kmeans_clust.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "84a295d5-4754-44ad-aa0a-aab06863ee8f",
   "metadata": {},
   "source": [
    "# k-Means Clustering from Scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "988facbc-c2a6-45b8-a68a-a2b485799199",
   "metadata": {},
   "source": [
    "## Prepare the Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "23c62ae1-7c5d-4f4c-9dfc-618010bdea2e",
   "metadata": {},
   "source": [
    "### Loading the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "f2cd018a-6283-4f66-92c8-b1da70c629c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d788e9ce-3ec8-472b-8199-3b1b5092f7ae",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Olivetti\\anaconda3\\lib\\site-packages\\IPython\\core\\interactiveshell.py:3444: DtypeWarning: Columns (25,108) have mixed types.Specify dtype option on import or set low_memory=False.\n",
      "  exec(code_obj, self.user_global_ns, self.user_ns)\n"
     ]
    }
   ],
   "source": [
    "# Read in the soccer_players CSV file\n",
    "players = pd.read_csv(\"players_22.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "fed6d165-0e70-469d-b9ef-446c45e8ed24",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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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>sofifa_id</th>\n",
       "      <th>player_url</th>\n",
       "      <th>short_name</th>\n",
       "      <th>long_name</th>\n",
       "      <th>player_positions</th>\n",
       "      <th>overall</th>\n",
       "      <th>potential</th>\n",
       "      <th>value_eur</th>\n",
       "      <th>wage_eur</th>\n",
       "      <th>age</th>\n",
       "      <th>...</th>\n",
       "      <th>lcb</th>\n",
       "      <th>cb</th>\n",
       "      <th>rcb</th>\n",
       "      <th>rb</th>\n",
       "      <th>gk</th>\n",
       "      <th>player_face_url</th>\n",
       "      <th>club_logo_url</th>\n",
       "      <th>club_flag_url</th>\n",
       "      <th>nation_logo_url</th>\n",
       "      <th>nation_flag_url</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>158023</td>\n",
       "      <td>https://sofifa.com/player/158023/lionel-messi/...</td>\n",
       "      <td>L. Messi</td>\n",
       "      <td>Lionel Andrés Messi Cuccittini</td>\n",
       "      <td>RW, ST, CF</td>\n",
       "      <td>93</td>\n",
       "      <td>93</td>\n",
       "      <td>78000000.0</td>\n",
       "      <td>320000.0</td>\n",
       "      <td>34</td>\n",
       "      <td>...</td>\n",
       "      <td>50+3</td>\n",
       "      <td>50+3</td>\n",
       "      <td>50+3</td>\n",
       "      <td>61+3</td>\n",
       "      <td>19+3</td>\n",
       "      <td>https://cdn.sofifa.net/players/158/023/22_120.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/73/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/fr.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/1369/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/ar.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>188545</td>\n",
       "      <td>https://sofifa.com/player/188545/robert-lewand...</td>\n",
       "      <td>R. Lewandowski</td>\n",
       "      <td>Robert Lewandowski</td>\n",
       "      <td>ST</td>\n",
       "      <td>92</td>\n",
       "      <td>92</td>\n",
       "      <td>119500000.0</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>32</td>\n",
       "      <td>...</td>\n",
       "      <td>60+3</td>\n",
       "      <td>60+3</td>\n",
       "      <td>60+3</td>\n",
       "      <td>61+3</td>\n",
       "      <td>19+3</td>\n",
       "      <td>https://cdn.sofifa.net/players/188/545/22_120.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/21/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/de.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/1353/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/pl.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20801</td>\n",
       "      <td>https://sofifa.com/player/20801/c-ronaldo-dos-...</td>\n",
       "      <td>Cristiano Ronaldo</td>\n",
       "      <td>Cristiano Ronaldo dos Santos Aveiro</td>\n",
       "      <td>ST, LW</td>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>45000000.0</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>36</td>\n",
       "      <td>...</td>\n",
       "      <td>53+3</td>\n",
       "      <td>53+3</td>\n",
       "      <td>53+3</td>\n",
       "      <td>60+3</td>\n",
       "      <td>20+3</td>\n",
       "      <td>https://cdn.sofifa.net/players/020/801/22_120.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/11/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/gb-eng.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/1354/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/pt.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>190871</td>\n",
       "      <td>https://sofifa.com/player/190871/neymar-da-sil...</td>\n",
       "      <td>Neymar Jr</td>\n",
       "      <td>Neymar da Silva Santos Júnior</td>\n",
       "      <td>LW, CAM</td>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>129000000.0</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>29</td>\n",
       "      <td>...</td>\n",
       "      <td>50+3</td>\n",
       "      <td>50+3</td>\n",
       "      <td>50+3</td>\n",
       "      <td>62+3</td>\n",
       "      <td>20+3</td>\n",
       "      <td>https://cdn.sofifa.net/players/190/871/22_120.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/73/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/fr.png</td>\n",
       "      <td>NaN</td>\n",
       "      <td>https://cdn.sofifa.net/flags/br.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>192985</td>\n",
       "      <td>https://sofifa.com/player/192985/kevin-de-bruy...</td>\n",
       "      <td>K. De Bruyne</td>\n",
       "      <td>Kevin De Bruyne</td>\n",
       "      <td>CM, CAM</td>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>125500000.0</td>\n",
       "      <td>350000.0</td>\n",
       "      <td>30</td>\n",
       "      <td>...</td>\n",
       "      <td>69+3</td>\n",
       "      <td>69+3</td>\n",
       "      <td>69+3</td>\n",
       "      <td>75+3</td>\n",
       "      <td>21+3</td>\n",
       "      <td>https://cdn.sofifa.net/players/192/985/22_120.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/10/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/gb-eng.png</td>\n",
