TP_N_4_Apprentissage_non_supervisé__Clustering_.ipynb

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      "name": "python3",
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    "language_info": {
      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Objectifs"
      ],
      "metadata": {
        "id": "3By7jIBAMXDz"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "L’objectif principal des méthodes d’apprentissage non supervisé est de grouper des éléments proches dans un même groupe d’une manière que deux éléments d’un même groupe soient le plus similaire possible et que deux éléments de deux groupes différents soient le plus dissemblables possible. \n",
        "Nous cherchons donc à minimiser la distance intra-classe et de maximiser la distance inter-classe. Plusieurs méthodes sont disponibles dans **Scikit- Learn**. Nous étudierons une d’entre elles de plus près dans ce TP."
      ],
      "metadata": {
        "id": "wQ5SGg9LMM-q"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Partie 1 : Données de travail"
      ],
      "metadata": {
        "id": "ztOH1yxbNNWn"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nous disposons d’un jeu de données **fromage.txt** qui comprend **29 instances de fromage**, représentées par **9 attributs** (**calories**, **sodium**, **calcium**, **lipides**, **retinol**, **folates**, **proteines**, **cholesterol** et **magnesium**).\n",
        "Les instructions Python suivantes permettent de charger le jeu de données **fromage.txt**."
      ],
      "metadata": {
        "id": "CyecIsr3NWJA"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "fromage=pd.read_table(r\"fromage.txt\",sep=\"\\t\",header=0,index_col=0)\n",
        "fromage"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 990
        },
        "id": "CypMkzsfPNff",
        "outputId": "ff140884-b534-4f24-9ef4-8b359cd7f210"
      },
      "execution_count": 91,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                    calories  sodium  calcium  lipides  retinol  folates  \\\n",
              "Fromages                                                                   \n",
              "CarredelEst              314   353.5     72.6     26.3     51.6     30.3   \n",
              "Babybel                  314   238.0    209.8     25.1     63.7      6.4   \n",
              "Beaufort                 401   112.0    259.4     33.3     54.9      1.2   \n",
              "Bleu                     342   336.0    211.1     28.9     37.1     27.5   \n",
              "Camembert                264   314.0    215.9     19.5    103.0     36.4   \n",
              "Cantal                   367   256.0    264.0     28.8     48.8      5.7   \n",
              "Chabichou                344   192.0     87.2     27.9     90.1     36.3   \n",
              "Chaource                 292   276.0    132.9     25.4    116.4     32.5   \n",
              "Cheddar                  406   172.0    182.3     32.5     76.4      4.9   \n",
              "Comte                    399    92.0    220.5     32.4     55.9      1.3   \n",
              "Coulomniers              308   222.0     79.2     25.6     63.6     21.1   \n",
              "Edam                     327   148.0    272.2     24.7     65.7      5.5   \n",
              "Emmental                 378    60.0    308.2     29.4     56.3      2.4   \n",
              "Fr.chevrepatemolle       206   160.0     72.8     18.5    150.5     31.0   \n",
              "Fr.fondu.45              292   390.0    168.5     24.0     77.4      5.5   \n",
              "Fr.frais20nat.            80    41.0    146.3      3.5     50.0     20.0   \n",
              "Fr.frais40nat.           115    25.0     94.8      7.8     64.3     22.6   \n",
              "Maroilles                338   311.0    236.7     29.1     46.7      3.6   \n",
              "Morbier                  347   285.0    219.0     29.5     57.6      5.8   \n",
              "Parmesan                 381   240.0    334.6     27.5     90.0      5.2   \n",
              "Petitsuisse40            142    22.0     78.2     10.4     63.4     20.4   \n",
              "PontlEveque              300   223.0    156.7     23.4     53.0      4.0   \n",
              "Pyrenees                 355   232.0    178.9     28.0     51.5      6.8   \n",
              "Reblochon                309   272.0    202.3     24.6     73.1      8.1   \n",
              "Rocquefort               370   432.0    162.0     31.2     83.5     13.3   \n",
              "SaintPaulin              298   205.0    261.0     23.3     60.4      6.7   \n",
              "Tome                     321   252.0    125.5     27.3     62.3      6.2   \n",
              "Vacherin                 321   140.0    218.0     29.3     49.2      3.7   \n",
              "Yaourtlaitent.nat.        70    91.0    215.7      3.4     42.9      2.9   \n",
              "\n",
              "                    proteines  cholesterol  magnesium  \n",
              "Fromages                                               \n",
              "CarredelEst              21.0           70         20  \n",
              "Babybel                  22.6           70         27  \n",
              "Beaufort                 26.6          120         41  \n",
              "Bleu                     20.2           90         27  \n",
              "Camembert                23.4           60         20  \n",
              "Cantal                   23.0           90         30  \n",
              "Chabichou                19.5           80         36  \n",
              "Chaource                 17.8           70         25  \n",
              "Cheddar                  26.0          110         28  \n",
              "Comte                    29.2          120         51  \n",
              "Coulomniers              20.5           80         13  \n",
              "Edam                     24.7           80         44  \n",
              "Emmental                 29.4          110         45  \n",
              "Fr.chevrepatemolle       11.1           50         16  \n",
              "Fr.fondu.45              16.8           70         20  \n",
              "Fr.frais20nat.            8.3           10         11  \n",
              "Fr.frais40nat.            7.0           30         10  \n",
              "Maroilles                20.4           90         40  \n",
              "Morbier                  23.6           80         30  \n",
              "Parmesan                 35.7           80         46  \n",
              "Petitsuisse40             9.4           20         10  \n",
              "PontlEveque              21.1           70         22  \n",
              "Pyrenees                 22.4           90         25  \n",
              "Reblochon                19.7           80         30  \n",
              "Rocquefort               18.7          100         25  \n",
              "SaintPaulin              23.3           70         26  \n",
              "Tome                     21.8           80         20  \n",
              "Vacherin                 17.6           80         30  \n",
