SMM_RecSys_Baseline_Approach_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "DZuJgz7f2IZ3"
   },
   "source": [
    "## Super Mario Maker Dataset - Network Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "ErHiyzZVVERF"
   },
   "source": [
    "### 1. Prerequisites"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "moaC0uhpU5i_"
   },
   "source": [
    "Import required libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "CqfsTYm83mip"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, precision_recall_fscore_support\n",
    "import os\n",
    "import gc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pHXQkBC7U-U3"
   },
   "source": [
    "Specify data files location."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "6Tm0Ut1d3UY2"
   },
   "outputs": [],
   "source": [
    "data_path = '/Users/pj/Documents/671_Project/'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "pcpsAYAOVLJt"
   },
   "source": [
    "Read player names data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "id": "s5al7sbB358P",
    "outputId": "6a30133d-71e7-46a7-dc59-439eecdfeaf0"
   },
   "outputs": [],
   "source": [
    "players = []\n",
    "with open(data_path + 'players_tsv.csv') as players_file:\n",
    "  for pl_data in players_file.readlines()[1:]:\n",
    "    player_name = pl_data.split(',')[0]\n",
    "    players.append(player_name)\n",
    "\n",
    "players_df=pd.DataFrame()\n",
    "players_df['player'] = players\n",
    "\n",
    "del(players)\n",
    "#gc.collect()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 212
    },
    "colab_type": "code",
    "id": "k4xW2xoGHE2U",
    "outputId": "ad0267b0-d0f1-41a7-8d18-61466221be04"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of players : 884300\n"
     ]
    },
    {
     "data": {
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>player</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NolramImpro</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>SGK2017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>preamstrikbiz0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>gotatari</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>skrufpanda</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           player\n",
       "0     NolramImpro\n",
       "1         SGK2017\n",
       "2  preamstrikbiz0\n",
       "3        gotatari\n",
       "4      skrufpanda"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Number of players : {}'.format(len(players_df)))\n",
    "players_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sshE2UkC3viZ"
   },
   "source": [
    "Read games data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jexJwiOWhd-o"
   },
   "outputs": [],
   "source": [
    "course = dict()\n",
    "with open(data_path + 'courses.csv') as course_file:\n",
    "  for game_data in course_file.readlines()[1:]:    \n",
    "    creator_name = game_data.split()[3]\n",
    "    game_id = game_data.split()[0]\n",
    "    course[game_id] = creator_name"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "GxCGGBiFVbPa"
   },
   "source": [
    "Create a dataframe for course data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "odYQWgV_4HbM"
   },
   "outputs": [],
   "source": [
    "course_df = pd.DataFrame(data=course.keys(), index=range(len(course)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "L2GAVAlHmVm5"
   },
   "outputs": [],
   "source": [
    "course_df.columns = ['game']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 212
    },
    "colab_type": "code",
    "id": "74IjM8fxVhdN",
    "outputId": "e5ef1921-9364-433e-89c8-3c3200cd2b33"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of courses : 115032\n"
     ]
    },
    {
     "data": {
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       "    }\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>game</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>079D-0000-0351-17E2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>07CD-0000-030D-EA60</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>07F7-0000-030F-A51B</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>080E-0000-0307-A394</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>082F-0000-0358-A218</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  game\n",
       "0  079D-0000-0351-17E2\n",
       "1  07CD-0000-030D-EA60\n",
       "2  07F7-0000-030F-A51B\n",
       "3  080E-0000-0307-A394\n",
       "4  082F-0000-0358-A218"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "del(course)\n",
    "gc.collect()\n",
    "print('Number of courses : {}'.format(len(course_df)))\n",
    "course_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "tuTybxy1WEeq"
   },
   "source": [
    "Read playes and likes data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "W0c3Ch3sid_G"
