01_Exploratory-Analysis-on-100K-data.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MovieLens Project Part 1: Exploratory Data Analysis on 100K Dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As part of a project sponsored by the data science team at [Air Liquide](https://www.airliquide.com/) here in Philadelphia, I'm diving deep into collaborative filtering algorithms. There are 2 main goals of this project:\n",
    "\n",
    "1. Gain understanding of a variety of collaborative filtering algorithms by implementing them myself\n",
    "2. Compare quality and speed of a variety of algorithms as a function of dataset size\n",
    "\n",
    "The data I'm using comes from the [GroupLens](https://grouplens.org/) research group, who has been collecting movie ratings from volunteers since 1995 and has curated datasets of a variety of sizes. For the initial development phase of the project, I'll focus on the 100K dataset, the smallest one, to enable faster iteration. I'll scale up to larger datasets later on.\n",
    "\n",
    "Before getting into any algorithm development, I want to get a picture of the data I'm working with, so I'll ask the questions on my mind and try to answer them with the data.\n",
    "\n",
    "## Get the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n",
      "                                 Dload  Upload   Total   Spent    Left  Speed\n",
      "100 4808k  100 4808k    0     0  1783k      0  0:00:02  0:00:02 --:--:-- 1783k\n",
      "Archive:  ml-100k.zip\n",
      "  inflating: raw/ml-100k/allbut.pl   \n",
      "  inflating: raw/ml-100k/mku.sh      \n",
      "  inflating: raw/ml-100k/README      \n",
      "  inflating: raw/ml-100k/u.data      \n",
      "  inflating: raw/ml-100k/u.genre     \n",
      "  inflating: raw/ml-100k/u.info      \n",
      "  inflating: raw/ml-100k/u.item      \n",
      "  inflating: raw/ml-100k/u.occupation  \n",
      "  inflating: raw/ml-100k/u.user      \n",
      "  inflating: raw/ml-100k/u1.base     \n",
      "  inflating: raw/ml-100k/u1.test     \n",
      "  inflating: raw/ml-100k/u2.base     \n",
      "  inflating: raw/ml-100k/u2.test     \n",
      "  inflating: raw/ml-100k/u3.base     \n",
      "  inflating: raw/ml-100k/u3.test     \n",
      "  inflating: raw/ml-100k/u4.base     \n",
      "  inflating: raw/ml-100k/u4.test     \n",
      "  inflating: raw/ml-100k/u5.base     \n",
      "  inflating: raw/ml-100k/u5.test     \n",
      "  inflating: raw/ml-100k/ua.base     \n",
      "  inflating: raw/ml-100k/ua.test     \n",
      "  inflating: raw/ml-100k/ub.base     \n",
      "  inflating: raw/ml-100k/ub.test     \n"
     ]
    }
   ],
   "source": [
    "!mkdir -p raw\n",
    "!curl -O http://files.grouplens.org/datasets/movielens/ml-100k.zip\n",
    "!unzip -o ml-100k.zip -d raw/\n",
    "!rm ml-100k.zip"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# <!-- collapse=True -->\n",
    "%matplotlib inline\n",
    "from datetime import datetime\n",
    "from IPython.display import Markdown\n",
    "from os.path import join\n",
    "from os.path import exists\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "# Use modified seaborn-darkgrid style with bigger text\n",
    "plt.style.use('big-darkgrid.mplstyle')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's load and examine the ratings data. I sort the data by `timestamp` and break the `timestamp` column out into `year` and `month` and display the first 5 and last 5 ratings in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "First 5:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userId</th>\n",
       "      <th>movieId</th>\n",
       "      <th>rating</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>214</th>\n",
       "      <td>259</td>\n",
       "      <td>255</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:05:10</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83965</th>\n",
       "      <td>259</td>\n",
       "      <td>286</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:05:27</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43027</th>\n",
       "      <td>259</td>\n",
       "      <td>298</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:05:54</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21396</th>\n",