       "      <td>https://cdn.sofifa.net/teams/1325/60.png</td>\n",
       "      <td>https://cdn.sofifa.net/flags/be.png</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 110 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   sofifa_id                                         player_url  \\\n",
       "0     158023  https://sofifa.com/player/158023/lionel-messi/...   \n",
       "1     188545  https://sofifa.com/player/188545/robert-lewand...   \n",
       "2      20801  https://sofifa.com/player/20801/c-ronaldo-dos-...   \n",
       "3     190871  https://sofifa.com/player/190871/neymar-da-sil...   \n",
       "4     192985  https://sofifa.com/player/192985/kevin-de-bruy...   \n",
       "\n",
       "          short_name                            long_name player_positions  \\\n",
       "0           L. Messi       Lionel Andrés Messi Cuccittini       RW, ST, CF   \n",
       "1     R. Lewandowski                   Robert Lewandowski               ST   \n",
       "2  Cristiano Ronaldo  Cristiano Ronaldo dos Santos Aveiro           ST, LW   \n",
       "3          Neymar Jr        Neymar da Silva Santos Júnior          LW, CAM   \n",
       "4       K. De Bruyne                      Kevin De Bruyne          CM, CAM   \n",
       "\n",
       "   overall  potential    value_eur  wage_eur  age  ...   lcb    cb   rcb  \\\n",
       "0       93         93   78000000.0  320000.0   34  ...  50+3  50+3  50+3   \n",
       "1       92         92  119500000.0  270000.0   32  ...  60+3  60+3  60+3   \n",
       "2       91         91   45000000.0  270000.0   36  ...  53+3  53+3  53+3   \n",
       "3       91         91  129000000.0  270000.0   29  ...  50+3  50+3  50+3   \n",
       "4       91         91  125500000.0  350000.0   30  ...  69+3  69+3  69+3   \n",
       "\n",
       "     rb    gk                                    player_face_url  \\\n",
       "0  61+3  19+3  https://cdn.sofifa.net/players/158/023/22_120.png   \n",
       "1  61+3  19+3  https://cdn.sofifa.net/players/188/545/22_120.png   \n",
       "2  60+3  20+3  https://cdn.sofifa.net/players/020/801/22_120.png   \n",
       "3  62+3  20+3  https://cdn.sofifa.net/players/190/871/22_120.png   \n",
       "4  75+3  21+3  https://cdn.sofifa.net/players/192/985/22_120.png   \n",
       "\n",
       "                            club_logo_url  \\\n",
       "0  https://cdn.sofifa.net/teams/73/60.png   \n",
       "1  https://cdn.sofifa.net/teams/21/60.png   \n",
       "2  https://cdn.sofifa.net/teams/11/60.png   \n",
       "3  https://cdn.sofifa.net/teams/73/60.png   \n",
       "4  https://cdn.sofifa.net/teams/10/60.png   \n",
       "\n",
       "                             club_flag_url  \\\n",
       "0      https://cdn.sofifa.net/flags/fr.png   \n",
       "1      https://cdn.sofifa.net/flags/de.png   \n",
       "2  https://cdn.sofifa.net/flags/gb-eng.png   \n",
       "3      https://cdn.sofifa.net/flags/fr.png   \n",
       "4  https://cdn.sofifa.net/flags/gb-eng.png   \n",
       "\n",
       "                            nation_logo_url  \\\n",
       "0  https://cdn.sofifa.net/teams/1369/60.png   \n",
       "1  https://cdn.sofifa.net/teams/1353/60.png   \n",
       "2  https://cdn.sofifa.net/teams/1354/60.png   \n",
       "3                                       NaN   \n",
       "4  https://cdn.sofifa.net/teams/1325/60.png   \n",
       "\n",
       "                       nation_flag_url  \n",
       "0  https://cdn.sofifa.net/flags/ar.png  \n",
       "1  https://cdn.sofifa.net/flags/pl.png  \n",
       "2  https://cdn.sofifa.net/flags/pt.png  \n",
       "3  https://cdn.sofifa.net/flags/br.png  \n",
       "4  https://cdn.sofifa.net/flags/be.png  \n",
       "\n",
       "[5 rows x 110 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take a look at the dataframe\n",
    "players.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "087b634c-db8c-4a06-9d0b-6c87cd171631",
   "metadata": {},
   "source": [
    "Specific info about this data can be found [here](https://www.kaggle.com/datasets/stefanoleone992/fifa-22-complete-player-dataset)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3321eefe-9809-4204-bb85-6ec55678e5de",
   "metadata": {},
   "source": [
    "### Selecting Features and Target Variable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "163bdf51-eb77-4a44-9c39-a9622acce1bd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# We will only use the following 5 features\n",
    "features = [\"overall\", \"potential\", \"wage_eur\", \"value_eur\", \"age\"]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3e64831f-1632-4185-81d7-3072718e1190",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Drop any row with missing values\n",
    "players = players.dropna(subset=features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3fedf944-a3ac-419f-932d-8a95b6ca3621",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Separate the data we'll work with\n",
    "data = players[features].copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f379689d-b1bd-417a-841b-bc453ca3c8ae",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>overall</th>\n",
       "      <th>potential</th>\n",
       "      <th>wage_eur</th>\n",
       "      <th>value_eur</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>93</td>\n",
       "      <td>93</td>\n",
       "      <td>320000.0</td>\n",
       "      <td>78000000.0</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>92</td>\n",
       "      <td>92</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>119500000.0</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>45000000.0</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>129000000.0</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>350000.0</td>\n",
       "      <td>125500000.0</td>\n",
       "      <td>30</td>\n",
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       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <th>19234</th>\n",
       "      <td>47</td>\n",
       "      <td>52</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>70000.0</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19235</th>\n",
       "      <td>47</td>\n",
       "      <td>59</td>\n",
       "      <td>500.0</td>\n",
       "      <td>110000.0</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19236</th>\n",
       "      <td>47</td>\n",
       "      <td>55</td>\n",
       "      <td>500.0</td>\n",
       "      <td>100000.0</td>\n",
