TP 5 RN2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TP 5 Réseaux de neurones - Multi classification et Propagation en arrière\n",
    "Dans ce TP, nous aimerions entrainer un réseau de neurones pour la tâche de classification en utilisant l'algorithme d propagation en arrière (backpropagation).\n",
    "\n",
    "L'ensemble de données que nous allons utiliser est le même que celui utilisé durant le TP1, i.e. les images de chiffres manuscrits.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Importation des librairies necessaires au travail"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy import random\n",
    "import cv2 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lecture des fichiers de données\n",
    "Pour ce TP, nous allons lire les données à partir d'un fichier csv."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 401)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# données\n",
    "data = np.genfromtxt('data.csv', delimiter=',', dtype=float)\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans ces données (data), les 400 premières colonnes representent les pixels de l'image (20x20), la dernière colonne represente la classe de l'image (chiffres de 0 à 9). (http://yann.lecun.com/exdb/mnist/)\n",
    "\n",
    "Chaque ligne represente un exemple de notre ensemble de données. \n",
    "\n",
    "Mettons ces données dans leus vecteurs correspondants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# rajoutons l'ordonnée à l'origine theta 0\n",
    "intercept=np.ones((data.shape[0],1))\n",
    "X=np.column_stack((intercept,data[:,:-1]))\n",
    "y=data[:,-1]\n",
    "# forcer y à avoir une seule colonne\n",
    "y = y.reshape( y.shape[0], 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X (5000, 401)  y  (5000, 1)\n"
     ]
    }
   ],
   "source": [
    "print('X', X.shape ,' y ', y.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualisation aléatoire de quelques données"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x800 with 13 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,8))\n",
    "for i in range(13):\n",
    "    c = random.randint(X.shape[0])\n",
    "    a = X[c,1:].reshape((20, 20)) ##premiere colonne de X est l'intercept\n",
    "    a=np.transpose(a)\n",
    "    plt.subplot(1,13,i+1)\n",
    "    plt.title('label '+ str(y[c]))\n",
    "    plt.imshow(a,cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transformer y de tel sorte à avoir un vecteur pour chaque exemple\n",
    "\n",
    "Equivalent de tocategorical\n",
    "\n",
    "transformer les étiquettes de classe y en vecteurs one-hot encoded, ce qui est souvent nécessaire pour les tâches de classification lorsque le modèle de réseau de neurones a une couche de sortie avec plusieurs neurones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 10)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# nombre de lignes = nbr d'exemples , nbr de colonnes = plus grand label+1\n",
    "YY=np.zeros((y.shape[0], int(np.max(y))+1))\n",
    "YY.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\taouc\\AppData\\Local\\Temp\\ipykernel_10052\\972189422.py:3: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)\n",
      "  YY[i,int(y[i])]=1\n"
     ]
    }
   ],
   "source": [
    "#cette ligne attribue 1 à la colonne correspondant à la classe de l'exemple dans y\n",
    "for i in range (YY.shape[0]):\n",
    "    YY[i,int(y[i])]=1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cela revient à la représentation one-hot encoding : une seule valeur est mise à 1 dans le vecteur, correspondant à la classe réelle de l'exemple, tandis que toutes les autres valeurs restent à 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Réseaux de neurones\n",