       "      <td>259</td>\n",
       "      <td>185</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:06:21</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82655</th>\n",
       "      <td>259</td>\n",
       "      <td>173</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:07:23</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       userId  movieId  rating           timestamp  year  month\n",
       "214       259      255       4 1997-09-19 23:05:10  1997      9\n",
       "83965     259      286       4 1997-09-19 23:05:27  1997      9\n",
       "43027     259      298       4 1997-09-19 23:05:54  1997      9\n",
       "21396     259      185       4 1997-09-19 23:06:21  1997      9\n",
       "82655     259      173       4 1997-09-19 23:07:23  1997      9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Last 5:\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userId</th>\n",
       "      <th>movieId</th>\n",
       "      <th>rating</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>46773</th>\n",
       "      <td>729</td>\n",
       "      <td>689</td>\n",
       "      <td>4</td>\n",
       "      <td>1998-04-22 19:10:38</td>\n",
       "      <td>1998</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73008</th>\n",
       "      <td>729</td>\n",
       "      <td>313</td>\n",
       "      <td>3</td>\n",
       "      <td>1998-04-22 19:10:38</td>\n",
       "      <td>1998</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46574</th>\n",
       "      <td>729</td>\n",
       "      <td>328</td>\n",
       "      <td>3</td>\n",
       "      <td>1998-04-22 19:10:38</td>\n",
       "      <td>1998</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64312</th>\n",
       "      <td>729</td>\n",
       "      <td>748</td>\n",
       "      <td>4</td>\n",
       "      <td>1998-04-22 19:10:38</td>\n",
       "      <td>1998</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>79208</th>\n",
       "      <td>729</td>\n",
       "      <td>272</td>\n",
       "      <td>4</td>\n",
       "      <td>1998-04-22 19:10:38</td>\n",
       "      <td>1998</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       userId  movieId  rating           timestamp  year  month\n",
       "46773     729      689       4 1998-04-22 19:10:38  1998      4\n",
       "73008     729      313       3 1998-04-22 19:10:38  1998      4\n",
       "46574     729      328       3 1998-04-22 19:10:38  1998      4\n",
       "64312     729      748       4 1998-04-22 19:10:38  1998      4\n",
       "79208     729      272       4 1998-04-22 19:10:38  1998      4"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# <!-- collapse=True -->\n",
    "ratings_df = pd.read_csv('raw/ml-100k/u.data', sep='\\t', header=None, \n",
    "                         names=['userId', 'movieId', 'rating', 'timestamp'])\n",
    "ratings_df['timestamp'] = ratings_df['timestamp'].apply(datetime.fromtimestamp)\n",
    "ratings_df['year'] = ratings_df['timestamp'].dt.year\n",
    "ratings_df['month'] = ratings_df['timestamp'].dt.month\n",
    "ratings_df = ratings_df.sort_values('timestamp')\n",
    "print('First 5:')\n",
    "display(ratings_df.head())\n",
    "print()\n",
    "print('Last 5:')\n",
    "display(ratings_df.tail())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from these rows that this part of the dataset is user-movie-rating triplets at different points in time. Let's ask some questions about the data to get a feel for what we're working with:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. How are the ratings distributed?\n",
    "\n",
