Labo_Machine_Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p align=\"center\"><font size=\"6\"><b>Notebook de Charles-Henri SAINT-MARS</b></font></p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Les fondamentaux du Machine Learning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importation des modules\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre de valeur :  21\n",
      "Liste triée par ordre croissant :  [ 2  5  6  7  8 11 15 25 27 31 31 32 36 39 41 43 48 50 61 80 82]\n"
     ]
    }
   ],
   "source": [
    "ages = [5,31,43,48,50,41,7,11,15,39,80,82,32,2,8,6,25,36,27,61,31]\n",
    "\n",
    "# Nombre de personnes\n",
    "print(\"Nombre de valeur : \", len(ages))\n",
    "\n",
    "# Trier la liste ages par ordre croissant\n",
    "print(\"Liste triée par ordre croissant : \", np.sort(ages))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "15.75"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "21*3/4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le 75e percentile est à la 16ème position dans la liste triée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "75e percentile :  43.0\n"
     ]
    }
   ],
   "source": [
    "x = np.percentile(ages, 75)\n",
    "print(\"75e percentile : \", x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Distribution des données</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tableau de 250 flottants aléatoires entre 0 et 5 :  [2.45977534 2.40511997 4.79595919 1.62475661 3.47148249 4.59154503\n",
      " 3.31201839 3.10616553 4.49638813 3.45364783 2.62719608 2.54140003\n",
      " 4.27093026 2.10058979 3.7610589  2.84557864 4.44750374 1.92206961\n",
      " 4.37550081 4.3122334  0.36976494 3.78827562 2.68607045 4.18547469\n",
      " 0.39734363 1.99244401 1.12027181 0.11545709 1.11813751 1.93608543\n",
      " 0.3709289  3.52979786 3.1738463  1.5517872  4.92069596 3.71368999\n",
      " 3.66854563 0.19624461 3.95578126 2.70609697 1.45783045 0.61852081\n",
      " 2.29133793 4.53305225 0.81326865 0.34860556 3.36056503 1.03399917\n",
      " 4.50192038 3.40095319 4.67339288 4.80091756 1.90101434 4.40595241\n",
      " 4.08866375 1.85285052 4.69484297 0.60705631 2.02301983 0.64235841\n",
      " 4.12839867 1.09457264 2.93752955 3.97479992 4.77895914 4.20104714\n",
      " 0.28084259 4.43192519 1.12130334 1.55442661 3.14202421 0.47879892\n",
      " 0.58762004 2.07930645 1.38354738 4.03180443 1.6086113  0.08344114\n",
      " 1.97512229 1.34587101 4.64717911 3.24955919 4.46721747 4.24762073\n",
      " 0.6345325  0.22719911 2.02768476 4.61697109 2.69077623 0.33065092\n",
      " 3.14751705 0.68058683 3.5800686  1.09676476 2.87341927 0.01820917\n",
      " 2.78236634 4.09998611 4.1086393  0.38878833 1.14322398 0.50192965\n",
      " 0.54098661 4.8734411  0.00985855 0.22500745 3.19461854 2.44525597\n",
      " 3.24763672 4.25251931 3.8902793  1.48275528 3.36684333 4.31486947\n",
      " 1.93541541 0.83070359 1.80021032 3.92798621 2.76185247 4.44534045\n",
      " 0.41659567 1.28453414 1.48463199 0.78889331 3.73223669 3.94186382\n",
      " 0.37021509 0.14700914 2.97113159 2.56049206 1.05449136 0.5584587\n",
      " 2.15258226 0.33357438 2.35255709 0.37516847 0.89765976 1.73978094\n",
      " 4.23799147 1.79163758 4.37338808 2.6053896  2.39007337 1.08779716\n",
      " 3.52386074 4.97339425 2.42853738 2.20280264 0.63570087 4.91694346\n",
      " 2.74190915 1.88036981 0.04767347 2.32019093 1.11898799 4.82497315\n",
      " 0.49375275 2.23417416 2.91725496 2.80627053 2.17456499 2.77587456\n",
      " 4.93364027 3.82252349 2.03311042 3.30703061 3.23645525 4.47970457\n",
      " 0.93193865 0.46160839 0.13570779 2.60585903 2.92788806 4.99709321\n",
      " 0.24117517 2.30114933 0.84826405 4.42172078 3.20095195 2.58811128\n",
      " 0.88648402 4.60527125 4.41604023 3.19118903 1.58710151 3.26258806\n",
      " 4.57904291 2.10244051 2.37210962 1.32540544 3.62707201 2.932764\n",
      " 1.13523533 3.28563623 2.13735878 1.33462586 3.42303333 1.4981511\n",
      " 1.48529055 1.94271641 3.17827646 3.89439888 3.14867048 1.8744893\n",
      " 3.78073169 2.63351607 1.79640553 1.14076816 0.72486023 0.04447942\n",
      " 4.43835418 2.48067609 3.88343078 2.92303418 1.87061919 4.6788197\n",
      " 2.49719362 0.11925257 1.9414299  1.54997127 4.06961121 1.82166782\n",
      " 0.13448287 2.02379837 2.86419267 3.06021127 1.3147519  4.97420603\n",
      " 1.2914665  2.69817024 2.59602541 0.12886297 1.12645796 0.68333376\n",
      " 2.92795726 0.2279109  4.17526117 3.74813605 3.74261834 3.0699959\n",
      " 1.82525517 1.64521212 3.01279434 0.45430696 1.92911407 4.88257953\n",
      " 2.56929358 0.12343489 3.82718278 2.40674429]\n"
     ]
    }
   ],
   "source": [
    "# Créez un tableau contenant 250 flottants aléatoires entre 0 et 5\n",
    "tab = np.random.uniform(0,5,250)\n",
    "print(\"Tableau de 250 flottants aléatoires entre 0 et 5 : \", tab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1atUqSWdGty5btkzr1q3TyZMnNWXKFD366KMaP378B3pNL8erHz9+XJf/Y4MyhuQzutcjrusq3tkuSeTsIXK2Q9Y2yNlGIueX/mGGhg8f7tt49XP+2KWpqUnr1q3ThAkTeh1fsWKFVq5cqdWrV6upqUnFxcWaMWOGTp06da5v1S8cx1FhYaEycwpY1B5yHEeZOQXk7DFytkPWNsjZRiLnwsJCX3M+p+bj9OnTuvXWW/X444/rwx/+cPK467patWqVli5dqtmzZ6uiokL19fXq6OjQhg0b+q1oAAAwcJ1T87FgwQLNmjVL11xzTa/jBw8eVEtLi6qqqpLHQqGQpk+fru3bt59fpecpEolowYIFOrFlLaN7PeT2dOvElrXk7DFytkPWNsjZRiLnBQsWDKzx6hs3btRLL72kurq6sx5raWmRJBUVFfU6XlRUlHzsvSKRiNrb23ttXujp6dGaNWt0+uVNjO71kBuP6fTLm8jZY+Rsh6xtkLONRM5r1qwZOOPVm5ubdffdd+tf/uVfNHjwn77i+72fI7mu+yc/W6qrq1NBQUFyKy0t7UtJAABggOlT87Fr1y61trZq4sSJysrKUlZWlhobG/Wd73xHWVlZyTMe7z3L0draetbZkIQlS5aora0tuTU3N5/jrwIAAAaCPs35+OxnP6s9e/b0Onb77bfrYx/7mO677z5deOGFKi4uVkNDgy677DJJUjQaVWNjo5YvX/6+rxkKhRQKhc6xfAAAMND0qfnIy8tTRUVFr2O5ubkaNmxY8nh1dbVqa2tVXl6u8vJy1dbWKicnR3PmzOm/qgEAwIDV7xNOFy9erM7OTs2fPz85ZGzLli3Ky8vr77cCAAAD0Hk3H1u3bu31s+M4qqmpUU1Nzfm+NAAASEPnNV7dC16NV4/H4zp8+LCuWv4zZeYXynH4Tj0vuG5csfZjkkTOHiJnO2Rtg5xtJHL+5X2f0ejRo5WR0X859+Xvd2C+WC4jI0Njx45VVsH733WD/uE4GWRsgJztkLUNcraRyHns2LG+1kFrCQAATAWm+YhGo/rqV7+qkz//vtwYo3u94sa6dfLn3ydnj5GzHbK2Qc42Ejl/9atfVTQa9a2OwDQf3d3d+sY3vqH2Xz8tN8boXq+4sZjaf/00OXuMnO2QtQ1ytpHI+Rvf+Ia6u/1r8gLTfAAAgNRA8wEAAEzRfAAAAFM0HwAAwBTNBwAAMEXzAQAATAVqvPqrr76qGSsbNWh4KaN7PeK6cXUfb5YkcvYQOdshaxvkbCORc8Oi6br44osZr+61jIwMjR8/XtmFh/wuJa05ToayC8f4XUbaI2c7ZG2DnG0kch4/fryvddBaAgAAU4FpPqLRqGpqavTHX/4ro3s95Ma69cdf/is5e4yc7ZC1DXK2kci5pqaG8eoWuru7tWzZMrX96geM7vWQG4up7Vc/IGePkbMdsrZBzjYSOS9btozx6gAAIDhoPgAAgCmaDwAAYIrmAwAAmKL5AAAApmg+AACAqcCMV4/FYnrppZf0P1f/UtlFH5GTkdlvr413uPGYom/9XpLI2UPkbIesbZCzjUTOzy28SpdffrkyM/svZ8arv4/MzExNnjxZoZGtfpeS1pyMTIVGjvO7jLRHznbI2gY520jkPHnyZF/r4GMXAABgKjDNRzQa1SOPPKK2//oxo3s95Ma61fZfPyZnj5GzHbK2Qc42Ejk/8sgjvo5XD8zHLt3d3Vq8eLEkKe+yWXIyB/lcUXpyYzH9cesTksjZS+Rsh6xtkLONRM6Lt0rz589Xdna2L3UE5swHAABIDTQfAADAFM0HAAAwRfMBAABM0XwAAABTNB8AAMBUYG61HTx4sH7+85/rC+v+U04Wt3B5xckapKJbapP78AY52yFrG+RsI5Hzxr+bqsGDB/tXR1C+2yVh7P2b+v01AQAYSA49PKvfX7Mvf7/52AUAAJgKTPPR3d2tRx99VKdeel5urMfvctKWG+vRqZeeJ2ePkbMdsrZBzjYSOT/66KPq7vZvjH1grvmIRqNauHChJCm34ho5mYH51U25sR79oeG7ksjZS+Rsh6xtkLONRM4LG6R58+Zp0CB/rq8JzJkPAACQGmg+AACAKZoPAABgiuYDAACYovkAAACmaD4AAICpwNzLFAqF9Pzzz+v29U2M7vWQkzVIhTc9mNyHN8jZDlnbIGcbiZyfmDdZoVDIvzoYrw4AQLAwXh0AAARKYJqP7u5urV+/Xqf3/Dujez3kxnp0es+/k7PHyNkOWdsgZxuJnNevX894dQvRaFS33367JCnnoqsY3esRN9ajE5tXSSJnL5GzHbK2Qc42Ejnfvlm6+eabB8Z49bVr12rChAnKz89Xfn6+pk6dqhdeeCH5uOu6qqmpUUlJiYYMGaLKykrt3bu334sGAAADV5+aj1GjRunhhx/Wzp07tXPnTn3mM5/RDTfckGwwVqxYoZUrV2r16tVqampScXGxZsyYoVOnTnlSPAAAGHj61Hxcf/31uvbaazVu3DiNGzdOX//61zV06FDt2LFDrutq1apVWrp0qWbPnq2KigrV19ero6NDGzZs8Kp+AAAwwJzzBaexWEwbN25UOBzW1KlTdfDgQbW0tKiqqir5nFAopOnTp2v79u1/8nUikYja29t7bQAAIH31ufnYs2ePhg4dqlAopLvuukvPPPOMLrnkErW0tEiSioqKej2/qKgo+dj7qaurU0FBQXIrLS3ta0kAAGAA6XPzcdFFF2n37t3asWOHvvzlL2vu3Lnat29f8nHHcXo933Xds46925IlS9TW1pbcmpub+1oSAAAYQPp8L1N2drY++tGPSpImTZqkpqYmffvb39Z9990nSWppadHIkSOTz29tbT3rbMi7hUIhkxGvoVBI//Zv/6b5//oSo3s95GQN0vAb7k/uwxvkbIesbZCzjUTOa2693Nfx6ud9I7XruopEIiorK1NxcbEaGhp02WWXSTozW6OxsVHLly8/70LPV1ZWlm6++WZ9dVeO36WkNScjU7kfu8rvMtIeOdshaxvkbCOR88039/949b7oU/PxwAMPaObMmSotLdWpU6e0ceNGbd26VS+++KIcx1F1dbVqa2tVXl6u8vJy1dbWKicnR3PmzPGqfgAAMMD0qfl46623dNttt+no0aMqKCjQhAkT9OKLL2rGjBmSpMWLF6uzs1Pz58/XyZMnNWXKFG3ZskV5eXmeFN8XPT09euaZZxT+75eUM26qnIxMv0tKS248po7f/qckkbOHyNkOWdsgZxuJnH/0ow791V/9lbKy/JkkG5hvtQ2Hwxo6dKgkqfSep5SRPbjfXhvviEe71PytmySRs5fI2Q5Z2yBnG+/O+fTp08rNze231+ZbbQEAQMqi+QAAAKZoPgAAgCmaDwAAYIrmAwAAmKL5AAAApvy5wdcH2dnZeuKJJ3Tvj/6fnMzA/NrmnMwsDbu2OrkPb5CzHbK2Qc42Ejl/4+aPKzs72786gjLnI2Hs/Zv6/TUBABhIDj3c/+PVmfMBAABSVmCaj56eHm3atEkdv2+SG4/5XU7acuMxdfy+iZw9Rs52yNoGOdtI5Lxp0yb19PT4VkdgPliLRCK67rrrJJ0Z3etk870BXnB7unXsqWWSyNlL5GyHrG2Qs41Eztc9dWa8ul/f7RKYMx8AACA10HwAAABTNB8AAMAUzQcAADBF8wEAAEzRfAAAAFOBudU2Oztbq1ev1v/9yW8Y3eshJzNLF8y4K7kPb5CzHbK2Qc42Ejl/7YYKxqu/G+PVAQDwFuPVAQBAoASm+YjFYtq6dau6Dr/C6F4PufGYug6/Qs4eI2c7ZG2DnG0kct66datiMf9yDswHa11dXbr66qslMbrXS25Pt976wQOSyNlL5GyHrG2Qs41Ezlf/4Mx49dzcXF/qCMyZDwAAkBpoPgAAgCmaDwAAYIrmAwAAmKL5AAAApmg+AACAqcDcajto0CCtWLFCtZtflZPJLVxecTIz9aHK25P78AY52yFrG+RsI5HzA9derEGDBvlXB+PVAQAIFsarAwCAQAlM8xGLxdTU1KTI0d8yutdDbjymyNHfkrPHyNkOWdsgZxuJnJuamnwdrx6Y5qOrq0uf/OQn1fLkIrk93X6Xk7bcnm61PLmInD1GznbI2gY520jk/MlPflJdXV2+1RGY5gMAAKQGmg8AAGCK5gMAAJii+QAAAKZoPgAAgCmaDwAAYCpQ49UffPBBrfr33zK610NOZqYKrrwluQ9vkLMdsrZBzjYSOVdfM47x6u/GeHUAALzFeHUAABAogWk+4vG49u7dq+ix1+W6cb/LSVuuG1f02Ovk7DFytkPWNsjZRiLnvXv3Kh73L+fANB+dnZ2qqKjQ0e8vkNsd9buctOV2R3X0+wvI2WPkbIesbZCzjUTOFRUV6uzs9K2OwDQfAAAgNdB8AAAAUzQfAADAFM0HAAAwRfMBAABM9an5qKur0+TJk5WXl6cRI0boxhtv1GuvvdbrOa7rqqamRiUlJRoyZIgqKyu1d+/efi0aAAAMXH0ar97Y2KgFCxZo8uTJ6unp0dKlS1VVVaV9+/YpNzdXkrRixQqtXLlS69ev17hx4/TQQw9pxowZeu2115SXl+fJL/FBDBo0SPfee6/WbTvA6F4POZmZyv/k7OQ+vEHOdsjaBjnbSOT8d5++cOCOVz927JhGjBihxsZGffrTn5bruiopKVF1dbXuu+8+SVIkElFRUZGWL1+uO++88y++JuPVAQDw1oAer97W1iZJuuCCCyRJBw8eVEtLi6qqqpLPCYVCmj59urZv3/6+rxGJRNTe3t5rAwAA6eucmw/XdbVo0SJdddVVqqiokCS1tLRIkoqKino9t6ioKPnYe9XV1amgoCC5lZaWnmtJf1Y8HtehQ4fU0/YWo3s95Lpx9bS9Rc4eI2c7ZG2DnG0kcj506NDAHK++cOFCvfLKK/rBD35w1mOO4/T62XXds44lLFmyRG1tbcmtubn5XEv6szo7O1VWVqY3vnsHo3s95HZH9cZ37yBnj5GzHbK2Qc42EjmXlZX5Ol69TxecJnzlK1/Rc889p23btmnUqFHJ48XFxZLOnAEZOXJk8nhra+tZZ0MSQqGQQqHQuZQBAAAGoD6d+XBdVwsXLtTTTz+tn/3sZyorK+v1eFlZmYqLi9XQ0JA8Fo1G1djYqGnTpvVPxQAAYEDr05mPBQsWaMOGDfrJT36ivLy85HUcBQUFGjJkiBzHUXV1tWpra1VeXq7y8nLV1tYqJydHc+bM8eQXAAAAA0ufmo+1a9dKkiorK3sdf+KJJzRv3jxJ0uLFi9XZ2an58+fr5MmTmjJlirZs2eLrjA8AAJA6+tR8fJCRII7jqKamRjU1NedaEwAASGN8twsAADB1Tne7DERZWVmaP3++nvzP1+VkMLrXK05GpoZeNiu5D2+Qsx2ytkHONhI5/6+pY5SV5V8LcF7j1b3AeHUAALw1oMerAwAA9FVgmg/XdXXs2DHFOto+0IWzODeu6yrW0UbOHiNnO2Rtg5xtJHI+duyYrzkHpvno6OjQiBEjdOSfbpXbHfG7nLTldkd05J9uJWePkbMdsrZBzjYSOY8YMUIdHR2+1RGY5gMAAKQGmg8AAGCK5gMAAJii+QAAAKZoPgAAgCmaDwAAYCpQ49Xnzp2rp3YdYXSvh5yMTOVWfDa5D2+Qsx2ytkHONhI53zRxFOPV343x6gAAeIvx6gAAIFAC03y4rqtwOKx4tIvRvR5yXVfxaBc5e4yc7ZC1DXK2kcg5HA4zXt1CR0eHhg4dquZv3cToXg+53RE1f+smcvYYOdshaxvkbCOR89ChQxmvDgAAgoPmAwAAmKL5AAAApmg+AACAKZoPAABgiuYDAACYCsx49czMTN10003avOeonAx6Lq84GRnKuejK5D68Qc52yNoGOdtI5HztpSOVmenfGHvGqwMAEDCMVwcAAIFC8wEAAEwFpvkIh8NyHEevL79O8WiX3+WkrXi0S68vv46cPUbOdsjaBjnbSOTsOI7C4bBvdQSm+QAAAKmB5gMAAJii+QAAAKZoPgAAgCmaDwAAYIrmAwAAmArUePVrr71WP//vVkb3esjJyNCQCycl9+ENcrZD1jbI2UYi56s/NoLx6u/GeHUAALzFeHUAABAoNB8AAMBUYJqPcDis3NxcHV75OUb3eige7dLhlZ8jZ4+Rsx2ytkHONhI55+bm+jpePTAXnEpSR0eH3yUEgtsd8buEQCBnO2Rtg5xtuN0RdXT7W0NgznwAAIDUQPMBAABM0XwAAABTNB8AAMAUzQcAADAVmLtdMjIyNH36dO04cEJyHL/LSV+Oo1BpRXIfHiFnO2Rtg5xtvJ3zFRcOU4aPY+wZrw4AQMAwXh0AAARKn5uPbdu26frrr1dJSYkcx9Gzzz7b63HXdVVTU6OSkhINGTJElZWV2rt3b3/VCwAABrg+Nx/hcFgf//jHtXr16vd9fMWKFVq5cqVWr16tpqYmFRcXa8aMGTp16tR5F3s+wuGwCgsL1fydOYzu9VA82qXm78whZ4+Rsx2ytkHONhI5FxYWDqzx6jNnztTMmTPf9zHXdbVq1SotXbpUs2fPliTV19erqKhIGzZs0J133nl+1Z6n48eP+/r+QRHvbPe7hEAgZztkbYOcbcQ723W8098a+vWaj4MHD6qlpUVVVVXJY6FQSNOnT9f27dv7860AAMAA1a+32ra0tEiSioqKeh0vKirS66+//r7/JhKJKBJ558uE2tvpfAEASGee3O3ivOcebdd1zzqWUFdXp4KCguRWWlrqRUkAACBF9GvzUVxcLOmdMyAJra2tZ50NSViyZIna2tqSW3Nzc3+WBAAAUky/Nh9lZWUqLi5WQ0ND8lg0GlVjY6OmTZv2vv8mFAopPz+/1wYAANJXn6/5OH36tH73u98lfz548KB2796tCy64QKNHj1Z1dbVqa2tVXl6u8vJy1dbWKicnR3PmzOnXwvsqIyNDkyZN0itH2hjd6yXHUXZxeXIfHiFnO2Rtg5xtvJ3zhFEFA2u8+tatW3X11VefdXzu3Llav369XNfVsmXL9Nhjj+nkyZOaMmWKHn30UVVUVHyg12e8OgAA3vJ7vDrf7QIAQMD43Xzw3S4AAMBUYJqPjo4OjR07VkfWflHxbkb3eiXe3aUja79Izh4jZztkbYOcbSRyHjt2rDo6Onyro1+HjKUy13XfGXSWUh80pRlXirW3JvfhEXK2Q9Y2yNnG2zm/3n7m76JfAnPmAwAApAaaDwAAYIrmAwAAmKL5AAAApmg+AACAqcDc7eI4ji655BLtf+u0xORe7zjSoGGjk/vwCDnbIWsb5Gzj7ZzLi4b+yW+bNymDCacAAAQLE04BAECg0HwAAABTgWk+Ojo6NH78eL35vfmM7vVQvLtLb35vPjl7jJztkLUNcraRyHn8+PGMV7fguq727dv39g/+1pLWXKn7xOHkPjxCznbI2gY523g7530nGK8OAAAChOYDAACYovkAAACmaD4AAIApmg8AAGAqMHe7OI6jMWPG6MjJTkb3esmRMvNHJPfhEXK2Q9Y2yNnG2zmP+vAQxqu/G+PVAQDwFuPVAQBAoNB8AAAAU4FpPjo7OzV58mQdrb9H8e6I3+WkrXh3REfr7yFnj5GzHbK2Qc42EjlPnjxZnZ2dvtURmAtO4/G4du7ceeaH1LrMJb24rqIt+5P78Ag52yFrG+Rs4+2cd7ac+bvol8Cc+QAAAKmB5gMAAJii+QAAAKZoPgAAgCmaDwAAYCowd7tI0vDhw/WHcNTvMtJexpD+n0yLs5GzHbK2Qc42Mobk64LcbF9rYLw6AAABw3h1AAAQKDQfAADAVGCaj87OTlVWVqplw/2M7vVQvDuilg33k7PHyNkOWdsgZxuJnCsrKxmvbiEej6uxsfHMD6l1mUt6cV1Fmn+T3IdHyNkOWdsgZxtv59zYzHh1AAAQIDQfAADAFM0HAAAwRfMBAABM0XwAAABTgbnbRZJycnLU2R3zu4y05wwK+V1CIJCzHbK2Qc42nEEhDRmU6W8NjFcHACBYGK8OAAACheYDAACYCkzz0dXVpVmzZqn1RzVye6J+l5O23J6oWn9UQ84eI2c7ZG2DnG0kcp41a5a6urp8qyMwF5zGYjFt3rxZkuTG43J8riddufG4Og/sTO6TszfI2Q5Z2yBnG4mcNx8483fRL4E58wEAAFIDzQcAADDlWfOxZs0alZWVafDgwZo4caJ+8YtfePVWAABgAPGk+fjhD3+o6upqLV26VC+//LI+9alPaebMmTp8+LAXbwcAAAYQT5qPlStX6o477tDf/u3f6uKLL9aqVatUWlqqtWvXevF2AABgAOn3u12i0ah27dql+++/v9fxqqoqbd++/aznRyIRRSKR5M9tbW2SzkxK60/hcDi5H490SG68X18fZ8Sj79y6Rc7eIWc7ZG2DnG28O+f29vZ+veMl8Xf7Aw1Od/vZG2+84Upyf/WrX/U6/vWvf90dN27cWc9/8MEHXUlsbGxsbGxsabA1Nzf/xV7BszkfjtP7Lm3Xdc86JklLlizRokWLkj/H43H94Q9/0LBhw973+eejvb1dpaWlam5u9uR7Y/AOsrZBznbI2g5Z2+nPrF3X1alTp1RSUvIXn9vvzcfw4cOVmZmplpaWXsdbW1tVVFR01vNDoZBCod7fZPihD32ov8vqJT8/nwVthKxtkLMdsrZD1nb6K+uCgoIP9Lx+v+A0OztbEydOVENDQ6/jDQ0NmjZtWn+/HQAAGGA8+dhl0aJFuu222zRp0iRNnTpV69at0+HDh3XXXXd58XYAAGAA8aT5+PznP68TJ07oa1/7mo4ePaqKigpt3rxZY8aM8eLtPrBQKKQHH3zwrI950P/I2gY52yFrO2Rtx6+sHdf9IPfEAAAA9A++2wUAAJii+QAAAKZoPgAAgCmaDwAAYCowzceaNWtUVlamwYMHa+LEifrFL37hd0lpadu2bbr++utVUlIix3H07LPP+l1SWqqrq9PkyZOVl5enESNG6MYbb9Rrr73md1lpae3atZowYUJyCNPUqVP1wgsv+F1W2qurq5PjOKqurva7lLRUU1Mjx3F6bcXFxWbvH4jm44c//KGqq6u1dOlSvfzyy/rUpz6lmTNn6vDhw36XlnbC4bA+/vGPa/Xq1X6XktYaGxu1YMEC7dixQw0NDerp6VFVVVWvL1BE/xg1apQefvhh7dy5Uzt37tRnPvMZ3XDDDdq7d6/fpaWtpqYmrVu3ThMmTPC7lLQ2fvx4HT16NLnt2bPH7L0DcavtlClTdPnll2vt2rXJYxdffLFuvPFG1dXV+VhZenMcR88884xuvPFGv0tJe8eOHdOIESPU2NioT3/6036Xk/YuuOACPfLII7rjjjv8LiXtnD59WpdffrnWrFmjhx56SJ/4xCe0atUqv8tKOzU1NXr22We1e/duX94/7c98RKNR7dq1S1VVVb2OV1VVafv27T5VBfSvtrY2SWf+KMI7sVhMGzduVDgc1tSpU/0uJy0tWLBAs2bN0jXXXON3KWlv//79KikpUVlZmb7whS/owIEDZu/t2bfaporjx48rFoud9aV2RUVFZ335HTAQua6rRYsW6aqrrlJFRYXf5aSlPXv2aOrUqerq6tLQoUP1zDPP6JJLLvG7rLSzceNGvfTSS2pqavK7lLQ3ZcoUPfnkkxo3bpzeeustPfTQQ5o2bZr27t2rYcOGef7+ad98JDiO0+tn13XPOgYMRAsXLtQrr7yiX/7yl36XkrYuuugi7d69W3/84x/14x//WHPnzlVjYyMNSD9qbm7W3XffrS1btmjw4MF+l5P2Zs6cmdy/9NJLNXXqVH3kIx9RfX29Fi1a5Pn7p33zMXz4cGVmZp51lqO1tfWssyHAQPOVr3xFzz33nLZt26ZRo0b5XU7ays7O1kc/+lFJ0qRJk9TU1KRvf/vbeuyxx3yuLH3s2rVLra2tmjhxYvJYLBbTtm3btHr1akUiEWVmZvpYYXrLzc3VpZdeqv3795u8X9pf85Gdna2JEyeqoaGh1/GGhgZNmzbNp6qA8+O6rhYuXKinn35aP/vZz1RWVuZ3SYHiuq4ikYjfZaSVz372s9qzZ492796d3CZNmqRbb71Vu3fvpvHwWCQS0auvvqqRI0eavF/an/mQpEWLFum2227TpEmTNHXqVK1bt06HDx/WXXfd5Xdpaef06dP63e9+l/z54MGD2r17ty644AKNHj3ax8rSy4IFC7Rhwwb95Cc/UV5eXvLMXkFBgYYMGeJzdenlgQce0MyZM1VaWqpTp05p48aN2rp1q1588UW/S0sreXl5Z12zlJubq2HDhnEtkwfuvfdeXX/99Ro9erRaW1v10EMPqb29XXPnzjV5/0A0H5///Od14sQJfe1rX9PRo0dVUVGhzZs3a8yYMX6XlnZ27typq6++Ovlz4rPDuXPnav369T5VlX4St41XVlb2Ov7EE09o3rx59gWlsbfeeku33Xabjh49qoKCAk2YMEEvvviiZsyY4XdpwDk7cuSIbrnlFh0/flyFhYW64oortGPHDrO/i4GY8wEAAFJH2l/zAQAAUgvNBwAAMEXzAQAATNF8AAAAUzQfAADAFM0HAAAwRfMBAABM0XwAAABTNB8AAMAUzQcAADBF8wEAAEzRfAAAAFP/H/ZHXvpAq7hlAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = numpy.random.uniform(0.0, 5.0, 250)\n",