              "Yaourtlaitent.nat.        4.1           13         14  "
            ],
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>calories</th>\n",
              "      <th>sodium</th>\n",
              "      <th>calcium</th>\n",
              "      <th>lipides</th>\n",
              "      <th>retinol</th>\n",
              "      <th>folates</th>\n",
              "      <th>proteines</th>\n",
              "      <th>cholesterol</th>\n",
              "      <th>magnesium</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Fromages</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>CarredelEst</th>\n",
              "      <td>314</td>\n",
              "      <td>353.5</td>\n",
              "      <td>72.6</td>\n",
              "      <td>26.3</td>\n",
              "      <td>51.6</td>\n",
              "      <td>30.3</td>\n",
              "      <td>21.0</td>\n",
              "      <td>70</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Babybel</th>\n",
              "      <td>314</td>\n",
              "      <td>238.0</td>\n",
              "      <td>209.8</td>\n",
              "      <td>25.1</td>\n",
              "      <td>63.7</td>\n",
              "      <td>6.4</td>\n",
              "      <td>22.6</td>\n",
              "      <td>70</td>\n",
              "      <td>27</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Beaufort</th>\n",
              "      <td>401</td>\n",
              "      <td>112.0</td>\n",
              "      <td>259.4</td>\n",
              "      <td>33.3</td>\n",
              "      <td>54.9</td>\n",
              "      <td>1.2</td>\n",
              "      <td>26.6</td>\n",
              "      <td>120</td>\n",
              "      <td>41</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Bleu</th>\n",
              "      <td>342</td>\n",
              "      <td>336.0</td>\n",
              "      <td>211.1</td>\n",
              "      <td>28.9</td>\n",
              "      <td>37.1</td>\n",
              "      <td>27.5</td>\n",
              "      <td>20.2</td>\n",
              "      <td>90</td>\n",
              "      <td>27</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Camembert</th>\n",
              "      <td>264</td>\n",
              "      <td>314.0</td>\n",
              "      <td>215.9</td>\n",
              "      <td>19.5</td>\n",
              "      <td>103.0</td>\n",
              "      <td>36.4</td>\n",
              "      <td>23.4</td>\n",
              "      <td>60</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cantal</th>\n",
              "      <td>367</td>\n",
              "      <td>256.0</td>\n",
              "      <td>264.0</td>\n",
              "      <td>28.8</td>\n",
              "      <td>48.8</td>\n",
              "      <td>5.7</td>\n",
              "      <td>23.0</td>\n",
              "      <td>90</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Chabichou</th>\n",
              "      <td>344</td>\n",
              "      <td>192.0</td>\n",
              "      <td>87.2</td>\n",
              "      <td>27.9</td>\n",
              "      <td>90.1</td>\n",
              "      <td>36.3</td>\n",
              "      <td>19.5</td>\n",
              "      <td>80</td>\n",
              "      <td>36</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Chaource</th>\n",
              "      <td>292</td>\n",
              "      <td>276.0</td>\n",
              "      <td>132.9</td>\n",
              "      <td>25.4</td>\n",
              "      <td>116.4</td>\n",
              "      <td>32.5</td>\n",
              "      <td>17.8</td>\n",
              "      <td>70</td>\n",
              "      <td>25</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Cheddar</th>\n",
              "      <td>406</td>\n",
              "      <td>172.0</td>\n",
              "      <td>182.3</td>\n",
              "      <td>32.5</td>\n",
              "      <td>76.4</td>\n",
              "      <td>4.9</td>\n",
              "      <td>26.0</td>\n",
              "      <td>110</td>\n",
              "      <td>28</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Comte</th>\n",
              "      <td>399</td>\n",
              "      <td>92.0</td>\n",
              "      <td>220.5</td>\n",
              "      <td>32.4</td>\n",
              "      <td>55.9</td>\n",
              "      <td>1.3</td>\n",
              "      <td>29.2</td>\n",
              "      <td>120</td>\n",
              "      <td>51</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Coulomniers</th>\n",
              "      <td>308</td>\n",
              "      <td>222.0</td>\n",
              "      <td>79.2</td>\n",
              "      <td>25.6</td>\n",
              "      <td>63.6</td>\n",
              "      <td>21.1</td>\n",
              "      <td>20.5</td>\n",
              "      <td>80</td>\n",
              "      <td>13</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Edam</th>\n",
              "      <td>327</td>\n",
              "      <td>148.0</td>\n",
              "      <td>272.2</td>\n",
              "      <td>24.7</td>\n",
              "      <td>65.7</td>\n",
              "      <td>5.5</td>\n",
              "      <td>24.7</td>\n",
              "      <td>80</td>\n",
              "      <td>44</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Emmental</th>\n",
              "      <td>378</td>\n",
              "      <td>60.0</td>\n",
              "      <td>308.2</td>\n",
              "      <td>29.4</td>\n",
              "      <td>56.3</td>\n",
              "      <td>2.4</td>\n",
              "      <td>29.4</td>\n",
              "      <td>110</td>\n",
              "      <td>45</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Fr.chevrepatemolle</th>\n",
              "      <td>206</td>\n",
              "      <td>160.0</td>\n",
              "      <td>72.8</td>\n",
              "      <td>18.5</td>\n",
              "      <td>150.5</td>\n",
              "      <td>31.0</td>\n",
              "      <td>11.1</td>\n",
              "      <td>50</td>\n",
              "      <td>16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Fr.fondu.45</th>\n",
              "      <td>292</td>\n",
              "      <td>390.0</td>\n",
              "      <td>168.5</td>\n",
              "      <td>24.0</td>\n",
              "      <td>77.4</td>\n",
              "      <td>5.5</td>\n",
              "      <td>16.8</td>\n",
              "      <td>70</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Fr.frais20nat.</th>\n",
              "      <td>80</td>\n",
              "      <td>41.0</td>\n",
              "      <td>146.3</td>\n",
              "      <td>3.5</td>\n",
              "      <td>50.0</td>\n",
              "      <td>20.0</td>\n",
              "      <td>8.3</td>\n",
              "      <td>10</td>\n",
              "      <td>11</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Fr.frais40nat.</th>\n",
              "      <td>115</td>\n",
              "      <td>25.0</td>\n",
              "      <td>94.8</td>\n",
              "      <td>7.8</td>\n",