    "I'd like to see what ratings are common and uncommon, so let's just plot counts of each rating:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYcAAAEoCAYAAACzVD1FAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4yLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvhp/UCwAAIABJREFUeJzt3XeYXGXZx/HvQkggJFRBIqih/iQUQw8tgCAI0rugiKAC6gsINl6pIqAg5UVQiiIgVUSKCAIRggSpEene0kINRTBAKAEk7x/PM8kwZyabzM7umez8Pte119k59Z6Z3XOfp53TNXXqVMzMzKrNUXYAZmbWfpwczMyswMnBzMwKnBzMzKzAycHMzAqcHMzMrGBA2QFYa0gaDjw5g1WmAu8ALwB3AydExD0tjmH5iHikZl6lr/RKEfFgK4/XU5ImAJ+cydWviohtey8aA5A0FtgA+J+IOK3kcDqak0P/dA8wpWZeF/ARYBlgSWBHSbtFxKU9PZikxYD/A5YC1ujp/krwKPBSN+s83BeBmLULJ4f+aaeImFBvgaQlgUtJJ/FfS7ohIv7Tw+N9DtgZGF9n2fJ5+kQPj9Gbjo2Ic8sOwgDYAxhMKuFaiZwcOkxEPClpF+BfwLzArsAve/F4/+ytfVv/ExFPlx2DJW6Q7kAR8SQQ+eXyM1rXzDqTSw6dq9JQ3FW7IFc9HQBsTGqwnRt4BbgDODUibq5adwLTG3VXyw3QT0XE8Ly80CAt6Vzgy8BOpPr+w4HRwFDgceBC4MSIqG03QdJqwCHA2sCCwD+BnwM3kxrkpx27t1Q1mq4L7A58KS+6C9g0Ij7I640Gvg2sAyxAate4ATguIh5rsO9Vge8D6wPzAw8Ax5GS+SPA+IhYvWr9hg3+koYAb+SXS9ZWNUr6NPA9YENSe9R/gFuA4yNifM26w0mf70PASOAgUhXQ0sBbwK3Aj+t1cpDUBewG7A2smN/XU8AVpCq916rWHUuDBun8d/kDYFPgY/m93QGcHBF/qXPcgcC3gB2AZUl/X88DN5H+vlyqnQGXHDqQJAEr5Jd31yzblHQCOAD4OOlk/TiwELAt8BdJX6ja5G7SCR5gMnBb7T5n4DOkE+pWpDrmF4ERwDHA7+rEvQtwO+mffWCOcxngHFKDeF87EfgG6UT3BjCxKjEcSjrRbkv6P3sAGALsBdwnafPanUnagfT+dia9v4dJ39OVwNdbGbikPUkdF3YjVS8+SLpQ2Bm4U9LeDTYdAFwD/JSUUB7J228DjJM0quY4A0lJ4AJgI9Ln9AjpguJ7eZv5ZiLezUif4deBRUnf/dvA54Exko6oWb8rH/dEYE3g3/m4iwJfBcZLWqu743YyJ4cOI2kkcDnpRPAkVSdhSYOA3wDzACcDH42IVSJieeATwJi83WGVbSJiJ+DY6S9jvTxvZuwH3Ah8PCJWiohPkpISwNaSpvV8kvTxHNtcwNHAsIhYAxiW5289859Cy4wCto+IlUiJ9IAc6/Y5xteBXSNikXy1vyjpsxsMXCLpE5UdSRpGSnIDSZ995f0tDvyBVAJpCUlrAmfnl98CFoqI1YDFgK8BHwBnSFq93ubAevl9LRYRq5J6vz0MDKLqbyP7X1LieAkYHRFLR8RIYDlSQlqRdAKfUbzDSX+n85I+1wUjYtWI+Hje9+vAkZKquxpvkX/+RSo1jcixfoyUbAcz/e/W6nBy6J8ukzSu5uduSc8B95KuRh8HPh8R71Rttxrp6vY54LvV1ToR8SJwVH4pSa3423mV1LPqxarjnJpjg1R1VPEdUtK6IiIOj4j38/pvkq4EZ7a0Us9vJE2dwc+BDba7PSKuyHF8EBGv5vlH5+mB1V2FI+K9iPgx6UQ3Hx8+4e+b5/0tIg6KiPfyNq+Tru7/1YP3V+sIUgng2Ig4vVLaiYipEfErUnIaAPywwfZH17yviaSqL6j6zvLFxkH55Z4RcWvVNk8BX8kvd87rNvJd0mdzfv7u363az9WkqqbK+6pYKU+vi4hnq9Z/g/S530gqfVgDTg790+qk+vDqn9VJ1QCXk6o2VqgdsBYRf4uI+YFlI+K/dfb7Vp7OQWqH6KmxEfF2nfmVxvLq6oat8vSswsrp5HZGD+J4lFQd1ujnuQbb3V47Q9LSpKqxD0hdhuu5OE+rq5a2yNPzalfOSbrwvpshaW5gk5o4GsX3WUn12iWvrTOv3ndWaUeaCPy5sEFqn1gVWKJe+1KVynffKN5LSG1oI3MJDKZfYOwl6auSFqo67oSI2DQi9p/BMTueG6T7p2mNj/mK7LPAKaTGwyHA1TP6Z4yIt3PD6Kp5m6VJV2KqWq0VFxaNTrqVhDEnTHsPS+Z59zfY5t4exNHsOIeJdeaNyNMPgBtS807B4DxdVlJXRExl+vtrdDXbk5JRtWVJVVeQSkz1LgLmzNN5SdVaT9Usr/e9feg7y5bO04fyeyyIiBl+b5KGkqrsAI7NbTn1/Jd0PluO9L1cBdwJrEWqQjtT0t3A9cAfW313gP7IyaGfy0ngGkn3kk4wmwF/krRRvav23MPmJFIVU8VU0tX1hcAXWxjeu90sr/SkWrhq3psN1n2jwfze9E6deZUr5wGkEtuMzEG6sn6d1IMHUqN+Pa82mD+rqq/sRzVca7r568zr7nurqHxvjd7TzKiOd5WZWH9+gIh4V9JGwMGknnHLkBLFWsDhkh4C9omI23oQW7/m5NAhIuI5SXuQulKuRUoA+1WvI2nFvHwQqWvib0lX6o9ExOuSlqO1yWFmVSeEocBrddYZ2kexdKcS64O5oXpmvUY6mTZ6H/N0s32hSzLTSyjVKvFNjoje/swq1ZDz9mAf1d/9RyLilZndMF/8/Bj4cf7b3ZjUDfZzpHa36yUpIhqVYDua2xw6SESMYXovlX0lbVyzyv6kxPAXYKOIODsi7syNogBL9FGoH5L7wVf+gRudcFfso3C6U+nWu1Tuxlkg6aOS1pO0eNXsyhiFkQ32O6LB/Eq1UL0G3WF15j2etxkiqe73KWmopA0lDc9dQptVaURvFDuSrpJ0paS660TEJODl/LLugE1Jc0raRNIykipVkQtLWlfSInk//4qIX0bEdqRSxAukpOWbKTbg5NB5vsf0+9acXnMCG56n9zdokK7u+15d6vwgT3tyIunO1Xn6lQbL9+rFY8+Kh4EJpKv2PRqscxypZHZJ1byr8nTvygmuxp4N9lW5L1a9xo1C997cW2dcfrlvg31+mzSocCw9O0eMI5UeFpf0mdqFebzN1qSxCi/XLq9SaQBvFO/upN5H/yC1qUGqAh3Hh/9mgVSKJo15gA+3kVgVJ4cOk6/Cv5tfijQat6JypbeLpGUqMyUtKOlkUpfKiureSpU65WGNrpZb4GekRs+dJB1adYU4SNJJpFG+pcsNr5WurKdI2rWyTNIASd9leoKr7t//K1LD70jSDRHnzdvMJelEGr+/v+XpoZWeOpK68nEPabDN0aR2pB9I2r/qs+yS9EWg0uh7coOLhJmS/9Yqo5zPUxrdTj7WcKb3PvptRMwoORxPat/ZXdIxucdVZT+bVh3j7KrR1hfl6Q/zOlRtsxNpBPoHpGpUq8PJoQNFxAWk0bsA/5u7X0Jqh5hEGij0iKQHJN1P6v1xIHAf6TYa5HUqHiSdbIYBj0oaR4tFxBOk0bEfkE5uEyXdRSoFfZs02hfg/VYfe1ZFxDmksQLzAhdLej73lHmBdKID+FFEXFm1zRvAdqSRvF8Gns/vbyJprMB9DQ53DOnE+SngCUl/B54hnXivI40qro3vL3mfc5BGlr+Yj/U8qZ1pLuB84NRmP4Mqh5Gu/JcA7pH0iKQHSBciqwB/Z/pYiLoi4mFSKWwKaVDdS3nczgRS76OhpAGa1Rc6vyV12x5Calt4pmqsz+9IJd9DfQuNxpwcOtc3gfdIJYDTYdoJeCSpr/3TpJLFJ0gnpoNIDdk35u0rfc+JiH+RBqI9Thplu7Skj7Y64JzURpNONgNI7Q+Pk6oVTsqr1Rs30eci4iBSz7CrSVUXI0nVbtcD20TEEXW2uRf4NGlMw2RgZeBZUrI4pcFx7iL1Orqc1Hi7PKln0wGke1d90GC7U/J2l5BOuiNJVWF/JVVh7dmo++msyAPWtib9ffyN1DV2OVLbzGHAurldobv9XJZj/DXp/a1MGrdzN+nCZYuawXFTgS+QPoc7SL2eRpLOeVcAG0fEcVhDXVOn9vj7NyudpP2AXwBjIuKzZcfTakr3QvoNNTfeM+stLjnYbEHSuZL+LmmrBqt8Lk97MhjOzDInB5tdPEiqo/5JbswE0l0/JX2fVHXxLunq2sx6yIPgbHbxS9JzE1YGHpP0KKmb5FKkZyW8B+xbe78oM2uOSw42W8h3Xx1Faki/m/R8iRVIvavOA0ZFhEsNZi3iBmkzMyvoF9VKL7/8hjOcmdksWmSRoQ3vauBqJTMzK3ByMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK3ByMDOzAicHMzMr6BcjpM2seQ/vsGXZIbTciMuvKTuE2Z5LDmZmVuDkYGZmBU4OZmZW4ORgZmYFTg5mZlbg5GBmZgVODmZmVuDkYGZmBU4OZmZW4ORgZmYFTg5mZlbg5GBmZgVODmZmVuDkYGZmBU4OZmZW4ORgZmYFTg5mZlbg5GBmZgVODmZmVlD6M6QlfQo4DRgFvAKcFhEn5GWfBM4G1gWeBg6KiOvKitXMrFOUWnKQNBdwHenEPxL4JnCYpN0ldQFXkRLGGsB5wOWSliwrXjOzTlF2yWFx4C7gmxHxNvCYpDHABsBEQMD6EfEG8LCkTYC9gUPLCtjMrBOUmhwiYgKwC0AuKawDjCaVIEYB9+bEUDEOWL+PwzQz6zjt1CD9LOnkfzvwe2AY8HzNOi8CS/RxXGZmHaedksM2+WdV4GRgMDClZp0pwKA+jsvMrOOU3eYwTUTcAyBpMKnx+Rxg/prVBgFv1W47ZMggBgyYs9djNLPZwwILDC47hNleqclB0uLAahFxddXsh4GBpAbplWo2WSzP/5DJk2sLGGbWySZNKlxDWh2LLDK04bKyq5WWB/4gadGqeasBL5PaH0ZKmrdq2XrAHX0Yn5lZRyq7WukWUknhXEkHA0sDPwGOycueysuOBLYk9WDau5xQzcw6R6klh4h4j3TSfx+4EzgTOAU4NSL+S2qgXhQYD+wBbJe7v5qZWS8qu+RARDwNbN1g2WOkAXFmZtaHym5zMDOzNuTkYGZmBU4OZmZW4ORgZmYFTg5mZlbg5GBmZgVODmZmVuDkYGZmBU4OZmZW4ORgZmYFTg5mZlZQ+r2VzMqw7SWfKzuEXnHlrn8uOwTrJ1xyMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK3ByMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK3ByMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK3ByMDOzAicHMzMrcHIwM7MCJwczMytwcjAzswInBzMzK5jl5CBptKRPdLPOCElfbj4sMzMrUzMlh5uB7k78XwZOb2LfZmbWBgZ0t4KkHYF1qmZ1AZtLWrDBJgOBXYA3ex6emZmVodvkANwHXEA66QNMBUblnxn5YQ/iMjOzEnWbHCLiUUlrAguSSg03AecC59VZfSrwHvBcRDzdwjjNzKwPzUzJgYi4v/K7pKOAmyPir70WlZmZlWqmkkO1iDiqNwIxM7P2McvJAUDSusDXgOWAQaTqplpTI2K1HsRmZmYlmeXkIGl74Hd03w12alMRmZlZ6ZopORxCanTeC7g2Il5rbUhmZla2ZpLDisAFEXFxq4MxM7P20ExymIQHuJlZP3TpT8aWHULL7fKDDZvarpnbZ1wJbC1p7qaOaGZmba/ZNofVgZsl/Rx4FJhSb8Xq8RGNSFoaOAVYj1QiuRT4YUS8I+mTwNnAusDTwEERcV0TMZuZ2SxoJjm8SuqJ1AWs2c26c85ooaSBwB+Bh0n3b1oUOCcv+w5wFfAIsAawNXC5pBUi4skm4jYzs5nUTHI4n9Z1U10TWAZYMyImA49IOgw4CfgTIGD9iHgDeFjSJsDewKEtOr6ZmdXRzAjpPVt4/AC2yImhYippYN0o4N6cGCrGAeu38PhmZlZHj58EJ2mYpBXy77OUbCLi5YgYU7WvOYBvAbcCw4DnazZ5EViiZxGbmVl3mr19xjzAEcBXgI+QrvYHAAdL2gzYLyKiiV2fBKxCamM4iGJD9xRSqeJDhgwZxIABM2zeMOsICywwuOwQ2oI/h+ma/SyauX3GEGAssCrwDPAEsFRePBjYELhV0poRMWEm99lF6rH0DWDHiHhI0jvA/DWrDgLeqt1+8uS6naXMOs6kSYV/j47kz2G6GX0WiywytOGyZqqVDiUlhv2B4cCFlQURcQTpEaELAYfNzM5yVdI5wH7ALhFxVV70HLBYzeqLARObiNnMzGZBM8lhZ+DPEXFaREylpudSRPwWuAbYaCb3dyKwG7B9RPyhav4dwEhJ81bNWy/PNzOzXtRMm8PHgEu6WSeAzbrbkaRRwIGkgXX3SKouKdwCPAWcK+lIYEtSD6a9m4jZzMxmQTMlh5eB5btZZ8W8Xnd2zNPjSNVF1T9dwDakgXHjgT2A7Wa2HcPMzJrXTMnhj8DXJW1e71YWknYANgfO6m5HEfEd4DszWOUxYIMmYjQzsx5oJjkcBWwF/FHStcDCALnqZ3VSYngJOLpFMZqZWR+b5WqliHiRdB+k64HPA2uTqoAOB7YgDWAbHRHPtTBOMzPrQ00NgouIZ4DP5wbkVYEFgMnA/W4TMDOb/TWVHAAkjQSmRMS1VfMOkXRDRIxvSXRmZlaKWa5WkjRA0rmkHkQ7Vc2fG/gxcJekE1sWoZmZ9blmurLuT+pWegNwddX8KcBo0q22D5S0f8/DMzOzMjRTrbQXcHdEbF49M4+Wvk3SNqRSxb7AqT0P0czM+lozJYclSTfeqysnib8w/WZ8ZmY2m2kmObwKfKqbdYYDrzWxbzMzawPNJIfrSd1Yt6m3UNKmwLbAjT0JzMzMytNMm8PRwHbA5ZJuJN0l9XVgKOmZ0Jvl10e0KkgzM+tbzTxD+ilJGwC/ICWC2ruv3g7sExGPtyA+MzMrQTNPghscEQ8CoyUtDqwMLEgaIf1ARDzZ4hjNzKyPNVOtNF7S2IjYL98/yfdQMjPrZ5rtyvpGqwMxM7P20UxyuI90a24zM+unmqlWOgS4UNLtwJXABODteitGxNX15puZWXtrJjmMydOPkrqu1tMFTAXmbCYoMzMrVzPJ4UekE7+ZmfVTzYxzOLIX4jAzszbS9MN+ACQtD4wEFoqI0yV9Ang1Iia3JDozMytFM72VkDRC0h3Ag8AFTL8191eAZyXt0qL4zMysBM08CW5J4K/AKsBFwE1Vi5/M+7xQ0notidDMzPpcMyWHo4HBwNoR8SVgXGVBRJwPjALeInV5NTOz2VAzyeGzwO8i4u/1FkbEw8BlwKo9CczMzMrTTHKYD3ipm3UmAfM3sW8zM2sDzSSHJ4D1Gy2U1AVsmNczM7PZUDPJ4QJgLUnHSvrQCGhJg4CTSN1bL2lBfGZmVoJmxjn8DNgE+AGwL/m+SpLGAisACwN3Aie0JkQzM+trs1xyiIj3SE9/+z6p7WEY6V5Ko4E3SbfX2CgiprQwTjMz60NNjZCOiPeBEyRdROqVNIT0JLhbI2JSC+MzM7MSNJUcJK0E/B+wQc2i9yVdCRwcEc/2NDgzMytHM8+QHgHcAixAGgB3F/BCfr0OsBMwStKoiJjYwljNzKyPNFNyOAYYCuwQEVfULpS0A3Apqe3haz0Lz8zMytBMV9bRwOX1EgNARFwOXAVs2ZPAzMysPM0khzmA7toTniHdf8nMzGZDzSSHa4BdJC1Yb6GkoaRSw7U9CczMzMrTTJvDQcB1wHhJR5Nu3/0cMA+wBnAU6f5LZ0hauXrDiLi/Z+GamVlfaCY5vEh6hnQX8Ks6y7vy9KY6y+asM8/MzNpMM8nhfFJyMDOzfmqWk0NE7NkLcZiZWRtp6hnSZmbWvzk5mJlZgZODmZkVODmYmVlBU3dltdnT279cp+wQesU8+/2t7BDM+h2XHMzMrMDJwczMCpwczMysoG3aHCQNAsYDB0bEmDxvIeBM0jOrXwWOiIjzyovSzKwztEXJQdLcwMXACjWLzgUWBtYlPTzoTEn9s1XVzKyNlF5yyI8dvYjpN+yrzF8a2ApYNiIeAx7IieEbgLunmJn1onYoOawP3ACsXTN/LWBiTgwV4+qsZ2ZmLVZ6ySEizqz8Lql60TDg+ZrVXwSW6IOwzMw6WunJYQYGA1Nq5k0BBkrqiohptw0fMmQQAwb4URHdebvsAHrJAgv4ibQV/iwSfw7TNftZtHNyeAcYVDNvEPB2dWIAmDy5NodYJ5k06a2yQ2gb/iwSfw7TzeizWGSRoQ2XtUObQyPPAYvVzFsMmFhCLGZmHaWdk8MdwOKShlfNWy/PNzOzXtS21UoR8YSk64HzJX0LWA3YHdio3MjMzPq/tk0O2R7Ar4A7gReAr0bE7eWGZGbW/7VVcoiIrprXLwFblxSOmVnHauc2BzMzK4mTg5mZFTg5mJlZgZODmZkVODmYmVmBk4OZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVODmYmVmBk4OZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVtNXDfnrD546/ouwQesWfv7dd2SGYWT/mkoOZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVODmYmVmBk4OZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVODmYmVmBk4OZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVODmYmVmBk4OZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVODmYmVmBk4OZmRU4OZiZWYGTg5mZFTg5mJlZgZODmZkVODmYmVmBk4OZmRUMKDuA7kgaBPwc2AmYApwUEceXG5WZWf82O5QcTgDWATYB9gEOlbRruSGZmfVvbZ0cJM0LfA04MCLGR8RVwPHAt8qNzMysf2vr5AB8GhgEjKuaNw5YQ1LbV4mZmc2u2j05DANejYh3qua9CAwEFiknJDOz/q9r6tSpZcfQkKQvAT+JiMWr5i0FPA4sGRETyorNzKw/a/eSwzukaqVqlddv9XEsZmYdo92Tw3PAgpIGVs1bjNSl9dVyQjIz6//aPTn8A3iX1JW1Yj1gfES8X05IZmb9X1u3OQBIOgMYDexJKjX8Fvh6RFxaZly18mC98aRut2PKjqcMkpYGTiEl8DeBS4Ef1nQo6AiSPgWcBowCXgFOi4gTyo2qfJJ+BSwTERuWHUsZJO0GXFgz+6qI2LaMeGak3UsOAAcBdwM3AWcAP2rDxDA3cDGwQtmxlCVX/f2RVOW3DrA7sC1wTJlxlUHSXMB1wNPASOCbwGGSdi81sJJJ2hjYu+w4SjYCuILUE7Pys2eZATXS9mMFIuIt4Mv5p+1IGgFcBHSVHUvJ1gSWAdaMiMnAI5IOA04CDi41sr63OHAX8M2IeBt4TNIYYAOKV40dIQ9oPQu4rexYSjYCuD8iXig7kO60fXKYDawP3AAcSapK6VQBbJETQ8VUir3N+r3cxXoXAEldpJLUaFIJolMdA4wFJpKqHTvVCOCysoOYGU4OPRQRZ1Z+l1RmKKWKiJeBaW0tkuYg3ebk1tKCag/PAh8DrgF+X3IspZC0NunGmSvSeaXIaXLV69LAlpJ+RKrWvww4IiKmlBpcHbNDm4PNnk4CVgEOKTuQkm2Tf1YFTi45lj6XO2r8mtRR4z9lx1OyZUkX5G8COwLfJbXNnVRmUI245GAtlatRTgG+AewYEQ+VHFKpIuIeAEmDgfMkfSci3i05rL50OPBoRMwWVSm9KSIekvSRiHglz7ov/79cLOmAduue7+RgLZOrkn5NuhraJd9Ft+NIWhxYLSKurpr9MOmeYPMB/y4lsHLsBgyTVGmLGgjMKWlyRAwpMa5SVCWGikeAuUj3ipvY9xE15mola6UTSSeD7SPiD2UHU6LlgT9IWrRq3mrAyxHRSYkBYENSW8PI/HM2cE/+vaNI2l7SizV3fFgFmAS0Xe8llxysJSSNAg4ktTHcI2mxyrLZodtei91CKimcK+lgUiPkT+jAMR8R8VT1a0n/Ad6OiMdKCqlMt5C6vJ8l6VhSG8QJwAkR0XajkV1ysFbZMU+PIxWPp/102rM3IuI9YEvgfeBO4ExSO8ypZcZl5cpVSpsBnwT+Thr3cQbpf6bttP3tM8zMrO+55GBmZgVODmZmVuDkYGZmBU4OZmZW4ORgZmYFTg5mZlbg5GDWIpK+IGmpqtd7Spoq6cAy4zJrhpODWQtI+inpoU/zVc3+B3AUcEcpQZn1QEeNXDXrRR+tnRER/yAlCLPZjksOZmZW4NtnWMeTNBYYDuwH/BJYFLgmInaWtAewF/BpYF7gFeAm4LCIeCJvP4F0v5yKpyJiuKQ9gd8A346IU6rWnZCPdTzp8aFzkJ6Yd0hE3FcT26rAj4C1SSX960hPU3sKuCAi9mzNp2D2YS45mCULA78DxgHnArdK+hlwHrBAnnca8DzptuRjJc2Ttz0FqJzUKzfZm5GPA7eRktBZpGcrbw7cLGloZaX8eM1bgU1ISeHXwLo5xq5m36jZzHCbg1kyBDgpIg6GaQ/seRr4K/CZiPhvZUVJfwK2ANYHboiIUySNJJUuzshtDTOyFHA68D+VWzVLOgv4GulZy+fk9c4kPRxn/Yi4I693NOlOr76ws17lPzCz6X5f9fs7wJeAA6oTQ3ZLni5K835acw//a/N0OZhWnbQScHElMQDk5zAf2YPjms0UlxzMpptQ+SXfe/8iSXNIWpH0dLelSKWDTfJqczZ5nHci4pmaea/l6aA8XSNP76qz/W1NHtdspjk5mE33dvULSduTnuC2bJ41GRhPal/YhObr/afUmVcpRVT2+ZE8rfcUveebPK7ZTHO1klkdktYCLiNdyX8BWAaYLyI2BMb0QQiv5+l8dZbVm2fWUi45mNW3K+ni6RsR8aeaZcvnaXXJodV9wsfn6ZpMb6CuWKvFxzIrcMlBUdzmAAABQUlEQVTBrL538vRDI58lbUzqygowV9Wi9/J0YIuOfzvwT+BLuXG6cvwFSOMezHqVSw5m9V1KGmz2C0kbABOBlUkPiP83qafSwlXrP5enJ0oaExFH9eTgETFV0j7AjcA4SZeTGq23Agbn1Wp7UZm1jEsOZnXksQpbkKp3tgW+DiwGHE7qsfRBXl5xOulEvjqwv6QhLYjhr8BGpFLEdqSutbeSxkIAvNXTY5g14ttnmLUhSXOTktEzteMsJG1EuoXH9yPi+DLis/7PJQez9jQUeBK4UdK0hm9JcwIH5Zc3lxGYdQaXHMzalKTLgB1JVVtjSYPuPgusAJwVEfuUF531d26QNmtfXyS1N+xBavOA1INpH+DssoKyzuCSg5mZFbjNwczMCpwczMyswMnBzMwKnBzMzKzAycHMzAqcHMzMrOD/AW0NEVdvt7ETAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# <!-- collapse=True -->\n",
    "norm_counts = (\n",
    "    ratings_df['rating']\n",
    "    .value_counts(normalize=True, sort=False)\n",
    "    .multiply(100)\n",
    "    .reset_index()\n",
    "    .rename(columns={'rating': 'percent', 'index': 'rating'})\n",
    ")\n",
    "ax = sns.barplot(x='rating', y='percent', data=norm_counts)\n",
    "ax.set_title('Rating Frequencies')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. How many ratings were submitted per month?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th># of Ratings</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1997-09-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "      <td>6808</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-10-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>10</td>\n",
       "      <td>10368</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-11-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>11</td>\n",
       "      <td>24073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-12-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>12</td>\n",
       "      <td>11695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-01-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>1</td>\n",
       "      <td>14100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-02-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>2</td>\n",
