example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The autoreload extension is already loaded. To reload it, use:\n",
      "  %reload_ext autoreload\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2\n",
    "\n",
    "from tqdm import tqdm_notebook\n",
    "\n",
    "from mhrw import MHRWSampler\n",
    "from mhrw.utils import start_session"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def degree_cdf(graph_neigh, k_range):\n",
    "    degree_dist = np.zeros_like(k_range)\n",
    "    count = graph_neigh.count()\n",
    "    \n",
    "    for i, k in enumerate(tqdm_notebook(k_range)):\n",
    "        degree_k = graph_neigh.filter(f\"degree <= {k}\").count()\n",
    "        degree_dist[i] = degree_k\n",
    "    \n",
    "    return degree_dist / count\n",
    "\n",
    "def process_fb(path, save_path=None, to_undirected=False, compression=\"UNCOMPRESSED\"):\n",
    "    get_edges = lambda row: row.split()[:2]\n",
    "    head = lambda itr, i: [next(itr) for _ in range(i)]\n",
    "    \n",
    "    with open(path, \"r\") as file:\n",
    "        edge_list = map(get_edges, file)\n",
    "        header = head(edge_list, 2)\n",
    "\n",
    "        df = pd.DataFrame(edge_list, columns=[\"user\", \"item\"]).drop_duplicates()\n",
    "        df = df.astype({\"user\": \"int64\", \"item\": \"int64\"})\n",
    "        \n",
    "        if to_undirected:\n",
    "            df_inv = df.rename(columns={\"user\": \"item\", \"item\": \"user\"})\n",
    "            df = df.append(df_inv)\n",
    "        \n",
    "        if save_path:\n",
    "            df.to_parquet(\"data/fb_edge_list\", index=False, compression=compression)\n",
    "    \n",
    "    return df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Network data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Facebook friendship graph](http://networkrepository.com/fb-wosn-friends.php) where nodes are users and edges between the users represent friendship relations/edges. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 4.93 s, sys: 557 ms, total: 5.49 s\n",
      "Wall time: 7.24 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "df = process_fb(\"data/fb-wosn-friends.edges\", \"data/fb_edge_list\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "spark, sc = start_session(\"test_sample\")\n",
    "\n",
    "import pyspark.sql.functions as F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph = spark.read.parquet(\"data/fb_edge_list\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampler = MHRWSampler(spark, ids_path=\"tmp\",seed_ratio=0.08, method=\"RCMH\", alpha=0.3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "INFO - 2019-09-16 22:27:11: sampled 3565 seed nodes, budget: 4509\n",
      "INFO - 2019-09-16 22:27:29: iteration 1, sampled 6027 nodes, progress: 133.67%\n",
      "INFO - 2019-09-16 22:27:29: the budget has been spent! stop sampling\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<mhrw.mhrw_sampler.MHRWSampler at 0x10dba9f28>"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampler.fit(graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "sampled_graph = sampler.transform(graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "full graph: 817090 edges\n",
      "sampled graph: 15808 edges\n"
     ]
    }
   ],
   "source": [
    "print(f\"full graph: {graph.count()} edges\")\n",
    "print(f\"sampled graph: {sampled_graph.count()} edges\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Node Degree Distribution "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_neigs(df):\n",
    "    return (df\n",
    "            .groupBy(\"user\")\n",
    "            .agg(F.collect_list(\"item\").alias(\"neigh\"))\n",
    "            .withColumn(\"degree\", arr_len(\"neigh\")))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mhrw.utils import arr_len\n",
    "from mhrw.utils import graph_filter_ids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "k_range = np.arange(1, 80, 2.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "graph_neig = get_neigs(graph)\n",
    "graph_random = graph_neig.sample(False, 0.1, seed=42)\n",
    "graph_mhrw = get_neigs(sampled_graph)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "500708aa2d4b45789fcb224a0d2e330c",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=32), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c310c4cdd8fc4c368c409bac8bf862a6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=32), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3dfe1f1aa4af48e5bf822ad897cba233",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(IntProgress(value=0, max=32), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "base_ndd = degree_cdf(graph_neig, k_range)\n",
    "random_ndd = degree_cdf(graph_random, k_range)\n",
    "mhrw_ndd = degree_cdf(graph_mhrw, k_range)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(12, 8))\n",
    "plt.plot(k_range, base_ndd, marker='o', color=\"red\", label=\"base\");\n",
    "plt.plot(k_range, random_ndd, marker='o', color=\"green\", label=\"random\");\n",
    "plt.plot(k_range, mhrw_ndd, marker='o', color=\"blue\", label=\"mhrw\");\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tmp'"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sampler.clear_ids()"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}