    "Pour cette partie, nous choisissons une réseau simple:\n",
    "\n",
    "- une couche d'entrée avec 400 noeuds (20 x 20 pixels) + le biais\n",
    "- une couche cachée avec 25 noeuds\n",
    "- une couche de sortie avec 10 noeuds (nombre de classes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25, 401)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# poids de la couche 1\n",
    "W1 = np.genfromtxt('W1.csv', delimiter=',', dtype=float)\n",
    "W1.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 26)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# poids de la couche 2\n",
    "W2 = np.genfromtxt('W2.csv', delimiter=',', dtype=float)\n",
    "W2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_layer_size  = 400\n",
    "hidden_layer_size = 25   \n",
    "num_labels = 10"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Calcul du coût"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO  1 calcul du coût\n",
    "**Tâche 1**: Modifier la fonction computeCost afin d'obtenir un coût avec régularisation\n",
    "\n",
    "Rappelons que le coût avec régularisation est calculé comme suit:\n",
    "\n",
    "$ J(\\theta)= \\frac{1}{m} \\sum_{i=1}^m\\sum_{k=1}^K \\left[ -y_k^{(i)} \\log (h_\\theta(x^{(i)}) )_k - (1-y_k^{(i)}) \\log (1-h_\\theta(x^{(i)}) )_k \\right] + \\frac{\\lambda}{2m} \\left[ \\sum_{j=1}^{25}\\sum_{k=1}^{400} \\left( \\theta_{j,k}^{(1)} \\right)^2 +   \\sum_{j=1}^{10}\\sum_{k=1}^{25} \\left( \\theta_{j,k}^{(2)} \\right)^2 \\right] $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "\n",
    "$ J(\\theta) = \\frac{1}{m} \\sum_{i=1}^m \\left[ \\text{Erreur}(x^{(i)}, y^{(i)}, \\theta) \\right] + \\frac{\\lambda}{2m} \\left[ \\text{Régularisation}(\\theta^{(1)}) + \\text{Régularisation}(\\theta^{(2)}) \\right] $\n",
    "\n",
    "Où :\n",
    "\n",
    "- m est le nombre total d'exemples d'entraînement.\n",
    "- i est l'indice de l'exemple d'entraînement actuel.\n",
    "- $ x^{(i)} $ représente les caractéristiques de l'exemple d'entraînement i.\n",
    "- $ y^{(i)} $ est la classe réelle de l'exemple d'entraînement i.\n",
    "- θ est l'ensemble des paramètres du modèle.\n",
    "- λ est le paramètre de régularisation.\n",
    "- $ \\theta^{(1)} $ et $ \\theta^{(2)} $ représentent respectivement les poids entre la couche d'entrée et la couche cachée, et entre la couche cachée et la couche de sortie.\n",
    "\n",
    "La fonction Erreur mesure l'erreur de prédiction pour chaque exemple d'entraînement et est définie comme suit :\n",
    "\n",
    "\n",
    "$ \\text{Erreur}(x^{(i)}, y^{(i)}, \\theta) = \\sum_{k=1}^K \\left[ -y_k^{(i)} \\log(h_\\theta(x^{(i)}))_k - (1 - y_k^{(i)}) \\log(1 - h_\\theta(x^{(i)}))_k \\right] $\n",
    "\n",
    "\n",
    "Où :\n",
    "\n",
    "- K est le nombre total de classes de sortie.\n",
    "- $ y_k^{(i)} $ est 1 si la classe réelle de l'exemple d'entraînement i est k, et 0 sinon.\n",
    "- $ h_\\theta(x^{(i)}) $ est la prédiction du modèle pour l'exemple d'entraînement i.\n",
    "\n",
    "La fonction Régularisation mesure la régularisation des poids du modèle et est définie comme suit :\n",
    "\n",
    "$ \\text{Régularisation}(\\theta^{(l)}) = \\sum_{j=1}^{n_l}\\sum_{k=1}^{n_{l-1}} (\\theta_{j,k}^{(l)})^2 $\n",
    "\n",
    "Où :\n",
    "\n",
    "- n_l est le nombre de neurones dans la couche l du réseau de neurones.\n",
    "- $ \\theta_{j,k}^{(l)} $ est le poids entre le neurone k de la couche (l-1) et le neurone j de la couche l.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\" Le np.clip(-z, -500, 500) assure que la valeur de -z reste dans la plage [-500, 500],\\n évitant ainsi les problèmes de débordement numérique lorsque z est trop grand ou trop petit.\\n   Cela garantit que l'exponentielle calculée ne dépasse pas les limites des valeurs numériques représentables \""