       "      <td>10961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-03-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>3</td>\n",
       "      <td>12987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-04-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>4</td>\n",
       "      <td>9008</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            year month  # of Ratings\n",
       "Date                                \n",
       "1997-09-01  1997     9          6808\n",
       "1997-10-01  1997    10         10368\n",
       "1997-11-01  1997    11         24073\n",
       "1997-12-01  1997    12         11695\n",
       "1998-01-01  1998     1         14100\n",
       "1998-02-01  1998     2         10961\n",
       "1998-03-01  1998     3         12987\n",
       "1998-04-01  1998     4          9008"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# <!-- collapse=True -->\n",
    "month_counts = ratings_df[['year', 'month', 'rating']].groupby(['year', 'month']).count()\n",
    "month_counts = month_counts.rename(index=str, columns={'rating': '# of Ratings'})\n",
    "month_counts = month_counts.reset_index()\n",
    "month_counts['Date'] = month_counts[['year', 'month']].apply(\n",
    "    lambda x: datetime(year=int(x[0]), month=int(x[1]), day=1), axis=1\n",
    ")\n",
    "month_counts = month_counts.set_index('Date', drop=True)\n",
    "display(month_counts)\n",
    "month_counts['# of Ratings'].plot(style='o-')\n",
    "plt.ylabel('# of Ratings')\n",
    "plt.title('# of Ratings per Month')\n",
    "plt.ylim([0, 25000])\n",
    "plt.gca().grid(which='minor')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of ratings had a fairly large spike in November of 1998, but otherwise was relatively constant.\n",
    "\n",
    "This leads to another question about changes over time:\n",
    "\n",
    "# 5. How consistent are the average ratings over time?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>Rating</th>\n",
       "      <th>std</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1997-09-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "      <td>3.541569</td>\n",
       "      <td>1.091807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-10-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>10</td>\n",
       "      <td>3.594425</td>\n",
       "      <td>1.097959</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-11-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>11</td>\n",
       "      <td>3.558759</td>\n",
       "      <td>1.110674</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1997-12-01</th>\n",
       "      <td>1997</td>\n",
       "      <td>12</td>\n",
       "      <td>3.578367</td>\n",
       "      <td>1.110067</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-01-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>1</td>\n",
       "      <td>3.397092</td>\n",
       "      <td>1.187497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-02-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>2</td>\n",
       "      <td>3.456619</td>\n",
       "      <td>1.128093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-03-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>3</td>\n",
       "      <td>3.548395</td>\n",
       "      <td>1.109802</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1998-04-01</th>\n",
       "      <td>1998</td>\n",
       "      <td>4</td>\n",
       "      <td>3.576710</td>\n",
       "      <td>1.142116</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            year month    Rating       std\n",
       "Date                                      \n",
       "1997-09-01  1997     9  3.541569  1.091807\n",
       "1997-10-01  1997    10  3.594425  1.097959\n",
       "1997-11-01  1997    11  3.558759  1.110674\n",
       "1997-12-01  1997    12  3.578367  1.110067\n",
       "1998-01-01  1998     1  3.397092  1.187497\n",
       "1998-02-01  1998     2  3.456619  1.128093\n",
       "1998-03-01  1998     3  3.548395  1.109802\n",
       "1998-04-01  1998     4  3.576710  1.142116"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# <!-- collapse=True -->\n",
    "month_counts = ratings_df.groupby(['year', 'month'])['rating'].agg([np.mean, np.std])\n",