              "      <td>64.3</td>\n",
              "      <td>22.6</td>\n",
              "      <td>7.0</td>\n",
              "      <td>30</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Maroilles</th>\n",
              "      <td>338</td>\n",
              "      <td>311.0</td>\n",
              "      <td>236.7</td>\n",
              "      <td>29.1</td>\n",
              "      <td>46.7</td>\n",
              "      <td>3.6</td>\n",
              "      <td>20.4</td>\n",
              "      <td>90</td>\n",
              "      <td>40</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Morbier</th>\n",
              "      <td>347</td>\n",
              "      <td>285.0</td>\n",
              "      <td>219.0</td>\n",
              "      <td>29.5</td>\n",
              "      <td>57.6</td>\n",
              "      <td>5.8</td>\n",
              "      <td>23.6</td>\n",
              "      <td>80</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Parmesan</th>\n",
              "      <td>381</td>\n",
              "      <td>240.0</td>\n",
              "      <td>334.6</td>\n",
              "      <td>27.5</td>\n",
              "      <td>90.0</td>\n",
              "      <td>5.2</td>\n",
              "      <td>35.7</td>\n",
              "      <td>80</td>\n",
              "      <td>46</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Petitsuisse40</th>\n",
              "      <td>142</td>\n",
              "      <td>22.0</td>\n",
              "      <td>78.2</td>\n",
              "      <td>10.4</td>\n",
              "      <td>63.4</td>\n",
              "      <td>20.4</td>\n",
              "      <td>9.4</td>\n",
              "      <td>20</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>PontlEveque</th>\n",
              "      <td>300</td>\n",
              "      <td>223.0</td>\n",
              "      <td>156.7</td>\n",
              "      <td>23.4</td>\n",
              "      <td>53.0</td>\n",
              "      <td>4.0</td>\n",
              "      <td>21.1</td>\n",
              "      <td>70</td>\n",
              "      <td>22</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Pyrenees</th>\n",
              "      <td>355</td>\n",
              "      <td>232.0</td>\n",
              "      <td>178.9</td>\n",
              "      <td>28.0</td>\n",
              "      <td>51.5</td>\n",
              "      <td>6.8</td>\n",
              "      <td>22.4</td>\n",
              "      <td>90</td>\n",
              "      <td>25</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Reblochon</th>\n",
              "      <td>309</td>\n",
              "      <td>272.0</td>\n",
              "      <td>202.3</td>\n",
              "      <td>24.6</td>\n",
              "      <td>73.1</td>\n",
              "      <td>8.1</td>\n",
              "      <td>19.7</td>\n",
              "      <td>80</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Rocquefort</th>\n",
              "      <td>370</td>\n",
              "      <td>432.0</td>\n",
              "      <td>162.0</td>\n",
              "      <td>31.2</td>\n",
              "      <td>83.5</td>\n",
              "      <td>13.3</td>\n",
              "      <td>18.7</td>\n",
              "      <td>100</td>\n",
              "      <td>25</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>SaintPaulin</th>\n",
              "      <td>298</td>\n",
              "      <td>205.0</td>\n",
              "      <td>261.0</td>\n",
              "      <td>23.3</td>\n",
              "      <td>60.4</td>\n",
              "      <td>6.7</td>\n",
              "      <td>23.3</td>\n",
              "      <td>70</td>\n",
              "      <td>26</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Tome</th>\n",
              "      <td>321</td>\n",
              "      <td>252.0</td>\n",
              "      <td>125.5</td>\n",
              "      <td>27.3</td>\n",
              "      <td>62.3</td>\n",
              "      <td>6.2</td>\n",
              "      <td>21.8</td>\n",
              "      <td>80</td>\n",
              "      <td>20</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Vacherin</th>\n",
              "      <td>321</td>\n",
              "      <td>140.0</td>\n",
              "      <td>218.0</td>\n",
              "      <td>29.3</td>\n",
              "      <td>49.2</td>\n",
              "      <td>3.7</td>\n",
              "      <td>17.6</td>\n",
              "      <td>80</td>\n",
              "      <td>30</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Yaourtlaitent.nat.</th>\n",
              "      <td>70</td>\n",
              "      <td>91.0</td>\n",
              "      <td>215.7</td>\n",
              "      <td>3.4</td>\n",
              "      <td>42.9</td>\n",
              "      <td>2.9</td>\n",
              "      <td>4.1</td>\n",
              "      <td>13</td>\n",
              "      <td>14</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-649c8661-76bc-4ae8-b813-e0a2c4a41ce3')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "        \n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
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              "    .colab-df-convert:hover {\n",
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              "      fill: #174EA6;\n",
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              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
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              "\n",
              "      <script>\n",
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              "          document.querySelector('#df-649c8661-76bc-4ae8-b813-e0a2c4a41ce3 button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
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              "          const element = document.querySelector('#df-649c8661-76bc-4ae8-b813-e0a2c4a41ce3');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
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              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 91
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(fromage.describe())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a3mEH6r7Tz12",
        "outputId": "a21bada6-3a17-4e06-e2a0-53bdf363e87d"
      },
      "execution_count": 92,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "         calories      sodium     calcium    lipides     retinol    folates  \\\n",
            "count   29.000000   29.000000   29.000000  29.000000   29.000000  29.000000   \n",
            "mean   300.034483  210.086207  185.734483  24.158621   67.562069  13.010345   \n",
            "std     91.914356  108.678923   72.528882   8.129642   24.163098  11.723339   \n",
            "min     70.000000   22.000000   72.600000   3.400000   37.100000   1.200000   \n",
            "25%    292.000000  140.000000  132.900000  23.400000   51.600000   4.900000   \n",
            "50%    321.000000  223.000000  202.300000  26.300000   62.300000   6.400000   \n",
            "75%    355.000000  276.000000  220.500000  29.100000   76.400000  21.100000   \n",
