TP_MNIS_Keras_dense-soluce.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    v1.1 2018/10/23 JLC Ajout image architecture réseau + correction fautes de frappe\n",
    "    v1.2 2019/06/13 BA  MAJ par Benjamin AILLOUD (stage L2 informatique)\n",
    "    v2.0 2019/06/16 JLC Reformulation version 2.\n",
    "    V2.1 2019/10/29 JLC Consolidation des versions keras 2.2.4 / tensorflow 1.13.1 / numpy 16.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-weight:bold;color:blue;font-family:arial;font-size:xx-large;\">\n",
    "    Machine learning avec les modules Python Keras & tensorflow \n",
    "</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"font-weight:bold;color:blue;font-family:arial;font-size:x-large;\">\n",
    "    Conception / entraînement / évaluation d'un réseau de neurones dédié à la reconnaissance de chiffres manuscrits.</span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "<b>Info:</b> Document initialement inspiré du travail de Jason Brownlee : *Handwritten Digit Recognition using Convolutional Neural Networks in Python with Keras* publié en juin 2016 à l'adresse https://machinelearningmastery.com/handwritten-digit-recognition-using-convolutional-neural-networks-python-keras/\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A/ Quelques concepts fondamentaux autour des réseaux de neurones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Le neurone artificiel\n",
    "C'est une unité de traitement informatique programmée pour calculer la valeur de sa **fonction d'activation** en un point défini par la **combinaison linéaire de ses entrées** $\\Sigma_i w_i x_i - b$ :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center; font-style:italic; font-size=xx-small\">\n",
    "    <img src=\"./figures/nn_1.png\" width=\"600\" >\n",
    "    (crédit image : JLC)\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "L'entrée *Bias* reçoit le stimuli `-1` affecté du poids $b$ pour donner une **translation** (décalage) dans la fonction d'activation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Fonction d'activation\n",
    "Les principaux rôles des fonctions d'activation des neurones artificiels sont :\n",
    "- donner au neurone artificiel un comportement **non linéaire** (avec par exemple des mécanismes de seuil, de saturation...)\n",
    "- fixer la plage de sortie de la valeur calculée par le neurone (par exemple sortie dans l'intervalle $[-1 ; 1]$, ou $[0 ; +\\infty[$\n",
    "\n",
    "Exemples de fonction d'activation couramment utilisées :<br />\n",
    "<p style=\"text-align:center; font-style:italic; font-size=xx-small\">\n",
    "    <img src=\"./figures/activationFunctions.png\"> \n",
    "    (crédit image : JLC)\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Banque d'images MNIST\n",
    "\n",
    "Dans ce travail, nous utiliserons les images de la banque MNIST disponible sur Internet (http://yann.lecun.com/exdb/mnist/).\n",
    "\n",
    "La banque MNIST propose des images en ton de gris de 28 $\\times$ 28 pixels, correspondant à des matrice de 28 $\\times$ 28 d'entiers compris entre 0 et 255 :\n",
    "<p style=\"text-align:center; font-style:italic; font-size=xx-small\">\n",
    "    <img src=\"./figures/MnistExamples.png\" width=\"500\" >\n",
    "    (crédit image : Josef Steppan — Travail personnel, CC BY-SA 4.0, commons.wikimedia.org/w/index.php?curid=64810040)\n",
    "</p>\n",
    "\n",
    "L'ensemble des images du jeu de données MNIST contient **60000 images d'apprentissage** et **10000 images de test**, soit en tout **70000 images** de 28 x 28 pixels."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Structure du réseau à construire \n",
    "Dans un premier temps nous allons construire un simple *réseau dense*, avec :\n",
    "- une **couche d'entrée** de 784 valeurs comprises entre 0 et 1 (les pixels de l'image 28 $\\times$ 28 mis sous forme d'un vecteur de 784 valeurs),\n",
    "- une **couche cachée** de 784 neurones utilisant la fonction d'activation `relu`,\n",
    "- une **couche de sortie** à 10 neurones, pour la classification des images en 10 classes associées aux chiffres {0,1,2...9}, utilisant la fonction d'activation `softmax` adaptée aux traitements de classification."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center; font-style:italic; font-size=xx-small\">\n",
    "    <img src=\"./figures/archiReseau.png\" width=\"900\">\n",