       "      <td>21</td>\n",
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       "    <tr>\n",
       "      <th>19237</th>\n",
       "      <td>47</td>\n",
       "      <td>60</td>\n",
       "      <td>500.0</td>\n",
       "      <td>110000.0</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19238</th>\n",
       "      <td>47</td>\n",
       "      <td>60</td>\n",
       "      <td>500.0</td>\n",
       "      <td>110000.0</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>19165 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       overall  potential  wage_eur    value_eur  age\n",
       "0           93         93  320000.0   78000000.0   34\n",
       "1           92         92  270000.0  119500000.0   32\n",
       "2           91         91  270000.0   45000000.0   36\n",
       "3           91         91  270000.0  129000000.0   29\n",
       "4           91         91  350000.0  125500000.0   30\n",
       "...        ...        ...       ...          ...  ...\n",
       "19234       47         52    1000.0      70000.0   22\n",
       "19235       47         59     500.0     110000.0   19\n",
       "19236       47         55     500.0     100000.0   21\n",
       "19237       47         60     500.0     110000.0   19\n",
       "19238       47         60     500.0     110000.0   19\n",
       "\n",
       "[19165 rows x 5 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take a look at the data\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7de92f3c-064b-48ad-9498-f8851adaa252",
   "metadata": {},
   "source": [
    "### Normalizing the Data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93d456c1-ae66-4eb2-8e77-456a6bf0cc71",
   "metadata": {},
   "source": [
    "Since k-Means Clustering uses the euclidean distance to assign the samples to the clusters, we need to normalize the data to make sure all features have the same bearing in the calculations. In this case, we will normalize the data pushing every feature into the range [0, 100]. We use this scale because, especially since we are talking about ratings and players strenght, it is somewhat more intuitive to interpret rather than the standard [0, 1] one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6e839c69-d1ba-4533-9f6b-c29b9925fe2a",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Normalize the data using the min/max scaler and pushing the data into the [0, 100] range\n",
    "data = (data - data.min()) / (data.max() - data.min()) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f15ed21f-ef0d-457e-a0e2-47e7aadb2fe7",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\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>overall</th>\n",
       "      <th>potential</th>\n",
       "      <th>wage_eur</th>\n",
       "      <th>value_eur</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>19165.000000</td>\n",
       "      <td>19165.000000</td>\n",
       "      <td>19165.000000</td>\n",
       "      <td>19165.000000</td>\n",
       "      <td>19165.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>40.783017</td>\n",
       "      <td>47.999977</td>\n",
       "      <td>2.438261</td>\n",
       "      <td>1.464734</td>\n",
       "      <td>34.037163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>14.962616</td>\n",
       "      <td>13.234175</td>\n",
       "      <td>5.572534</td>\n",
       "      <td>3.924770</td>\n",
       "      <td>17.509315</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>30.434783</td>\n",
       "      <td>39.130435</td>\n",
       "      <td>0.143062</td>\n",
       "      <td>0.240217</td>\n",
       "      <td>18.518519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>41.304348</td>\n",
       "      <td>47.826087</td>\n",
       "      <td>0.715308</td>\n",
       "      <td>0.497961</td>\n",
       "      <td>33.333333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>50.000000</td>\n",
       "      <td>56.521739</td>\n",
       "      <td>2.145923</td>\n",
       "      <td>1.026336</td>\n",
       "      <td>48.148148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>100.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            overall     potential      wage_eur     value_eur           age\n",
       "count  19165.000000  19165.000000  19165.000000  19165.000000  19165.000000\n",
       "mean      40.783017     47.999977      2.438261      1.464734     34.037163\n",
       "std       14.962616     13.234175      5.572534      3.924770     17.509315\n",
       "min        0.000000      0.000000      0.000000      0.000000      0.000000\n",
       "25%       30.434783     39.130435      0.143062      0.240217     18.518519\n",
       "50%       41.304348     47.826087      0.715308      0.497961     33.333333\n",
       "75%       50.000000     56.521739      2.145923      1.026336     48.148148\n",
       "max      100.000000    100.000000    100.000000    100.000000    100.000000"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f8302e6-b64e-4920-9b71-3063a02c0a87",
   "metadata": {},
   "source": [
    "## Implement k-Means Clustering from Scratch"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65a3361c-c131-43e3-ab23-e72676f36249",
   "metadata": {},
   "source": [
    "### Pseudo Code of the k-Means Clustering Algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6df503b4-4530-458f-9e00-a6d184afaafa",
   "metadata": {},
   "source": [
    "0. Initialize a counter $i = 0$ for the number of iterations performed.\n",
    "1. Start the algorithm choosing randomly `n_clusters` centroids (here the `n_clusters` is an integer hyperparameter that is set at the beginning of the algorithm). Each of this centroids represents the center of a cluster.\n",
    "2. Assign each sample to the cluster corresponding to the centroid with minimal distance to it.\n",
    "3. Update the centroids using the geometric mean of all samples in each cluster.  \n",
    "4. Increase $i$ by 1.\n",
    "5. If $i >$ `max_iterations` (where `max_iterations` is an integer hyperparameter fixed at the beginning) or if the centroids haven't moved, stop; else go back to step 2."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "817b2a84-1e48-4a31-b7db-5000da722449",
   "metadata": {},
   "source": [
    "### Coding Step 1"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0f8c625-24f1-43db-aa05-91932d35edb0",
   "metadata": {},
   "source": [