    "\n",
    "# Créez un histogramme avec 5 barres\n",
    "counts, bins, patches = plt.hist(x, 5)\n",
    "\n",
    "# Ajoutez des lignes verticales entre chaque barre\n",
    "for bin_edge in bins:\n",
    "    plt.axvline(bin_edge, color='k', linestyle='--') # k = black\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Distribution normale des données</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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KT0+XJE2YMEEDBw5UeXm5U1NfX6/Tp08rJydHkpSdna1QKKQTJ044NcePH1coFHJqAAAAbqdLt6uWLVum/fv367XXXlNSUpIzP8ayLA0aNEjNzc3auHGj5s2bp/T0dF24cEEbNmxQWlqaHnvsMad20aJFWr16tVJTU5WSkqI1a9Zo/PjxztNWY8aM0axZs7R48WJt27ZNkrRkyRLl5eXxZBUAALgjXQo5W7dulSRNmTIl6viuXbv0xBNPKCEhQadOndLLL7+spqYmpaen65FHHtGBAweUlJTk1G/ZskUDBgzQ/Pnz1dLSomnTpmn37t1KSEhwavbt26eVK1c6T2Hl5+erpKSku9cJAADijMu2bTvWg+gN4XBYlmUpFAoxPwdxjUfIvxoXnn001kMAjNCT39+8uwoAABiJkAMAAIxEyAEAAEYi5AAAACMRcgAAgJEIOQAAwEiEHAAAYKRuv6ATAPB/OluPiLVzgNiikwMAAIxEyAEAAEYi5AAAACMRcgAAgJEIOQAAwEiEHAAAYCRCDgAAMBIhBwAAGImQAwAAjETIAQAARiLkAAAAIxFyAACAkQg5AADASIQcAABgJEIOAAAwEiEHAAAYiZADAACMRMgBAABGIuQAAAAjEXIAAICRCDkAAMBIhBwAAGCkAbEeAICe9a11h2I9BADoE+jkAAAAIxFyAACAkbhdBQC9pP2twwvPPhqjkQDxiU4OAAAwEp0coB9jkjEA3BqdHAAAYCRCDgAAMFKXQk5xcbEeeOABJSUlyePxaO7cuTp37lxUjW3b2rhxo/x+vwYNGqQpU6bozJkzUTWRSEQrVqxQWlqahgwZovz8fF28eDGqprGxUYFAQJZlybIsBQIBNTU1de8qAQBA3OlSyKmoqNCyZctUVVWl8vJyffrpp8rNzdX169edmk2bNmnz5s0qKSlRdXW1fD6fZsyYoWvXrjk1hYWFOnjwoEpLS3X06FE1NzcrLy9PbW1tTk1BQYFqa2tVVlamsrIy1dbWKhAI9MAlAwCAeOCybdvu7g9fuXJFHo9HFRUVevjhh2Xbtvx+vwoLC7V27VpJn3VtvF6vnnvuOS1dulShUEj33HOP9uzZowULFkiSLl26pIyMDB0+fFgzZ87U2bNnNXbsWFVVVSkrK0uSVFVVpezsbH344YcaPXr0l44tHA7LsiyFQiElJyd39xKBPo2Jx/0Lj5ADX64nv7/vak5OKBSSJKWkpEiSzp8/r2AwqNzcXKfG7XZr8uTJqqyslCTV1NToxo0bUTV+v1+ZmZlOzbFjx2RZlhNwJGnSpEmyLMupaS8SiSgcDkdtAAAgfnU75Ni2rVWrVumhhx5SZmamJCkYDEqSvF5vVK3X63U+CwaDSkxM1NChQ29b4/F4OvxOj8fj1LRXXFzszN+xLEsZGRndvTQAAGCAboec5cuX6/3339c//MM/dPjM5XJF7du23eFYe+1rOqu/3XnWr1+vUCjkbHV1dXdyGQAAwFDdCjkrVqzQ66+/rnfeeUfDhg1zjvt8Pknq0G1paGhwujs+n0+tra1qbGy8bc3ly5c7/N4rV6506BJ9zu12Kzk5OWoDAADxq0shx7ZtLV++XK+88oqOHDmikSNHRn0+cuRI+Xw+lZeXO8daW1tVUVGhnJwcSdKECRM0cODAqJr6+nqdPn3aqcnOzlYoFNKJEyecmuPHjysUCjk1ANDffGvdoQ4bgN7Tpdc6LFu2TPv379drr72mpKQkp2NjWZYGDRokl8ulwsJCFRUVadSoURo1apSKioo0ePBgFRQUOLWLFi3S6tWrlZqaqpSUFK1Zs0bjx4/X9OnTJUljxozRrFmztHjxYm3btk2StGTJEuXl5d3Rk1UAAABdCjlbt26VJE2ZMiXq+K5du/TEE09Ikp5++mm1tLToySefVGNjo7KysvTWW28pKSnJqd+yZYsGDBig+fPnq6WlRdOmTdPu3buVkJDg1Ozbt08rV650nsLKz89XSUlJd64RAADEobtaJ6cvY50cxANud/R/rJ0DROsz6+QAAAD0VYQcAABgJEIOAAAwEiEHAAAYiZADAACMRMgBAABGIuQAAAAjdWkxQACxxbo4AHDn6OQAAAAjEXIAAICRCDkAAMBIhBwAAGAkQg4AADASIQcAABiJkAMAAIxEyAEAAEYi5AAAACOx4jEAxFD7VawvPPtojEYCmIdODgAAMBIhBwAAGImQAwAAjETIAQAARiLkAAAAIxFyAACAkQg5AADASIQcAABgJEIOAAAwEiEHAAAYiZADAACMRMgBAABGIuQAAAAj8RZyoI9q/3ZqAEDX0MkBAABGIuQAAAAjEXIAAICRmJMDAH1IZ3OxLjz7aAxGAvR/dHIAAICRCDkAAMBIXQ457733nubMmSO/3y+Xy6VXX3016vMnnnhCLpcraps0aVJUTSQS0YoVK5SWlqYhQ4YoPz9fFy9ejKppbGxUIBCQZVmyLEuBQEBNTU1dvkAAABCfujwn5/r167r//vv113/915o3b16nNbNmzdKuXbuc/cTExKjPCwsL9cYbb6i0tFSpqalavXq18vLyVFNTo4SEBElSQUGBLl68qLKyMknSkiVLFAgE9MYbb3R1yEC/wLo4ANCzuhxyZs+erdmzZ9+2xu12y+fzdfpZKBTSzp07tWfPHk2fPl2StHfvXmVkZOjtt9/WzJkzdfbsWZWVlamqqkpZWVmSpB07dig7O1vnzp3T6NGjuzpsAAAQZ3plTs67774rj8ej73znO1q8eLEaGhqcz2pqanTjxg3l5uY6x/x+vzIzM1VZWSlJOnbsmCzLcgKOJE2aNEmWZTk17UUiEYXD4agNAADErx4PObNnz9a+fft05MgRvfDCC6qurtbUqVMViUQkScFgUImJiRo6dGjUz3m9XgWDQafG4/F0OLfH43Fq2isuLnbm71iWpYyMjB6+MgAA0J/0+Do5CxYscP6dmZmpiRMnasSIETp06JAef/zxW/6cbdtyuVzO/hf/fauaL1q/fr1WrVrl7IfDYYIOAABxrNcfIU9PT9eIESP00UcfSZJ8Pp9aW1vV2NgYVdfQ0CCv1+vUXL58ucO5rly54tS053a7lZycHLUBAID41esh5+rVq6qrq1N6erokacKECRo4cKDKy8udmvr6ep0+fVo5OTmSpOzsbIVCIZ04ccKpOX78uEKhkFMDAABwO12+XdXc3KyPP/7Y2T9//rxqa2uVkpKilJQUbdy4UfPmzVN6erouXLigDRs2KC0tTY899pgkybIsLVq0SKtXr1ZqaqpSUlK0Zs0ajR8/3nnaasyYMZo1a5YWL16sbdu2SfrsEfK8vDyerAIAAHekyyHn5MmTeuSRR5z9z+fBLFy4UFu3btWpU6f08ssvq6mpSenp6XrkkUd04MABJSUlOT+zZcsWDRgwQPPnz1dLS4umTZum3bt3O2vkSNK+ffu0cuVK5yms/Px8lZSUdPtCAQBAfHHZtm3HehC9IRwOy7IshUIh5uegX2AxQNwKL+hEPOnJ72/eXQUAAIzU44+QAwB6VvsuH50d4M7QyQEAAEYi5AAAACMRcgAAgJEIOQAAwEiEHAAAYCRCDgAAMBIhBwAAGIl1coAYYHVjAOh9dHIAAICRCDkAAMBIhBwAAGAkQg4AADASIQcAABiJkAMAAIxEyAEAAEYi5AAAACMRcgAAgJEIOQAAwEiEHAAAYCRCDgAAMBIv6AS+AryQEwC+enRyAACAkQg5AADASNyuAoB+prPbnxeefTQGIwH6Njo5AADASIQcAABgJG5XAYAB2t/C4vYVQCcHAAAYipADAACMRMgBAABGIuQAAAAjEXIAAICRCDkAAMBIhBwAAGAkQg4AADASIQcAABiJFY+BHtbZyxMBAF+9Lndy3nvvPc2ZM0d+v18ul0uvvvpq1Oe2bWvjxo3y+/0aNGiQpkyZojNnzkTVRCIRrVixQmlpaRoyZIjy8/N18eLFqJrGxkYFAgFZliXLshQIBNTU1NTlCwQAAPGpyyHn+vXruv/++1VSUtLp55s2bdLmzZtVUlKi6upq+Xw+zZgxQ9euXXNqCgsLdfDgQZWWluro0aNqbm5WXl6e2tranJqCggLV1taqrKxMZWVlqq2tVSAQ6MYlAgCAeOSybdvu9g+7XDp48KDmzp0r6bMujt/vV2FhodauXSvps66N1+vVc889p6VLlyoUCumee+7Rnj17tGDBAknSpUuXlJGRocOHD2vmzJk6e/asxo4dq6qqKmVlZUmSqqqqlJ2drQ8//FCjR4/+0rGFw2FZlqVQKKTk5OTuXiLQZdyuQl/ACzrRX/Xk93ePTjw+f/68gsGgcnNznWNut1uTJ09WZWWlJKmmpkY3btyIqvH7/crMzHRqjh07JsuynIAjSZMmTZJlWU5Ne5FIROFwOGoDAADxq0dDTjAYlCR5vd6o416v1/ksGAwqMTFRQ4cOvW2Nx+PpcH6Px+PUtFdcXOzM37EsSxkZGXd9PQAAoP/qlUfIXS5X1L5t2x2Otde+prP6251n/fr1CoVCzlZXV9eNkQMAAFP06CPkPp9P0medmPT0dOd4Q0OD093x+XxqbW1VY2NjVDenoaFBOTk5Ts3ly5c7nP/KlSsdukSfc7vdcrvdPXYtANCfdTY3jHk6iDc92skZOXKkfD6fysvLnWOtra2qqKhwAsyECRM0cODAqJr6+nqdPn3aqcnOzlYoFNKJEyecmuPHjysUCjk1AAAAt9PlTk5zc7M+/vhjZ//8+fOqra1VSkqKhg8frsLCQhUVFWnUqFEaNWqUioqKNHjwYBUUFEiSLMvSokWLtHr1aqWmpiolJUVr1qzR+PHjNX36dEnSmDFjNGvWLC1evFjbtm2TJC1ZskR5eXl39GQVAABAl0POyZMn9cgjjzj7q1atkiQtXLhQu3fv1tNPP62WlhY9+eSTamxsVFZWlt566y0lJSU5P7NlyxYNGDBA8+fPV0tLi6ZNm6bdu3crISHBqdm3b59WrlzpPIWVn59/y7V5gFjikXEA6Jvuap2cvox1cvBVIeSgv2BODvqDPrtODgAAQF9ByAEAAEYi5AAAACMRcgAAgJEIOQAAwEiEHAAAYCRCDgAAMFKPvrsKANB3tV/TiXVzYDo6OQAAwEiEHAAAYCRCDgAAMBIhBwAAGImQAwAAjETIAQAARiLkAAAAI7FODtAF7dcZAQD0XXRyAACAkQg5AADASIQcAABgJEIOAAAwEhOPASBOdTaRnpd2wiR0cgAAgJEIOQAAwEiEHAAAYCRCDgAAMBIhBwAAGImQAwAAjETIAQAARiLkAAAAI7EYIHAbvHUcAPovOjkAAMBIhBwAAGAkblcBABztb9HyLiv0Z3RyAACAkejkAP+LScYAYBY6OQAAwEiEHAAAYCRCDgAAMFKPh5yNGzfK5XJFbT6fz/nctm1t3LhRfr9fgwYN0pQpU3TmzJmoc0QiEa1YsUJpaWkaMmSI8vPzdfHixZ4eKgAAMFivdHLGjRun+vp6Zzt16pTz2aZNm7R582aVlJSourpaPp9PM2bM0LVr15yawsJCHTx4UKWlpTp69Kiam5uVl5entra23hguAAAwUK88XTVgwICo7s3nbNvWiy++qJ/97Gd6/PHHJUm//e1v5fV6tX//fi1dulShUEg7d+7Unj17NH36dEnS3r17lZGRobffflszZ87sjSEDAADD9ErI+eijj+T3++V2u5WVlaWioiLde++9On/+vILBoHJzc51at9utyZMnq7KyUkuXLlVNTY1u3LgRVeP3+5WZmanKyspbhpxIJKJIJOLsh8Ph3rg0AIgrnS2twAKB6C96/HZVVlaWXn75Zf3+97/Xjh07FAwGlZOTo6tXryoYDEqSvF5v1M94vV7ns2AwqMTERA0dOvSWNZ0pLi6WZVnOlpGR0cNXBgAA+pMeDzmzZ8/WvHnzNH78eE2fPl2HDn32/wJ++9vfOjUulyvqZ2zb7nCsvS+rWb9+vUKhkLPV1dXdxVUAAID+rtdXPB4yZIjGjx+vjz76SHPnzpX0WbcmPT3dqWloaHC6Oz6fT62trWpsbIzq5jQ0NCgnJ+eWv8ftdsvtdvfORQAAHLzfCv1Fr6+TE4lEdPbsWaWnp2vkyJHy+XwqLy93Pm9tbVVFRYUTYCZMmKCBAwdG1dTX1+v06dO3DTkAAABf1OOdnDVr1mjOnDkaPny4Ghoa9Ktf/UrhcFgLFy6Uy+VSYWGhioqKNGrUKI0aNUpFRUUaPHiwCgoKJEmWZWnRokVavXq1UlNTlZKSojVr1ji3vwAAAO5Ej4ecixcv6kc/+pH++Mc/6p577tGkSZNUVVWlESNGSJKefvpptbS06Mknn1RjY6OysrL01ltvKSkpyTnHli1bNGDAAM2fP18tLS2aNm2adu/erYSEhJ4eLgAAMJTLtm071oPoDeFwWJZlKRQKKTk5OdbDQT/AW8iB7mFODnpST35/8+4qAABgpF5/ugroi+jaAID56OQAAAAj0clBXKBzAwDxh04OAAAwEiEHAAAYiZADAACMRMgBAABGYuIxjMMkY+Cr1dl/51ggEH0BnRwAAGAkQg4AADASIQcAABiJkAMAAIzExGMAQI9rPxmZiciIBTo5AADASIQcAABgJEIOAAAwEnNy0O+x+B8AoDN0cgAAgJHo5AAAeh2vfkAsEHLQr3BrCgBwp7hdBQAAjETIAQAARuJ2Ffo0bk8B5mJVZPQ2OjkAAMBIhBwAAGAkQg4AADASc3IAAH0Ca+mgpxFyEDNMKgYA9CZuVwEAACMRcgAAgJEIOQAAwEjMyQEA9Fl3MnePycm4FUIOvhJMMgYAfNW4XQUAAIxEJwe9gs4NgK8K78DCrdDJAQAARqKTAwAwCisn43N9PuS89NJLev7551VfX69x48bpxRdf1J/8yZ/Eelhxg9tOAExA8IlPfTrkHDhwQIWFhXrppZf04IMPatu2bZo9e7Y++OADDR8+PNbDMxKhBkC8YC6P+Vy2bduxHsStZGVl6Qc/+IG2bt3qHBszZozmzp2r4uLi2/5sOByWZVkKhUJKTk7u7aH2SwQaAPg/hJy+oSe/v/tsJ6e1tVU1NTVat25d1PHc3FxVVlZ2qI9EIopEIs5+KBSS9Nl/WPEo8+e/j/UQAKBfGf7T/9dr5z79i5m9dm7TfP693RM9mD4bcv74xz+qra1NXq836rjX61UwGOxQX1xcrF/84hcdjmdkZPTaGAEAuBPWi7EeQf9z9epVWZZ1V+fosyHncy6XK2rftu0OxyRp/fr1WrVqlbN/8+ZN/dd//ZdSU1M7rUf3hcNhZWRkqK6ujluBfQh/l76Jv0vfxd+mbwqFQho+fLhSUlLu+lx9NuSkpaUpISGhQ9emoaGhQ3dHktxut9xud9Sxb37zm705xLiXnJzM/zD0Qfxd+ib+Ln0Xf5u+6Wtfu/ul/PrsYoCJiYmaMGGCysvLo46Xl5crJycnRqMCAAD9RZ/t5EjSqlWrFAgENHHiRGVnZ2v79u36j//4D/3kJz+J9dAAAEAf16dDzoIFC3T16lX98pe/VH19vTIzM3X48GGNGDEi1kOLa263Wz//+c873B5EbPF36Zv4u/Rd/G36pp78u/TpdXIAAAC6q8/OyQEAALgbhBwAAGAkQg4AADASIQcAABiJkIM7UlxcrAceeEBJSUnyeDyaO3euzp07F+thoZ3i4mK5XC4VFhbGeiiQ9J//+Z/6y7/8S6Wmpmrw4MH63ve+p5qamlgPK659+umn+ru/+zuNHDlSgwYN0r333qtf/vKXunnzZqyHFnfee+89zZkzR36/Xy6XS6+++mrU57Zta+PGjfL7/Ro0aJCmTJmiM2fOdOl3EHJwRyoqKrRs2TJVVVWpvLxcn376qXJzc3X9+vVYDw3/q7q6Wtu3b9d9990X66FAUmNjox588EENHDhQb775pj744AO98MILrMQeY88995z+/u//XiUlJTp79qw2bdqk559/Xr/5zW9iPbS4c/36dd1///0qKSnp9PNNmzZp8+bNKikpUXV1tXw+n2bMmKFr167d8e/gEXJ0y5UrV+TxeFRRUaGHH3441sOJe83NzfrBD36gl156Sb/61a/0ve99Ty+++GKshxXX1q1bp3/+53/WP/3TP8V6KPiCvLw8eb1e7dy50zk2b948DR48WHv27InhyOKby+XSwYMHNXfuXEmfdXH8fr8KCwu1du1aSVIkEpHX69Vzzz2npUuX3tF56eSgW0KhkCT1yAvUcPeWLVumRx99VNOnT4/1UPC/Xn/9dU2cOFF/9md/Jo/Ho+9///vasWNHrIcV9x566CH94z/+o/7whz9Ikv7t3/5NR48e1Z/+6Z/GeGT4ovPnzysYDCo3N9c55na7NXnyZFVWVt7xefr0isfom2zb1qpVq/TQQw8pMzMz1sOJe6WlpfqXf/kXVVdXx3oo+IJ///d/19atW7Vq1Spt2LBBJ06c0MqVK+V2u/VXf/VXsR5e3Fq7dq1CoZC++93vKiEhQW1tbXrmmWf0ox/9KNZDwxd8/nLu9i/k9nq9+uSTT+74PIQcdNny5cv1/vvv6+jRo7EeStyrq6vTU089pbfeektf//rXYz0cfMHNmzc1ceJEFRUVSZK+//3v68yZM9q6dSshJ4YOHDigvXv3av/+/Ro3bpxqa2tVWFgov9+vhQsXxnp4aMflckXt27bd4djtEHLQJStWrNDrr7+u9957T8OGDYv1cOJeTU2NGhoaNGHCBOdYW1ub3nvvPZWUlCgSiSghISGGI4xf6enpGjt2bNSxMWPG6He/+12MRgRJ+tu//VutW7dOf/7nfy5JGj9+vD755BMVFxcTcvoQn88n6bOOTnp6unO8oaGhQ3fndpiTgzti27aWL1+uV155RUeOHNHIkSNjPSRImjZtmk6dOqXa2lpnmzhxov7iL/5CtbW1BJwYevDBBzsss/CHP/yBFwzH2H//93/ra1+L/upLSEjgEfI+ZuTIkfL5fCovL3eOtba2qqKiQjk5OXd8Hjo5uCPLli3T/v379dprrykpKcm5X2pZlgYNGhTj0cWvpKSkDvOihgwZotTUVOZLxdhPf/pT5eTkqKioSPPnz9eJEye0fft2bd++PdZDi2tz5szRM888o+HDh2vcuHH613/9V23evFk//vGPYz20uNPc3KyPP/7Y2T9//rxqa2uVkpKi4cOHq7CwUEVFRRo1apRGjRqloqIiDR48WAUFBXf+S2zgDkjqdNu1a1esh4Z2Jk+ebD/11FOxHgZs237jjTfszMxM2+1229/97nft7du3x3pIcS8cDttPPfWUPXz4cPvrX/+6fe+999o/+9nP7EgkEuuhxZ133nmn0++VhQsX2rZt2zdv3rR//vOf2z6fz3a73fbDDz9snzp1qku/g3VyAACAkZiTAwAAjETIAQAARiLkAAAAIxFyAACAkQg5AADASIQcAABgJEIOAAAwEiEHAAAYiZADAACMRMgBAABGIuQAAAAjEXIAAICR/j9iRuX/JJuJwAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Créez un tableau contenant 100000 valeurs aléatoires, avec une moyenne de 5 et un écart-type de 1\n",
    "x = numpy.random.normal(5, 1, 100000)\n",
    "\n",
    "plt.hist(x, 100)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous spécifions que la valeur moyenne est 5,0 et que l’écart-type est 1,0.\n",
    "\n",
    "Cela signifie que les valeurs doivent être concentrées autour de 5,0, et rarement au-delà de plus de 1,0 par rapport à la moyenne.\n",
    "\n",
    "Et comme vous pouvez le voir sur l’histogramme, la plupart des valeurs sont comprises entre 4.0 et 6.0, avec un sommet à environ 5,0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Régression linéaire avec SciPy</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy import stats\n",
    "\n",
    "x = [5,7,8,7,2,17,2,9,4,11,12,9,6]\n",
    "y = [99,86,87,88,111,86,103,87,94,78,77,85,86]\n",
    "\n",
    "# Calculer la pente, l'interception, la corrélation, la p-valeur et l'erreur standard\n",
    "slope, intercept, r, p, std_err = stats.linregress(x, y)\n",
    "\n",
    "def myfunc(x):\n",
    "  return slope * x + intercept\n",
    "\n",
    "mymodel = list(map(myfunc, x))\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, mymodel)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Régression polynomiale</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "coeffs [-3.03208795e-02  1.34333191e+00 -1.55383039e+01  1.13768037e+02]\n",
      "a:  -0.030320879528678697\n",
      "b:  1.3433319130832158\n",
      "c:  -15.538303872236863\n",
      "d:  113.76803676835567\n",
      "mymodel:            3         2\n",
      "-0.03032 x + 1.343 x - 15.54 x + 113.8\n",
      "myline:  [ 1.          1.21212121  1.42424242  1.63636364  1.84848485  2.06060606\n",
      "  2.27272727  2.48484848  2.6969697   2.90909091  3.12121212  3.33333333\n",
      "  3.54545455  3.75757576  3.96969697  4.18181818  4.39393939  4.60606061\n",
      "  4.81818182  5.03030303  5.24242424  5.45454545  5.66666667  5.87878788\n",
      "  6.09090909  6.3030303   6.51515152  6.72727273  6.93939394  7.15151515\n",
      "  7.36363636  7.57575758  7.78787879  8.          8.21212121  8.42424242\n",
      "  8.63636364  8.84848485  9.06060606  9.27272727  9.48484848  9.6969697\n",
      "  9.90909091 10.12121212 10.33333333 10.54545455 10.75757576 10.96969697\n",
      " 11.18181818 11.39393939 11.60606061 11.81818182 12.03030303 12.24242424\n",
      " 12.45454545 12.66666667 12.87878788 13.09090909 13.3030303  13.51515152\n",
      " 13.72727273 13.93939394 14.15151515 14.36363636 14.57575758 14.78787879\n",
      " 15.         15.21212121 15.42424242 15.63636364 15.84848485 16.06060606\n",
      " 16.27272727 16.48484848 16.6969697  16.90909091 17.12121212 17.33333333\n",
      " 17.54545455 17.75757576 17.96969697 18.18181818 18.39393939 18.60606061\n",
      " 18.81818182 19.03030303 19.24242424 19.45454545 19.66666667 19.87878788\n",
      " 20.09090909 20.3030303  20.51515152 20.72727273 20.93939394 21.15151515\n",
      " 21.36363636 21.57575758 21.78787879 22.        ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = [1,2,3,5,6,7,8,9,10,12,13,14,15,16,18,19,21,22]\n",
    "y = [100,90,80,60,60,55,60,65,70,70,75,76,78,79,90,99,99,100]\n",
    "\n",
    "# Retourne tableau de coefficients d'un polynome de degré 3 à partir des données fournies dans les tableaux x et y\n",
    "(a,b,c,d) = numpy.polyfit(x, y, 3)\n",
    "print(\"coeffs\", numpy.polyfit(x, y, 3))\n",
    "print(\"a: \", a)\n",
    "print(\"b: \", b)\n",
    "print(\"c: \", c)\n",
    "print(\"d: \", d)\n",
    "\n",
    "# Crée un objet polynomial avec les coefficients obtenus\n",
    "# Cet objet polynomial est une fonction de x et sert de modèle de prédiction\n",
    "mymodel = numpy.poly1d([a, b, c, d])\n",
    "print(\"mymodel: \", mymodel)\n",
    "\n",
    "# Génère un tableau de valeurs de 100 nombres allant de 1 à 22 et également espacés\n",
    "values_table = numpy.linspace(1, 22, 100)\n",
    "print(\"myline: \", values_table)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(values_table, mymodel(values_table))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Coefficient de détérmination R² (R-squared)</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le coefficient de détermination, noté R², est la proportion de la variance de la variable dépendante qui est prévisible à partir de la variable indépendante. Il est comprise entre 0 et 1 où 0 signifie qu’il n’y a pas de relation et 1 signifie 100% lié. Il fournit ainsi une mesure de la qualité de l'ajustement du modèle. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9432150416451026\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "from sklearn.metrics import r2_score\n",
    "\n",
    "x = [1,2,3,5,6,7,8,9,10,12,13,14,15,16,18,19,21,22]\n",
    "y = [100,90,80,60,60,55,60,65,70,70,75,76,78,79,90,99,99,100]\n",
    "\n",
    "mymodel = numpy.poly1d(numpy.polyfit(x, y, 3))\n",
    "\n",
    "print(r2_score(y, mymodel(x)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Régression multiple</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>Car</th>\n",