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def Sigmoid(z):\n",
    "    # pour une valeur donnée, cette fonction calculera sa sigmoid\n",
    "    return 1 / (1+np.exp(np.clip(-z, -500, 500)))\n",
    "\n",
    "\n",
    "\"\"\" Le np.clip(-z, -500, 500) assure que la valeur de -z reste dans la plage [-500, 500],\n",
    " évitant ainsi les problèmes de débordement numérique lorsque z est trop grand ou trop petit.\n",
    "   Cela garantit que l'exponentielle calculée ne dépasse pas les limites des valeurs numériques représentables \"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeCost(X: np.ndarray, YY: np.ndarray, *thetas:np.ndarray, lambda_=0):\n",
    "    m = X.shape[0]\n",
    "    a1 = X\n",
    "    theta1, theta2 = thetas\n",
    "    \n",
    "\n",
    "    #la couche cachee\n",
    "    intercept = np.ones((m,1))\n",
    "    z2 = np.column_stack((intercept, np.matmul(a1, np.transpose(theta1))))\n",
    "    a2 = Sigmoid(z2)\n",
    "    a2[:,0] = 1 \n",
    "    \n",
    "    #la couche de sortie\n",
    "    z3 = np.matmul(a2, np.transpose(theta2))\n",
    "    a3 = Sigmoid(z3)\n",
    "\n",
    "    reg = (lambda_/(2*m)) * np.sum([np.sum(theta[:,1:]**2) for theta in thetas])\n",
    "    J = (-np.sum((YY*np.log(a3)) + (1-YY) * np.log(1-a3))) / m + reg\n",
    "\n",
    "    return J"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$ J(\\theta) = \\frac{1}{m} \\sum_{i=1}^m \\left[ \\text{Erreur}(x^{(i)}, y^{(i)}, \\theta) \\right] + \\frac{\\lambda}{2m} \\left[ \\text{Régularisation}(\\theta^{(1)}) + \\text{Régularisation}(\\theta^{(2)}) \\right] $\n",
    "\n",
    "$ \\text{Régularisation}(\\theta^{(l)}) = \\sum_{j=1}^{n_l}\\sum_{k=1}^{n_{l-1}} (\\theta_{j,k}^{(l)})^2 $\n",
    "\n",
    "$ \\text{Erreur}(x^{(i)}, y^{(i)}, \\theta) = \\sum_{k=1}^K \\left[ -y_k^{(i)} \\log(h_\\theta(x^{(i)}))_k - (1 - y_k^{(i)}) \\log(1 - h_\\theta(x^{(i)}))_k \\right] $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO  2 calcul du gradient\n",
    "**Tâche 2**: Implémenter la fonction NNCostFunction afin de retourner:\n",
    "\n",
    "- Le coût avec régularisation\n",
    "- Le gardient du coût par rapport à chaqu'un des paramètres du réseau\n",
    "\n",
    "Rappelons le gradient de la sigmoid:\n",
    "\n",
    "$ sigmoid(z) =\\sigma(z)= \\frac{1}{1-e^{-z}}$\n",
    "\n",
    "$ \\sigma(z)^\\prime = \\sigma(z)(1-\\sigma(z)) =a(1-a)$ tel que $a$ est l'activation d'une couche donnée\n",
    "\n",
    "L'algorithme à implementer est comme suit:\n",
    "\n",
    "Pour chaque exemple de l'ensemble d'apprentissage faire\n",
    "\n",
    "Pour chaque noeud de la couche de sortie, calculer la dérivée (gradient):\n",
    "\n",
    "$\\delta_k^{(3)} = \\left( a_k^{(3)}- y_k \\right)  $\n",
    "\n",
    "Pour chaque noeud de la couche caché calculer la dérivée (gradient):\n",
    "\n",
    "$\\delta^{(2)} =  \\left(\\Theta^{(2)}\\right)^T \\delta^{(3)} \\quad .* \\quad \\sigma^\\prime\\left(z^{(2)} \\right) $\n",
    "\n",
    "Notons que l'opérateur $.*$ represente la multiplication élement par élement et non pas la multiplication matricielle\n",
    "\n",
    "Le gradient de chaque noeud et de chaque couche sera finalement:\n",
    "\n",
    "$\\Delta^{(l)} =  \\Delta^{(l)} + \\delta^{(l)} * \\left( a^{(l)} \\right)^T $\n",
    "\n",
    "Fin pour\n",
    "\n",
    "Fin pour\n",
    "\n",
    "Diviser le gradient cumulé par le nombre d'exemples:\n",
    "\n",
    "$ \\frac{\\partial J(\\Theta)} { \\partial \\Theta_{i,j)}^{(l)}} = \\frac{1}{m} \\Delta_{i,j)}^{(l)}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_activations(X: np.ndarray, *thetas: np.ndarray) -> list[np.ndarray]:\n",