    "The general goal when picking the initial centroids is to do it so that they are as \"spread out\" as possible. This usually helps the algorithm converging faster. There are known strategies that achieve this task efficiently (those who are curious to learn more about this topic can refer to [this paper](https://theory.stanford.edu/~sergei/papers/kMeansPP-soda.pdf)). Here we will just choose the centroids picking each time a random sample coordinate. This will at least minimize the risk of getting centroids that are really close to each other.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "fc408750-83d7-4e3d-bebc-c9879213b4d8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_centroids(data, n_clusters):\n",
    "    \"\"\"\n",
    "    Choose the samples which will serve as the initial centroids.\n",
    "    \n",
    "    :param data: the samples to cluster\n",
    "    :type data: pandas.DataFrame of shape (n_samples, n_features)\n",
    "    :param n_cluster: the number of clusters to use\n",
    "    :type n_cluster: int\n",
    "    \n",
    "    :return: a pandas.DataFrame whose columns correspond to the centroids\n",
    "    \"\"\"\n",
    "    \n",
    "    # Initialize an empty list to contain the centroids\n",
    "    centroids = []\n",
    "    \n",
    "    # Start the iterations to choose the centroids\n",
    "    for i in range(n_clusters):\n",
    "        \n",
    "        # Choose the centroid pciking random values from each column\n",
    "        centroid = data.apply(lambda x : float(x.sample()))\n",
    "        # Add the centroid we picked to the list of all centroids\n",
    "        centroids.append(centroid)\n",
    "        \n",
    "    return pd.concat(centroids, axis = 1)    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "db6a6881-51c5-4386-a92e-99efe680c2a4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>overall</th>\n",
       "      <td>28.260870</td>\n",
       "      <td>8.695652</td>\n",
       "      <td>28.260870</td>\n",
       "      <td>36.956522</td>\n",
       "      <td>39.130435</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>potential</th>\n",
       "      <td>52.173913</td>\n",
       "      <td>50.000000</td>\n",
       "      <td>84.782609</td>\n",
       "      <td>23.913043</td>\n",
       "      <td>56.521739</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wage_eur</th>\n",
       "      <td>7.010014</td>\n",
       "      <td>0.429185</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.143062</td>\n",
       "      <td>0.143062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value_eur</th>\n",
       "      <td>0.214443</td>\n",
       "      <td>0.150007</td>\n",
       "      <td>0.162894</td>\n",
       "      <td>0.317541</td>\n",
       "      <td>0.923239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>40.740741</td>\n",
       "      <td>44.444444</td>\n",
       "      <td>14.814815</td>\n",
       "      <td>59.259259</td>\n",
       "      <td>18.518519</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0          1          2          3          4\n",
       "overall    28.260870   8.695652  28.260870  36.956522  39.130435\n",
       "potential  52.173913  50.000000  84.782609  23.913043  56.521739\n",
       "wage_eur    7.010014   0.429185   0.000000   0.143062   0.143062\n",
       "value_eur   0.214443   0.150007   0.162894   0.317541   0.923239\n",
       "age        40.740741  44.444444  14.814815  59.259259  18.518519"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test the function\n",
    "centroids = random_centroids(data, 5)\n",
    "centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4273010e-25ac-4ac2-bcc0-bbeb158bbd2d",
   "metadata": {},
   "source": [
    "### Coding Step 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1aeaf106-c3b1-427a-87c1-6b7d7b7cedc5",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_labels(data, centroids):\n",
    "    \"\"\"\n",
    "    Assigns to each sample the label of the cluster it belongs to.\n",
    "    The cluster assignment is based on the Euclidean distance between the sample and the centroids.\n",
    "    \n",
    "    :param data: the samples to cluster\n",
    "    :type data: pandas.DataFrame of shape (n_samples, n_features)\n",
    "    :param centroids: the clusters' centroids\n",
    "    :type centroids: pandas.DataFrame of shape (n_features, n_clusters)\n",
    "    \n",
    "    :return: a pandas.Series of shape (n_samples,) with the labels of the clusters each sample was assigned to\n",
    "    \"\"\"\n",
    "    \n",
    "    # Calculate the distance between each sample and each centroid\n",
    "    distances = centroids.apply(lambda x : np.sqrt((data - x) ** 2).sum(axis = 1))\n",
    "    \n",
    "    # For each sample find the centroid with minimal distance\n",
    "    nearest_centroids = distances.idxmin(axis = 1)\n",
    "    \n",
    "    return nearest_centroids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "eee5be9e-93b4-4b03-a032-e8a8b1c306a7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4    8809\n",
       "0    4863\n",
       "3    4227\n",
       "1     934\n",
       "2     332\n",
       "dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test the function\n",
    "labels = get_labels(data, centroids)\n",
    "labels.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "97ca2a7b-3d07-49ea-b888-10335eaf6137",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>overall</th>\n",
       "      <th>potential</th>\n",
       "      <th>wage_eur</th>\n",
       "      <th>value_eur</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>100.000000</td>\n",
       "      <td>95.652174</td>\n",
       "      <td>91.416309</td>\n",
       "      <td>40.203411</td>\n",
       "      <td>66.666667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>97.826087</td>\n",
       "      <td>93.478261</td>\n",
       "      <td>77.110157</td>\n",
       "      <td>61.596157</td>\n",
       "      <td>59.259259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>95.652174</td>\n",
       "      <td>91.304348</td>\n",
       "      <td>77.110157</td>\n",
       "      <td>23.192313</td>\n",
       "      <td>74.074074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>95.652174</td>\n",
       "      <td>91.304348</td>\n",
       "      <td>77.110157</td>\n",
       "      <td>66.493291</td>\n",
       "      <td>48.148148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>95.652174</td>\n",