       "      <th>Model</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Weight</th>\n",
       "      <th>CO2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Toyoty</td>\n",
       "      <td>Aygo</td>\n",
       "      <td>1000</td>\n",
       "      <td>790</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Mitsubishi</td>\n",
       "      <td>Space Star</td>\n",
       "      <td>1200</td>\n",
       "      <td>1160</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Skoda</td>\n",
       "      <td>Citigo</td>\n",
       "      <td>1000</td>\n",
       "      <td>929</td>\n",
       "      <td>95</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Fiat</td>\n",
       "      <td>500</td>\n",
       "      <td>900</td>\n",
       "      <td>865</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Mini</td>\n",
       "      <td>Cooper</td>\n",
       "      <td>1500</td>\n",
       "      <td>1140</td>\n",
       "      <td>105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>VW</td>\n",
       "      <td>Up!</td>\n",
       "      <td>1000</td>\n",
       "      <td>929</td>\n",
       "      <td>105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>Skoda</td>\n",
       "      <td>Fabia</td>\n",
       "      <td>1400</td>\n",
       "      <td>1109</td>\n",
       "      <td>90</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Mercedes</td>\n",
       "      <td>A-Class</td>\n",
       "      <td>1500</td>\n",
       "      <td>1365</td>\n",
       "      <td>92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Ford</td>\n",
       "      <td>Fiesta</td>\n",
       "      <td>1500</td>\n",
       "      <td>1112</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>Audi</td>\n",
       "      <td>A1</td>\n",
       "      <td>1600</td>\n",
       "      <td>1150</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Car       Model  Volume  Weight  CO2\n",
       "0      Toyoty        Aygo    1000     790   99\n",
       "1  Mitsubishi  Space Star    1200    1160   95\n",
       "2       Skoda      Citigo    1000     929   95\n",
       "3        Fiat         500     900     865   90\n",
       "4        Mini      Cooper    1500    1140  105\n",
       "5          VW         Up!    1000     929  105\n",
       "6       Skoda       Fabia    1400    1109   90\n",
       "7    Mercedes     A-Class    1500    1365   92\n",
       "8        Ford      Fiesta    1500    1112   98\n",
       "9        Audi          A1    1600    1150   99"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from sklearn import linear_model\n",
    "\n",
    "df = pd.read_csv(\"data.csv\")\n",
    "\n",
    "df.head(10)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X    Weight  Volume\n",
      "0     790    1000\n",
      "1    1160    1200\n",
      "2     929    1000\n",
      "3     865     900\n",
      "4    1140    1500\n",
      "5     929    1000\n",
      "6    1109    1400\n",
      "7    1365    1500\n",
      "8    1112    1500\n",
      "9    1150    1600\n",
      "\n",
      "\n",
      "y 0     99\n",
      "1     95\n",
      "2     95\n",
      "3     90\n",
      "4    105\n",
      "5    105\n",
      "6     90\n",
      "7     92\n",
      "8     98\n",
      "9     99\n",
      "Name: CO2, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "X = df[['Weight', 'Volume']]\n",
    "y = df['CO2']\n",
    "\n",
    "print(\"X\", X.head(10))\n",
    "print(\"\\n\")\n",
    "print(\"y\", y.head(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[107.2087328]\n"
     ]
    }
   ],
   "source": [
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X, y)\n",
    "\n",
    "# Predict the CO2 emission of a car where the weight is 2300kg, and the volume is 1300cm3:\n",
    "new_car = pd.DataFrame({\n",
    "  \"Weight\": [2300], \n",
    "  \"Volume\": [1300]\n",
    "})\n",
    "\n",
    "predictedCO2 = regr.predict(new_car)\n",
    "\n",
    "print(predictedCO2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.00755095 0.00780526]\n"
     ]
    }
   ],
   "source": [
    "# Valeurs des coefficients respectivement pour le poids et le volume\n",
    "print(regr.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces valeurs nous indiquent que si le poids augmente de 1kg, le CO2 Les émissions augmentent de 0,00755095 g.\n",
    "\n",
    "Et si la taille du moteur (Volume) augmente de 1 cm3, l’émission de CO2 augmente de 0,00780526 g.\n",
    "\n",
    "Je pense que c’est une supposition juste, mais testons-la !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[114.75968007]\n"
     ]
    }
   ],
   "source": [
    "# Predict the CO2 emission of a car where the weight is 3300kg, and the volume is 1300cm3:\n",
    "new_car = pd.DataFrame({\n",
    "  \"Weight\": [3300], \n",
    "  \"Volume\": [1300]\n",
    "})\n",
    "\n",
    "predictedCO2 = regr.predict(new_car)\n",
    "\n",
    "print(predictedCO2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons prédit qu’une voiture avec un moteur de 1,3 litre, et un poids de 3300 kg, libérera environ 115 grammes de CO2 pour chaque kilomètre parcouru.\n",
    "\n",
    "Ce qui montre que le coefficient de 0,00755095 est correct :\n",
    "\n",
    "107,2087328 + (1000 * 0,00755095) = 114,75968"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Mise à l'échelle (scaling)</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be difficult to compare the volume 1.0 with the weight 790, but if we scale them both into comparable values, we can easily see how much one value is compared to the other.\n",
    "\n",
    "There are different methods for scaling data, in this tutorial we will use a method called standardization.\n",
    "\n",
    "The standardization method uses this formula:\n",
    "\n",
    "<font color=\"red\"> z = (x - u) / s</font>\n",
    "\n",
    "Where <font color=\"red\">z</font> is the new value, <font color=\"red\">x</font> is the original value, <font color=\"red\">u</font> is the mean and s is the standard deviation.\n",
    "\n",
    "If you take the weight column from the data set above, the first value is 790, and the scaled value will be:\n",
    "\n",
    "<font color=\"red\">(790 - 1292.23) / 238.74 = -2.1</font>\n",
    "\n",
    "If you take the volume column from the data set above, the first value is 1.0, and the scaled value will be:\n",
    "\n",
    "<font color=\"red\">(1.0 - 1.61) / 0.38 = -1.59</font>\n",
    "\n",
    "Now you can compare -2.1 with -1.59 instead of comparing 790 with 1.0.\n",
    "\n",
    "You do not have to do this manually, the Python sklearn module has a method called <font color=\"red\">StandardScaler()</font> which returns a Scaler object with methods for transforming data sets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.10389253 -1.59336644]\n",
      " [-0.55407235 -1.07190106]\n",
      " [-1.52166278 -1.59336644]\n",
      " [-1.78973979 -1.85409913]\n",
      " [-0.63784641 -0.28970299]\n",
      " [-1.52166278 -1.59336644]\n",
      " [-0.76769621 -0.55043568]\n",
      " [ 0.3046118  -0.28970299]\n",
      " [-0.7551301  -0.28970299]\n",
      " [-0.59595938 -0.0289703 ]]\n"
     ]
    }
   ],
   "source": [
    "import pandas\n",
    "from sklearn import linear_model\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scale = StandardScaler()\n",
    "\n",
    "df = pandas.read_csv(\"data_2.csv\")\n",
    "\n",
    "X = df[['Weight', 'Volume']]\n",
    "\n",
    "scaledX = scale.fit_transform(X)\n",
    "\n",
    "print(scaledX[0:10,:]) # Affiche les 10 premières lignes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le code suivant utilise la méthode `fit_transform` de l'objet `scale` pour ajuster et transformer les données `X`.\n",
    "\n",
    "```python\n",
    "scaledX = scale.fit_transform(X)\n",
    "```\n",
    "\n",
    "Voici une explication détaillée :\n",
    "\n",
    "1. `scale.fit_transform(X)` :\n",
    "   - `scale` est un objet de transformation, probablement un scaler de `sklearn` comme `StandardScaler` ou `MinMaxScaler`.\n",
    "   - La méthode `fit_transform` effectue deux opérations :\n",
    "     - `fit` : elle ajuste le scaler aux données `X`, c'est-à-dire qu'elle calcule les paramètres nécessaires à la transformation (par exemple, la moyenne et l'écart-type pour `StandardScaler`).\n",
    "     - `transform` : elle applique la transformation aux données `X` en utilisant les paramètres calculés.\n",
    "\n",
    "2. `scaledX` :\n",
    "   - La variable `scaledX` stocke les données transformées (normalisées ou mises à l'échelle).\n",
    "\n",
    "En résumé, ce code ajuste le scaler aux données `X` et applique la transformation, puis stocke les données transformées dans `scaledX`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4.22104928 -0.81116837]]\n",
      "[107.2087328]\n"
     ]
    }
   ],
   "source": [
    "# Predict CO2 Values\n",
    "\n",
    "regr = linear_model.LinearRegression() # Crée un objet de régression linéaire\n",
    "regr.fit(scaledX, y) # Entraîne le modèle avec les données d'entrée et de sortie\n",
    "\n",
    "# Mise à l'échelle des valeurs de poids et de volume pour une nouvelle voiture\n",
    "new_car = pd.DataFrame({\n",
    "  \"Weight\": [2300], \n",
    "  \"Volume\": [1.3]\n",
    "})\n",
    "\n",
    "new_car_scaled = scale.transform(new_car) \n",
    "print(new_car_scaled)\n",
    "\n",
    "predictedCO2 = regr.predict(new_car_scaled)\n",
    "print(predictedCO2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le code suivant utilise la méthode `transform` de l'objet `scale` pour normaliser les nouvelles données d'une voiture.\n",
    "\n",
    "```python\n",
    "new_car_scaled = scale.transform(pd.DataFrame({\"Weight\": [2300], \"Volume\": [1.3]})) \n",
    "```\n",
    "\n",
    "Voici une explication détaillée :\n",
    "\n",
    "1. `pd.DataFrame({\"Weight\": [2300], \"Volume\": [1.3]})` :\n",
    "   - Crée un DataFrame pandas avec deux colonnes : `Weight` (poids) et `Volume`.\n",
    "   - Les valeurs de ces colonnes sont respectivement 2300 et 1.3.\n",
    "\n",
    "2. `scale.transform(...)` :\n",
    "   - `scale` est un objet de transformation, probablement un scaler de `sklearn` comme `StandardScaler` ou `MinMaxScaler`.\n",
    "   - La méthode `transform` applique la transformation (normalisation ou mise à l'échelle) aux nouvelles données fournies.\n",
    "\n",
    "3. `new_car_scaled` :\n",
    "   - La variable `new_car_scaled` stocke les données transformées (normalisées).\n",
    "\n",
    "En résumé, ce code normalise les nouvelles données d'une voiture (poids de 2300 et volume de 1.3) en utilisant un scaler préalablement ajusté, et stocke les données normalisées dans `new_car_scaled`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Entraîner / Tester</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x:  [2.58324215 2.94373317 0.8638039  4.64027081 1.20656441 2.15825263\n",
      " 3.50288142 1.75471191 1.94204778 2.09099239 3.55145404 5.29220801\n",
      " 3.04153939 1.88207455 3.53905832 2.4038403  2.9808695  4.17500122\n",
      " 2.25212905 3.00902525 2.12189211 2.84356583 3.25657045 2.01122095\n",
      " 2.66117803 2.76381597 2.36234499 1.81238771 1.57878277 2.8465048\n",
      " 2.73094304 5.23136679 0.56523242 3.1127265  3.37044454 4.35963386\n",
      " 3.50185721 2.1557863  3.00000976 3.54235257 2.6864918  3.77101174\n",
      " 1.13190935 4.73118467 4.46767801 2.66432266 3.61134078 3.04797059\n",
      " 2.17086471 3.08771022 4.00036589 2.61890748 2.62433058 2.92552924\n",
      " 3.43349633 4.27837923 2.36532069 3.50839624 3.21611601 1.14138761\n",
      " 2.58068352 2.8676711  2.96042976 3.32600343 0.95967695 3.04625552\n",
      " 2.32232442 1.56056097 3.52429643 3.73527958 2.34674973 3.84245628\n",
      " 2.61848352 3.06648901 1.90126105 4.58448706 0.34055054 2.90854738\n",
      " 3.69511961 0.96653345 2.81053074 2.92278133 3.82470301 4.24821292\n",
      " 2.59610773 1.61548133 4.36723542 4.21788563 2.53799465 3.35088849\n",
      " 3.38186623 3.56627544 3.20420798 4.40669624 1.2620405  4.04082395\n",
      " 3.38047197 2.78286473 4.1735315  0.65639681]\n",
      "y:  [ 76.05204933  56.20180641 121.17874037  36.05903817 114.23885932\n",
      " 117.41526024  63.77986643  95.52998052  62.4237197   60.57574247\n",
      "  38.57519009  24.10914678  37.45148182  67.13926856  39.26265343\n",
      "  53.79918302  40.94657678  27.02857247 111.90190427  30.26663537\n",
      "  51.4368334   58.83311239  42.08623741  83.01076429  68.37843898\n",
      "  72.54627253  76.22874513  60.83111238 123.11113005  27.89501382\n",
      "  53.25015791  24.86406278 190.30762228  55.79245737  42.32964984\n",
      "  43.76381026  25.90093643  85.28325651  56.63901768  43.77321677\n",
      "  34.70979433  37.10649687  77.86225629  14.09666443  62.93869329\n",
      "  70.87521926  61.39097018  43.58292288  81.92492065  57.61442568\n",
      "  43.5111781   57.3316853   53.67848811  22.97550427  50.79538368\n",
      "  39.01941998  82.32095959  39.62788318  68.30365792 115.73628743\n",
      "  38.66530343  65.39332448  44.34023444  30.00934597 161.50533328\n",
      "  59.1743156   68.74904453 108.8692008   89.19445659  48.95077634\n",
      "  90.02681869  18.36485932  62.86162946  59.01318439  71.22685026\n",
      "  25.07604874 487.03726791  47.24533754  34.16662793 202.76589695\n",
      "  72.37873053  55.46264153  34.46826737  40.15213735  70.55883508\n",
      " 108.46604975  21.035144    32.35727584  64.76189111  52.19177448\n",
      "  55.71813453  50.5667094   32.65308038  27.61777936  80.14230427\n",
      "  54.98360439  46.50723143  61.85229524  45.84155234 208.47130994]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "numpy.random.seed(2) # Pour obtenir les mêmes valeurs aléatoires à chaque exécution\n",
    "\n",
    "x = numpy.random.normal(3, 1, 100)\n",
    "y = numpy.random.normal(150, 40, 100) / x\n",
    "\n",
    "print(\"x: \", x)\n",
    "print(\"y: \", y)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L’ensemble d’apprentissage doit être une sélection aléatoire de 80 % des données d’origine.\n",
    "\n",
    "L’ensemble de test doit être constitué des 20 % restants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_x = x[:80]\n",
    "train_y = y[:80]\n",
    "\n",
    "test_x = x[80:]\n",
    "test_y = y[80:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Afficher les données d'entraînement\n",
    "plt.scatter(train_x, train_y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Afficher les données de test\n",
    "plt.scatter(test_x, test_y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ajuster l’ensemble de données\n",
    "À quoi ressemble l’ensemble de données ? À mon avis, je pense que la meilleure solution serait une régression polynomiale, alors traçons la courbe de régression polynomiale."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Modèle de régression polynomiale de degré 4 pour les données d'entraînement\n",
    "mymodel = numpy.poly1d(numpy.polyfit(train_x, train_y, 4))\n",
    "\n",
    "# Tableau de valeurs de 0 à 6 avec 100 nombres\n",
    "values_table = numpy.linspace(0, 6, 100)\n",
    "\n",
    "plt.scatter(train_x, train_y)\n",