    "    (crédit image : JLC)\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La fonction d'activation `softmax` utilisée pour les 10 neurones de la couche de sortie permet de \"faire ressortir\" la sortie $y_i$ de valeur la plus grande : `softmax` donne une valeur très proche de 1 pour le neurone fournissant la plus grande valeur $y_i$, alors que pour tous les autres neurones, la valeur calculée par `softmax` sera proche de zero."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center; font-style:italic; font-size=xx-small\">\n",
    "    <img src=\"./figures/softmax.png\" width=\"400\">\n",
    "    (crédit image : JLC)\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remarques : \n",
    "- Chaque neurone de la première couche cachée reçoit 785 entrées : les 784 valeurs des pixels de l'image plus l'entrée -1. \n",
    "- Il y a dons 785 inconnues pour chaque neurone : les 784 poids $w_i$ affectés à chaque entrée $x_i$, plus le  poids $b$ affecté à l'entrée -1 (le biais).\n",
    "- on compte donc 785 $\\times$ 784 inconnues pour la couche cachée et 785 $\\times$ 10 inconnues pour la couche de sortie : soit un total de 623290 inconnues dont la valeur doit être optimisée par l'algorithme d'apprentissage du réseau.\n",
    "\n",
    "C'est un algorithme de **retropropagation de l'erreur** entre valeur attendue et valeur prédite par le réseau qui permet de modifier les valeurs des poids des différentes couches pour minimiser l'erreur. Au fur et à mesure des apprentissages successifs, cette modification des poids du réseau de neurones tend vers un état qui constitue le réseau entraîné."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  B/ Environnement Python de travail"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "<span style=\"color:brown;font-family:arial;font-size:large\"> \n",
    "    Les développement en Python doivent se faire dans un <span style=\"font-weight:bold;\">environnement Python 3.6 dédié</span> : voir le document <span style=\"font-style:italic\">EnvironnementPython.pdf</span> si vous n'avez pas encore créé d'environnement Python dédié pour le travail avec les modules Keras et tensorflow.\n",
    "</span>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Environnement Python dédié\n",
    "Vérification :\n",
    "- de la version de Python : doit être 3.6.8 ou 3.6.9\n",
    "- de la version de keras : doit être 2.2.4\n",
    "- de la version de tensorflow : doit être 1.13.1\n",
    "- de la version de OpenCV : doit être 3.4.x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Version de Python    : 3.6.9\n",
      "Version, de Keras    : 2.2.4\n",
      "Version de tensorflow: 1.13.1\n",
      "Version, de OpenCV   : 3.4.2\n"
     ]
    }
   ],
   "source": [
    "import sys, keras, cv2\n",
    "import tensorflow as tf\n",
    "print(f\"Version de Python    : {sys.version.split()[0]}\")\n",
    "print(f\"Version, de Keras    : {keras.__version__}\")\n",
    "print(f\"Version de tensorflow: {tf.__version__}\")\n",
    "print(f\"Version, de OpenCV   : {cv2.__version__}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La documentation du module Python Keras (en anglais) est disponible sur https://keras.io."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Incrustation des tracés matplotlib dans le cahier IPython et import de modules utiles :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from IPython.display import Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# C/ Travail à faire"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1 -- Récupération du jeu de données MNIST :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "https://fr.wikipedia.org/wiki/Base_de_données_MNIST : La base de données MNIST (*Mixed National Institute of Standards and Technology*), est une base de données de chiffres écrits à la main. C'est un jeu de données très utilisé en apprentissage automatique.<br /><br />\n",
    "L'ensemble des images du jeu de données MNIST contient **60000 images d'apprentissage** et **10000 images de test**, soit en tout **70000 images** de 28 x 28 pixels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load data from https://www.openml.org/d/554\n",
    "from keras.datasets import mnist\n",
    "(image_train, etiq_train), (image_test, etiq_test) = mnist.load_data() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Faire afficher le type des objets `image_train`, `etiq_train`, `image_test` et `etiq_test` :</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n",
      "<class 'numpy.ndarray'>\n",
      "<class 'numpy.ndarray'>\n",
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "objs = (image_train, etiq_train, image_test, etiq_test)\n",
    "for o in objs: print(type(o))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Faire afficher les attributs `shape` et `dtype` des tableaux `image_train`, `etiq_train`, `image_test` et `etiq_test` -> interpréter les réponses :</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 28, 28) uint8\n",