       "      <td>91.304348</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>64.689084</td>\n",
       "      <td>51.851852</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "      overall  potential    wage_eur  value_eur        age\n",
       "0  100.000000  95.652174   91.416309  40.203411  66.666667\n",
       "1   97.826087  93.478261   77.110157  61.596157  59.259259\n",
       "2   95.652174  91.304348   77.110157  23.192313  74.074074\n",
       "3   95.652174  91.304348   77.110157  66.493291  48.148148\n",
       "4   95.652174  91.304348  100.000000  64.689084  51.851852"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f7e1132-87c2-4de8-afba-ba8a2b13689d",
   "metadata": {},
   "source": [
    "### Coding Step 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ae27d6c5-14cc-4b72-9aa1-815f4ef47e97",
   "metadata": {},
   "outputs": [],
   "source": [
    "def new_centroids(data, labels, n_clusters):\n",
    "    \"\"\"\n",
    "    Update the centroids using the geometric mean of the samples in each cluster.\n",
    "    \n",
    "    :param data: the samples to cluster\n",
    "    :type data: pandas.DataFrame of shape (n_samples, n_features)\n",
    "    :param labels: the labels denoting the cluster each sample belongs to\n",
    "    :type labels: pandas.Series of shape (n_samples,)\n",
    "    :param n_cluster: the number of clusters to use\n",
    "    :type n_cluster: int  \n",
    "    \n",
    "    :return: a pandas.DataFrame whose columns correspond to the new centroids\n",
    "    \"\"\"\n",
    "    \n",
    "    # Group the samples in clusters following the labels\n",
    "    clusters = data.groupby(labels)\n",
    "    # Find the new centroids by calculating the geometric mean of the samples in each cluster\n",
    "    updated_centroids = clusters.apply(lambda x : x.mean()).T # We transpose to make sure we get\n",
    "                                                                              # the centroids on the columns as\n",
    "                                                                              # that's what we did before\n",
    "        \n",
    "    return updated_centroids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "4b420694-bcc6-4583-968c-4ad3346519ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>overall</th>\n",
       "      <td>50.787222</td>\n",
       "      <td>10.515781</td>\n",
       "      <td>54.963332</td>\n",
       "      <td>40.066447</td>\n",
       "      <td>38.278786</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>potential</th>\n",
       "      <td>49.700042</td>\n",
       "      <td>31.163300</td>\n",
       "      <td>78.116815</td>\n",
       "      <td>36.049825</td>\n",
       "      <td>53.445834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wage_eur</th>\n",
       "      <td>5.214497</td>\n",
       "      <td>0.156433</td>\n",
       "      <td>10.896117</td>\n",
       "      <td>0.811234</td>\n",
       "      <td>1.609544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value_eur</th>\n",
       "      <td>2.482813</td>\n",
       "      <td>0.079966</td>\n",
       "      <td>12.191733</td>\n",
       "      <td>0.325706</td>\n",
       "      <td>1.191804</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>43.564786</td>\n",
       "      <td>17.320961</td>\n",
       "      <td>15.316823</td>\n",
       "      <td>55.232237</td>\n",
       "      <td>21.084917</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0          1          2          3          4\n",
       "overall    50.787222  10.515781  54.963332  40.066447  38.278786\n",
       "potential  49.700042  31.163300  78.116815  36.049825  53.445834\n",
       "wage_eur    5.214497   0.156433  10.896117   0.811234   1.609544\n",
       "value_eur   2.482813   0.079966  12.191733   0.325706   1.191804\n",
       "age        43.564786  17.320961  15.316823  55.232237  21.084917"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Test the function\n",
    "updated_centroids = new_centroids(data, labels, 5)\n",
    "updated_centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90941e60-b932-44b1-8758-9faed0789a02",
   "metadata": {},
   "source": [
    "### Coding Function to Visualize Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8e7d24e8-b5c8-44ce-932d-1f8ac26f5763",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import clear_output\n",
    "\n",
    "def plot_clusters(data, labels, centroids, iteration):\n",
    "    \"\"\"\n",
    "    Visualize the clusters generated by the k-Means Algorithm at a given iteration.\n",
    "    \n",
    "    :param data: the samples to cluster\n",
    "    :type data: pandas.DataFrame of shape (n_samples, n_features)\n",
    "    :param labels: the labels denoting the cluster each sample belongs to\n",
    "    :type labels: pandas.Series of shape (n_samples,)\n",
    "    :param centroids: the clusters' centroids\n",
    "    :type centroids: pandas.DataFrame of shape (n_features, n_clusters)\n",
    "    :param iteration: the number of iterations already performed by the k-Means Algorithm  \n",
    "    :type iteration: int\n",
    "    \"\"\"\n",
    "    # Perform dimensionality reduction in order to be able to visualize the samples and the clusters\n",
    "    pca = PCA(n_components = 2)    # We use 2 components so that we can use planar plots \n",
    "    data_2d = pca.fit_transform(data)\n",
    "    centroids_2d = pca.fit_transform(centroids.T) # We transpose again to put the centroids back on the columns\n",
    "    \n",
    "    # Delete the picture created in the previous iteration\n",
    "    clear_output(wait = True)\n",
    "    \n",
    "    # Draw the picture for the current iteration\n",
    "    plt.title(f\"Iteration {iteration}\")\n",
    "    plt.scatter(x = data_2d[:, 0], y = data_2d[:,1], c = labels) # We use different colors to draw each cluster\n",
    "    plt.scatter(x = centroids_2d[:, 0], y = centroids_2d[:,1], c = \"r\")\n",
    "    plt.show()\n",
    "    \n",
    "    return"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9198f8f-2dcf-48b1-98d4-69abe9797c31",
   "metadata": {},
   "source": [
    "### Coding the Entire Algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5c03cf8d-164c-457c-94c6-d0f8dcf2062c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def k_means_clustering(X, n_clusters = 8, max_iterations = 300): # We set the same hyperparameter default values used by\n",