    "plt.plot(values_table, mymodel(values_table))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le résultat peut étayer ma suggestion de l’ensemble de données ajustant un polynôme régression, même si cela nous donnerait des résultats étranges si nous essayions de prédire valeurs en dehors de l’ensemble de données. Exemple : la ligne indique qu’un client qui passe 6 minutes dans la boutique ferait un achat d’une valeur de 200. C’est probablement un signe de surapprentissage.\n",
    "\n",
    "Mais qu’en est-il du score R au carré ? Le score R au carré est un bon indicateur de la façon dont mon modèle s’adapte à l'ensemble de données."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2:  0.7988645544629797\n"
     ]
    }
   ],
   "source": [
    "# Calculer le R2 pour les données d'entraînement\n",
    "r2 = r2_score(train_y, mymodel(train_x))\n",
    "print(\"R2: \", r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Le résultat 0,799 montre qu’il existe une relation correcte."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous avons maintenant créé un modèle qui est correct, du moins en ce qui concerne les données d’entraînement.\n",
    "\n",
    "Maintenant, nous voulons tester le modèle avec les données de test également, pour voir s'il nous donne le même résultat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R2:  0.8086921460343659\n"
     ]
    }
   ],
   "source": [
    "# Calculer le R2 pour les données de test\n",
    "r2 = r2_score(test_y, mymodel(test_x))\n",
    "print(\"R2: \", r2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: Le résultat 0,809 montre que le modèle s’adapte à la et nous sommes convaincus que nous pouvons utiliser le modèle pour prédire valeurs futures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant que nous avons établi que notre modèle est OK, nous pouvons commencer à prédire de nouvelles valeurs. Exemple : Combien d’argent un client acheteur dépensera-t-il s’il reste dans le magasin pendant 5 minutes ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "22.879625918118336\n"
     ]
    }
   ],
   "source": [
    "# Combien d’argent un client acheteur dépensera-t-il s’il reste dans le magasin pendant 5 minutes ?\n",
    "print(mymodel(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le modèle estime que le client dépenserait 22,88 dollars s’il restait dans le magasin pendant 5 minutes. Voir la correspondance sur la figure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "mode": "markers",
         "name": "Nuage de points",
         "type": "scatter",
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           "sequential": [
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             0,
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            ],
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             0.2222222222222222,
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            ],
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             0.3333333333333333,
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            ],
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             0.4444444444444444,
             "#bd3786"
            ],
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             0.5555555555555556,
             "#d8576b"
            ],
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             0.6666666666666666,
             "#ed7953"
            ],
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             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
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             0.6666666666666666,
             "#ed7953"
            ],
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             0.7777777777777778,
             "#fb9f3a"
            ],
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             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        }
       }
      }
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.graph_objects as go\n",
    "\n",
    "# Créer une figure vide\n",
    "fig = go.Figure()\n",
    "\n",
    "# Ajouter le nuage de points\n",
    "fig.add_trace(go.Scatter(x=train_x, y=train_y, mode='markers', name='Nuage de points'))\n",
    "\n",
    "# Ajouter la ligne\n",
    "fig.add_trace(go.Scatter(x=values_table, y=mymodel(values_table), mode='lines', name='Ligne'))\n",
    "\n",
    "# Ajouter une annotation pour la valeur précise de 5\n",
    "fig.add_annotation(\n",
    "    x=5,\n",
    "    y=mymodel(5),\n",
    "    text=f\"({5}, {mymodel(5)})\",\n",
    "    showarrow=True,\n",
    "    arrowhead=3  # grande flèche\n",
    ")\n",
    "\n",
    "# Afficher la figure\n",
    "fig.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"img_traintest_predict.png\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Arbres de décision</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    Age  Experience  Rank  Nationality  Go\n",
      "0    36          10     9            0   0\n",
      "1    42          12     4            1   0\n",
      "2    23           4     6            2   0\n",
      "3    52           4     4            1   0\n",
      "4    43          21     8            1   1\n",
      "5    44          14     5            0   0\n",
      "6    66           3     7            2   1\n",
      "7    35          14     9            0   1\n",
      "8    52          13     7            2   1\n",
      "9    35           5     9            2   1\n",
      "10   24           3     5            1   0\n",
      "11   18           3     7            0   1\n",
      "12   45           9     9            0   1\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from sklearn import tree\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "df = pd.read_csv(\"comedies.csv\")\n",
    "\n",
    "# Transformation des valeurs de chaîne en valeurs numériques pour créer l'arbre de décision\n",
    "d = {'UK': 0, 'USA': 1, 'N': 2}\n",
    "df['Nationality'] = df['Nationality'].map(d)\n",
    "d = {'YES': 1, 'NO': 0}\n",
    "df['Go'] = df['Go'].map(d)\n",
    "\n",
    "print(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Création d'un arbre de décision\n",
    "features = ['Age', 'Experience', 'Rank', 'Nationality']\n",
    "\n",
    "X = df[features]\n",
    "y = df['Go']\n",
    "\n",
    "dtree = DecisionTreeClassifier()\n",
    "dtree = dtree.fit(X, y)\n",
    "\n",
    "# Affichage de l'arbre de décision\n",
    "tree.plot_tree(dtree, feature_names=features)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "REMARQUE : Vous verrez que l’arbre de décision vous donne des résultats différents si vous exécutez le code plusieurs fois, même si vous le nourrissez avec les mêmes données.\n",
    "\n",
    "C’est parce que l’arbre de décision ne nous donne pas une réponse certaine à 100%. Il est basé sur le probabilité d’un résultat, et donc la réponse variera."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant, nous pouvons utiliser l’arbre de décision pour prédire de nouvelles valeurs.\n",
    "\n",
    "Exemple : Dois-je aller voir un spectacle mettant en vedette un comédien américain de 40 ans, avec 10 ans d’expérience, et un classement de comédie de 7 ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]\n",
      "[1] means 'GO'\n",
      "[0] means 'NO'\n"
     ]
    }
   ],
   "source": [
    "new_comedian = pd.DataFrame({\n",
    "  \"Age\": [40], \n",
    "  \"Experience\": [10], \n",
    "  \"Rank\": [7], \n",
    "  \"Nationality\": [1]\n",
    "})\n",
    "\n",
    "print(dtree.predict(new_comedian))\n",
    "\n",
    "print(\"[1] means 'GO'\")\n",
    "print(\"[0] means 'NO'\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La réponse est oui, selon l’arbre de décision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple 2 : Dois-je aller voir un spectacle mettant en vedette un comédien américain de 40 ans, avec 10 ans d’expérience, et un classement de comédie de 6 ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0]\n",
      "[1] means 'GO'\n",
      "[0] means 'NO'\n"
     ]
    }
   ],
   "source": [
    "new_comedian = pd.DataFrame({\n",
    "  \"Age\": [40], \n",
    "  \"Experience\": [10], \n",
    "  \"Rank\": [6], \n",
    "  \"Nationality\": [1]\n",
    "})\n",
    "\n",
    "print(dtree.predict(new_comedian))\n",
    "\n",
    "print(\"[1] means 'GO'\")\n",
    "print(\"[0] means 'NO'\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La réponse est non, selon l’arbre de décision."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Matrice de confusion</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy\n",
    "from sklearn import metrics\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Génère 1000 valeurs aléatoires binomiales (0 ou 1) avec une probabilité de 0.9 (90%) pour chaque valeur\n",
    "actual = numpy.random.binomial(1,.9,size = 1000)\n",
    "predicted = numpy.random.binomial(1,.9,size = 1000)\n",
    "\n",
    "# Crée une matrice de confusion\n",
    "confusion_matrix = metrics.confusion_matrix(actual, predicted)\n",
    "\n",
    "# Affiche la matrice de confusion\n",
    "cm_display = metrics.ConfusionMatrixDisplay(confusion_matrix = confusion_matrix, display_labels = [0, 1])\n",
    "\n",
    "cm_display.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explication des résultats\n",
    "La matrice de confusion créée comporte quatre quadrants différents :\n",
    "\n",
    "- Vrai Négatif (quadrant supérieur gauche)\n",
    "\n",
    "- Faux positif (quadrant supérieur droit)\n",
    "\n",
    "- Faux négatif (quadrant inférieur gauche)\n",
    "\n",
    "- Vrai positif (quadrant inférieur droit)\n",
    "\n",
    "Vrai signifie que les valeurs ont été prédites avec précision, Faux signifie qu’il y a eu une erreur ou une prédiction erronée.\n",
    "\n",
    "La diagonale principale (en haut à gauche jusqu'en bas à droite) indique les prédictions correctes pour chaque classe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Métriques créées :\n",
    "La matrice de confusion nous fournit de nombreuses mesures utiles qui nous aident à évaluer notre modèle de classification.\n",
    "\n",
    "Les différentes mesures comprennent : l’exactitude, la précision, la sensibilité (rappel), la spécificité et le score F, expliqués ci-dessous."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ⭐ Accuracy (Exactitude)\n",
    "L'exactitude (ou la justesse) mesure la fréquence à laquelle le modèle est correct.\n",
    "\n",
    "Comment calculer :\n",
    "\n",
    "<font color=\"red\">Exactitude = (Vrai positif + Vrai négatif) / Total des prédictions</font>\n",
    "\n",
    "Diagonale principale / Total des prédictions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:  0.834\n"
     ]
    }
   ],
   "source": [
    "Accuracy = metrics.accuracy_score(actual, predicted)\n",
    "print(\"Accuracy: \", Accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ⭐ Precision (Précision)\n",
    "Parmi les positifs prédits, quel pourcentage est vraiment positif ?\n",
    "\n",
    "Comment calculer :\n",
    "\n",
    "<font color=\"red\">Précision = Vrai positif / (Vrai positif + Faux positif)</font>\n",
    "\n",
    "La précision n’évalue pas les cas négatifs correctement prédits :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Precision:  0.9029443838604144\n"
     ]
    }
   ],
   "source": [
    "Precision = metrics.precision_score(actual, predicted)\n",
    "print(\"Precision: \", Precision)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ⭐ Sensitivity (Sensibilité ou Rappel)\n",
    "De tous les cas positifs, quel pourcentage sont prédits positifs ?\n",
    "\n",
    "La sensibilité (parfois appelée rappel) mesure la capacité du modèle à prédire les résultats positifs.\n",
    "\n",
    "Cela signifie qu’il examine les vrais positifs et les faux négatifs (qui sont des positifs qui ont été prédits à tort comme négatifs).\n",
    "\n",
    "Comment calculer :\n",
    "\n",
    "<font color=\"red\">Sensibilité = Vrai positif / (Vrai positif + Faux négatif)</font>\n",
    "\n",
    "La sensibilité est bonne pour comprendre dans quelle mesure le modèle prédit quelque chose de positif."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sensitivity_recall:  0.9149171270718232\n"
     ]
    }
   ],
   "source": [
    "Sensitivity_recall = metrics.recall_score(actual, predicted)\n",
    "print(\"Sensitivity_recall: \", Sensitivity_recall)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ⭐ Specificity (Spécificité)\n",
    "Dans quelle mesure le modèle est-il capable de prédire des résultats négatifs ?\n",
    "\n",
    "La spécificité est <font color=\"red\">similaire à la sensibilité</font>, mais elle est considérée <font color=\"red\">du point de vue des résultats négatifs.</font>\n",
    "\n",
    "Comment calculer :\n",
    "\n",
    "<font color=\"red\">Spécificité = Vrai négatif / (Vrai négatif + Faux positif)</font>\n",
    "\n",
    "Comme il s’agit de l’opposé de Rappel, nous utilisons la fonction recall_score, en prenant l’étiquette de position opposée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Specificity:  0.06315789473684211\n"
     ]
    }
   ],
   "source": [
    "Specificity = metrics.recall_score(actual, predicted, pos_label=0)\n",
    "print(\"Specificity: \", Specificity)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ⭐ F-Score (Score F)\n",
    "Le score F est la « moyenne harmonique » de la précision et de la sensibilité.\n",
    "\n",
    "Il prend en compte à la fois les cas faux positifs et faux négatifs et est bon pour les ensembles de données déséquilibrés.\n",
    "\n",
    "Comment calculer :\n",
    "\n",
    "<font color=\"red\">F-Score = 2 * ((Précision * Sensibilité) / (Précision + Sensibilité))</font>\n",
    "\n",
    "Ce score ne prend pas en compte les valeurs Vrai Négatif."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "F1_score:  0.9088913282107574\n"
     ]
    }
   ],
   "source": [
    "F1_score = metrics.f1_score(actual, predicted)\n",
    "print(\"F1_score: \", F1_score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calcul des métriques en une seule ligne"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'Accuracy': 0.834, 'Precision': 0.9029443838604144, 'Sensitivity_recall': 0.9149171270718232, 'Specificity': 0.06315789473684211, 'F1_score': 0.9088913282107574}\n"
     ]
    }
   ],
   "source": [
    "#metrics\n",
    "print({\"Accuracy\":Accuracy,\"Precision\":Precision,\"Sensitivity_recall\":Sensitivity_recall,\"Specificity\":Specificity,\"F1_score\":F1_score})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Clustering hiérarchique</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. Méthode de clustering hiérarchique à l'aide de la bibliothèque `scipy.cluster.hierarchy`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "\n",
    "x = [4, 5, 10, 4, 3, 11, 14 , 6, 10, 12]\n",
    "y = [21, 19, 24, 17, 16, 25, 24, 22, 21, 21]\n",
    "\n",
    "data = list(zip(x, y))\n",
    "\n",
    "# Crée un objet de liaison en utilisant les données et la méthode de liaison 'ward' (méthode de liaison minimisant la variance)\n",
    "linkage_data = linkage(data, method='ward', metric='euclidean') \n",
    "dendrogram(linkage_data)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'axe des x représente les échantillons (ici chaque point) et l'axe des y représente la distance entre ces échantillons."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. Méthode de clustering hiérarchique à l'aide de la bibliothèque `sklearn.cluster`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "x = [4, 5, 10, 4, 3, 11, 14 , 6, 10, 12]\n",