            "max    406.000000  432.000000  334.600000  33.300000  150.500000  36.400000   \n",
            "\n",
            "       proteines  cholesterol  magnesium  \n",
            "count  29.000000    29.000000  29.000000  \n",
            "mean   20.168966    74.586207  26.965517  \n",
            "std     6.959788    28.245755  11.318388  \n",
            "min     4.100000    10.000000  10.000000  \n",
            "25%    17.800000    70.000000  20.000000  \n",
            "50%    21.000000    80.000000  26.000000  \n",
            "75%    23.400000    90.000000  30.000000  \n",
            "max    35.700000   120.000000  51.000000  \n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "nombre_instances,nombre_attributs=fromage.shape\n",
        "print('Le jeu de données fromage.txt comprend', nombre_instances, 'instances représentées chacune par', nombre_attributs , 'attributs :' , \", \".join(fromage.columns),'.')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Za-8ed_FTDVN",
        "outputId": "2b035a34-fdfc-48e2-a9a9-01751afda4ab"
      },
      "execution_count": 93,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Le jeu de données fromage.txt comprend 29 instances représentées chacune par 9 attributs : calories, sodium, calcium, lipides, retinol, folates, proteines, cholesterol, magnesium .\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**À vous !**\n",
        "\n",
        "**Comment sont réparties les données ?**\n",
        "\n",
        "Le jeu de données **fromage.txt** comprend **29 instances** de fromage représentées par **9 attributs**.\n",
        "\n",
        "**Quels sont les attributs de ce jeu de données ?**\n",
        "\n",
        "Les attributs de ce jeu de données sont **calories**, **sodium**, **calcium**, **lipides**, **retinol**, **folates**, **proteines**, **cholesterol** et **magnesium**.\n",
        "\n",
        "Nous allons visualiser la **matrice de distribution de données** grâce aux instructions ci-dessous :"
      ],
      "metadata": {
        "id": "-Jlo8xsXQiht"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from pandas.plotting import scatter_matrix\n",
        "# Croisement 2 à 2 des variables\n",
        "scatter_matrix(fromage, figsize=(9,9))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "0yRBPzdSSrFG",
        "outputId": "b1e9d952-e625-4d0c-ee9b-f72e92a99df0"
      },
      "execution_count": 94,
      "outputs": [
        {
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nous remarquons que les attributs suivants sont **positivement corrélés** :\n",
        "- **calories - cholesterol**\n",
        "- **calories - lipides**\n",
        "- **lipides - cholesterol**\n",
        "- **retinol - folates**"
      ],
      "metadata": {
        "id": "sxg6xQIkXOAN"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Partie 2 : Méthode des centres mobiles"
      ],
      "metadata": {
        "id": "n9eJYB7GYyH3"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Dans l’algorithme **k-Means**, le nombre **k** de **clusters** est **fixé au départ**. A partir d'une partition initiale, nous cherchons à améliorer itérativement la partition en minimisant un certain critère.\n",
        "\n",
        "Nous importerons le paquet **sklearn.cluster** pour utiliser la méthode **k-Means** de la classe **sklearn.cluster.KMeans**.\n",
        "\n",
        "**À vous !**"
      ],
      "metadata": {
        "id": "WSHUGFD0Y_me"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "from sklearn import cluster\n",
        "np.random.seed(0)\n",
        "# Créer un modèle pour un ensemble de k centres\n",
        "kmeans = cluster.KMeans(n_clusters = 4)\n",
        "# Utiliser les données pour définir le modèle de clustering\n",
        "kmeans.fit(fromage)\n",
        "idk = np.argsort(kmeans.labels_)\n",
        "print(pd.DataFrame(fromage.index[idk],kmeans.labels_[idk]))\n",
        "print(kmeans.transform(fromage))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "buy1W3gzbSi0",
        "outputId": "2335bafb-67bd-42d0-e8a2-6e5ba2ea09be"
      },
      "execution_count": 95,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "             Fromages\n",
            "0         CarredelEst\n",
            "0                Tome\n",
            "0         PontlEveque\n",
            "0           Chabichou\n",
            "0            Chaource\n",
            "0         Coulomniers\n",
            "0  Fr.chevrepatemolle\n",
            "1            Beaufort\n",
            "1         SaintPaulin\n",
            "1             Cheddar\n",
            "1               Comte\n",
            "1                Edam\n",
            "1            Emmental\n",
            "1            Vacherin\n",
            "1            Parmesan\n",
            "2       Petitsuisse40\n",
            "2  Yaourtlaitent.nat.\n",
            "2      Fr.frais20nat.\n",
            "2      Fr.frais40nat.\n",
            "3           Maroilles\n",
            "3             Morbier\n",
            "3              Cantal\n",
            "3           Camembert\n",
            "3            Pyrenees\n",
            "3           Reblochon\n",
            "3          Rocquefort\n",
            "3                Bleu\n",
            "3             Babybel\n",
            "3         Fr.fondu.45\n",
            "[[123.59715669 285.36163076 384.27301005 145.46927992]\n",
            " [110.54651897 118.43379084 303.10311983  71.72681089]\n",
            " [235.25665316  56.72603293 349.91323389 218.1879268 ]\n",
            " [159.09984736 200.30401971 393.76898843  45.60922494]\n",
            " [141.19170858 210.31138298 332.43471728  84.66051854]\n",
            " [180.75982487 111.73150994 371.97076666  86.99931839]\n",
            " [ 72.0404549  182.80599775 298.65300308 170.2611917 ]\n",
            " [ 57.86280572 204.98823213 311.48990553 105.53037193]\n",
            " [156.41570984  92.26223665 348.48685233 159.88151676]\n",
            " [224.31195752  79.32509258 333.83554522 230.88643399]\n",
            " [ 39.94716153 204.4018782  285.29211565 155.61953412]\n",
            " [197.13338124  43.74211715 293.81905359 172.55995306]\n",
            " [289.57992728 102.59674855 343.1669947  273.3780741 ]\n",
            " [144.41931015 265.24828993 195.86579908 252.80069897]\n",
            " [164.74401355 271.72958122 400.47054979 101.45152241]\n",
            " [307.24796873 336.96303256  27.57918146 378.20198492]\n",
            " [286.92623741 330.65941362  48.43507252 376.38946771]\n",
            " [163.69886115 169.20512053 379.74839203  39.80348477]\n",
            " [137.46307556 146.31641334 360.87135     31.87791398]\n",
            " [247.92574637 127.37007228 405.05415842 157.0268493 ]\n",
            " [275.48594208 322.76561591  73.02996816 370.72406639]\n",
            " [ 66.39975258 145.61200264 273.9400961  103.74546448]\n",
            " [103.21034693 118.1602421  327.69454718  85.09362726]\n",
            " [106.4868939  149.56115075 323.02206001  41.96502591]\n",
            " [215.62761551 302.57210349 480.78906108 141.69363218]\n",
            " [163.61948015  93.47945128 289.74900561 120.31124386]\n",
