavelet `scales` to use. This is a graph and task dependent hyperparameter. Larger scales extract larger scale features and smaller scales extract more local structural features. Experiment with different values. \n",
    "- the `sample_points` at which to sample the characteristic function. This should be of the form `sample_points=np.linspace(0, max_val, number_of_samples)`. The best value depends on the graph.\n",
    "- the `degree` of Chebyshev poly\n",
    "\n",
    "The dimension of the embeddings are `2 * len(scales) * len(sample_points)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "G = StellarGraph.from_networkx(gnx)\n",
    "sample_points = np.linspace(0, 100, 50).astype(np.float32)\n",
    "degree = 20\n",
    "scales = [5, 10]\n",
    "\n",
    "generator = GraphWaveGenerator(G, scales=scales, degree=degree)\n",
    "\n",
    "embeddings_dataset = generator.flow(\n",
    "    node_ids=G.nodes(), sample_points=sample_points, batch_size=1, repeat=False\n",
    ")\n",
    "\n",
    "embeddings = [x.numpy() for x in embeddings_dataset]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualisation\n",
    "\n",
    "The nodes are coloured by their structural role, e.g. in the fully connected sections, first node in the chain, second node in the chain etc. We can see that all nodes of the same colour completely overlap in this visualisation, indicating that structurally equivalent nodes are very close in the embedding space.\n",
    "\n",
    "The plot here doesn't exactly match the one in the paper, which we think is because the details of approximating the wavelet diffusion differ, the paper uses `pygsp` to calculate the Chebyshev coefficient while `StellarGraph` uses `numpy` to calculate the coefficients. Some brief experiments have shown that the `numpy` Chebyshev coefficients are more accurate than the `pygsp` coefficients."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "trans_emb = PCA(n_components=2).fit_transform(np.vstack(embeddings))\n",
    "\n",
    "plt.scatter(\n",
    "    trans_emb[:, 0], trans_emb[:, 1], c=classes, cmap=\"jet\", alpha=0.7,\n",
    ")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "nbsphinx": "hidden",
    "tags": [
     "CloudRunner"
    ]
   },
   "source": [
    "<table><tr><td>Run the latest release of this notebook:</td><td><a href=\"https://mybinder.org/v2/gh/stellargraph/stellargraph/master?urlpath=lab/tree/demos/embeddings/graphwave-embeddings.ipynb\" alt=\"Open In Binder\" target=\"_parent\"><img src=\"https://mybinder.org/badge_logo.svg\"/></a></td><td><a href=\"https://colab.research.google.com/github/stellargraph/stellargraph/blob/master/demos/embeddings/graphwave-embeddings.ipynb\" alt=\"Open In Colab\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\"/></a></td></tr></table>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}