   },
   "outputs": [],
   "source": [
    "plays_df = pd.read_csv(data_path + 'plays.csv', sep=\"\\t\", usecols=['id', 'player'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 212
    },
    "colab_type": "code",
    "id": "GRJAsxt6j99Z",
    "outputId": "71191f8b-984c-4883-99af-e29470373dfd"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of plays-player data : 3941378\n"
     ]
    },
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>player</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>darter60k</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>davidchofis</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>fabioviana</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>gorigokky</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>groebenzell</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    id       player\n",
       "0  0000-0000-0353-3D35    darter60k\n",
       "1  0000-0000-0353-3D35  davidchofis\n",
       "2  0000-0000-0353-3D35   fabioviana\n",
       "3  0000-0000-0353-3D35    gorigokky\n",
       "4  0000-0000-0353-3D35  groebenzell"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Number of plays-player data : {}'.format(len(plays_df)))\n",
    "plays_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "KvZnfXsAlZFs"
   },
   "outputs": [],
   "source": [
    "likes_df = pd.read_csv(data_path + 'likes.csv', sep=\"\\t\", usecols=['id', 'player'], )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 212
    },
    "colab_type": "code",
    "id": "NIcOdl6bkdE8",
    "outputId": "d936d036-a263-4475-f062-e65c2ee7cbe6"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of likes-player data : 3941378\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>player</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0000-0000-0353-3D35</td>\n",
       "      <td>groebenzell</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0000-0000-035A-9F14</td>\n",
       "      <td>jlan6e</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0001-0000-0347-486A</td>\n",
       "      <td>cat38690</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0001-0000-0347-486A</td>\n",
       "      <td>raulcaba</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0001-0000-0359-B3CD</td>\n",
       "      <td>Tugaeddy</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    id       player\n",
       "0  0000-0000-0353-3D35  groebenzell\n",
       "1  0000-0000-035A-9F14       jlan6e\n",
       "2  0001-0000-0347-486A     cat38690\n",
       "3  0001-0000-0347-486A     raulcaba\n",
       "4  0001-0000-0359-B3CD     Tugaeddy"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Number of likes-player data : {}'.format(len(plays_df)))\n",
    "likes_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2hZdb4FQXzvR"
   },
   "source": [
    "### 2. Data attributes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "uzbM_qRiYYjg"
   },
   "source": [
    "Check distribution of games played and liked."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "colab_type": "code",
    "id": "mFvzDElYYPak",
    "outputId": "199b860f-c8b8-4800-f0e4-a443897bcf28"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('ggplot')\n",
    "plt.hist(plays_df['player'].value_counts().values, rwidth=0.9)\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Number of games played')\n",
    "plt.ylabel('Number of players')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "colab_type": "code",
    "id": "X-T79HNpZWFX",
    "outputId": "dfb74c47-fa55-4058-8cb6-05a63d574154"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('ggplot')\n",
    "plt.hist(likes_df['player'].value_counts().values, rwidth=0.9)\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Number of games liked')\n",
    "plt.ylabel('Number of players')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "colab_type": "code",
    "id": "zgivXh0OZg6x",
    "outputId": "5669f591-4f19-41e0-8f68-6c7471461ec0"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('ggplot')\n",
    "plt.hist(plays_df['id'].value_counts().values, rwidth=0.9)\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Number of players playing the game')\n",
    "plt.ylabel('Number of games')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 282
    },
    "colab_type": "code",
    "id": "BjrGwdmNZhR8",
    "outputId": "0912a681-831b-42f1-bb8d-97ba3f290217"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.style.use('ggplot')\n",
    "plt.hist(likes_df['id'].value_counts().values, rwidth=0.9)\n",
    "plt.yscale('log')\n",
    "plt.xlabel('Number of players liking the game')\n",
    "plt.ylabel('Number of games')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "rWu8c9FPVl4b"
   },
   "source": [
    "### 3. Baseline recommendation system."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "qF_vrW0rVvAo"