    "y = [21, 19, 24, 17, 16, 25, 24, 22, 21, 21]\n",
    "\n",
    "# Crée une liste de tuples contenant les coordonnées x et y\n",
    "data = list(zip(x, y))\n",
    "\n",
    "# Crée un objet de clustering hiérarchique avec 2 clusters et la méthode de liaison 'ward'\n",
    "hierarchical_cluster = AgglomerativeClustering(n_clusters=2, metric='euclidean', linkage='ward')\n",
    "# Prédit les clusters avec les données et retoune un tableau d'étiquettes (0 ou 1)\n",
    "labels = hierarchical_cluster.fit_predict(data)\n",
    "\n",
    "plt.scatter(x, y, c=labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Régression logistique</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La régression logistique vise à résoudre les problèmes de classification. Pour ce faire, il prédit des résultats catégoriels, contrairement à la régression linéaire qui prédit un résultat continu.\n",
    "\n",
    "Dans le cas le plus simple, il y a deux résultats, ce qu’on appelle le binôme, dont un exemple est de prédire si une tumeur est maligne ou bénigne. D’autres cas ont plus de deux issues à classer, dans ce cas on parle de multinôme. Un exemple courant de régression logistique multinomiale serait de prédire la classe d’une fleur d’iris entre 3 espèces différentes.\n",
    "\n",
    "Ici, nous allons utiliser la régression logistique de base pour prédire une variable binomiale. Cela signifie qu’il n’y a que deux issues possibles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "from sklearn import linear_model\n",
    "\n",
    "#X represents the size of a tumor in centimeters.\n",
    "X = numpy.array([3.78, 2.44, 2.09, 0.14, 1.72, 1.65, 4.92, 4.37, 4.96, 4.52, 3.69, 5.88]).reshape(-1,1)\n",
    "#Note: X has to be reshaped into a column from a row for the LogisticRegression() function to work.\n",
    "\n",
    "#y represents whether or not the tumor is cancerous (0 for \"No\", 1 for \"Yes\").\n",
    "y = numpy.array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1])\n",
    "\n",
    "# Create a logistic regression object\n",
    "logr = linear_model.LogisticRegression() \n",
    "logr.fit(X,y) # Train the model\n",
    "\n",
    "#  Determine if tumor is cancerous where the size is 3.78cm:\n",
    "predicted = logr.predict(numpy.array([3.78]).reshape(-1,1))\n",
    "\n",
    "print(predicted)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0]\n"
     ]
    }
   ],
   "source": [
    "# Determine if tumor is cancerous where the size is 3.46cm:\n",
    "predicted = logr.predict(numpy.array([3.46]).reshape(-1,1))\n",
    "\n",
    "print(predicted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Coefficient\n",
    "Dans la régression logistique, le coefficient est la variation attendue des logarithmes des chances d’avoir le résultat par unité de variation en X."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[4.03541657]]\n"
     ]
    }
   ],
   "source": [
    "log_odds = logr.coef_\n",
    "odds = numpy.exp(log_odds)\n",
    "\n",
    "print(odds)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cela nous dit que lorsque la taille d’une tumeur augmente de 1 mm, les chances qu’il s’agisse d’une La tumeur cancéreuse augmente de 4 fois."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probabilité\n",
    "Les valeurs du coefficient et de l’ordonnée à l’origine peuvent être utilisées pour déterminer la probabilité que chaque tumeur soit cancéreuse.\n",
    "\n",
    "Créez une fonction qui utilise les valeurs de coefficient et d’interception du modèle pour renvoyer une nouvelle valeur. Cette nouvelle valeur représente la probabilité que l’observation donnée soit une tumeur :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.60749955]\n",
      " [0.19268876]\n",
      " [0.12775886]\n",
      " [0.00955221]\n",
      " [0.08038616]\n",
      " [0.07345637]\n",
      " [0.88362743]\n",
      " [0.77901378]\n",
      " [0.88924409]\n",
      " [0.81293497]\n",
      " [0.57719129]\n",
      " [0.96664243]]\n"
     ]
    }
   ],
   "source": [
    "import numpy\n",
    "from sklearn import linear_model\n",
    "\n",
    "X = numpy.array([3.78, 2.44, 2.09, 0.14, 1.72, 1.65, 4.92, 4.37, 4.96, 4.52, 3.69, 5.88]).reshape(-1,1)\n",
    "y = numpy.array([0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1])\n",
    "\n",
    "logr = linear_model.LogisticRegression()\n",
    "logr.fit(X,y)\n",
    "\n",
    "# Calcule la probabilité qu'une tumeur soit cancéreuse\n",
    "def logit2prob(logr, X):\n",
    "  log_odds = logr.coef_ * X + logr.intercept_\n",
    "  odds = numpy.exp(log_odds)\n",
    "  probability = odds / (1 + odds)\n",
    "  return(probability)\n",
    "\n",
    "print(logit2prob(logr, X))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explication des résultats :\n",
    "\n",
    "(3.78, 0.61) La probabilité qu’une tumeur de 3,78 cm soit cancéreuse est de 61 %.\n",
    "\n",
    "(2.44, 0.19) La probabilité qu’une tumeur de 2,44 cm soit cancéreuse est de 19 %.\n",
    "\n",
    "(2.09, 0.13) La probabilité qu’une tumeur de 2,09 cm soit cancéreuse est de 13 %."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Régession logistique : Recherche par grille de valeurs (Grid Search)</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La majorité des modèles d’apprentissage automatique contiennent des paramètres qui peuvent être ajustés pour varier la façon dont le modèle apprend. Par exemple, le modèle de régression logistique à partir de `sklearn` a un paramètre `C` qui contrôle la régularisation. Ceci affecte la complexité du modèle.\n",
    "\n",
    "Avant d’entrer dans l’exemple, il est bon de savoir ce que fait le paramètre que nous modifions. Des valeurs plus élevées de `C` indiquent au modèle que les données d’entraînement ressemblent à des informations du majoritéonde réel. Accordez plus d’importance aux données d’entraînement. Alors que des valeurs inférieures de `C` font le contraire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_iris.html\n",
    "iris = datasets.load_iris() # Charge le jeu de données 'Iris flowers' dans la variable iris\n",
    "print(iris.DESCR)\n",
    "\n",
    "X = iris['data']\n",
    "y = iris['target']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En créant le modèle, nous définissons max_iter sur une valeur plus élevée pour s’assurer que le modèle trouve un résultat.\n",
    "\n",
    "Gardez à l’esprit que la valeur par défaut de `C` d’un modèle de régression logistique est `1`. Nous la comparerons plus tard.\n",
    "\n",
    "Dans l’exemple ci-dessous, nous examinons le jeu de données de l’iris et essayons d’entraîner un modèle en variant les valeurs de `C`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LogisticRegression(max_iter=10000)\n",
      "0.9733333333333334\n"
     ]
    }
   ],
   "source": [
    "logit = LogisticRegression(max_iter = 10000)\n",
    "\n",
    "# After we create the model, we must fit the model to the data.\n",
    "print(logit.fit(X,y))\n",
    "\n",
    "# To evaluate the model we run the score method.\n",
    "print(logit.score(X,y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
    "                   intercept_scaling=1, l1_ratio=None, max_iter=10000,\n",
    "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
    "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
    "                   warm_start=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec le réglage par défaut de `C = 1`, nous avons obtenu un score de 0,973.\n",
    "\n",
    "Voyons si nous pouvons faire mieux en implémentant une recherche par grille avec différentes valeurs de `C`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous suivrons les mêmes étapes que précédemment, sauf que cette fois nous définirons une plage de valeurs pour `C`.\n",
    "\n",
    "Savoir quelles valeurs définir pour les paramètres recherchés nécessitera une combinaison de connaissances du domaine et de pratique.\n",
    "\n",
    "Étant donné que la valeur par défaut de C est 1, nous allons définir une plage de valeurs qui l’entoure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.9666666666666667, 0.9666666666666667, 0.9733333333333334, 0.9733333333333334, 0.98, 0.98, 0.9866666666666667, 0.9866666666666667]\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "\n",
    "X = iris['data']\n",
    "y = iris['target']\n",
    "\n",
    "logit = LogisticRegression(max_iter = 10000)\n",
    "\n",
    "C = [0.25, 0.5, 0.75, 1, 1.25, 1.5, 1.75, 2]\n",
    "\n",
    "scores = []\n",
    "\n",
    "for choice in C:\n",
    "  logit.set_params(C=choice)\n",
    "  logit.fit(X, y)\n",
    "  scores.append(logit.score(X, y))\n",
    "\n",
    "print(scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Observations :\n",
    "\n",
    "We can see that the lower values of C performed worse than the base parameter of 1. However, as we increased the value of C to 1.75 the model experienced increased accuracy.\n",
    "\n",
    "It seems that increasing C beyond this amount does not help increase model accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note sur les bonnes pratiques\n",
    "\n",
    "Nous avons évalué notre modèle de régression logistique en utilisant les mêmes données que celles utilisées pour l'entraîner. Si le modèle correspond trop étroitement à ces données, il risque de ne pas être très efficace pour prédire les données invisibles. Cette erreur statistique est connue sous le nom de surajustement .\n",
    "\n",
    "Pour éviter d'être induit en erreur par les scores des données d'entraînement, nous pouvons mettre de côté une partie de nos données et les utiliser spécifiquement dans le but de tester le modèle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Données catégorielles</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of unique values in the 'Car' column:  17\n",
      "[110.26943394]\n"
     ]
    }
   ],
   "source": [
    "import pandas\n",
    "from sklearn import linear_model\n",
    "import numpy as np\n",
    "\n",
    "cars = pandas.read_csv(\"data.csv\")\n",
    "\n",
    "# Number of unique values in the 'Car' column\n",
    "print(\"Number of unique values in the 'Car' column: \", cars['Car'].nunique())\n",
    "\n",
    "# One-hot encode the 'Car' column\n",
    "ohe_cars = pandas.get_dummies(cars[['Car']]) \n",
    "\n",
    "# Concatenate the 'Volume' and 'Weight' columns with the one-hot encoded data\n",
    "X = pandas.concat([cars[['Volume', 'Weight']], ohe_cars], axis=1) \n",
    "#print(X.to_string())\n",
    "\n",
    "y = cars['CO2']\n",
    "\n",
    "regr = linear_model.LinearRegression()\n",
    "regr.fit(X,y)\n",
    "\n",
    "# Predict the CO2 emission of a Volvo where the weight is 2300kg, and the volume is 1300cm3:\n",
    "\n",
    "# new_car = np.array([[2300, 1300, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]])\n",
    "\n",
    "new_car = pandas.DataFrame({\n",
    "  \"Volume\": [1300],\n",
    "  \"Weight\": [2300],\n",
    "  \"Car_Audi\": [0],\n",
    "  \"Car_BMW\": [0],\n",
    "  \"Car_Fiat\": [0],\n",
    "  \"Car_Ford\": [0],\n",
    "  \"Car_Honda\": [0],\n",
    "  \"Car_Hundai\": [0],\n",
    "  \"Car_Hyundai\": [0],\n",
    "  \"Car_Mazda\": [0],\n",
    "  \"Car_Mercedes\": [0],\n",
    "  \"Car_Mini\": [0],\n",
    "  \"Car_Mitsubishi\": [0],\n",
    "  \"Car_Opel\": [0],\n",
    "  \"Car_Skoda\": [0],\n",
    "  \"Car_Suzuki\": [0],\n",
    "  \"Car_Toyoty\": [0],\n",
    "  \"Car_VW\": [0],\n",
    "  \"Car_Volvo\": [1]\n",
    "})\n",
    "\n",
    "# Prédire la valeur de CO2 pour la nouvelle voiture\n",
    "predictedCO2 = regr.predict(new_car)\n",
    "\n",
    "print(predictedCO2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">K-means</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "K-means est une méthode d'apprentissage non supervisée permettant de regrouper des points de données. L'algorithme divise de manière itérative les points de données en K clusters en minimisant la variance dans chaque cluster.\n",
    "\n",
    "Ici, nous vous montrerons comment estimer la meilleure valeur pour K en utilisant la méthode du coude, puis utiliser le clustering K-means pour regrouper les points de données en clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comment ça marche ?\n",
    "\n",
    "Tout d'abord, chaque point de données est attribué de manière aléatoire à l'un des K clusters. Ensuite, nous calculons le centroïde (fonctionnellement le centre) de chaque cluster et réaffectons chaque point de données au cluster ayant le centroïde le plus proche. Nous répétons ce processus jusqu'à ce que les attributions de cluster pour chaque point de données ne changent plus.\n",
    "\n",
    "Le clustering K-means nécessite de sélectionner K, le nombre de clusters dans lesquels nous souhaitons regrouper les données. La méthode du coude nous permet de représenter graphiquement l'inertie (une mesure basée sur la distance) et de visualiser le point auquel elle commence à diminuer linéairement. Ce point est appelé le « coude » et constitue une bonne estimation de la meilleure valeur pour K en fonction de nos données."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Commencez par visualiser quelques points de données :\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = [4, 5, 10, 4, 3, 11, 14 , 6, 10, 12]\n",
    "y = [21, 19, 24, 17, 16, 25, 24, 22, 21, 21]\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Nous utilisons maintenant la méthode du coude pour visualiser l’inertie pour différentes valeurs de K :\n",
    "\n",
    "# Créer une variable d'environnement OMP_NUM_THREAD avec la valeur 1\n",
    "# setx OMP_NUM_THREADS \"1\"\n",
    "# echo %OMP_NUM_THREADS%\n",
    "\n",
    "from sklearn.cluster import KMeans\n",
    "\n",
    "data = list(zip(x, y))\n",
    "inertias = []\n",
    "\n",
    "for i in range(1,11):\n",
    "    kmeans = KMeans(n_clusters=i, n_init=10) # Crée un objet KMeans avec i clusters\n",
    "    kmeans.fit(data) # Entraîne le modèle avec les données\n",
    "    inertias.append(kmeans.inertia_) # Ajoute l'inertie à la liste\n",
    "\n",
    "# Afficher l'inertie\n",
    "plt.plot(range(1,11), inertias, marker='o')\n",
    "plt.title('Elbow method')\n",
    "plt.xlabel('Number of clusters')\n",
    "plt.ylabel('Inertia')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La méthode du coude montre que 2 est une bonne valeur pour K, nous entraînons donc le modèle à nouveau et visualisons le résultat :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Crée un objet de clustering KMeans avec 2 clusters\n",
    "kmeans = KMeans(n_clusters=2, n_init=10)\n",
    "\n",
    "# Entraîne le modèle avec les données\n",
    "kmeans.fit(data) \n",
    "\n",
    "plt.scatter(x, y, c=kmeans.labels_)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Bootstrap Aggregating (Bagging)</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _wine_dataset:\n",
      "\n",
      "Wine recognition dataset\n",
      "------------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 178\n",
      "    :Number of Attributes: 13 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      " \t\t- Alcohol\n",
      " \t\t- Malic acid\n",
      " \t\t- Ash\n",
      "\t\t- Alcalinity of ash  \n",
      " \t\t- Magnesium\n",
      "\t\t- Total phenols\n",
