docs/tutorials/clustering/louvain.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Louvain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "This notebook illustrates the clustering of a graph by the [Louvain algorithm](https://scikit-network.readthedocs.io/en/latest/reference/clustering.html#module-sknetwork.clustering)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "from IPython.display import SVG"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-25T09:04:07.335572Z",
     "start_time": "2019-11-25T09:04:07.330695Z"
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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     "end_time": "2019-11-25T09:03:43.045120Z",
     "start_time": "2019-11-25T09:03:43.041227Z"
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   "outputs": [],
   "source": [
    "from sknetwork.data import karate_club, painters, movie_actor\n",
    "from sknetwork.clustering import Louvain, get_modularity\n",
    "from sknetwork.linalg import normalize\n",
    "from sknetwork.utils import get_membership\n",
    "from sknetwork.visualization import visualize_graph, visualize_bigraph"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "graph = karate_club(metadata=True)\n",
    "adjacency = graph.adjacency\n",
    "position = graph.position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-11-25T09:03:44.149657Z",
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
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    "scrolled": true
   },
   "outputs": [],
   "source": [
    "louvain = Louvain()\n",
    "labels = louvain.fit_predict(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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    "pycharm": {
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   },
   "outputs": [],
   "source": [
    "labels_unique, counts = np.unique(labels, return_counts=True)\n",
    "print(labels_unique, counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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     "end_time": "2019-11-25T09:03:45.166971Z",
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
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   },
   "outputs": [],
   "source": [
    "image = visualize_graph(adjacency, position, labels=labels)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:37:17.935102Z",
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   },
   "outputs": [],
   "source": [
    "# metric\n",
    "get_modularity(adjacency, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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   "outputs": [],
   "source": [
    "# aggregate graph (one node per cluster)\n",
    "adjacency_aggregate = louvain.aggregate_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
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   "outputs": [],
   "source": [
    "average = normalize(get_membership(labels).T)\n",
    "position_aggregate = average.dot(position)\n",
    "labels_unique, counts = np.unique(labels, return_counts=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_graph(adjacency_aggregate, position_aggregate, counts, labels=labels_unique,\n",
    "                  display_node_weight=True, node_weights=counts)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# probability distribution over clusters\n",
    "probs = louvain.predict_proba()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# scores for cluster 1\n",
    "scores = probs[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_graph(adjacency, position, scores=scores)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Directed graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:37:49.296788Z",
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "graph = painters(metadata=True)\n",
    "adjacency = graph.adjacency\n",
    "names = graph.names\n",
    "position = graph.position"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:37:50.496413Z",
     "start_time": "2019-10-30T14:37:50.486975Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# clustering\n",
    "louvain = Louvain()\n",
    "labels = louvain.fit_predict(adjacency)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:38:09.086642Z",
     "start_time": "2019-10-30T14:38:09.080982Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "labels_unique, counts = np.unique(labels, return_counts=True)\n",
    "print(labels_unique, counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:38:10.029486Z",
     "start_time": "2019-10-30T14:38:10.025845Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_graph(adjacency, position, names=names, labels=labels)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:38:13.415879Z",
     "start_time": "2019-10-30T14:38:13.406435Z"
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
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   },
   "outputs": [],
   "source": [
    "get_modularity(adjacency, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# aggregate graph\n",
    "adjacency_aggregate = louvain.aggregate_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "average = normalize(get_membership(labels).T)\n",
    "position_aggregate = average.dot(position)\n",
    "labels_unique, counts = np.unique(labels, return_counts=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_graph(adjacency_aggregate, position_aggregate, counts, labels=labels_unique,\n",
    "                    display_node_weight=True, node_weights=counts)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# probability distribution over clusters\n",
    "probs = louvain.predict_proba()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# scores for cluster 1\n",
    "scores = probs[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_graph(adjacency, position, scores=scores)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Bipartite graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:38:14.429988Z",
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
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   },
   "outputs": [],
   "source": [
    "graph = movie_actor(metadata=True)\n",
    "biadjacency = graph.biadjacency\n",
    "names_row = graph.names_row\n",
    "names_col = graph.names_col"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:38:34.386474Z",
     "start_time": "2019-10-30T14:38:34.372114Z"
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    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# clustering\n",
    "louvain = Louvain()\n",
    "louvain.fit(biadjacency)\n",
    "labels_row = louvain.labels_row_\n",
    "labels_col = louvain.labels_col_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_bigraph(biadjacency, names_row, names_col, labels_row, labels_col)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2019-10-30T14:46:02.572278Z",
     "start_time": "2019-10-30T14:46:02.558375Z"
    },
    "pycharm": {
     "is_executing": false,
     "name": "#%%\n"
    },
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# metric\n",
    "get_modularity(biadjacency, labels_row, labels_col)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# aggregate graph\n",
    "biadjacency_aggregate = louvain.aggregate_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "labels_unique_row, counts_row = np.unique(labels_row, return_counts=True)\n",
    "labels_unique_col, counts_col = np.unique(labels_col, return_counts=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_bigraph(biadjacency_aggregate, counts_row, counts_col, labels_unique_row, labels_unique_col,\n",
    "                    display_node_weight=True, node_weights_row=counts_row, node_weights_col=counts_col)\n",
    "SVG(image)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# probability distribution over clusters\n",
    "probs_row = louvain.predict_proba()\n",
    "probs_col = louvain.predict_proba(columns=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# soft clustering\n",
    "scores_row = probs_row[:,1]\n",
    "scores_col = probs_col[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "image = visualize_bigraph(biadjacency, names_row, names_col, scores_row=scores_row, scores_col=scores_col)\n",
    "SVG(image)\n"
   ]
  }
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