    "    \"\"\"     Cette fonction calcule les \n",
    "    activations pour chaque couche du reseau\n",
    "    \"\"\"    \n",
    "    activations = []\n",
    "    a = X\n",
    "\n",
    "    for theta in thetas:\n",
    "        a = Sigmoid(np.matmul(a, np.transpose(theta)))\n",
    "        activations.append(a)\n",
    "        # ajout d'un biais au activations pour la prochaine couche\n",
    "        a = np.column_stack((np.ones((a.shape[0],1)), a))\n",
    "    return activations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def NNCostFunction(X: np.ndarray, YY: np.ndarray, *thetas: list[np.ndarray], lambda_=0):\n",
    "    m = X.shape[0]\n",
    "    # calcul des activations pour chaque exemple d'entrainement * une liste de listes \n",
    "    activations = compute_activations(X, *thetas)\n",
    "    Deltas = [np.zeros_like(theta) for theta in thetas] # initialisation des gradients pour chaque couche\n",
    "    \n",
    "    for i in range(m):\n",
    "        #une liste de tableaux où chaque élément de la liste représente les activations de chaque couche pour un seul exemple d'entraînement spécifique\n",
    "        A = [a[i].reshape(-1,1) for a in activations]\n",
    "        a_l = A.pop(-1) #extrait l'activation de la couche de sortie de la liste A\n",
    "\n",
    "        #calcul de l'erreur pour la couche de sortie\n",
    "        prev_delta = a_l - YY[i].reshape(-1,1)\n",
    "\n",
    "        # Boucle sur chaque couche cachee en partant de la couche de sortie\n",
    "        for Delta, theta, a in zip(Deltas[::-1], thetas[::-1], A[::-1]):\n",
    "            # Ajoute un biais aux activations de chaque couche\n",
    "            a = np.vstack((np.ones((1, a.shape[1])), a))\n",
    "            \n",
    "            Delta += np.matmul(prev_delta, np.transpose(a))\n",
    "            #Calcule l'erreur (delta) pour la couche actuelle en utilisant la rétropropagation du gradient\n",
    "            prev_delta = np.matmul(np.transpose(theta), prev_delta) * a * (1-a)\n",
    "\n",
    "    # Calcul des termes de régularisation pour chaque couche (pour chaque matrice de poids)\n",
    "    regularizations = [np.hstack((np.zeros((theta.shape[0],1)), theta[:,1:])) for theta in thetas]\n",
    "    # Calcul des gradients avec régularisation\n",
    "    grad = [Delta/m + (lambda_/m)*reg for Delta, reg in zip(Deltas, regularizations)]\n",
    "    J = computeCost(X, YY, *thetas, lambda_=lambda_)\n",
    "\n",
    "    return J, grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO  3 entrainement du réseau\n",
    "**Tâche 3**: Entrainer le réseau en utilisant la descente du gradient:\n",
    "Ici il faudra reprendre l'algorithme de la descente du gradient afin de mettre à jour les paramètres du réseau\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradientDescent(X: np.ndarray, y: np.ndarray, Theta: list[np.ndarray], alpha: float, iterations: int, lambda_=0):\n",
    "    # Initialise un tableau pour stocker l'historique des coûts pour chaque itération\n",
    "    J_history = np.zeros((iterations, 1))\n",
    "    \n",
    "    # Boucle sur le nombre d'itérations spécifié\n",
    "    for i in range(iterations):\n",
    "        # Calcule le coût et les gradients en utilisant la fonction de coût de réseau de neurones\n",
    "        J, grad = NNCostFunction(X, y, *Theta, lambda_=lambda_)\n",
    "        \n",
    "        # Enregistre le coût actuel dans l'historique des coûts\n",
    "        J_history[i] = J\n",
    "        \n",
    "        # Affiche le coût tous les 10 itérations\n",