      "(60000,) uint8\n",
      "(10000, 28, 28) uint8\n",
      "(10000,) uint8\n"
     ]
    }
   ],
   "source": [
    "for o in objs: print(o.shape, o.dtype)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a bien 60000 matrice d'entiers 28 x 28 avec les 60000 étiquettes et les 10000 matrice d'entiers 28 x 28 avec les 10000 étiquettes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 -- Vérification des étiquettes des données : "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Faire afficher les 10 premières valeurs de `etiq_train` et `etiq_test` ; interpréter les réponses. </span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5 0 4 1 9 2 1 3 1 4]\n"
     ]
    }
   ],
   "source": [
    "print(etiq_train[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7 2 1 0 4 1 4 9 5 9]\n"
     ]
    }
   ],
   "source": [
    "print(etiq_test[:10])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 -- Visualisation des images MNIST  :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial;\">Avec la fonction `imshow` du module `matplotlib.pyplot` faire afficher la 601-ème image du tableau `image_train`. Indications :<br />\n",
    "\n",
    "- utiliser `plt.figure(figsize=(4,4))`;<br />\n",
    "- passer l'argument `cmap='binary'` à la fonction `imshow`;<br/>\n",
    "- enlever les graduations en X et Y avec l'instruction  `plt.xticks([]); plt.yticks([])`.</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(4,4))\n",
    "import matplotlib.pyplot as plt\n",
    "plt.imshow(image_train[600],cmap='binary')\n",
    "plt.xticks([]) ; plt.yticks([]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Vérifier que l'étiquette associée à `image_train[600]` est bien `9` :</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "etiq_train[600]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Écrire une fonction `plot_image` qui prend les arguments 'qui vont bien' pour afficher les images MNIST commençant au rang `r` sur `L` lignes et `C` colonnes (utiliser `plt.subplot` pour faire un quadrillage d'images). La figure affichée doit avoir pour dimensions 10 x 10 pouces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_image(r,L,C):\n",
    "    plt.figure(figsize=(10,10))\n",
    "    for i in range(L*C):\n",
    "        plt.subplot(L, C, i+1)\n",
    "        plt.imshow(image_train[r+i],cmap='binary', interpolation='none')\n",
    "        plt.xticks([])\n",
    "        plt.yticks([])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Fait afficher 100 images à partir de la 600 ème dans une grille de 10x10 : </span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 100 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_image(599, 10, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2 -- Pré-traitement des données"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Le pré-traitement des données constitue une des étapes fondamentales de l'apprentissage des réseaux de neurones.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour adapter les données au réseau de neurones, on doit transformer les matrice d'entiers `uint8` représentant les images 28 x 28 pixels en vecteurs **normalisés** $(V_i)_{i=0..783}$ de 784 valeurs réelles $V_i$  avec $ 0 \\leqslant V_i \\leqslant 1.$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 -- Transformation des matrices d'entrée en vecteurs normalisés :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_image_train, nb_image_test = image_train.shape[0], image_test.shape[0]\n",
    "nb_pixels = image_train.shape[1] * image_train.shape[2]   # 28 x 28 = 784 pixels\n",
    "\n",
    "# mise 'à plat' des matrices sous forme de vecteurs de floats \n",
    "# Indications: utiliser les méthodes 'reshape(new_shape)' et astype('float32') de ndarray).\n",
    "x_train = image_train.reshape((nb_image_train, nb_pixels)).astype('float32')\n",
    "x_test  = image_test.reshape((nb_image_test, nb_pixels)).astype('float32')\n",
    "\n",
    "# normalisation des tableaux X_train et X_test :\n",
    "x_train = x_train/255\n",
    "x_test  = x_test/255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Vérifier la tailles des tableaux `x_train` et `x_test`  :</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dimensions du tableu x_train: (60000, 784)\n",
      "Dimensions du tableu x_test : (10000, 784)\n"
     ]
    }
   ],
   "source": [
    "print(f\"Dimensions du tableu x_train: {x_train.shape}\")\n",