      " \t\t- Flavanoids\n",
      " \t\t- Nonflavanoid phenols\n",
      " \t\t- Proanthocyanins\n",
      "\t\t- Color intensity\n",
      " \t\t- Hue\n",
      " \t\t- OD280/OD315 of diluted wines\n",
      " \t\t- Proline\n",
      "\n",
      "    - class:\n",
      "            - class_0\n",
      "            - class_1\n",
      "            - class_2\n",
      "\t\t\n",
      "    :Summary Statistics:\n",
      "    \n",
      "    ============================= ==== ===== ======= =====\n",
      "                                   Min   Max   Mean     SD\n",
      "    ============================= ==== ===== ======= =====\n",
      "    Alcohol:                      11.0  14.8    13.0   0.8\n",
      "    Malic Acid:                   0.74  5.80    2.34  1.12\n",
      "    Ash:                          1.36  3.23    2.36  0.27\n",
      "    Alcalinity of Ash:            10.6  30.0    19.5   3.3\n",
      "    Magnesium:                    70.0 162.0    99.7  14.3\n",
      "    Total Phenols:                0.98  3.88    2.29  0.63\n",
      "    Flavanoids:                   0.34  5.08    2.03  1.00\n",
      "    Nonflavanoid Phenols:         0.13  0.66    0.36  0.12\n",
      "    Proanthocyanins:              0.41  3.58    1.59  0.57\n",
      "    Colour Intensity:              1.3  13.0     5.1   2.3\n",
      "    Hue:                          0.48  1.71    0.96  0.23\n",
      "    OD280/OD315 of diluted wines: 1.27  4.00    2.61  0.71\n",
      "    Proline:                       278  1680     746   315\n",
      "    ============================= ==== ===== ======= =====\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: class_0 (59), class_1 (71), class_2 (48)\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "This is a copy of UCI ML Wine recognition datasets.\n",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data\n",
      "\n",
      "The data is the results of a chemical analysis of wines grown in the same\n",
      "region in Italy by three different cultivators. There are thirteen different\n",
      "measurements taken for different constituents found in the three types of\n",
      "wine.\n",
      "\n",
      "Original Owners: \n",
      "\n",
      "Forina, M. et al, PARVUS - \n",
      "An Extendible Package for Data Exploration, Classification and Correlation. \n",
      "Institute of Pharmaceutical and Food Analysis and Technologies,\n",
      "Via Brigata Salerno, 16147 Genoa, Italy.\n",
      "\n",
      "Citation:\n",
      "\n",
      "Lichman, M. (2013). UCI Machine Learning Repository\n",
      "[https://archive.ics.uci.edu/ml]. Irvine, CA: University of California,\n",
      "School of Information and Computer Science. \n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "  (1) S. Aeberhard, D. Coomans and O. de Vel, \n",
      "  Comparison of Classifiers in High Dimensional Settings, \n",
      "  Tech. Rep. no. 92-02, (1992), Dept. of Computer Science and Dept. of  \n",
      "  Mathematics and Statistics, James Cook University of North Queensland. \n",
      "  (Also submitted to Technometrics). \n",
      "\n",
      "  The data was used with many others for comparing various \n",
      "  classifiers. The classes are separable, though only RDA \n",
      "  has achieved 100% correct classification. \n",
      "  (RDA : 100%, QDA 99.4%, LDA 98.9%, 1NN 96.1% (z-transformed data)) \n",
      "  (All results using the leave-one-out technique) \n",
      "\n",
      "  (2) S. Aeberhard, D. Coomans and O. de Vel, \n",
      "  \"THE CLASSIFICATION PERFORMANCE OF RDA\" \n",
      "  Tech. Rep. no. 92-01, (1992), Dept. of Computer Science and Dept. of \n",
      "  Mathematics and Statistics, James Cook University of North Queensland. \n",
      "  (Also submitted to Journal of Chemometrics).\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 900x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "\n",
    "# Charge le jeu de données 'Wine' dans la variable data\n",
    "# Contient des informations chimiques sur différents types de vins\n",
    "# https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_wine.html\n",
    "data = datasets.load_wine()\n",
    "print(data.DESCR)\n",
    "\n",
    "X = data.data\n",
    "y = data.target\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, random_state = 22)\n",
    "\n",
    "estimator_range = [2,4,6,8,10,12,14,16]\n",
    "\n",
    "models = []\n",
    "scores = []\n",
    "\n",
    "for n_estimators in estimator_range:\n",
    "    \n",
    "    # Create bagging classifier model\n",
    "    clf = BaggingClassifier(n_estimators = n_estimators, random_state = 22)\n",
    "    \n",
    "    # Fit the model\n",
    "    clf.fit(X_train, y_train)\n",
    "    \n",
    "    # Append the model and score to their respective list\n",
    "    models.append(clf)\n",
    "    scores.append(accuracy_score(y_true = y_test, y_pred = clf.predict(X_test)))\n",
    "    \n",
    "# Generate the plot of scores against number of estimators\n",
    "plt.figure(figsize=(9,6))\n",
    "plt.plot(estimator_range, scores)\n",
    "\n",
    "# Adjust labels and font (to make visable)\n",
    "plt.xlabel(\"n_estimators\", fontsize = 18)\n",
    "plt.ylabel(\"score\", fontsize = 18)\n",
    "plt.tick_params(labelsize = 16)\n",
    "\n",
    "# Visualize plot\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Résultats expliqués :</b>\n",
    "\n",
    "En itérant sur différentes valeurs pour le nombre d'estimateurs, nous pouvons constater une augmentation des performances du modèle de 82,2 % à 95,5 %. Après 14 estimateurs, l'exactitude (accuracy) commence à diminuer. Encore une fois, si vous définissez un nombre différent pour random_state, les valeurs que vous voyez varieront. C'est pourquoi il est recommandé d'utiliser la `validation croisée` pour garantir des résultats stables.\n",
    "\n",
    "Dans ce cas, nous constatons une augmentation de 13,3 % de l'exactitude lorsqu’il s’agit d’identifier le type de vin (blanc, rosé, rouge)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Remarque :</b>\n",
    "\n",
    "Voici une explication détaillée :\n",
    "\n",
    "1. `datasets.load_wine(as_frame=True)` :\n",
    "   - `datasets` : fait référence au module `datasets` de la bibliothèque `scikit-learn`, qui contient plusieurs jeux de données intégrés pour les tests et les démonstrations.\n",
    "   - `load_wine` : est une fonction de ce module qui charge le jeu de données \"wine\". Ce jeu de données est utilisé pour la classification et contient des informations chimiques sur différents types de vins.\n",
    "   - `as_frame=True` : est un paramètre qui, lorsqu'il est défini sur `True`, retourne les données sous forme de `pandas.DataFrame` au lieu de `numpy.ndarray`. Cela facilite la manipulation et l'analyse des données en utilisant les fonctionnalités de `pandas`.\n",
    "\n",
    "2. `data` :\n",
    "   - La variable `data` stocke le jeu de données chargé. Lorsque `as_frame=True`, `data` est un dictionnaire contenant les éléments suivants :\n",
    "     - `data` : un DataFrame contenant les caractéristiques (features) du jeu de données.\n",
    "     - `target` : un DataFrame contenant les étiquettes de classe (target) du jeu de données.\n",
    "     - `frame` : un DataFrame combinant les caractéristiques et les étiquettes.\n",
    "     - `DESCR` : une description du jeu de données.\n",
    "     - `feature_names` : une liste des noms des caractéristiques.\n",
    "     - `target_names` : une liste des noms des classes.\n",
    "\n",
    "En résumé, cette ligne de code charge le jeu de données \"wine\" de `scikit-learn` sous forme de DataFrame pandas et le stocke dans la variable `data` pour une manipulation et une analyse plus faciles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Une autre forme d’évaluation\n",
    "\n",
    "Comme le bootstrapping choisit des sous-ensembles aléatoires d'observations pour créer des classificateurs, certaines observations sont laissées de côté dans le processus de sélection. Ces observations « out-of-bag » peuvent ensuite être utilisées pour évaluer le modèle, de la même manière que celles d'un ensemble de tests. Gardez à l'esprit que l'estimation out-of-bag peut surestimer l'erreur dans les problèmes de classification binaire et ne doit être utilisée qu'en complément d'autres mesures.\n",
    "\n",
    "Nous avons vu dans le dernier exercice que 12 estimateurs ont donné la plus grande précision. Nous allons donc utiliser cela pour créer notre modèle. Cette fois, nous définissons le paramètre oob_score sur true pour évaluer le modèle avec le score out-of-bag."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X    alcohol  malic_acid   ash  alcalinity_of_ash  magnesium  total_phenols  flavanoids  nonflavanoid_phenols  proanthocyanins  color_intensity   hue  od280/od315_of_diluted_wines  proline\n",
      "0    14.23        1.71  2.43               15.6      127.0           2.80        3.06                  0.28             2.29             5.64  1.04                          3.92   1065.0\n",
      "1    13.20        1.78  2.14               11.2      100.0           2.65        2.76                  0.26             1.28             4.38  1.05                          3.40   1050.0\n",
      "2    13.16        2.36  2.67               18.6      101.0           2.80        3.24                  0.30             2.81             5.68  1.03                          3.17   1185.0\n",
      "3    14.37        1.95  2.50               16.8      113.0           3.85        3.49                  0.24             2.18             7.80  0.86                          3.45   1480.0\n",
      "4    13.24        2.59  2.87               21.0      118.0           2.80        2.69                  0.39             1.82             4.32  1.04                          2.93    735.0\n",
      "5    14.20        1.76  2.45               15.2      112.0           3.27        3.39                  0.34             1.97             6.75  1.05                          2.85   1450.0\n",
      "6    14.39        1.87  2.45               14.6       96.0           2.50        2.52                  0.30             1.98             5.25  1.02                          3.58   1290.0\n",
      "7    14.06        2.15  2.61               17.6      121.0           2.60        2.51                  0.31             1.25             5.05  1.06                          3.58   1295.0\n",
      "8    14.83        1.64  2.17               14.0       97.0           2.80        2.98                  0.29             1.98             5.20  1.08                          2.85   1045.0\n",
      "9    13.86        1.35  2.27               16.0       98.0           2.98        3.15                  0.22             1.85             7.22  1.01                          3.55   1045.0\n",
      "\n",
      "\n",
      "y 0      0\n",
      "1      0\n",
      "2      0\n",
      "3      0\n",
      "4      0\n",
      "5      0\n",
      "6      0\n",
      "7      0\n",
      "8      0\n",
      "9      0\n",
      "10     0\n",
      "11     0\n",
      "12     0\n",
      "13     0\n",
      "14     0\n",
      "15     0\n",
      "16     0\n",
      "17     0\n",
      "18     0\n",
      "19     0\n",
      "20     0\n",
      "21     0\n",
      "22     0\n",
      "23     0\n",
      "24     0\n",
      "25     0\n",
      "26     0\n",
      "27     0\n",
      "28     0\n",
      "29     0\n",
      "30     0\n",
      "31     0\n",
      "32     0\n",
      "33     0\n",
      "34     0\n",
      "35     0\n",
      "36     0\n",
      "37     0\n",
      "38     0\n",
      "39     0\n",
      "40     0\n",
      "41     0\n",
      "42     0\n",
      "43     0\n",
      "44     0\n",
      "45     0\n",
      "46     0\n",
      "47     0\n",
      "48     0\n",
      "49     0\n",
      "50     0\n",
      "51     0\n",
      "52     0\n",
      "53     0\n",
      "54     0\n",
      "55     0\n",
      "56     0\n",
      "57     0\n",
      "58     0\n",
      "59     1\n",
      "60     1\n",
      "61     1\n",
      "62     1\n",
      "63     1\n",
      "64     1\n",
      "65     1\n",
      "66     1\n",
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      "70     1\n",
      "71     1\n",
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      "73     1\n",
      "74     1\n",
      "75     1\n",
      "76     1\n",
      "77     1\n",
      "78     1\n",
      "79     1\n",
      "80     1\n",
      "81     1\n",
      "82     1\n",
      "83     1\n",
      "84     1\n",
      "85     1\n",
      "86     1\n",
      "87     1\n",
      "88     1\n",
      "89     1\n",
      "90     1\n",
      "91     1\n",
      "92     1\n",
      "93     1\n",
      "94     1\n",
      "95     1\n",
      "96     1\n",
      "97     1\n",
      "98     1\n",
      "99     1\n",
      "100    1\n",
      "101    1\n",
      "102    1\n",
      "103    1\n",
      "104    1\n",
      "105    1\n",
      "106    1\n",
      "107    1\n",
      "108    1\n",
      "109    1\n",
      "110    1\n",
      "111    1\n",
      "112    1\n",
      "113    1\n",
      "114    1\n",
      "115    1\n",
      "116    1\n",
      "117    1\n",
      "118    1\n",
      "119    1\n",
      "120    1\n",
      "121    1\n",
      "122    1\n",
      "123    1\n",
      "124    1\n",
      "125    1\n",
      "126    1\n",
      "127    1\n",
      "128    1\n",
      "129    1\n",
      "130    2\n",
      "131    2\n",
      "132    2\n",
      "133    2\n",
      "134    2\n",
      "135    2\n",
      "136    2\n",
      "137    2\n",
      "138    2\n",
      "139    2\n",
      "140    2\n",
      "141    2\n",
      "142    2\n",
      "143    2\n",
      "144    2\n",
      "145    2\n",
      "146    2\n",
      "147    2\n",
      "148    2\n",
      "149    2\n",
      "150    2\n",
      "151    2\n",
      "152    2\n",
      "153    2\n",
      "154    2\n",
      "155    2\n",
      "156    2\n",
      "157    2\n",
      "158    2\n",
      "159    2\n",
      "160    2\n",
      "161    2\n",
      "162    2\n",
      "163    2\n",
      "164    2\n",
      "165    2\n",
      "166    2\n",
      "167    2\n",
      "168    2\n",
      "169    2\n",
      "170    2\n",
      "171    2\n",
      "172    2\n",
      "173    2\n",
      "174    2\n",
      "175    2\n",
      "176    2\n",
      "177    2\n",
      "\n",
      "\n",
      "oob_model.oob_score_ :  0.9398496240601504\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "\n",
    "data = datasets.load_wine(as_frame = True)\n",
    "\n",
    "X = data.data\n",
    "y = data.target\n",
    "\n",
    "print(\"X\", X.head(10).to_string())\n",
    "print(\"\\n\")\n",
    "print(\"y\", y.to_string())\n",
    "print(\"\\n\")\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, random_state = 22)\n",
    "\n",
    "oob_model = BaggingClassifier(n_estimators = 12, oob_score = True, random_state = 22)\n",
    "\n",
    "oob_model.fit(X_train, y_train)\n",
    "\n",
    "print(\"oob_model.oob_score_ : \", oob_model.oob_score_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Étant donné que les échantillons utilisés dans OOB et l'ensemble de test sont différents et que l'ensemble de données est relativement petit, il existe une différence de précision. Il est rare qu'ils soient exactement identiques. Là encore, OOB doit être utilisé comme moyen rapide d'estimation de l'erreur, mais ce n'est pas la seule mesure d'évaluation.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Génération d'arbres de décision à partir du classificateur Bagging\n",