    "        if i % 10 == 0:\n",
    "            print(f'Iteration {i} - Cost {J}')\n",
    "        \n",
    "        # Met à jour les paramètres (poids) du réseau en utilisant la descente de gradient\n",
    "        Theta = [theta - alpha * g for theta, g in zip(Theta, grad)]\n",
    "    \n",
    "    # Retourne les paramètres mis à jour et l'historique des coûts\n",
    "    return Theta, J_history\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Rassemble les poids dans une liste\n",
    "Theta1 = [W1, W2]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ce coût total est une mesure de l'erreur globale du modèle pour toutes les classes. Il est calculé en prenant en compte les prédictions du modèle pour toutes les classes et en les comparant aux valeurs réelles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 - Cost 10.441433938769038\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 10 - Cost 7.1201402950392625\n",
      "Iteration 20 - Cost 4.384267671880341\n",
      "Iteration 30 - Cost 2.714331055867724\n",
      "Iteration 40 - Cost 1.9051315488904337\n",
      "Iteration 50 - Cost 1.485498356253914\n",
      "Iteration 60 - Cost 1.2430338090439261\n",
      "Iteration 70 - Cost 1.087858013374782\n",
      "Iteration 80 - Cost 0.9799633434108926\n",
      "Iteration 90 - Cost 0.9000961542155177\n",
      "Iteration 100 - Cost 0.8381407289477022\n",
      "Iteration 110 - Cost 0.7883443004100443\n",
      "Iteration 120 - Cost 0.7472105422013605\n"
     ]
    }
   ],
   "source": [
    "# entrainement\n",
    "Theta1, J_history = gradientDescent(X, YY, Theta1, 0.7, 121)  #0.5 0.1 0.3 0.7 0.4  # pour le nbr d'iterations 100 suffit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "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",
    "\n",
    "# Création de la figure\n",
    "plt.figure()\n",
    "\n",
    "# Tracé du coût en fonction des itérations\n",
    "plt.plot(range(len(J_history)), J_history, marker='o', linestyle='-')\n",
    "\n",
    "# Ajout de titres et de labels\n",
    "plt.title('Évolution du coût en fonction des itérations')\n",
    "plt.xlabel('Nombre d\\'itérations')\n",
    "plt.ylabel('Coût')\n",
    "\n",
    "# Affichage de la grille\n",
    "plt.grid(True)\n",
    "\n",
    "# Affichage du graphique\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO 4 : Régularisation\n",
    "Mettre à jour le calcul du coût en ajoutant le terme de régularisation et comparer les résultats (avec et sans régularisation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initialisation des poids\n",
    "Theta2 = [W1, W2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Données d'entraînement appropriées : Si les données d'entraînement sont suffisamment riches et représentatives, le modèle peut déjà généraliser correctement sans nécessiter de régularisation supplémentaire.\n",
    "* Complexité du modèle : Si le modèle est relativement simple ou si le nombre de paramètres est limité, la régularisation peut ne pas avoir un impact significatif sur sa performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration 0 - Cost 10.465469065283514\n",
      "Iteration 10 - Cost 6.278918580079564\n",
      "Iteration 20 - Cost 3.295867651046883\n",
      "Iteration 30 - Cost 2.000448153484694\n",
      "Iteration 40 - Cost 1.45731062069938\n",
      "Iteration 50 - Cost 1.1853950302079301\n",
      "Iteration 60 - Cost 1.0252673990928283\n",
      "Iteration 70 - Cost 0.919054082823337\n",
      "Iteration 80 - Cost 0.842596971250321\n",
      "Iteration 90 - Cost 0.784330372819421\n",
      "Iteration 100 - Cost 0.7380694163001515\n",
      "Iteration 110 - Cost 0.7002070931649258\n",
      "Iteration 120 - Cost 0.6684902138133046\n"