            " [ 44.67517687 176.06769384 309.5039923   98.83002277]\n",
            " [158.9611408   63.47704556 263.14012664 168.16769428]\n",
            " [304.65582689 316.6232269  101.24362326 346.9503587 ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Donner les attributs des centres de chaque cluster\n",
        "print(kmeans.cluster_centers_)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "6yS-kiWc7GY_",
        "outputId": "e1a8c879-74f4-4c95-91fa-0045da1aa5d7"
      },
      "execution_count": 96,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[297.85714286 239.78571429 103.84285714  24.91428571  83.92857143\n",
            "   23.05714286  18.97142857  71.42857143  21.71428571]\n",
            " [363.875      146.125      257.025       29.05        63.6\n",
            "    3.8625      26.5625      96.25        38.875     ]\n",
            " [101.75        44.75       133.75         6.275       55.15\n",
            "   16.475        7.2         18.25        11.25      ]\n",
            " [329.8        306.6        206.82        26.87        64.24\n",
            "   11.91        21.08        82.          27.4       ]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Aide à la détection du nombre adéquat de groupes**\n",
        "\n",
        "**K-Means**, ne fournit pas d’outils d’aide à la détection du nombre de classes. Nous devons les programmer sous Python ou utiliser des procédures proposées par des packages dédiés. Le schéma est souvent le même: nous faisons varier le nombre de groupes et nous surveillons l’évolution d’un indicateur de qualité de la solution c'est à dire l’aptitude des individus à être plus proches de ses congénères du même groupe que des individus des autres groupes.\n",
        "Dans ce qui suit, nous allons calculer la métrique '**Silhouette**' pour différents nombres de groupes issus de la méthode des centres mobiles.\n",
        "\n",
        "**À vous !**"
      ],
      "metadata": {
        "id": "JQI-m8dYc4hs"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import metrics\n",
        "# Utilisation de la métrique \"Silhouette\"\n",
        "res = np.arange(9, dtype =\"double\")\n",
        "for k in np.arange(9):\n",
        "  km = cluster.KMeans(n_clusters = k+2)\n",
        "  km.fit(fromage)\n",
        "  res[k] = metrics.silhouette_score(fromage,km.labels_)\n",
        "print(res)\n",
        "# Graphique\n",
        "import matplotlib.pyplot as plt\n",
        "plt.title(\"Silhouette\")\n",
        "plt.xlabel(\"# of clusters\")\n",
        "plt.plot(np.arange(2,11,1),(res))\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 330
        },
        "id": "OgnC2u-wd40d",
        "outputId": "5a473c30-0693-49ed-b4ad-e3b34cc670a2"
      },
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[0.50681355 0.37299771 0.3282387  0.35737616 0.32267618 0.28114392\n",
            " 0.29450378 0.23904343 0.25006247]\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Quelle est la meilleure valeur de k (nombre de clusters) selon la métrique 'Silhouette' ?**\n",
        "\n",
        "Le **score le plus élevé** est d'environ **0,5** pour un **nombre de clusters** égal à **2**. Cependant, il faut éviter d'utiliser une valeur de k égal à **2** car il s'agit d'un **cas limite**. Nous choisissons donc la valeur **5** qui a le meilleur score selon cette métrique.\n",
        "\n",
        "Si nous choisissons un k qui est :\n",
        "\n",
        "* **Très faible**: Risque que des éléments appartenant à un **même cluster** présentent des **dissimilitudes**.\n",
        "* **Très élevé**: Risque que des éléments **n'appartenant pas au même cluster** soient **similaires**."
      ],
      "metadata": {
        "id": "hSPrRWNRevyc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Partie 3 : Classification ascendante hiérarchique"
      ],
      "metadata": {
        "id": "1qF4xei2e5TA"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "La **classification ascendante hiérarchique** (ou **CAH**) procède par fusions successives d'ensembles de points (clusters), en considérant initialement tous les points comme des clusters singletons, nous fusionnons à chaque étape les 2 clusters les plus proches au sens d'une\n",
        "distance, jusqu'à obtenir un seul cluster contenant tous les points.\n",
        "Nous allons exécuter l’algorithme **CAH** en utilisant le package **scipy**.\n",
        "\n",
        "**À vous !**\n"
      ],
      "metadata": {
        "id": "ZHBOQrsJfBJd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas\n",
        "import numpy as np\n",
        "# Librairies pour la CAH\n",
        "from matplotlib import pyplot as plt\n",
        "from scipy.cluster.hierarchy import dendrogram, linkage, fcluster\n",
        "Z = linkage(fromage,method='ward', metric='euclidean')\n",
        "# Affichage du dendrogramme\n",
        "plt.title(\"CAH\")\n",
        "plt.title('CAH avec matérialisation des 4 classes')\n",
        "dendrogram(Z,labels=fromage.index,orientation='left',color_threshold=255)\n",
        "plt.show()\n",
        "groupes_cah = fcluster(Z, t = 255,criterion='distance')\n",
        "print(groupes_cah)\n",
        "# Index triés des groupes\n",
        "idg = np.argsort(groupes_cah)\n",
        "# Affichage des observations et leurs groupes\n",
        "print(pandas.DataFrame(fromage.index[idg],groupes_cah[idg]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 819
        },
        "id": "CmTF3fn-fbY6",
        "outputId": "b490c64e-b1d9-4e91-bd81-aaedb83fd01c"
      },
      "execution_count": 98,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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          },
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            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[3 4 2 3 3 2 4 4 2 2 4 2 2 4 3 1 1 3 3 2 1 4 4 4 3 2 4 2 1]\n",
            "             Fromages\n",
            "1  Yaourtlaitent.nat.\n",
            "1       Petitsuisse40\n",
            "1      Fr.frais40nat.\n",
            "1      Fr.frais20nat.\n",
            "2         SaintPaulin\n",
            "2            Beaufort\n",
            "2              Cantal\n",
            "2            Parmesan\n",
            "2             Cheddar\n",
            "2               Comte\n",
            "2                Edam\n",
            "2            Emmental\n",
            "2            Vacherin\n",
            "3          Rocquefort\n",
            "3             Morbier\n",
            "3           Maroilles\n",
            "3         CarredelEst\n",
            "3           Camembert\n",
            "3                Bleu\n",
            "3         Fr.fondu.45\n",
            "4         Coulomniers\n",
            "4            Chaource\n",
            "4           Chabichou\n",
            "4         PontlEveque\n",
            "4            Pyrenees\n",
            "4           Reblochon\n",
            "4             Babybel\n",
            "4                Tome\n",
            "4  Fr.chevrepatemolle\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Pour une **distance minimale de 255** entre **2 clusters**, nous obtenons **4 clusters**."