    "Comme nous l'avons vu dans la leçon sur l'arbre de décision , il est possible de représenter graphiquement l'arbre de décision créé par le modèle. Il est également possible de voir les arbres de décision individuels qui ont été intégrés au classificateur agrégé. Cela nous aide à mieux comprendre comment le modèle de bagging parvient à ses prédictions.\n",
    "\n",
    "Remarque : ceci n'est fonctionnel qu'avec des ensembles de données plus petits, où les arbres sont relativement peu profonds et étroits, ce qui les rend faciles à visualiser.\n",
    "\n",
    "Nous devrons importer plot_tree, une fonction depuis sklearn.tree. Les différents arbres peuvent être représentés graphiquement en changeant l'estimateur que vous souhaitez visualiser."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[Text(0.4583333333333333, 0.875, 'x[12] <= 727.5\\ngini = 0.611\\nsamples = 82\\nvalue = [54, 60, 19]'),\n",
       " Text(0.25, 0.625, 'x[6] <= 1.335\\ngini = 0.339\\nsamples = 47\\nvalue = [0, 58, 16]'),\n",
       " Text(0.16666666666666666, 0.375, 'x[10] <= 0.92\\ngini = 0.266\\nsamples = 15\\nvalue = [0, 3, 16]'),\n",
       " Text(0.08333333333333333, 0.125, 'gini = 0.0\\nsamples = 13\\nvalue = [0, 0, 16]'),\n",
       " Text(0.25, 0.125, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 3, 0]'),\n",
       " Text(0.3333333333333333, 0.375, 'gini = 0.0\\nsamples = 32\\nvalue = [0, 55, 0]'),\n",
       " Text(0.6666666666666666, 0.625, 'x[6] <= 1.605\\ngini = 0.159\\nsamples = 35\\nvalue = [54, 2, 3]'),\n",
       " Text(0.5, 0.375, 'x[9] <= 4.325\\ngini = 0.375\\nsamples = 3\\nvalue = [0, 1, 3]'),\n",
       " Text(0.4166666666666667, 0.125, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]'),\n",
       " Text(0.5833333333333334, 0.125, 'gini = 0.0\\nsamples = 2\\nvalue = [0, 0, 3]'),\n",
       " Text(0.8333333333333334, 0.375, 'x[4] <= 147.0\\ngini = 0.036\\nsamples = 32\\nvalue = [54, 1, 0]'),\n",
       " Text(0.75, 0.125, 'gini = 0.0\\nsamples = 31\\nvalue = [54, 0, 0]'),\n",
       " Text(0.9166666666666666, 0.125, 'gini = 0.0\\nsamples = 1\\nvalue = [0, 1, 0]')]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 3000x2000 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.ensemble import BaggingClassifier\n",
    "from sklearn.tree import plot_tree\n",
    "\n",
    "data = datasets.load_wine()\n",
    "\n",
    "X = data.data\n",
    "y = data.target\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, random_state = 22)\n",
    "\n",
    "clf = BaggingClassifier(n_estimators = 12, oob_score = True,random_state = 22)\n",
    "clf.fit(X_train, y_train)\n",
    "\n",
    "plt.figure(figsize=(30, 20))\n",
    "\n",
    "plot_tree(clf.estimators_[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Remarque : </b>\n",
    "\n",
    "⭐ Voici une explication détaillée pour la classe `BaggingClassifier`:\n",
    "\n",
    "1. `BaggingClassifier` :\n",
    "   - C'est une classe de `sklearn.ensemble` qui implémente l'algorithme de Bagging pour les modèles de classification.\n",
    "   - Bagging est une méthode d'ensemble qui améliore la stabilité et la précision des algorithmes de machine learning en combinant les résultats de plusieurs modèles de base (estimateurs).\n",
    "\n",
    "2. `n_estimators = 12` :\n",
    "   - `n_estimators` spécifie le nombre d'estimateurs de base (par défaut, des arbres de décision) à utiliser dans le modèle de Bagging.\n",
    "   - Ici, 12 estimateurs de base seront utilisés.\n",
    "\n",
    "3. `oob_score = True` :\n",
    "   - `oob_score` (Out-Of-Bag score) est un paramètre qui, lorsqu'il est défini sur `True`, permet d'utiliser les échantillons non sélectionnés (out-of-bag) pour évaluer la performance du modèle.\n",
    "   - Cela fournit une estimation de la précision du modèle sans avoir besoin d'une validation croisée explicite.\n",
    "\n",
    "4. `random_state = 22` :\n",
    "   - `random_state` est un paramètre qui contrôle la graine aléatoire (seed) utilisée pour la reproductibilité des résultats.\n",
    "   - En fixant `random_state` à 22, vous vous assurez que les résultats seront les mêmes à chaque exécution du code.\n",
    "\n",
    "En résumé, `BaggingClassifier` initialise un classificateur de Bagging avec 12 estimateurs, utilise les échantillons out-of-bag pour évaluer la performance du modèle, et fixe la graine aléatoire à 22 pour garantir la reproductibilité des résultats.\n",
    "\n",
    "\n",
    "⭐ Voici une explication détaillée pour la fonction `train_test_split()`:\n",
    "\n",
    "1. `train_test_split(X, y, test_size=0.25, random_state=22)` :\n",
    "   - `train_test_split` : est une fonction de `sklearn.model_selection` qui divise les matrices ou les tableaux en sous-ensembles aléatoires pour l'entraînement et le test.\n",
    "   - `X` : représente les caractéristiques (features) de vos données.\n",
    "   - `y` : représente les étiquettes (labels) de vos données.\n",
    "   - `test_size=0.25` : spécifie que 25% des données seront utilisées pour l'ensemble de test, et les 75% restants seront utilisés pour l'ensemble d'entraînement.\n",
    "   - `random_state=22` : fixe la graine aléatoire (seed) pour garantir la reproductibilité des résultats. En utilisant la même valeur de `random_state`, vous obtiendrez la même division des données à chaque exécution.\n",
    "\n",
    "2. `X_train, X_test, y_train, y_test` :\n",
    "   - `X_train` : contient les caractéristiques de l'ensemble d'entraînement.\n",
    "   - `X_test` : contient les caractéristiques de l'ensemble de test.\n",
    "   - `y_train` : contient les étiquettes de l'ensemble d'entraînement.\n",
    "   - `y_test` : contient les étiquettes de l'ensemble de test.\n",
    "\n",
    "En résumé, cette ligne de code divise les données `X` et `y` en ensembles d'entraînement et de test, en utilisant 75% des données pour l'entraînement et 25% pour le test, tout en garantissant la reproductibilité avec `random_state=22`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(45, 13)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([1, 2, 2, 2, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1,\n",
       "       2, 1, 1, 2, 0, 1, 2, 2, 1, 1, 2, 1, 0, 2, 2, 0, 2, 1, 2, 1, 0, 0,\n",
       "       2])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Identification du type de vin à l'aide des données de test en fonction des caractéristiques chimiques\n",
    "print(X_test.shape)\n",
    "clf.predict(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">La Validation Croisée</font>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La validation croisée est une technique d'évaluation des performances des modèles de machine learning. Elle consiste à diviser l'ensemble de données en plusieurs sous-ensembles, à entraîner le modèle sur certains sous-ensembles et à le tester sur d'autres, puis à répéter ce processus pour chaque sous-ensemble. Cela permet d'obtenir une estimation plus fiable de la performance du modèle que l'utilisation d'un seul ensemble de test."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lors de l'ajustement des modèles, nous cherchons à augmenter les performances globales du modèle sur des données invisibles. Le réglage des hyperparamètres peut conduire à de bien meilleures performances sur les ensembles de tests. Cependant, l'optimisation des paramètres de l'ensemble de tests peut entraîner une fuite d'informations, ce qui entraîne une moins bonne performance du modèle sur des données inconnues. Pour corriger cela, nous pouvons effectuer une validation croisée.\n",
    "\n",
    "Il existe de nombreuses méthodes de validation croisée. Nous commencerons par examiner la validation croisée k-fold."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validation croisée K-Fold"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme nous allons essayer de classer différentes espèces de fleurs d'iris, nous devrons importer un modèle de classificateur. Pour cet exercice, nous utiliserons `DecisionTreeClassifier`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross Validation Scores:  [1.         1.         0.83333333 0.93333333 0.8       ]\n",
      "Average CV Score:  0.9133333333333333\n",
      "Number of CV Scores used in Average:  5\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import KFold, cross_val_score\n",
    "\n",
    "# https://scikit-learn.org/stable/modules/generated/sklearn.datasets.load_iris.html\n",
    "X, y = datasets.load_iris(return_X_y=True)\n",
    "#print(datasets.load_iris().DESCR)\n",
    "\n",
    "clf = DecisionTreeClassifier(random_state=42)\n",
    "\n",
    "# Crée un objet KFold avec 5 dossiers\n",
    "k_folds = KFold(n_splits = 5)\n",
    "\n",
    "# Calcule les scores de validation croisée (CV)\n",
    "scores = cross_val_score(clf, X, y, cv = k_folds)\n",
    "\n",
    "print(\"Cross Validation Scores: \", scores)\n",
    "print(\"Average CV Score: \", scores.mean())\n",
    "print(\"Number of CV Scores used in Average: \", len(scores))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CV K-Fold stratifié\n",
    "\n",
    "La validation croisée k-fold stratifiée est une variante de la validation croisée k-fold qui garantit que chaque dossier contient une proportion égale de chaque classe cible. Cela est particulièrement utile lorsque les classes cibles sont déséquilibrées.\n",
    "\n",
    "Dans les cas où les classes sont déséquilibrées, nous devons trouver un moyen de tenir compte du déséquilibre dans les ensembles d'apprentissage et de validation. Pour ce faire, nous pouvons stratifier les classes cibles, ce qui signifie que les deux ensembles auront une proportion égale de toutes les classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross Validation Scores:  [0.96666667 0.96666667 0.9        0.93333333 1.        ]\n",
      "Average CV Score:  0.9533333333333334\n",
      "Number of CV Scores used in Average:  5\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import StratifiedKFold, cross_val_score\n",
    "\n",
    "X, y = datasets.load_iris(return_X_y=True)\n",
    "\n",
    "clf = DecisionTreeClassifier(random_state=42)\n",
    "\n",
    "sk_folds = StratifiedKFold(n_splits = 5)\n",
    "\n",
    "# Calcule les scores de validation croisée (CV)\n",
    "scores = cross_val_score(clf, X, y, cv = sk_folds)\n",
    "\n",
    "print(\"Cross Validation Scores: \", scores)\n",
    "print(\"Average CV Score: \", scores.mean())\n",
    "print(\"Number of CV Scores used in Average: \", len(scores))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bien que le nombre de plis soit le même, le CV moyen augmente à partir du k-fold de base lorsqu'on s'assure qu'il existe des classes stratifiées.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CV Leave-One-Out (LOO) ou Laisser un échantillon de côté\n",
    "La validation croisée Leave-One-Out (LOO) est une méthode de validation croisée où un seul échantillon est retenu pour l'ensemble de test et tous les autres échantillons sont utilisés pour l'ensemble d'entraînement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross Validation Scores:  [1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
      " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
      " 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1.\n",
      " 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1.\n",
      " 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 1. 0.\n",
      " 1. 1. 1. 1. 1. 1. 1. 1. 1. 0. 1. 1. 1. 0. 1. 1. 1. 1. 0. 1. 1. 1. 1. 1.\n",
      " 1. 1. 1. 1. 1. 1.]\n",
      "Average CV Score:  0.94\n",
      "Number of CV Scores used in Average:  150\n",
      ".. _iris_dataset:\n",
      "\n",
      "Iris plants dataset\n",
      "--------------------\n",
      "\n",
      "**Data Set Characteristics:**\n",
      "\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "                \n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
      "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
      "Machine Learning Repository, which has two wrong data points.\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      ".. topic:: References\n",
      "\n",
      "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import LeaveOneOut, cross_val_score\n",
    "\n",
    "X, y = datasets.load_iris(return_X_y=True)\n",
    "\n",
    "clf = DecisionTreeClassifier(random_state=42)\n",
    "\n",
    "# Crée un objet LeaveOneOut pour la validation croisée en laissant une observation à chaque fois\n",
    "loo = LeaveOneOut()\n",
    "\n",
    "# Calcule les scores de validation croisée (CV)\n",
    "scores = cross_val_score(clf, X, y, cv = loo)\n",
    "\n",
    "print(\"Cross Validation Scores: \", scores)\n",
    "print(\"Average CV Score: \", scores.mean())\n",
    "print(\"Number of CV Scores used in Average: \", len(scores))\n",
    "print(datasets.load_iris().DESCR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nous pouvons observer que le nombre de scores de validation croisée effectués est égal au nombre d'observations dans l'ensemble de données. Dans ce cas, il y a 150 observations dans l'ensemble de données d'iris.\n",
    "\n",
    "Le score moyen du CV est de 94%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CV Leave-P-Out (LPO)\n",
    "La validation croisée Leave-P-Out (LPO) est une méthode de validation croisée où p échantillons sont retenus pour l'ensemble de test et les autres échantillons sont utilisés pour l'ensemble d'entraînement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross Validation Scores:  [1. 1. 1. ... 1. 1. 1.]\n",
      "Average CV Score:  0.9382997762863534\n",
      "Number of CV Scores used in Average:  11175\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import LeavePOut, cross_val_score\n",
    "\n",
    "X, y = datasets.load_iris(return_X_y=True)\n",
    "\n",
    "clf = DecisionTreeClassifier(random_state=42)\n",
    "\n",
    "# Crée un objet LeavePOut pour la validation croisée en laissant p observations à chaque fois\n",
    "lpo = LeavePOut(p=2)\n",
    "\n",
    "scores = cross_val_score(clf, X, y, cv = lpo)\n",
    "\n",
    "print(\"Cross Validation Scores: \", scores)\n",
    "print(\"Average CV Score: \", scores.mean())\n",
    "print(\"Number of CV Scores used in Average: \", len(scores))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Comme nous pouvons le voir, il s'agit d'une méthode exhaustive avec beaucoup plus de scores calculés que Leave-One-Out, même avec ap = 2, mais elle atteint à peu près le même score CV moyen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### CV ShuffleSplit\n",
    "La validation croisée ShuffleSplit est une méthode de validation croisée qui génère un nombre prédéfini de jeux de données d'entraînement et de test en mélangeant les données. Pour ce faire, nous devons décider de la taille des ensembles d'entraînement et de test, ainsi que du nombre de divisions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cross Validation Scores:  [0.93333333 0.91111111 0.91111111 0.93333333 0.91111111]\n",
      "Average CV Score:  0.9200000000000002\n",