     ]
    }
   ],
   "source": [
    "Theta2, J_history = gradientDescent(X, YY, Theta2, 0.9, 121, lambda_=0.25)"
   ]
  },
  {
   "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": [
    "# Création de la figure\n",
    "plt.figure()\n",
    "\n",
    "# Tracé du coût en fonction des itérations\n",
    "plt.plot(range(len(J_history)), J_history, marker='o', linestyle='-')\n",
    "\n",
    "# Ajout de titres et de labels\n",
    "plt.title('Évolution du coût en fonction des itérations')\n",
    "plt.xlabel('Nombre d\\'itérations')\n",
    "plt.ylabel('Coût')\n",
    "\n",
    "# Affichage de la grille\n",
    "plt.grid(True)\n",
    "\n",
    "# Affichage du graphique\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TODO 5 : Prédiction\n",
    "\n",
    "Appliquer une propagation en avant en utilisant les paramètres données pour prédir les classes de l'ensemble d'apprentissage.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict (X, W1, W2):\n",
    "     # appliquer une propagation en avant\n",
    "    # !--- n'oubliez pas d'appliquer la sigmoid à chaque couche afin d'avoir les probabilités ---!\n",
    "    \n",
    "    # prédire la classe en choisissant la probabilité maximale parmi les 10 noeuds de sortie\n",
    "    activations = compute_activations(X, W1, W2)\n",
    "    output = activations[-1]\n",
    "    y_pred = np.argmax(output, axis=1).reshape(-1, 1)\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# calcul de precision = nombre de valeurs bien prédites (ici sur toute la base X)\n",
    "y_pred=predict(X, W1, W2)\n",
    "precision = np.mean(y==y_pred)*100\n",
    "precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "91.58"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred=predict(X, *Theta1)\n",
    "precision = np.mean(y==y_pred)*100\n",
    "precision"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "92.96"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred=predict(X, *Theta2)\n",
    "precision_reg = np.mean(y==y_pred)*100\n",
    "precision_reg"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x1000 with 25 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "' les \"poids 2\" représentent les poids associés au deuxième neurone de la couche cachée\\n '"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Extraction des poids de la première couche\n",
    "weights = Theta1[0][:, 1:]  # Ignorer la première colonne correspondant aux biais\n",
    "\n",
    "# Reshape des poids pour les adapter à une image 20x20\n",
    "num_images = weights.shape[0]\n",
    "images_per_row = 5  # Nombre d'images à afficher par ligne\n",
    "num_rows = (num_images // images_per_row) + (1 if num_images % images_per_row != 0 else 0)\n",
    "\n",
    "plt.figure(figsize=(images_per_row * 2, num_rows * 2))  # Taille de la figure en pouces\n",
    "\n",
    "for i in range(num_images):\n",
    "    plt.subplot(num_rows, images_per_row, i + 1)  # Sélection de la sous-figure actuelle\n",
    "    plt.imshow(weights[i].reshape(20, 20).T, cmap='gray')  # Affichage de l'image correspondant au poids\n",
    "    plt.title(f'Poids {i+1}')  # Titre de la sous-figure\n",
    "\n",
    "plt.tight_layout()  # Ajustement automatique des sous-figures pour éviter les chevauchements\n",
    "plt.show()  # Affichage de la figure\n",
    "\n",
    "\"\"\" les \"poids 2\" représentent les poids associés au deuxième neurone de la couche cachée\n",
    " \"\"\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ces images montrent comment les entrées sont pondérées et influencent l'activation de chaque neurone dans la couche cachée. \n",