    "                                                                 # sklearn's instance of k-Means Clustering \n",
    "    \"\"\"\n",
    "    Run the k-Means Algorithm and draw a scatterplot of the data at each iteration.\n",
    "    \n",
    "    :param X: the samples to cluster\n",
    "    :type X: pandas.DataFrame of shape (n_samples, n_features)\n",
    "    :param n_cluster: the number of clusters to use\n",
    "    :type n_cluster: int, default = 8\n",
    "    :param max_iterations: the max number of iterations to perform\n",
    "    :type max_iterations: int, default = 300\n",
    "    \n",
    "    :return: centroids, the clusters' centroids at the moment the algorithm stops\n",
    "             labels, the labels denoting the cluster each sample belongs to \n",
    "    \"\"\"\n",
    "    \n",
    "    # STEP 0: initialize the iterations count\n",
    "    iteration = 0\n",
    "    \n",
    "    # STEP 1: pick randomly the initial centroids\n",
    "    centroids = random_centroids(data, n_clusters)\n",
    "    \n",
    "    # Initialize a dataframe to keep track of the centroids at each previous step\n",
    "    old_centroids = pd.DataFrame()\n",
    "    \n",
    "    # test STEP 5 conditions: keep iterating until we reach the max number of iterations or the centroids don't change\n",
    "    while (iteration < max_iterations) and not (centroids.equals(old_centroids)):\n",
    "        \n",
    "        # The current centroids become outdated\n",
    "        old_centroids = centroids\n",
    "        \n",
    "        # STEP 2: assign the samples to the clusters\n",
    "        labels = get_labels(data, centroids)\n",
    "        \n",
    "        # STEP 3: calculate the new centroids\n",
    "        centroids = new_centroids(data, labels, n_clusters)\n",
    "        \n",
    "        # Plot the data\n",
    "        plot_clusters(data, labels, centroids, iteration)\n",
    "        \n",
    "        # STEP 4: increase the iterations count\n",
    "        iteration +=1\n",
    "        \n",
    "    return centroids, labels"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "914e4196-b71a-49d6-ba04-402e864e6dff",
   "metadata": {},
   "source": [
    "### Visualizing the Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "1d1be853-24e3-469c-90c3-8fc4593925e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Set the hyperparameters and run the algorithm\n",
    "n_clusters = 3\n",
    "max_iterations = 100\n",
    "\n",
    "final_centroids, labels = k_means_clustering(data, n_clusters, max_iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e221d509-c1b2-4320-ac1e-68e982c36da4",
   "metadata": {},
   "source": [
    "### Exploring the Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "7875ac2d-54b0-44d0-9f2c-3c0a493189ec",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2    8317\n",
       "0    7081\n",
       "1    3767\n",
       "dtype: int64"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print the number of players in each cluster\n",
    "labels.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a31fc2c0-f08c-467e-824b-8c6b18c05bcb",
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>overall</th>\n",
       "      <td>42.094890</td>\n",
       "      <td>61.360672</td>\n",
       "      <td>30.345913</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>potential</th>\n",
       "      <td>39.308192</td>\n",
       "      <td>63.785621</td>\n",
       "      <td>48.250310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wage_eur</th>\n",
       "      <td>1.183889</td>\n",
       "      <td>8.936522</td>\n",
       "      <td>0.562976</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value_eur</th>\n",
       "      <td>0.464327</td>\n",
       "      <td>5.512439</td>\n",
       "      <td>0.483151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>49.384634</td>\n",
       "      <td>38.648497</td>\n",
       "      <td>18.881897</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0          1          2\n",
       "overall    42.094890  61.360672  30.345913\n",
       "potential  39.308192  63.785621  48.250310\n",
       "wage_eur    1.183889   8.936522   0.562976\n",
       "value_eur   0.464327   5.512439   0.483151\n",
       "age        49.384634  38.648497  18.881897"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print the final centroids\n",
    "final_centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f66ff18-9029-408d-9f99-a2d2a1272cf6",
   "metadata": {},
   "source": [
    "Inspecting the coordinate of the centroids, it looks like cluster 2 represent young players with low rating, low salaries but good potential."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "84f84d0d-4e02-4621-9910-9993e3958be0",
   "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>short_name</th>\n",
       "      <th>overall</th>\n",
       "      <th>potential</th>\n",
       "      <th>wage_eur</th>\n",
       "      <th>value_eur</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2248</th>\n",
       "      <td>Caio Nunson</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>4400000.0</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2258</th>\n",
       "      <td>Victorino Magela</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>6000.0</td>\n",
       "      <td>3700000.0</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2866</th>\n",
       "      <td>Osvaldão Murilo</td>\n",
       "      <td>73</td>\n",
       "      <td>73</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>3100000.0</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2871</th>\n",
       "      <td>Nicolás Formido</td>\n",
       "      <td>73</td>\n",
       "      <td>73</td>\n",
       "      <td>16000.0</td>\n",
       "      <td>3600000.0</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2877</th>\n",
       "      <td>Neviano Neves</td>\n",
       "      <td>73</td>\n",
       "      <td>73</td>\n",
       "      <td>17000.0</td>\n",
       "      <td>3600000.0</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19234</th>\n",
       "      <td>Song Defu</td>\n",
       "      <td>47</td>\n",
       "      <td>52</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>70000.0</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19235</th>\n",
       "      <td>C. Porter</td>\n",