      ],
      "metadata": {
        "id": "U3ZG1gUUgk32"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Donner la correspondance entre les groupes de la CAH et les clusters de Kmeans\n",
        "pd.crosstab(kmeans.labels_,groupes_cah, rownames=['k-Means'], colnames=['Linkage',])"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "ZK5O3nSNh1lt",
        "outputId": "03bca81a-85bd-4079-fccf-8ce36e1d3121"
      },
      "execution_count": 99,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Linkage  1  2  3  4\n",
              "k-Means            \n",
              "0        0  0  1  6\n",
              "1        0  8  0  0\n",
              "2        4  0  0  0\n",
              "3        0  1  6  3"
            ],
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              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-8273d33f-10af-4b76-8b29-6d82ce871f9e button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-8273d33f-10af-4b76-8b29-6d82ce871f9e');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 99
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Cluster **0** de **k-Means** (=) Cluster **4** de **Linkage**\n",
        "\n",
        "Cluster **1** de **k-Means** (=) Cluster **2** de **Linkage**\n",
        "\n",
        "Cluster **2** de **k-Means** (=) Cluster **1** de **Linkage**\n",
        "\n",
        "Cluster **3** de **k-Means** (=) Cluster **3** de **Linkage**\n",
        "\n",
        "Avec 2 exceptions : \n",
        "- **4 échantillons** du **4ème** cluster de **k-Means** ne font pas partie du **3ème** cluster de **Linkage**.\n",
        "- **Un échantillon** du **1er** cluster de **k-Means** ne fait pas partie du **4ème** cluster de **Linkage**."
      ],
      "metadata": {
        "id": "d1Jqhd_ECSYg"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Partie 4 : Interprétation des classes"
      ],
      "metadata": {
        "id": "UROsB2pjjNec"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Analyse en composantes principales (ACP)**\n",
        "\n",
        "L'ACP est une méthode de réduction de la dimensionnalité qui transforme un grand ensemble de variables en un ensemble plus petit qui contient toujours la plupart des informations du grand ensemble. Cela rend l'ensemble de données plus simple et donc plus facile à explorer, à visualiser et à analyser, au détriment de la précision.\n",
        "\n",
        "\n",
        "**À vous !**"
      ],
      "metadata": {
        "id": "iQCs8MD1j4_X"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.decomposition import PCA\n",
        "acp = PCA(n_components =2).fit_transform(fromage)\n",
        "for couleur,k in zip(['red','blue','lawngreen', 'aqua'],[0,1,2,3]):\n",
        "    plt.scatter(acp[kmeans.labels_==k,0],acp[kmeans.labels_==k,1],c=couleur)\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "eobiHWimiIzN",
        "outputId": "1e2dbc07-d659-472b-ae2e-40aebfd1d720"
      },
      "execution_count": 100,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Compte rendu"
      ],
      "metadata": {
        "id": "BmHtTs8Bn4qE"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Nous allons appliquer sur le même jeu de données, la méthode de **clustering CAH** du package **sklearn.cluster.AgglomerativeClustering**."
      ],
      "metadata": {
        "id": "nrYHlpOAxqhR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# AgglomerativeClustering utilise la distance de liaison pour fusionner récursivement les paires de clusters\n",
        "from sklearn.cluster import AgglomerativeClustering\n",
        "np.random.seed(0)\n",
        "# Fournir le nombre de clusters à l'avance\n",
        "agg_c = AgglomerativeClustering(n_clusters=4) \n",
        "agg_c.fit(fromage)\n",
        "idk_ = np.argsort(agg_c.labels_)\n",
        "print(pd.DataFrame(fromage.index[idk_],agg_c.labels_[idk_]))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2IHTGORIxxNl",
        "outputId": "bcdafdcb-db4b-40b5-c040-3556dd5702a9"
      },
      "execution_count": 101,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "             Fromages\n",
            "0         SaintPaulin\n",
            "0            Beaufort\n",
            "0            Parmesan\n",
            "0              Cantal\n",
            "0             Cheddar\n",
            "0               Comte\n",
            "0            Vacherin\n",
            "0                Edam\n",
            "0            Emmental\n",
            "1         CarredelEst\n",
            "1          Rocquefort\n",
            "1             Morbier\n",
            "1           Maroilles\n",
            "1         Fr.fondu.45\n",
            "1           Camembert\n",
            "1                Bleu\n",
            "2         Coulomniers\n",
            "2            Chaource\n",
            "2           Chabichou\n",
            "2         PontlEveque\n",
            "2            Pyrenees\n",
            "2           Reblochon\n",
            "2             Babybel\n",
            "2                Tome\n",
            "2  Fr.chevrepatemolle\n",
            "3      Fr.frais20nat.\n",
            "3      Fr.frais40nat.\n",
            "3       Petitsuisse40\n",
            "3  Yaourtlaitent.nat.\n"
          ]
        }
      ]
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        "# Donner la correspondance entre les clusters de Kmeans et AgglomerativeClustering\n",
        "pd.crosstab(kmeans.labels_,agg_c.labels_, rownames=['k-Means'], colnames=['AgglomerativeClustering',])"
      ],
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              "AgglomerativeClustering  0  1  2  3\n",
              "k-Means                            \n",
              "0                        0  1  6  0\n",
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              "2                        0  0  0  4\n",
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      "source": [
        "Cluster **0** de **k-Means** (=) Cluster **2** de **AgglomerativeClustering**\n",
        "\n",
        "Cluster **1** de **k-Means** (=) Cluster **0** de **AgglomerativeClustering**\n",
        "\n",
        "Cluster **2** de **k-Means** (=) Cluster **3** de **AgglomerativeClustering**\n",
        "\n",
        "Cluster **3** de **k-Means** (=) Cluster **1** de **AgglomerativeClustering**\n",
        "\n",
        "Avec 2 exceptions : \n",
        "- **4 échantillons** du **4ème** cluster de **k-Means** ne font pas partie du **2ème** cluster de **AgglomerativeClustering**.\n",
        "- **Un échantillon** du **1er** cluster de **k-Means** ne fait pas partie du **3ème** cluster de **AgglomerativeClustering**.\n",
        "\n"
      ],
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      "cell_type": "code",
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        "# Donner la correspondance entre les clusters de Linkage et AgglomerativeClustering\n",
        "pd.crosstab(agg_c.labels_,groupes_cah, rownames=['Linkage'], colnames=['AgglomerativeClustering',])"
      ],
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              "AgglomerativeClustering  1  2  3  4\n",
              "Linkage                            \n",
              "0                        0  9  0  0\n",
              "1                        0  0  7  0\n",
              "2                        0  0  0  9\n",
              "3                        4  0  0  0"
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      "cell_type": "markdown",
      "source": [
        "Cluster **0** de **Linkage** (=) Cluster **2** de **AgglomerativeClustering**\n",
        "\n",
        "Cluster **1** de **Linkage** (=) Cluster **3** de **AgglomerativeClustering**\n",
        "\n",
        "Cluster **2** de **Linkage** (=) Cluster **4** de **AgglomerativeClustering**\n",
        "\n",
        "Cluster **3** de **Linkage** (=) Cluster **1** de **AgglomerativeClustering**\n",
        "\n",
        "Il existe une **forte correspondance** entre les clusters générés par les deux algorithmes **Linkage** et **AgglomerativeClustering**."