    "* Plus les pixels d'une image sont brillants (ou sombres), plus les poids associés à ces pixels ont une influence élevée (ou faible) sur l'activation du neurone correspondant."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# optionnel 1 : Vérification de l'implementation\n",
    "Comparer vos algorithmes à ceux de scikitlearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neural_network import MLPClassifier\n",
    "\n",
    "nn = MLPClassifier(hidden_layer_sizes=(25,), activation='logistic', solver='sgd', max_iter=500, batch_size=y.shape[0], learning_rate_init=0.4, alpha=0.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\taouc\\AppData\\Roaming\\Python\\Python312\\site-packages\\sklearn\\neural_network\\_multilayer_perceptron.py:691: ConvergenceWarning: Stochastic Optimizer: Maximum iterations (500) reached and the optimization hasn't converged yet.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: black;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: block;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 1ex;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>MLPClassifier(activation=&#x27;logistic&#x27;, alpha=0.4, batch_size=5000,\n",
       "              hidden_layer_sizes=(25,), learning_rate_init=0.4, max_iter=500,\n",
       "              solver=&#x27;sgd&#x27;)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow fitted\">&nbsp;&nbsp;MLPClassifier<a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.4/modules/generated/sklearn.neural_network.MLPClassifier.html\">?<span>Documentation for MLPClassifier</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></label><div class=\"sk-toggleable__content fitted\"><pre>MLPClassifier(activation=&#x27;logistic&#x27;, alpha=0.4, batch_size=5000,\n",
       "              hidden_layer_sizes=(25,), learning_rate_init=0.4, max_iter=500,\n",
       "              solver=&#x27;sgd&#x27;)</pre></div> </div></div></div></div>"
      ],
      "text/plain": [
       "MLPClassifier(activation='logistic', alpha=0.4, batch_size=5000,\n",
       "              hidden_layer_sizes=(25,), learning_rate_init=0.4, max_iter=500,\n",
       "              solver='sgd')"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nn.fit(X, YY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "94.06"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = nn.predict(X)\n",
    "y_pred = np.argmax(y_pred, axis=1).reshape(-1)\n",
    "precision_sk = np.mean(y_pred == y.astype(int).reshape(-1)) * 100\n",
    "precision_sk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optionnel 2 : Renforcement de l'apprentissage\n",
    "Mettre ici toute idée qui pourrait renforcer votre apprentissage"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Augmentation des données : Créez de nouvelles variations des données en appliquant des transformations.\n",
    "2. Optimisation des hyperparamètres : Trouvez les meilleurs paramètres pour votre modèle en expérimentant avec différentes valeurs.\n",
    "3. Utilisation d'algorithmes avancés : Explorez des modèles plus complexes adaptés à vos données, comme les réseaux de neurones convolutionnels ou récurrents.\n",
    "4. Ensemble Learning : Améliorez les performances en combinant les prédictions de plusieurs modèles.\n",
    "5. Validation croisée : Évaluez la performance de manière fiable en utilisant la validation croisée.\n",
    "6. Analyse des erreurs : Comprenez les faiblesses du modèle en analysant les prédictions incorrectes.\n",
    "7. Réduction de la dimensionnalité : Réduisez le nombre de caractéristiques tout en préservant les informations importantes.\n",
    "8. Interprétabilité du modèle : Analysez le comportement du modèle pour comprendre ses prédictions."
   ]
  }
 ],
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