       "      <td>47</td>\n",
       "      <td>59</td>\n",
       "      <td>500.0</td>\n",
       "      <td>110000.0</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19236</th>\n",
       "      <td>N. Logue</td>\n",
       "      <td>47</td>\n",
       "      <td>55</td>\n",
       "      <td>500.0</td>\n",
       "      <td>100000.0</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19237</th>\n",
       "      <td>L. Rudden</td>\n",
       "      <td>47</td>\n",
       "      <td>60</td>\n",
       "      <td>500.0</td>\n",
       "      <td>110000.0</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19238</th>\n",
       "      <td>E. Lalchhanchhuaha</td>\n",
       "      <td>47</td>\n",
       "      <td>60</td>\n",
       "      <td>500.0</td>\n",
       "      <td>110000.0</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8317 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "               short_name  overall  potential  wage_eur  value_eur  age\n",
       "2248          Caio Nunson       74         74    9000.0  4400000.0   21\n",
       "2258     Victorino Magela       74         74    6000.0  3700000.0   21\n",
       "2866      Osvaldão Murilo       73         73    9000.0  3100000.0   21\n",
       "2871      Nicolás Formido       73         73   16000.0  3600000.0   21\n",
       "2877        Neviano Neves       73         73   17000.0  3600000.0   21\n",
       "...                   ...      ...        ...       ...        ...  ...\n",
       "19234           Song Defu       47         52    1000.0    70000.0   22\n",
       "19235           C. Porter       47         59     500.0   110000.0   19\n",
       "19236            N. Logue       47         55     500.0   100000.0   21\n",
       "19237           L. Rudden       47         60     500.0   110000.0   19\n",
       "19238  E. Lalchhanchhuaha       47         60     500.0   110000.0   19\n",
       "\n",
       "[8317 rows x 6 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print players in cluster 2\n",
    "players[labels == 2][[\"short_name\"] + features]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "946520d6-ebe5-4143-8c80-df8d62bf90b5",
   "metadata": {},
   "source": [
    "Cluster 0 consists of experienced players medium rating, low potential and decent salaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "49405bf2-b606-4066-a772-93d07ecdd00e",
   "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>short_name</th>\n",
       "      <th>overall</th>\n",
       "      <th>potential</th>\n",
       "      <th>wage_eur</th>\n",
       "      <th>value_eur</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1967</th>\n",
       "      <td>J. Hansen</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>7000.0</td>\n",
       "      <td>475000.0</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1970</th>\n",
       "      <td>S. Viera</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>475000.0</td>\n",
       "      <td>38</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1979</th>\n",
       "      <td>L. Schøne</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>1700000.0</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1986</th>\n",
       "      <td>R. Fährmann</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>9000.0</td>\n",
       "      <td>2100000.0</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1987</th>\n",
       "      <td>Fernandinho Silva</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>7000.0</td>\n",
       "      <td>1700000.0</td>\n",
       "      <td>35</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19012</th>\n",
       "      <td>A. Paul</td>\n",
       "      <td>50</td>\n",
       "      <td>55</td>\n",
       "      <td>500.0</td>\n",
       "      <td>50000.0</td>\n",
       "      <td>26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19032</th>\n",
       "      <td>Song Yue</td>\n",
       "      <td>50</td>\n",
       "      <td>50</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>40000.0</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19100</th>\n",
       "      <td>J. Russell</td>\n",
       "      <td>49</td>\n",
       "      <td>49</td>\n",
       "      <td>500.0</td>\n",
       "      <td>15000.0</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19118</th>\n",
       "      <td>Gao Xiang</td>\n",
       "      <td>49</td>\n",
       "      <td>49</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>35000.0</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19139</th>\n",
       "      <td>V. Singh</td>\n",
       "      <td>49</td>\n",
       "      <td>52</td>\n",
       "      <td>500.0</td>\n",
       "      <td>45000.0</td>\n",
       "      <td>27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>7081 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "              short_name  overall  potential  wage_eur  value_eur  age\n",
       "1967           J. Hansen       74         74    7000.0   475000.0   36\n",
       "1970            S. Viera       74         74    2000.0   475000.0   38\n",
       "1979           L. Schøne       74         74    9000.0  1700000.0   35\n",
       "1986         R. Fährmann       74         74    9000.0  2100000.0   32\n",
       "1987   Fernandinho Silva       74         74    7000.0  1700000.0   35\n",
       "...                  ...      ...        ...       ...        ...  ...\n",
       "19012            A. Paul       50         55     500.0    50000.0   26\n",
       "19032           Song Yue       50         50    2000.0    40000.0   29\n",
       "19100         J. Russell       49         49     500.0    15000.0   36\n",
       "19118          Gao Xiang       49         49    2000.0    35000.0   32\n",
       "19139           V. Singh       49         52     500.0    45000.0   27\n",
       "\n",
       "[7081 rows x 6 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print players in cluster 0\n",
    "players[labels == 0][[\"short_name\"] + features]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5c591c4-b992-455e-98ad-23bf6b164784",
   "metadata": {},
   "source": [
    "Finally, Cluster 0 consists of players in their prime with high rating, high potential and high salaries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "35e4daca-06b6-4639-b898-36c388f71e02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\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>short_name</th>\n",