   },
   "source": [
    "A baseline recommendation system can be developed as below:\n",
    "1. An average like score $G_L$ for each game can be calculated as a fraction of the players liking the game out of all players that played the game.\n",
    "2. Simillarly, for each player, a like score $P_L$ can be calculated as fraction of games liked by the user, out of all games played by the user.\n",
    "3. For the games NOT played by the user $i$ the probability of player $i$ liking game $j$ can be calculated as:\n",
    "$P_{i,j} = P_L^i \\times G_L^j$\n",
    "4. For the purpose of testing this system. We will set aside $1000$ players and $1000$ games as test data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "2IjdnVWRZ8tp"
   },
   "source": [
    "Selecting test dataset:\n",
    "\n",
    "*   Since the game plays and likes matrix is sparse, randomly selecting 1000 users and 1000 games will not work, as it is likely that we will get very few plays or likes out of possible $1000 \\times 1000 = 10^6$ possible data points.\n",
    "*   To address this problem we use a simple strategy of selecting 500 players with highest number of games played and 500 players with highest number of games liked, for test dataset.\n",
    "*   Simillarly, 500 games which are played most and 500 games which are liked most are selected for test dataset.\n",
    "*   This strategy is quite crude and needs to be refined further to select players and games from all over the distribution and not just most frequent ones.\n",
    "\n",
    "\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "XnineO7LaBlO"
   },
   "outputs": [],
   "source": [
    "test_players = list(plays_df['player'].value_counts().index[:500]) + list(likes_df['player'].value_counts().index[:500])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "IZn6c9J_awmj"
   },
   "outputs": [],
   "source": [
    "test_games = list(plays_df['id'].value_counts().index[:500]) + list(likes_df['id'].value_counts().index[:500])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "1LrTv2jAL_fD",
    "outputId": "4de47a08-b96a-4cf7-ab62-f0478b3a41ab"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>player</th>\n",
       "      <th>plays</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Conducteur59220</td>\n",
       "      <td>2585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>dellbox2</td>\n",
       "      <td>1949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>AE4WiiU</td>\n",
       "      <td>1666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>revolv23</td>\n",
       "      <td>1423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>demonhunter47223</td>\n",
       "      <td>1240</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             player  plays\n",
       "0   Conducteur59220   2585\n",
       "1          dellbox2   1949\n",
       "2           AE4WiiU   1666\n",
       "3          revolv23   1423\n",
       "4  demonhunter47223   1240"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plays_df_train = plays_df[~plays_df['id'].isin(test_games)]\n",
    "p_plays_data = pd.DataFrame(plays_df_train['player'].value_counts())\n",
    "p_plays_data.reset_index(inplace=True)\n",
    "p_plays_data.columns = ['player', 'plays']\n",
    "p_plays_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "-mAbi8fWR9yN",
    "outputId": "e858d9c5-c368-4b19-e41f-8a69861ddbec"
   },
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>player</th>\n",
       "      <th>likes</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <td>Conducteur59220</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>dellbox2</td>\n",
       "      <td>1934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Leeshino</td>\n",
       "      <td>1786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>revolv23</td>\n",
       "      <td>1564</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>WIIMoustique</td>\n",
       "      <td>1505</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "            player  likes\n",
       "0  Conducteur59220   3223\n",
       "1         dellbox2   1934\n",
       "2         Leeshino   1786\n",
       "3         revolv23   1564\n",
       "4     WIIMoustique   1505"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likes_df_train = likes_df[~likes_df['id'].isin(test_games)]\n",
    "p_likes_data = pd.DataFrame(likes_df_train['player'].value_counts())\n",
    "p_likes_data.reset_index(inplace=True)\n",
    "p_likes_data.columns = ['player', 'likes']\n",
    "p_likes_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "XoVy3EM8UHl8"
   },
   "source": [
    "Combine these with players dataframe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "rKqPM661SRQp",