      ],
      "metadata": {
        "id": "v8U2qw_MQujV"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Implémentation d'un algorithme hiérarchique descendant (divisive clustering) basé sur l’utilisation de k-means**"
      ],
      "metadata": {
        "id": "wZ6_Sdl8RLjM"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from sklearn import cluster\n",
        "from sklearn import metrics\n",
        "def divisive_clustering_using_kMeans(oldDataset, step_nbre = 0):\n",
        "    if len(oldDataset)==1:\n",
        "        step_nbre = step_nbre+1\n",
        "        print(\"\\n\")\n",
        "        print(\"###### Final Step\",step_nbre,\"######\")\n",
        "        print(\" \\n\".join(pd.DataFrame(oldDataset).index))\n",
        "        return\n",
        "    else:\n",
        "        # Préparer l'algorithme k-Means avec k = 2 pour séparer l'ensemble de données en deux nouveaux clusters\n",
        "        km = cluster.KMeans(n_clusters = 2)\n",
        "        km.fit(oldDataset)\n",
        "        # Séparer le jeu de données en deux clusters\n",
        "        tab0=[] # Les numéros des lignes du premier cluster\n",
        "        tab1=[] # Les numéros des lignes du deuxième cluster\n",
        "        for i  in np.arange(len(km.labels_)):\n",
        "            if km.labels_[i]==0:\n",
        "                tab0.append(i)\n",
        "            elif km.labels_[i]==1:\n",
        "                tab1.append(i)\n",
        "        # Extraire les échantillons de chaque cluster\n",
        "        sub0=oldDataset.iloc[tab0]\n",
        "        sub1=oldDataset.iloc[tab1]\n",
        "        step_nbre=step_nbre+1\n",
        "        # Afficher les deux clusters\n",
        "        print(\"\\n\")\n",
        "        print(\"###### Step\",step_nbre,\"######\")\n",
        "        print(\"\\n\")\n",
        "        print(\"First cluster for this step :\\n\")\n",
        "        print(\" \\n\".join(pd.DataFrame(sub0).index))\n",
        "        print(\"\\n\")\n",
        "        print(\"Second cluster for this step :\\n\")\n",
        "        print(\" \\n\".join(pd.DataFrame(sub1).index))\n",
        "        # Continuez à diviser les clusters résultants\n",
        "        divisive_clustering_using_kMeans(sub0,step_nbre)\n",
        "        divisive_clustering_using_kMeans(sub1,step_nbre)\n",
        "# Appeler la fonction divisive_clustering_using_kMeans\n",
        "divisive_clustering_using_kMeans(fromage)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8nfMqiAu0Pt7",
        "outputId": "1cf26c4b-6ef3-4d8a-e323-8bd33b448ea6"
      },
      "execution_count": 104,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "###### Step 1 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "CarredelEst \n",
            "Babybel \n",
            "Beaufort \n",
            "Bleu \n",
            "Camembert \n",
            "Cantal \n",
            "Chabichou \n",
            "Chaource \n",
            "Cheddar \n",
            "Comte \n",
            "Coulomniers \n",
            "Edam \n",
            "Emmental \n",
            "Fr.fondu.45 \n",
            "Maroilles \n",
            "Morbier \n",
            "Parmesan \n",
            "PontlEveque \n",
            "Pyrenees \n",
            "Reblochon \n",
            "Rocquefort \n",
            "SaintPaulin \n",
            "Tome \n",
            "Vacherin\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Fr.chevrepatemolle \n",
            "Fr.frais20nat. \n",
            "Fr.frais40nat. \n",
            "Petitsuisse40 \n",
            "Yaourtlaitent.nat.\n",
            "\n",
            "\n",
            "###### Step 2 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "CarredelEst \n",
            "Babybel \n",
            "Bleu \n",
            "Camembert \n",
            "Chabichou \n",
            "Chaource \n",
            "Coulomniers \n",
            "Fr.fondu.45 \n",
            "Maroilles \n",
            "Morbier \n",
            "PontlEveque \n",
            "Pyrenees \n",
            "Reblochon \n",
            "Rocquefort \n",
            "Tome\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Beaufort \n",
            "Cantal \n",
            "Cheddar \n",
            "Comte \n",
            "Edam \n",
            "Emmental \n",
            "Parmesan \n",
            "SaintPaulin \n",
            "Vacherin\n",
            "\n",
            "\n",
            "###### Step 3 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Babybel \n",
            "Chabichou \n",
            "Chaource \n",
            "Coulomniers \n",
            "PontlEveque \n",
            "Pyrenees \n",
            "Reblochon \n",
            "Tome\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "CarredelEst \n",
            "Bleu \n",
            "Camembert \n",
            "Fr.fondu.45 \n",
            "Maroilles \n",
            "Morbier \n",
            "Rocquefort\n",
            "\n",
            "\n",
            "###### Step 4 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Chabichou \n",
            "Chaource \n",
            "Coulomniers \n",
            "Tome\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Babybel \n",
            "PontlEveque \n",
            "Pyrenees \n",
            "Reblochon\n",
            "\n",
            "\n",
            "###### Step 5 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Chabichou \n",
            "Coulomniers \n",
            "Tome\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Chaource\n",
            "\n",
            "\n",
            "###### Step 6 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Coulomniers \n",
            "Tome\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Chabichou\n",
            "\n",
            "\n",
            "###### Step 7 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Tome\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Coulomniers\n",
            "\n",
            "\n",
            "###### Final Step 8 ######\n",
            "Tome\n",
            "\n",
            "\n",
            "###### Final Step 8 ######\n",
            "Coulomniers\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Chabichou\n",
            "\n",
            "\n",
            "###### Final Step 6 ######\n",
            "Chaource\n",
            "\n",
            "\n",
            "###### Step 5 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Babybel \n",
            "Reblochon\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "PontlEveque \n",
            "Pyrenees\n",
            "\n",
            "\n",
            "###### Step 6 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Babybel\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Reblochon\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Babybel\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Reblochon\n",