       "      <th>overall</th>\n",
       "      <th>potential</th>\n",
       "      <th>wage_eur</th>\n",
       "      <th>value_eur</th>\n",
       "      <th>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>L. Messi</td>\n",
       "      <td>93</td>\n",
       "      <td>93</td>\n",
       "      <td>320000.0</td>\n",
       "      <td>78000000.0</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>R. Lewandowski</td>\n",
       "      <td>92</td>\n",
       "      <td>92</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>119500000.0</td>\n",
       "      <td>32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Cristiano Ronaldo</td>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>45000000.0</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Neymar Jr</td>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>270000.0</td>\n",
       "      <td>129000000.0</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>K. De Bruyne</td>\n",
       "      <td>91</td>\n",
       "      <td>91</td>\n",
       "      <td>350000.0</td>\n",
       "      <td>125500000.0</td>\n",
       "      <td>30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6983</th>\n",
       "      <td>J. Simpson</td>\n",
       "      <td>68</td>\n",
       "      <td>76</td>\n",
       "      <td>15000.0</td>\n",
       "      <td>2500000.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7103</th>\n",
       "      <td>R. Meshino</td>\n",
       "      <td>68</td>\n",
       "      <td>76</td>\n",
       "      <td>35000.0</td>\n",
       "      <td>2700000.0</td>\n",
       "      <td>23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7115</th>\n",
       "      <td>H. Abe</td>\n",
       "      <td>68</td>\n",
       "      <td>78</td>\n",
       "      <td>35000.0</td>\n",
       "      <td>2700000.0</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7116</th>\n",
       "      <td>E. Zaldívar</td>\n",
       "      <td>68</td>\n",
       "      <td>77</td>\n",
       "      <td>5000.0</td>\n",
       "      <td>2500000.0</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8315</th>\n",
       "      <td>Álex Collado</td>\n",
       "      <td>67</td>\n",
       "      <td>79</td>\n",
       "      <td>33000.0</td>\n",
       "      <td>2500000.0</td>\n",
       "      <td>22</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>3767 rows × 6 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             short_name  overall  potential  wage_eur    value_eur  age\n",
       "0              L. Messi       93         93  320000.0   78000000.0   34\n",
       "1        R. Lewandowski       92         92  270000.0  119500000.0   32\n",
       "2     Cristiano Ronaldo       91         91  270000.0   45000000.0   36\n",
       "3             Neymar Jr       91         91  270000.0  129000000.0   29\n",
       "4          K. De Bruyne       91         91  350000.0  125500000.0   30\n",
       "...                 ...      ...        ...       ...          ...  ...\n",
       "6983         J. Simpson       68         76   15000.0    2500000.0   24\n",
       "7103         R. Meshino       68         76   35000.0    2700000.0   23\n",
       "7115             H. Abe       68         78   35000.0    2700000.0   22\n",
       "7116        E. Zaldívar       68         77    5000.0    2500000.0   24\n",
       "8315       Álex Collado       67         79   33000.0    2500000.0   22\n",
       "\n",
       "[3767 rows x 6 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print players in cluster 1\n",
    "players[labels == 1][[\"short_name\"] + features]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "806cd894-04f5-4302-a152-57e54bc1a4fc",
   "metadata": {},
   "source": [
    "## Comparing my Algorithm to sklearn's Implementation of k-Means Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "0d412bd3-9f73-4bc4-b833-ef4c7bf50d33",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(n_clusters=3)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "# Instantiate and fit an instance of sklearn's k-Means Clustering algorithm\n",
    "kmeans = KMeans(n_clusters = 3)\n",
    "kmeans.fit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "b6692cc3-8814-4f48-831e-824115949ce3",
   "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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>overall</th>\n",
       "      <td>28.855991</td>\n",
       "      <td>58.071374</td>\n",
       "      <td>42.227897</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>potential</th>\n",
       "      <td>46.720262</td>\n",
       "      <td>62.448090</td>\n",
       "      <td>38.926672</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>wage_eur</th>\n",
       "      <td>0.443119</td>\n",
       "      <td>7.277191</td>\n",
       "      <td>1.253223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>value_eur</th>\n",
       "      <td>0.396673</td>\n",
       "      <td>4.581982</td>\n",
       "      <td>0.444290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>age</th>\n",
       "      <td>19.003805</td>\n",
       "      <td>34.872954</td>\n",
       "      <td>51.214468</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   0          1          2\n",
       "overall    28.855991  58.071374  42.227897\n",
       "potential  46.720262  62.448090  38.926672\n",
       "wage_eur    0.443119   7.277191   1.253223\n",
       "value_eur   0.396673   4.581982   0.444290\n",
       "age        19.003805  34.872954  51.214468"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print the final centroids\n",
    "pd.DataFrame(kmeans.cluster_centers_.T, index = features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "52687b30-abbe-4e6c-88f4-0f7aa985ebbb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "13"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Print the number of iterations performed\n",
    "kmeans.n_iter_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c67079c-7781-4b13-87cb-f512d099b0ea",
   "metadata": {},
   "source": [
    "Modulo a permutation of the labels (which doesn't really have any intrinsic meaning), the clusters obtained by sklearn are similar to the ones we got. Our algorithm, however, needed more iterations to converge; this is most likely because sklearn initializes the centroids using a method more efficient than the one we used.  "
   ]
  }
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