    "outputId": "4e1d991c-34fb-4dad-d6c4-359b6ba126c7"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>player</th>\n",
       "      <th>plays</th>\n",
       "      <th>likes</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>NolramImpro</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>SGK2017</td>\n",
       "      <td>50.0</td>\n",
       "      <td>19.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>preamstrikbiz0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>gotatari</td>\n",
       "      <td>51.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>skrufpanda</td>\n",
       "      <td>264.0</td>\n",
       "      <td>23.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           player  plays  likes\n",
       "0     NolramImpro    4.0    3.0\n",
       "1         SGK2017   50.0   19.0\n",
       "2  preamstrikbiz0   13.0    2.0\n",
       "3        gotatari   51.0    1.0\n",
       "4      skrufpanda  264.0   23.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plr_ply_df = players_df.merge(p_plays_data, how='left', on='player')\n",
    "plr_ply_like_df = plr_ply_df.merge(p_likes_data, how='left', on='player')\n",
    "plr_ply_like_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "sRl2-AvFUP1r"
   },
   "source": [
    "Calculate score for each player as ration of games liked to games played. There is small fraction of players where number of games liked is more than number of games played. We will set score for these cases to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "0FWlkpVPSzmk"
   },
   "outputs": [],
   "source": [
    "def calc_frac(a):\n",
    "  if a[1]==0:\n",
    "    return 0\n",
    "  else:\n",
    "    return(min(a[2]/a[1], 1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "UVJlAaHDTdBv"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>player</th>\n",
       "      <th>plays</th>\n",
       "      <th>likes</th>\n",
       "      <th>score</th>\n",
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       "      <th>0</th>\n",
       "      <td>NolramImpro</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>0.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>SGK2017</td>\n",
       "      <td>50.0</td>\n",
       "      <td>19.0</td>\n",
       "      <td>0.380000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>preamstrikbiz0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.153846</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>gotatari</td>\n",
       "      <td>51.0</td>\n",
       "      <td>1.0</td>\n",
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       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>skrufpanda</td>\n",
       "      <td>264.0</td>\n",
       "      <td>23.0</td>\n",
       "      <td>0.087121</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           player  plays  likes     score\n",
       "0     NolramImpro    4.0    3.0  0.750000\n",
       "1         SGK2017   50.0   19.0  0.380000\n",
       "2  preamstrikbiz0   13.0    2.0  0.153846\n",
       "3        gotatari   51.0    1.0  0.019608\n",
       "4      skrufpanda  264.0   23.0  0.087121"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plr_ply_like_df['score'] = plr_ply_like_df.apply(calc_frac, axis=1)\n",
    "plr_ply_like_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "SFAM-ujLY9ED"
   },
   "source": [
    "Repeat same calculations for games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "fxJjb2snY8EJ",
    "outputId": "0b404930-3bc7-4a98-84c7-203dc4ccc204"
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "                  game  plays\n",
       "0  5AB9-0000-038F-A23E   1641\n",
       "1  F44D-0000-035E-496C   1119\n",
       "2  DE4D-0000-035D-3AE1   1061\n",
       "3  A4E1-0000-038D-0EBC   1003\n",
       "4  8F40-0000-0391-4B50    959"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plays_df_train = plays_df[~plays_df['player'].isin(test_players)]\n",
    "g_plays_data = pd.DataFrame(plays_df_train['id'].value_counts())\n",
    "g_plays_data.reset_index(inplace=True)\n",
    "g_plays_data.columns = ['game', 'plays']\n",
    "g_plays_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "urBYFi9LZQa2",
    "outputId": "de436728-f1b7-4982-a747-083e338b9e79"
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "                  game  likes\n",
       "0  DE4D-0000-035D-3AE1    429\n",
       "1  BAC8-0000-036A-7EE1    308\n",
       "2  5AB9-0000-038F-A23E    297\n",
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      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likes_df_train = likes_df[~likes_df['player'].isin(test_players)]\n",
    "g_likes_data = pd.DataFrame(likes_df_train['id'].value_counts())\n",
    "g_likes_data.reset_index(inplace=True)\n",
    "g_likes_data.columns = ['game', 'likes']\n",
    "g_likes_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 195