    "print(f\"Dimensions du tableu x_test : {x_test.shape}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Vérifier les valeurs min et max des tableaux `x_train` et `x_test`  :</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min et max de x_train: 0.0, 1.0\n",
      "min et max de x_test : 0.0, 1.0\n"
     ]
    }
   ],
   "source": [
    "print(f\"min et max de x_train: {x_train.min()}, {x_train.max()}\")\n",
    "print(f\"min et max de x_test : {x_test.min()}, {x_test.max()}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 -- *Hot coding* des étiquettes :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les étiquettes des images sont des valeurs entières comprises entre 0 et 9. Pour traiter efficacement le problème de classification, on utilise la technique de `hot coding` qui remplace les valeurs des différentes classes par un vecteur comportant autant d'éléments que de classes à choisir.<br />\n",
    "Par exemple :\n",
    "- l'étiquette `0` sera transformée en le vecteur `[1 0 0 0 0 0 0 0 0 0]`.\n",
    "- l'étiquette `3` sera transformée en le vecteur `[0 0 0 1 0 0 0 0 0 0]`.\n",
    "- l'étiquette `9` sera transformée en le vecteur `[0 0 0 0 0 0 0 0 0 9]`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour réaliser le codage des étiquettes, on utilise la fonction `to_categorical` du module `keras.utils.np_utils` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "from keras.utils.np_utils import to_categorical\n",
    "# 'hot encoding' des sorties :\n",
    "y_train = to_categorical(etiq_train)\n",
    "y_test  = to_categorical(etiq_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Faire afficher les 10 premières valeurs de `etiq_train` et les 10 premières valeurs `hot encoded` de `y_train` :</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 0, 4, 1, 9, 2, 1, 3, 1, 4], dtype=uint8)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "etiq_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0., 1., 0., 0., 0., 0.],\n",
       "       [1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 0., 1.],\n",
       "       [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0., 0., 0., 0.]], dtype=float32)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(y_train[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3 -- Construction du réseau de neurones :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va maintenant construire un réseau de neurone **séquentiel** (cf https://keras.io/models/sequential ) en **4 lignes** Python à l'aide du module **keras** qui permet une manipulation de haut niveau des outils proposés par le module **tensorflow**.<br />\n",
    "\n",
    "Les spécifications du réseau de neurones à construire sont :\n",
    "- les entrées sont constituées des 784 pixels, mis sous forme d'un vecteur normalisé ;\n",
    "- le réseau de neurones comporte une première couche de 784 neurones utilisant la fonction d'activation `relu` (*retified linear unit*, voir https://keras.io/activations) ;\n",
    "- la couche de sortie comporte 10 neurones utilisant la fonction d'activation `softmax` pour convertir les sorties en valeur de probalibilités permettant de choisir une des 10 classes ;\n",
    "- la fonction d'erreur (différence entre étiquette et valeur prédite par le réseau) est `Logarithmic loss` (dans Keras elle coorepnd à la *loss function* `categorical_crossentropy`) ;\n",
    "- l'algorithme de descente de gradient ADAM est utilisé pour l'optimisation des poids des neurones par rétro-progation de l'erreur. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La **fonction d'erreur** (*loss function*) utilisée pour quantifier l'erreur entre l'étiquette associée aux données d'entrée est disponible dans keras sous le nom `categorical_crossentropy`:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p style=\"text-align:center; font-style:italic; font-size=xx-small\">\n",
    "    <img src=\"./figures/CrossEntropy.png\" width=650>\n",
    "    (crédit image : vidéo \"Deep Learning TensorFlow\" de Martin Gorner)\n",
    "</p>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rendre les tirages aléatoires reproductibles"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les poids d'un réseau de neurones sont initialisés par tirage aléatoire. Lorsqu'on invoque plusieurs fois de suite des générateurs aléatoires comme `numpy.random.rand` par exemple, on cconstate qu'à chaque invocation, on obtient une suite de valeurs aléatoires différentes :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.28900251 0.77152225 0.47383632 0.53065993 0.48269495]\n"
     ]
    }
   ],
   "source": [
    "print(np.random.rand(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.22847063 0.9282376  0.56364877 0.13138361 0.87592869]\n"
     ]
    }
   ],
   "source": [