    "month_counts = month_counts.rename(index=str, columns={'mean': 'Rating'})\n",
    "month_counts = month_counts.reset_index()\n",
    "month_counts['Date'] = month_counts[['year', 'month']].apply(\n",
    "    lambda x: datetime(year=int(x[0]), month=int(x[1]), day=1), axis=1\n",
    ")\n",
    "month_counts = month_counts.set_index('Date', drop=True)\n",
    "display(month_counts)\n",
    "month_counts['Rating'].plot(style='o-')\n",
    "plt.fill_between(month_counts.index,\n",
    "                 month_counts['Rating'] - month_counts['std'],\n",
    "                 month_counts['Rating'] + month_counts['std'],\n",
    "                 alpha=0.3,\n",
    "                )\n",
    "plt.ylim([0, 5])\n",
    "plt.ylabel('Rating')\n",
    "plt.gca().grid(which='minor')\n",
    "plt.title('Rating Consistency over Time')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This average ratings were fairly consistent around 3.5. The lack of large changes over time will simplify modeling a little bit.\n",
    "\n",
    "One last thing I'm curious about (for now) when it comes to changes over time:\n",
    "\n",
    "# 6. How quickly do the movie and user bases grow over time?\n",
    "\n",
    "I'll assume that a user has joined on her first rating, and that she remains a user from then on."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>userId</th>\n",
       "      <th>movieId</th>\n",
       "      <th>rating</th>\n",
       "      <th>timestamp</th>\n",
       "      <th>year</th>\n",
       "      <th>month</th>\n",
       "      <th>Date</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>214</th>\n",
       "      <td>259</td>\n",
       "      <td>255</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:05:10</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "      <td>1997-09-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83965</th>\n",
       "      <td>259</td>\n",
       "      <td>286</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:05:27</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "      <td>1997-09-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43027</th>\n",
       "      <td>259</td>\n",
       "      <td>298</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:05:54</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "      <td>1997-09-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21396</th>\n",
       "      <td>259</td>\n",
       "      <td>185</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:06:21</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "      <td>1997-09-01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82655</th>\n",
       "      <td>259</td>\n",
       "      <td>173</td>\n",
       "      <td>4</td>\n",
       "      <td>1997-09-19 23:07:23</td>\n",
       "      <td>1997</td>\n",
       "      <td>9</td>\n",
       "      <td>1997-09-01</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       userId  movieId  rating           timestamp  year  month       Date\n",
       "214       259      255       4 1997-09-19 23:05:10  1997      9 1997-09-01\n",
       "83965     259      286       4 1997-09-19 23:05:27  1997      9 1997-09-01\n",
       "43027     259      298       4 1997-09-19 23:05:54  1997      9 1997-09-01\n",
       "21396     259      185       4 1997-09-19 23:06:21  1997      9 1997-09-01\n",
       "82655     259      173       4 1997-09-19 23:07:23  1997      9 1997-09-01"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# <!-- collapse=True -->\n",
    "ratings_df['Date'] = ratings_df[['year', 'month']].apply(\n",
    "    lambda x: datetime(year=int(x[0]), month=int(x[1]), day=1), axis=1\n",
    ")\n",
    "display(ratings_df.head())\n",
    "n_users = []\n",
    "n_movies = []\n",
    "dates = np.unique(ratings_df['Date'])\n",
    "for date in dates:\n",
    "    n_users.append(ratings_df[ratings_df['Date'] <= date]['userId'].nunique())\n",
    "    n_movies.append(ratings_df[ratings_df['Date'] <= date]['movieId'].nunique())\n",
    "df_users = pd.DataFrame({'Date': dates, '# of Users': n_users}).set_index('Date')\n",
    "df_movies = pd.DataFrame({'Date': dates, '# of Movies': n_movies}).set_index('Date')\n",
    "fig, ax = plt.subplots()\n",