    },
    "colab_type": "code",
    "id": "Bx1yPWlaZalh",
    "outputId": "c60e03bf-27fa-40e8-a799-979980e9246c"
   },
   "outputs": [
    {
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      "text/plain": [
       "                  game  plays  likes     score\n",
       "0  079D-0000-0351-17E2     18    1.0  0.055556\n",
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     "execution_count": 35,
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     "output_type": "execute_result"
    }
   ],
   "source": [
    "gm_ply_df = course_df.merge(g_plays_data, how='left', on='game')\n",
    "gm_ply_like_df = gm_ply_df.merge(g_likes_data, how='left', on='game')\n",
    "gm_ply_like_df['score'] = gm_ply_like_df.apply(calc_frac, axis=1)\n",
    "gm_ply_like_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "KOnK12_2L2_0"
   },
   "source": [
    "Create a matrix for true labels on test data sets of 1000 players vs 1000 games."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "jogkGDBEPVSm"
   },
   "outputs": [],
   "source": [
    "true_labels = np.ones((1000, 1000)) * -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "igmQWtmYPfAX"
   },
   "outputs": [],
   "source": [
    "for p, plr in enumerate(test_players):\n",
    "  temp_plays_df = plays_df[plays_df['player']==plr]\n",
    "  temp_likes_df =  likes_df[likes_df['player']==plr]\n",
    "  for g, gm in enumerate(test_games):\n",
    "    # check if player 'plr' has played the game 'gm', then set label to zero\n",
    "    if gm in temp_plays_df['id'].values:\n",
    "      true_labels[p, g] = 0\n",
    "    # check if player 'plr has liked the game 'gm', then set label to 1.\n",
    "    if gm in temp_likes_df['id'].values:\n",
    "      true_labels[p, g] = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "4ZVncTx9SxRO"
   },
   "outputs": [],
   "source": [
    "predicted_labels = np.ones((1000,1000)) * -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "gH7JfjN5eNo8"
   },
   "source": [
    "Calculate the probability of a player liking a game on test dataset (predictions)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "cJeKabiseo_X"
   },
   "outputs": [],
   "source": [
    "for p, plr in enumerate(test_players):\n",
    "  temp_plays_df = plr_ply_like_df[plr_ply_like_df['player']==plr]  \n",
    "  for g, gm in enumerate(test_games):\n",
    "    if true_labels[p, g] != -1:\n",
    "      p_s = temp_plays_df['score'].values[0]\n",
    "      g_s = gm_ply_like_df[gm_ply_like_df['game']==gm]['score'].values[0]\n",
    "      predicted_labels[p, g] =  p_s * g_s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "wrLXI5B4pv8N"
   },
   "source": [
    "Flatten the true and predicted label matrices and remove entries of -1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "R4MgOr5Fgkfi"
   },
   "outputs": [],
   "source": [
    "threshold = 0.5 # Default threshold 0f 0.5\n",
    "true_flattened = []\n",
    "predicted_flattened = []\n",
    "predicted_prob_flattened = []\n",
    "for i in range(1000):\n",
    "  for j in range(1000):\n",
    "    if true_labels[i,j]!=-1:\n",
    "      true_flattened.append(true_labels[i,j])\n",
    "      predicted_prob_flattened.append(predicted_labels[i,j])\n",
    "      if predicted_labels[i,j]>threshold:\n",
    "        predicted_flattened.append(1)\n",
    "      else:\n",
    "        predicted_flattened.append(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "6GDmWBpbkNHJ"
   },
   "source": [
    "Calculate accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 67
    },
    "colab_type": "code",
    "id": "U6K4DpBUkWxQ",
    "outputId": "77464654-ce08-4099-f7fe-e660ba07a257"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on test dataset: 35.66%\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 5318,   240],\n",
       "       [26776,  9653]])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Accuracy on test dataset: {0:4.2f}%'.format(accuracy_score(true_flattened, predicted_flattened)*100))\n",
    "#labels = ['true_flattened', 'predicted_flattened']\n",
    "cm = confusion_matrix(true_flattened, predicted_flattened)\n",
    "cm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "U2ufrpb4ksLI"
   },
   "source": [
    "Comments:\n",
    "The low accuracy of the baseline method can be due to following factor:\n",
    "*  We have selected test players and games from high frequecy region of the distribution. A more balanced selection of test data might be better representative of overall data. Our selected data is having high probablility of liking the game, but the average on overall dataset might be much lower, hence out predictions will be biased towards **dislike** (0 score) as indicated by the results above."
   ]
  }
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