      "Number of CV Scores used in Average:  5\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.model_selection import ShuffleSplit, cross_val_score\n",
    "\n",
    "X, y = datasets.load_iris(return_X_y=True)\n",
    "\n",
    "clf = DecisionTreeClassifier(random_state=42)\n",
    "\n",
    "# Crée un objet ShuffleSplit pour la validation croisée en mélangeant les données et en les divisant en train et test\n",
    "# train_size = 0.6 signifie que 60% des données sont utilisées pour l'entraînement et 30% pour le test\n",
    "ss = ShuffleSplit(train_size=0.7, test_size=0.3, n_splits = 5)\n",
    "\n",
    "scores = cross_val_score(clf, X, y, cv = ss)\n",
    "\n",
    "print(\"Cross Validation Scores: \", scores)\n",
    "print(\"Average CV Score: \", scores.mean())\n",
    "print(\"Number of CV Scores used in Average: \", len(scores))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Remarque :</b>\n",
    "\n",
    "Ce ne sont là que quelques-unes des méthodes CV qui peuvent être appliquées aux modèles. Il existe de nombreuses autres classes de validation croisée, la plupart des modèles ayant leur propre classe. Découvrez la validation croisée de sklearns pour plus d'options de validation croisée."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">Courbe AUC-ROC (Area Under the Curve - Receiver Operating Characteristic)</font>\n",
    "La courbe AUC-ROC est un graphique qui montre la performance d'un modèle de classification à différents seuils de classification. L'AUC-ROC est une mesure de la performance d'un modèle de classification binaire, qui est souvent utilisée pour comparer différents modèles.\n",
    "\n",
    " La courbe caractéristique de fonctionnement du récepteur trace le taux de vrais positifs ( TP ) par rapport au taux de faux positifs ( FP ) à différents seuils de classification. Les seuils sont différents seuils de probabilité qui séparent les deux classes dans la classification binaire. Elle utilise la probabilité pour nous dire dans quelle mesure un modèle sépare les classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Données déséquilibrées\n",
    "Supposons que nous ayons un ensemble de données déséquilibré dans lequel la majorité de nos données est d'une valeur unique. Nous pouvons obtenir une grande précision pour le modèle en prédisant la classe majoritaire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy score: 0.95\n",
      "Confusion matrix\n",
      "[[   0  500]\n",
      " [   0 9500]]\n",
      "class 0 accuracy: 0.0\n",
      "class 1 accuracy: 1.0\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix\n",
    "\n",
    "n = 10000\n",
    "ratio = .95\n",
    "n_0 = int((1-ratio) * n)\n",
    "n_1 = int(ratio * n)\n",
    "\n",
    "y = np.array([0] * n_0 + [1] * n_1)\n",
    "# below are the probabilities obtained from a hypothetical model that always predicts the majority class\n",
    "# probability of predicting class 1 is going to be 100%\n",
    "y_proba = np.array([1]*n)\n",
    "y_pred = y_proba > .5\n",
    "\n",
    "print(f'accuracy score: {accuracy_score(y, y_pred)}')\n",
    "cf_mat = confusion_matrix(y, y_pred)\n",
    "print('Confusion matrix')\n",
    "print(cf_mat)\n",
    "print(f'class 0 accuracy: {cf_mat[0][0]/n_0}')\n",
    "print(f'class 1 accuracy: {cf_mat[1][1]/n_1}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bien que nous obtenions une très grande précision, le modèle ne fournit aucune information sur les données et n'est donc pas utile. Nous prédisons avec précision la classe 1 dans 100 % des cas, tandis que nous prédisons de manière inexacte la classe 0 dans 0 % des cas. Au détriment de la précision, il pourrait être préférable d'avoir un modèle capable de séparer quelque peu les deux classes.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy score: 0.7083\n",
      "Confusion matrix\n",
      "[[ 371  129]\n",
      " [2788 6712]]\n",
      "class 0 accuracy: 0.742\n",
      "class 1 accuracy: 0.7065263157894737\n"
     ]
    }
   ],
   "source": [
    "# below are the probabilities obtained from a hypothetical model that doesn't always predict the mode\n",
    "y_proba_2 = np.array(\n",
    "    np.random.uniform(0, .7, n_0).tolist() +\n",
    "    np.random.uniform(.3, 1, n_1).tolist()\n",
    ")\n",
    "y_pred_2 = y_proba_2 > .5\n",
    "\n",
    "print(f'accuracy score: {accuracy_score(y, y_pred_2)}')\n",
    "cf_mat = confusion_matrix(y, y_pred_2)\n",
    "print('Confusion matrix')\n",
    "print(cf_mat)\n",
    "print(f'class 0 accuracy: {cf_mat[0][0]/n_0}')\n",
    "print(f'class 1 accuracy: {cf_mat[1][1]/n_1}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour le deuxième ensemble de prédictions, nous n'avons pas un score de précision aussi élevé que le premier, mais la précision de chaque classe est plus équilibrée. En utilisant la précision comme mesure d'évaluation, nous donnerions au premier modèle une note plus élevée que le deuxième, même s'il ne nous dit rien sur les données.\n",
    "\n",
    "Dans des cas comme celui-ci, il serait préférable d’utiliser une autre mesure d’évaluation comme l’AUC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "model 1 AUC score: 0.5\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.metrics import roc_auc_score, roc_curve\n",
    "\n",
    "n = 10000\n",
    "ratio = .95\n",
    "n_0 = int((1-ratio) * n)\n",
    "n_1 = int(ratio * n)\n",
    "\n",
    "y = np.array([0] * n_0 + [1] * n_1)\n",
    "\n",
    "# below are the probabilities obtained from a hypothetical model that always predicts the majority class\n",
    "# probability of predicting class 1 is going to be 100%\n",
    "y_proba = np.array([1]*n)\n",
    "y_pred = y_proba > .5\n",
    "\n",
    "def plot_roc_curve(true_y, y_prob):\n",
    "    \"\"\"\n",
    "    plots the roc curve based of the probabilities\n",
    "    \"\"\"\n",
    "    \n",
    "    fpr, tpr, thresholds = roc_curve(true_y, y_prob)\n",
    "    plt.plot(fpr, tpr)\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "\n",
    "plot_roc_curve(y, y_proba)\n",
    "print(f'model 1 AUC score: {roc_auc_score(y, y_proba)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "model 2 AUC score: 0.8291787368421053\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, roc_auc_score, roc_curve\n",
    "\n",
    "n = 10000\n",
    "ratio = .95\n",
    "n_0 = int((1-ratio) * n)\n",
    "n_1 = int(ratio * n)\n",
    "\n",
    "y = np.array([0] * n_0 + [1] * n_1)\n",
    "\n",
    "# below are the probabilities obtained from a hypothetical model that doesn't always predict the mode\n",
    "y_proba_2 = np.array(\n",
    "    np.random.uniform(0, .7, n_0).tolist() +\n",
    "    np.random.uniform(.3, 1, n_1).tolist()\n",
    ")\n",
    "y_pred_2 = y_proba_2 > .5\n",
    "\n",
    "def plot_roc_curve(true_y, y_prob):\n",
    "    \"\"\"\n",
    "    plots the roc curve based of the probabilities\n",
    "    \"\"\"\n",
    "    \n",
    "    fpr, tpr, thresholds = roc_curve(true_y, y_prob)\n",
    "    plt.plot(fpr, tpr)\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "\n",
    "plot_roc_curve(y, y_proba_2)\n",
    "print(f'model 2 AUC score: {roc_auc_score(y, y_proba_2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un score AUC d'environ 0,5 signifierait que le modèle est incapable de faire une distinction entre les deux classes et la courbe ressemblerait à une ligne avec une pente de 1. Un score AUC plus proche de 1 signifie que le modèle a la capacité de séparer les deux classes et la courbe se rapprocherait du coin supérieur gauche du graphique."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probabilité\n",
    "Étant donné que l’AUC est une mesure qui utilise les probabilités des prédictions de classe, nous pouvons être plus confiants dans un modèle qui a un score AUC plus élevé que dans un modèle avec un score plus faible, même s’ils ont des précisions similaires.\n",
    "\n",
    "Dans les données ci-dessous, nous avons deux ensembles de probabilités issues de modèles hypothétiques. Le premier a des probabilités qui ne sont pas aussi « sûres » pour prédire les deux classes (les probabilités sont proches de 0,5). Le second a des probabilités qui sont plus « sûres » pour prédire les deux classes (les probabilités sont proches des extrêmes de 0 ou 1)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exemple"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "model 1 accuracy score: 0.7531\n",
      "model 2 accuracy score: 0.7435\n",
      "model 1 AUC score: 0.77717584\n",
      "model 2 AUC score: 0.85582564\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, roc_auc_score, roc_curve\n",
    "\n",
    "n = 10000\n",
    "y = np.array([0] * n + [1] * n)\n",
    "# \n",
    "y_prob_1 = np.array(\n",
    "    np.random.uniform(.25, .5, n//2).tolist() + \n",
    "    np.random.uniform(.3, .7, n).tolist() + \n",
    "    np.random.uniform(.5, .75, n//2).tolist()\n",
    ")\n",
    "y_prob_2 = np.array(\n",
    "    np.random.uniform(0, .4, n//2).tolist() + \n",
    "    np.random.uniform(.3, .7, n).tolist() + \n",
    "    np.random.uniform(.6, 1, n//2).tolist()\n",
    ")\n",
    "\n",
    "print(f'model 1 accuracy score: {accuracy_score(y, y_prob_1>.5)}')\n",
    "print(f'model 2 accuracy score: {accuracy_score(y, y_prob_2>.5)}')\n",
    "\n",
    "print(f'model 1 AUC score: {roc_auc_score(y, y_prob_1)}')\n",
    "print(f'model 2 AUC score: {roc_auc_score(y, y_prob_2)}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modèle de tracé 1 :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, roc_auc_score, roc_curve\n",
    "\n",
    "n = 10000\n",
    "y = np.array([0] * n + [1] * n)\n",
    "# \n",
    "y_prob_1 = np.array(\n",
    "    np.random.uniform(.25, .5, n//2).tolist() + \n",
    "    np.random.uniform(.3, .7, n).tolist() + \n",
    "    np.random.uniform(.5, .75, n//2).tolist()\n",
    ")\n",
    "y_prob_2 = np.array(\n",
    "    np.random.uniform(0, .4, n//2).tolist() + \n",
    "    np.random.uniform(.3, .7, n).tolist() + \n",
    "    np.random.uniform(.6, 1, n//2).tolist()\n",
    ")\n",
    "\n",
    "def plot_roc_curve(true_y, y_prob):\n",
    "    \"\"\"\n",
    "    plots the roc curve based of the probabilities\n",
    "    \"\"\"\n",
    "    \n",
    "    fpr, tpr, thresholds = roc_curve(true_y, y_prob)\n",
    "    plt.plot(fpr, tpr)\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "\n",
    "plot_roc_curve(y, y_prob_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modèle de tracé 2 :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x213fbe7e950>]"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, roc_auc_score, roc_curve\n",
    "\n",
    "n = 10000\n",
    "y = np.array([0] * n + [1] * n)\n",
    "# \n",
    "y_prob_1 = np.array(\n",
    "    np.random.uniform(.25, .5, n//2).tolist() + \n",
    "    np.random.uniform(.3, .7, n).tolist() + \n",
    "    np.random.uniform(.5, .75, n//2).tolist()\n",
    ")\n",
    "y_prob_2 = np.array(\n",
    "    np.random.uniform(0, .4, n//2).tolist() + \n",
    "    np.random.uniform(.3, .7, n).tolist() + \n",
    "    np.random.uniform(.6, 1, n//2).tolist()\n",
    ")\n",
    "\n",
    "def plot_roc_curve(true_y, y_prob):\n",
    "    \"\"\"\n",
    "    plots the roc curve based of the probabilities\n",
    "    \"\"\"\n",
    "    \n",
    "    fpr, tpr, thresholds = roc_curve(true_y, y_prob)\n",
    "    plt.plot(fpr, tpr)\n",
    "    plt.xlabel('False Positive Rate')\n",
    "    plt.ylabel('True Positive Rate')\n",
    "\n",
    "fpr, tpr, thresholds = roc_curve(y, y_prob_2)\n",
    "plt.plot(fpr, tpr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Même si les précisions des deux modèles sont similaires, le modèle avec le score AUC le plus élevé sera plus fiable car il prend en compte la probabilité prédite. Il est plus susceptible de vous offrir une plus grande précision lors de la prédiction des données futures."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## <font color=\"red\">K-nearest neighbors (KNN)</font>\n",
    "\n",
    "KNN est un algorithme d'apprentissage automatique (ML) supervisé simple qui peut être utilisé pour des tâches de classification ou de régression - et est également fréquemment utilisé dans l'imputation de valeurs manquantes. Il est basé sur l'idée que les observations les plus proches d'un point de données sont les observations les plus « similaires » dans un ensemble de données, et nous pouvons donc classer les points imprévus en fonction des valeurs des points existants les plus proches. En choisissant K, l'utilisateur peut sélectionner le nombre d'observations proches à utiliser dans l'algorithme.\n",
    "\n",
    "K est le nombre de voisins les plus proches à utiliser. Pour la classification, un vote majoritaire est utilisé pour déterminer dans quelle classe une nouvelle observation doit être classée. Les valeurs plus élevées de K sont souvent plus résistantes aux valeurs aberrantes et produisent des limites de décision plus stables que les valeurs très petites ( K=3 serait mieux que K=1 , ce qui pourrait produire des résultats indésirables).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Commencez par visualiser quelques points de données :\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = [4, 5, 10, 4, 3, 11, 14 , 8, 10, 12]\n",
    "y = [21, 19, 24, 17, 16, 25, 24, 22, 21, 21]\n",
    "classes = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1]\n",
    "\n",
    "plt.scatter(x, y, c=classes)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "x = [4, 5, 10, 4, 3, 11, 14 , 8, 10, 12]\n",
    "y = [21, 19, 24, 17, 16, 25, 24, 22, 21, 21]\n",
    "classes = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1]\n",
    "\n",
    "data = list(zip(x, y))\n",
    "\n",
    "# Crée un objet KNeighborsClassifier avec 1 voisin le plus proche\n",
    "knn = KNeighborsClassifier(n_neighbors=1) \n",
    "\n",
    "# Entraîne le modèle avec les données et les classes\n",
    "knn.fit(data, classes)\n",
    "\n",
    "new_x = 8\n",
    "new_y = 21\n",
    "new_point = [(new_x, new_y)]\n",
    "\n",
    "# Prédire la classe du nouveau point\n",
    "prediction = knn.predict(new_point)\n",
    "\n",
    "plt.scatter(x + [new_x], y + [new_y], c=classes + [prediction[0]])\n",
    "plt.text(x=new_x-1.7, y=new_y-0.7, s=f\"new point, class: {prediction[0]}\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Maintenant, nous faisons la même chose, mais avec une valeur K plus élevée qui modifie la prédiction :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "\n",
    "x = [4, 5, 10, 4, 3, 11, 14 , 8, 10, 12]\n",
    "y = [21, 19, 24, 17, 16, 25, 24, 22, 21, 21]\n",
    "classes = [0, 0, 1, 0, 0, 1, 1, 0, 1, 1]\n",
    "\n",
    "data = list(zip(x, y))\n",
    "knn = KNeighborsClassifier(n_neighbors=5)\n",
    "\n",
    "knn.fit(data, classes)\n",
    "\n",
    "new_x = 8\n",
    "new_y = 21\n",
    "new_point = [(new_x, new_y)]\n",
    "\n",
    "# Prédire la classe du nouveau point\n",
    "prediction = knn.predict(new_point) \n",
    "\n",
    "plt.scatter(x + [new_x], y + [new_y], c=classes + [prediction[0]])\n",
    "plt.text(x=new_x-1.7, y=new_y-0.7, s=f\"new point, class: {prediction[0]}\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cependant, lorsque nous modifions le nombre de voisins à 5, le nombre de points utilisés pour classer notre nouveau point change. Par conséquent, la classification du nouveau point change également :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}