    "df_movies['# of Movies'].plot(style='o-', ax=ax)\n",
    "df_users['# of Users'].plot(style='o-', ax=ax)\n",
    "plt.ylabel('Count')\n",
    "plt.ylim([0, 2000])\n",
    "ax.grid(which='minor')\n",
    "plt.tight_layout()\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "New users seen in the dataset look fairly linear over time, although the number of movies start out withover 1000 already in the system.\n",
    "\n",
    "# 7. How sparse is the user/movies matrix we'll be dealing with?\n",
    "\n",
    "Sparsity is a very common challenge to overcome in many collaborative filtering applications. By sparsity, I mean that if we create a matrix $R$ with dimensions $n_{users} \\times n_{movies}$ where each element $r_{ij}$ is a single rating by user $i$ of movie $j$, this matrix will be very empty because most users have only rated a few of the 25,000+ movies available. Let's see how bad it is."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's one way to visualize the sparsity. The plot below shows a single, tiny black square for every user/movie combination we have. If everyone rated every movie, you'd see a solid black rectangle. Instead what we see is a lot of white--lots of user/movie combinations for which we don't have a rating (yet). You especially see a lot of white in the top right corner. This is probably because early raters had access to fewer movies to rate, and new users progressively had more movies to rate as they were added to the system.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/markdown": [
       "The matrix density is $n_{ratings}/(n_{users} \\times n_{movies}) = 0.063$"
      ],
      "text/plain": [
       "<IPython.core.display.Markdown object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# <!-- collapse=True -->\n",
    "from cf_utils import get_rating_matrix\n",
    "rating_matrix, user_map, item_map = get_rating_matrix(ratings_df)\n",
    "with plt.style.context('seaborn-white'):\n",
    "    rating_matrix_binary = rating_matrix > 0\n",
    "    plt.imshow(rating_matrix_binary)\n",
    "    plt.xlabel('Movie')\n",
    "    plt.ylabel('User')\n",
    "    plt.show()\n",
    "\n",
    "Markdown(\n",
    "    r\"The matrix density is $n_{{ratings}}/(n_{{users}} \\times n_{{movies}}) = {:0.3f}$\"\n",
    "    .format(np.sum(rating_matrix_binary) / np.prod(rating_matrix.shape))\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above you also notice that there are a few darker rows and columns, but most rows and columns are pretty bare. Let's visualize the distributions of number of ratings by user and by movie. The way I chose to visualize this is with an [Empirical Cumulative Distribution Function (ECDF) plot](https://www.youtube.com/watch?v=ap4mfGvgDsM). An ECDF plot has an advantage compared to a histogram that all data points can be plotted in a meaningful way, and no bin size has to be chosen to average arbitrary chunks of it. This is especially helpful with the long-tailed distributions here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# <!-- collapse=True -->\n",
    "user_counts = ratings_df['userId'].value_counts(ascending=True)\n",
    "user_counts.index = np.arange(len(user_counts)) / len(user_counts)\n",
    "plt.plot(user_counts, user_counts.index, '.', label='Users')\n",
    "movie_counts = ratings_df['movieId'].value_counts(ascending=True)\n",
    "movie_counts.index = np.arange(len(movie_counts)) / len(movie_counts)\n",
    "plt.plot(movie_counts, movie_counts.index, '.', label='Movies')\n",
    "plt.xlabel('Number of Ratings')\n",
    "plt.ylabel('ECDF')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot above, you can learn, for example, that 40% of all users rated 50 or less movies, and 90% of movies have 169 or less ratings. In general, we seen that a large fraction of movies and users have few ratings associated with them, but a few movies and users have many more ratings.\n",
    "\n",
    "The main thing to take from this though is that the matrix of possible ratings is quite sparse, and that we need to use models that deal with this lack of data."
   ]
  }
 ],
 "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": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}