    "print(np.random.rand(5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ceci présente un gros inconvénient car les poids d'un réseau de neurones sont initialisés à la construction du réseau par tirage aléatoire : ceci veut dire qu'à chaque fois qu'on relance le cahier IPYthon par exemple on obtiendra un état initial du réseau différent conduisant à un résultat de réseau entraîné différent !\n",
    "\n",
    "Pour corriger ce comportement, on fixe la **graine** (*seed*) du générateur `numpy.random` de façon à générer des suites de nombres aléatoires reproductibles :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "seed = 43"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.11505457, 0.60906654, 0.13339096, 0.24058962, 0.32713906])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(seed)\n",
    "np.random.rand(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.11505457, 0.60906654, 0.13339096, 0.24058962, 0.32713906])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(seed)\n",
    "np.random.rand(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construction du réseau de neurones dense en 4 lignes avec le module Keras :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense \n",
    "\n",
    "tf.logging.set_verbosity(tf.logging.ERROR)  # n'afficher que les ERREURS tf, pas les warnings....\n",
    "nb_classes = len(y_train[0])\n",
    "np.random.seed(43)\n",
    "\n",
    "# les 4 lignes pour construire le réseau de neurones:\n",
    "model = Sequential()\n",
    "model.add(Dense(nb_pixels, input_dim=nb_pixels, kernel_initializer='normal', activation='relu'))\n",
    "model.add(Dense(nb_classes, kernel_initializer='normal', activation='softmax'))\n",
    "model.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Avec la méthode `summary` de l'objet `model`, faire afficher la description du modèle : expliquer les valeurs des paramètres ?</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 784)               615440    \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 10)                7850      \n",
      "=================================================================\n",
      "Total params: 623,290\n",
      "Trainable params: 623,290\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Peux-tu retrouver le nombre total de paramètres avec une formule simple ?</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "nombre total de paramètres : 623290\n"
     ]
    }
   ],
   "source": [
    "print(f\"nombre total de paramètres : {784*785 + 10*785}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4 -- Entraînement du réseau :"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le modèle est entraîné sur les $60\\,000$ images,\n",
    "- 10 fois de suite (paramètre `epochs`), \n",
    "- avec mises à jour des poids toutes les 200 images (paramètre `batch_size`),\n",
    "- en utilisant :\n",
    "    - les données d'entrée `x_train` (images)\n",
    "    - les données de sortie `y_train` (étiquettes)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/10\n",
      "60000/60000 [==============================] - 6s 103us/step - loss: 0.2751 - acc: 0.9211 - val_loss: 0.1445 - val_acc: 0.9570\n",
      "Epoch 2/10\n",
      "60000/60000 [==============================] - 6s 100us/step - loss: 0.1112 - acc: 0.9680 - val_loss: 0.0933 - val_acc: 0.9723\n",
      "Epoch 3/10\n",
      "60000/60000 [==============================] - 5s 90us/step - loss: 0.0710 - acc: 0.9796 - val_loss: 0.0766 - val_acc: 0.9765\n",
      "Epoch 4/10\n",
      "60000/60000 [==============================] - 6s 94us/step - loss: 0.0504 - acc: 0.9856 - val_loss: 0.0685 - val_acc: 0.9791\n",
      "Epoch 5/10\n",
      "60000/60000 [==============================] - 5s 85us/step - loss: 0.0362 - acc: 0.9896 - val_loss: 0.0632 - val_acc: 0.9787\n",
      "Epoch 6/10\n",
      "60000/60000 [==============================] - 5s 87us/step - loss: 0.0260 - acc: 0.9932 - val_loss: 0.0591 - val_acc: 0.9805\n",
      "Epoch 7/10\n",
      "60000/60000 [==============================] - 5s 91us/step - loss: 0.0205 - acc: 0.9950 - val_loss: 0.0590 - val_acc: 0.9821\n",
      "Epoch 8/10\n",
      "60000/60000 [==============================] - 5s 84us/step - loss: 0.0146 - acc: 0.9965 - val_loss: 0.0598 - val_acc: 0.9821\n",
      "Epoch 9/10\n",
      "60000/60000 [==============================] - 5s 84us/step - loss: 0.0095 - acc: 0.9983 - val_loss: 0.0578 - val_acc: 0.9825\n",
      "Epoch 10/10\n",
      "60000/60000 [==============================] - 6s 97us/step - loss: 0.0078 - acc: 0.9986 - val_loss: 0.0588 - val_acc: 0.9822\n"
     ]
    }
   ],
   "source": [