            "\n",
            "\n",
            "###### Step 6 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "PontlEveque\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Pyrenees\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "PontlEveque\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Pyrenees\n",
            "\n",
            "\n",
            "###### Step 4 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Bleu \n",
            "Camembert \n",
            "Maroilles \n",
            "Morbier\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "CarredelEst \n",
            "Fr.fondu.45 \n",
            "Rocquefort\n",
            "\n",
            "\n",
            "###### Step 5 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Bleu \n",
            "Maroilles \n",
            "Morbier\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Camembert\n",
            "\n",
            "\n",
            "###### Step 6 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Bleu\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Maroilles \n",
            "Morbier\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Bleu\n",
            "\n",
            "\n",
            "###### Step 7 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Morbier\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Maroilles\n",
            "\n",
            "\n",
            "###### Final Step 8 ######\n",
            "Morbier\n",
            "\n",
            "\n",
            "###### Final Step 8 ######\n",
            "Maroilles\n",
            "\n",
            "\n",
            "###### Final Step 6 ######\n",
            "Camembert\n",
            "\n",
            "\n",
            "###### Step 5 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Fr.fondu.45 \n",
            "Rocquefort\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "CarredelEst\n",
            "\n",
            "\n",
            "###### Step 6 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Rocquefort\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Fr.fondu.45\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Rocquefort\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Fr.fondu.45\n",
            "\n",
            "\n",
            "###### Final Step 6 ######\n",
            "CarredelEst\n",
            "\n",
            "\n",
            "###### Step 3 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Beaufort \n",
            "Cheddar \n",
            "Comte \n",
            "Edam \n",
            "Emmental \n",
            "Vacherin\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Cantal \n",
            "Parmesan \n",
            "SaintPaulin\n",
            "\n",
            "\n",
            "###### Step 4 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Cheddar \n",
            "Edam \n",
            "Vacherin\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Beaufort \n",
            "Comte \n",
            "Emmental\n",
            "\n",
            "\n",
            "###### Step 5 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Edam \n",
            "Vacherin\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Cheddar\n",
            "\n",
            "\n",
            "###### Step 6 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Vacherin\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Edam\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Vacherin\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Edam\n",
            "\n",
            "\n",
            "###### Final Step 6 ######\n",
            "Cheddar\n",
            "\n",
            "\n",
            "###### Step 5 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Emmental\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Beaufort \n",
            "Comte\n",
            "\n",
            "\n",
            "###### Final Step 6 ######\n",
            "Emmental\n",
            "\n",
            "\n",
            "###### Step 6 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Beaufort\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Comte\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Beaufort\n",
            "\n",
            "\n",
            "###### Final Step 7 ######\n",
            "Comte\n",
            "\n",
            "\n",
            "###### Step 4 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Cantal \n",
            "Parmesan\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "SaintPaulin\n",
            "\n",
            "\n",
            "###### Step 5 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Parmesan\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Cantal\n",
            "\n",
            "\n",
            "###### Final Step 6 ######\n",
            "Parmesan\n",
            "\n",
            "\n",
            "###### Final Step 6 ######\n",
            "Cantal\n",
            "\n",
            "\n",
            "###### Final Step 5 ######\n",
            "SaintPaulin\n",
            "\n",
            "\n",
            "###### Step 2 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Fr.frais20nat. \n",
            "Fr.frais40nat. \n",
            "Petitsuisse40 \n",
            "Yaourtlaitent.nat.\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Fr.chevrepatemolle\n",
            "\n",
            "\n",
            "###### Step 3 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Fr.frais20nat. \n",
            "Yaourtlaitent.nat.\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Fr.frais40nat. \n",
            "Petitsuisse40\n",
            "\n",
            "\n",
            "###### Step 4 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Yaourtlaitent.nat.\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Fr.frais20nat.\n",
            "\n",
            "\n",
            "###### Final Step 5 ######\n",
            "Yaourtlaitent.nat.\n",
            "\n",
            "\n",
            "###### Final Step 5 ######\n",
            "Fr.frais20nat.\n",
            "\n",
            "\n",
            "###### Step 4 ######\n",
            "\n",
            "\n",
            "First cluster for this step :\n",
            "\n",
            "Petitsuisse40\n",
            "\n",
            "\n",
            "Second cluster for this step :\n",
            "\n",
            "Fr.frais40nat.\n",
            "\n",
            "\n",
            "###### Final Step 5 ######\n",
            "Petitsuisse40\n",
            "\n",
            "\n",
            "###### Final Step 5 ######\n",
            "Fr.frais40nat.\n",
            "\n",
            "\n",
            "###### Final Step 3 ######\n",
            "Fr.chevrepatemolle\n"
          ]
        }
      ]
    }
  ]
}