distributions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Explorations of Goodreads User-Book Interactions\n",
    "\n",
    "**Run this notebook only when you have LARGE memory (recommend 32g+)!**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import gzip\n",
    "import json\n",
    "import os\n",
    "import sys\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "pd.options.display.float_format = '{:,}'.format\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and process the dataset\n",
    "\n",
    "**Specify your directory here:**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "DIR = './'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Load the huge '.csv' file**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "PATH_IN = os.path.join(DIR, 'goodreads_interactions.csv')\n",
    "df_interactions = pd.read_csv(PATH_IN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Take a look of the first 5 lines;**\n",
    "\n",
    "**Check if there're any duplicated (user_id, book_id) pairs in the file.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== first 5 records ===\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>book_id</th>\n",
       "      <th>is_read</th>\n",
       "      <th>rating</th>\n",
       "      <th>is_reviewed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>948</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>947</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>946</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>945</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>944</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   user_id  book_id  is_read  rating  is_reviewed\n",
       "0        0      948        1       5            0\n",
       "1        0      947        1       5            1\n",
       "2        0      946        1       5            0\n",
       "3        0      945        1       5            0\n",
       "4        0      944        1       5            0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "=== duplicated records ===\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>user_id</th>\n",
       "      <th>book_id</th>\n",
       "      <th>is_read</th>\n",
       "      <th>rating</th>\n",
       "      <th>is_reviewed</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [user_id, book_id, is_read, rating, is_reviewed]\n",
       "Index: []"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ideally you will not see any rows displayed above, then we are good now, no duplicates.\n"
     ]
    }
   ],
   "source": [
    "print('=== first 5 records ===')\n",
    "display(df_interactions.head())\n",
    "print('=== duplicated records ===')\n",
    "display(df_interactions[df_interactions.duplicated(['user_id', 'book_id'], keep=False)])\n",
    "print('ideally you will not see any rows displayed above, then we are good now, no duplicates.')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Display basic statistics\n",
    "\n",
    "'# shelved': the total number of records in this file\n",
    "\n",
    "'# read': the number of records where users read the books\n",
    "\n",
    "'# rated': the number of records where users provided rating scores for the books\n",
    "\n",
    "'# reviewed': the number of records where the book review texts are not empty"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th># shelve</th>\n",
       "      <td>228,648,342.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th># read</th>\n",
       "      <td>112,131,203.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th># rate</th>\n",
       "      <td>104,551,549.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th># review</th>\n",
       "      <td>16,219,149.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 count\n",
       "# shelve 228,648,342.0\n",
       "# read   112,131,203.0\n",
       "# rate   104,551,549.0\n",
       "# review  16,219,149.0"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_stats = pd.DataFrame([df_interactions.shape[0],\n",
    "                         df_interactions['is_read'].sum(),\n",
    "                         (df_interactions['rating']>0).sum(),\n",
    "                         df_interactions['is_reviewed'].sum()], dtype = float, \n",
    "                        columns = ['count'],\n",
    "                        index = ['# shelve', '# read', '# rate', '# review'])\n",
    "display(df_stats)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "display rating distribution ('0' indicates rating score is not provided)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0   124,096,793.0\n",
       "4    37,497,451.0\n",
       "5    35,506,166.0\n",
       "3    23,307,457.0\n",
       "2     6,189,946.0\n",
       "1     2,050,529.0\n",
       "Name: rating, dtype: float64"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_rating_count = df_interactions['rating'].value_counts().astype(float)\n",
    "display(df_rating_count)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualize user/item distributions\n",
    "\n",
    "**1) count the number of interactions for each user/item**\n",
    "\n",
    "**2) count the frequency of these numbers (i.e., ranks)**\n",
    "\n",
    "**3) visulize for each type of interaction (log-log plots)**\n",
    "\n",
    "we'll see distributions are long-tailed, approximately follow power-law (zipf's law)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "shelve_user = df_interactions['user_id'].value_counts().value_counts().reset_index().sort_values('index').values\n",
    "read_user = df_interactions['user_id'].loc[df_interactions['is_read']>0].value_counts().value_counts().reset_index().sort_values('index').values\n",
    "rate_user = df_interactions['user_id'].loc[df_interactions['rating']>0].value_counts().value_counts().reset_index().sort_values('index').values\n",
    "review_user = df_interactions['user_id'].loc[df_interactions['is_reviewed']>0].value_counts().value_counts().reset_index().sort_values('index').values\n",
    "\n",
    "shelve_book = df_interactions['book_id'].value_counts().value_counts().reset_index().sort_values('index').values\n",
    "read_book = df_interactions['book_id'].loc[df_interactions['is_read']>0].value_counts().value_counts().reset_index().sort_values('index').values\n",
    "rate_book = df_interactions['book_id'].loc[df_interactions['rating']>0].value_counts().value_counts().reset_index().sort_values('index').values\n",
    "review_book = df_interactions['book_id'].loc[df_interactions['is_reviewed']>0].value_counts().value_counts().reset_index().sort_values('index').values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f5ae0e5f9e8>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Rphv3i144xOi/fqGaWwCf7PmEmAQ9lJ6WNzIbpq5Zs2bs3buXr776Kl3zHaBF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\nkZBUQEVEQlIBFREJSQVURCSk/wMuxrW6b5Xu3wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5ae0da2320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "plt.loglog(shelve_user[:,0], shelve_user[:,1], label='shelve')\n",
    "plt.loglog(read_user[:,0], read_user[:,1], label='read')\n",
    "plt.loglog(rate_user[:,0], rate_user[:,1], label='rate')\n",
    "plt.loglog(review_user[:,0], review_user[:,1], label='review')\n",
    "plt.xlabel('rank')\n",
    "plt.ylabel('frequency')\n",
    "plt.title('Log-Log Plot of the Distribution of Users')\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f5addb3e0f0>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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v+jloBYQezs5SoRvOztVqoMnC3noTo58fZ4YNQyUmptlWPjiErzvPI0k8eU/2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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5addc0d080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "plt.loglog(shelve_book[:,0], shelve_book[:,1], label='shelve')\n",
    "plt.loglog(read_book[:,0], read_book[:,1], label='read')\n",
    "plt.loglog(rate_book[:,0], rate_book[:,1], label='rate')\n",
    "plt.loglog(review_book[:,0], review_book[:,1], label='review')\n",
    "plt.xlabel('rank')\n",
    "plt.ylabel('frequency')\n",
    "plt.title('Log-Log Plot of the Distribution of Books')\n",
    "plt.legend(loc='upper right')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}