    "history = model.fit(x_train, y_train, validation_data=(x_test, y_test), epochs=10, batch_size=200, verbose=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tracé des courbes `accuracy` et `loss` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(history):\n",
    "    # Plot training & validation accuracy values\n",
    "    plt.figure(figsize=(15,5))\n",
    "    ax1 = plt.subplot(1,2,1)\n",
    "    ax1.plot(history.history['acc'], 'o-',label='Train')\n",
    "    ax1.plot(history.history['val_acc'], 'o-', label='Test')\n",
    "    ax1.set_title('Model accuracy')\n",
    "    ax1.set_ylabel('Accuracy')\n",
    "    ax1.set_xlabel('Epoch') \n",
    "    ax1.grid()\n",
    "    ax1.legend(loc='best')\n",
    "    # Plot training & validation loss values\n",
    "    ax2 = plt.subplot(1,2,2)\n",
    "    ax2.plot(history.history['loss'], 'o-', label='Train')\n",
    "    ax2.plot(history.history['val_loss'], 'o-',  label='Test')\n",
    "    ax2.set_title('Model loss')\n",
    "    ax2.set_ylabel('Loss')\n",
    "    ax2.set_xlabel('Epoch')\n",
    "    ax2.legend(loc='best')\n",
    "    ax2.grid()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(history)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entrainer le réseau plus longtemps (par augmentation du paramètre `epochs` peut permettre d'aumengenter les performances du réseau... mais les courbes de précision du test (*test accuracy*) restent asymptotiquement voisinnes des 98 %.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5/ Vérication de l'apprentissage avec le jeu de test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La méthode `predict`permet de demander au modèle sa prédiction pour une ou plusieurs entrées.<BR />\n",
    "Exemple de prédition pour une image test numéro i dans le jeu d'images de test (0 <= i <= 10000) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "valeur trouvée par le réseau de neurones : [0.0000 0.0000 0.0000 0.0013 0.0000 0.0000 0.0000 0.0001 0.0000 0.9986]\n",
      "valeur trouvée arrondie  : [0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0]\n",
      "rep[0].argmax() donne    : 9\n",
      "\n",
      "La bonne réponse est 9, soit en 'hot coded' : [0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0]\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "i = 1000\n",
    "rep = model.predict(x_test[i:i+1])\n",
    "\n",
    "np.set_printoptions(formatter={'float':'{:0.4f}'.format})\n",
    "print(\"valeur trouvée par le réseau de neurones :\", rep[0])\n",
    "\n",
    "np.set_printoptions(formatter={'float':'{:0.1f}'.format})\n",
    "print(\"valeur trouvée arrondie  : {}\".format(rep[0]))\n",
    "print(\"rep[0].argmax() donne    : {}\".format(rep[0].argmax()))\n",
    "\n",
    "plt.figure(figsize=(1,1))\n",
    "digit = image_test[i]\n",
    "plt.xticks([]); plt.yticks([])\n",
    "plt.imshow(digit, cmap='binary');\n",
    "print(f\"\\nLa bonne réponse est {etiq_test[i]}, soit en 'hot coded' : {y_test[i]}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Écrire les instructions Python pour calculer avec les données de test le pourcentage d'erreur du réseau entrainé.... <br/> \n",
    "Conseil: la variable rep contient pour chaque image une liste de 10 probabilités, il pourra être utile d'utiliser la fonction argmax de la librairie numpy pour obtenir le chiffre de plus haute probabilité.</span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "taux de réussite : 98.22 %\n"
     ]
    }
   ],
   "source": [
    "results = model.predict_on_batch(x_test)\n",
    "bonne_rep = 0\n",
    "for i, res in enumerate(results):\n",
    "    bonne_rep += (np.argmax(res) == etiq_test[i])\n",
    "print(f\"taux de réussite : {bonne_rep/len(x_test)*100:.2f} %\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6/ Évolution du réseau : augmentation du nombre de couches cahées "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut essayer de construire un réseau avec plus de couches. Par exemple :\n",
    "- couche d'entrée avec les 784 pixels\n",
    "- couche cachée 1 : 784 neurones, fonction d'activation `relu`\n",
    "- couche cachée 2 : 300 neurones, fonction d'activation `relu`\n",
    "- couche cachée 3 : 100 neurones, fonction d'activation `relu`    \n",
    "- couche de sortie : 10 neurone, fonction d'activation `softmax`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Peux-tu conctruire le réseau `model2` correspondant avec Keras :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_classes = len(y_train[0])\n",
    "\n",
    "np.random.seed(43)\n",
    "model2 = Sequential()\n",
    "model2.add(Dense(784, input_dim=nb_pixels, kernel_initializer='normal', activation='relu'))\n",
    "model2.add(Dense(300, kernel_initializer='normal', activation='relu'))\n",
    "model2.add(Dense(100, kernel_initializer='normal', activation='relu'))\n",
    "model2.add(Dense(nb_classes, kernel_initializer='normal', activation='softmax'))\n",
    "model2.compile(loss='categorical_crossentropy', optimizer='adam', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\">Avec la méthode `summary` de l'objet `model2`, faire afficher la description du modèle : expliquer les valeurs des paramètres ?</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_3 (Dense)              (None, 784)               615440    \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 300)               235500    \n",
      "_________________________________________________________________\n",
      "dense_5 (Dense)              (None, 100)               30100     \n",
      "_________________________________________________________________\n",
      "dense_6 (Dense)              (None, 10)                1010      \n",
      "=================================================================\n",
      "Total params: 882,050\n",
      "Trainable params: 882,050\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "model2.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Entraîner le réseau `model2` avec les mêmes données que `model`, et faire tracer les courbes de précission et d'erreur :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/10\n",
      "60000/60000 [==============================] - 9s 142us/step - loss: 0.2929 - acc: 0.9177 - val_loss: 0.1241 - val_acc: 0.9608\n",
      "Epoch 2/10\n",
      "60000/60000 [==============================] - 7s 124us/step - loss: 0.0994 - acc: 0.9697 - val_loss: 0.0958 - val_acc: 0.9710\n",
      "Epoch 3/10\n",
      "60000/60000 [==============================] - 7s 114us/step - loss: 0.0579 - acc: 0.9823 - val_loss: 0.0718 - val_acc: 0.9778\n",
      "Epoch 4/10\n",
      "60000/60000 [==============================] - 7s 114us/step - loss: 0.0398 - acc: 0.9874 - val_loss: 0.0695 - val_acc: 0.9783\n",
      "Epoch 5/10\n",
      "60000/60000 [==============================] - 6s 105us/step - loss: 0.0296 - acc: 0.9907 - val_loss: 0.0704 - val_acc: 0.9793\n",
      "Epoch 6/10\n",
      "60000/60000 [==============================] - 7s 120us/step - loss: 0.0227 - acc: 0.9929 - val_loss: 0.0794 - val_acc: 0.9764\n",
      "Epoch 7/10\n",
      "60000/60000 [==============================] - 7s 115us/step - loss: 0.0181 - acc: 0.9940 - val_loss: 0.0657 - val_acc: 0.9823\n",
      "Epoch 8/10\n",
      "60000/60000 [==============================] - 7s 113us/step - loss: 0.0145 - acc: 0.9950 - val_loss: 0.0741 - val_acc: 0.9814\n",
      "Epoch 9/10\n",
      "60000/60000 [==============================] - 6s 103us/step - loss: 0.0136 - acc: 0.9954 - val_loss: 0.0742 - val_acc: 0.9819\n",
      "Epoch 10/10\n",
      "60000/60000 [==============================] - 7s 118us/step - loss: 0.0143 - acc: 0.9950 - val_loss: 0.1032 - val_acc: 0.9757\n"
     ]
    }
   ],
   "source": [
    "history2 = model2.fit(x_train, y_train, validation_data=(x_test, y_test), epochs=10, batch_size=200, verbose=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(history2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:blue;font-family:arial\"> Augmenter le nombre de couches a t'il un impact sur les performances du réseau ?<br />\n",
    "Que peut on conclure sur l'utilité de complexifier ce type de réseau ? </span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "À priori, on peut voir que l'augmentation du nombre de couches cachées n'a pas un grand impact sur la précision du résea : la reconnaissance lors des tests tourne toujours autour des 98%.\n",
    "Il semble donc peu utile de complexifier ce type de réseau..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7/ Utiliser le réseau avec ses propres images"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va utiliser le réseau entrainé pour voir comment il réagit avec des chiffres \"écrits à la main\" différents des chiffres de la banque MNIST...<br />\n",
    "Pour cela on utilise les images du dossier `chiffres` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Images du dossier 'chiffres' : ['chiffres/0_jlc.png', 'chiffres/1_jlc.png', 'chiffres/2_jlc.png', 'chiffres/3_jlc.png', 'chiffres/4_jlc.png', 'chiffres/5_jlc.png', 'chiffres/6_jlc.png', 'chiffres/7_jlc.png', 'chiffres/8_jlc.png', 'chiffres/9_jlc.png']\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "images = ['chiffres/'+f for f in os.listdir('chiffres') if f.endswith(\".png\") or f.endswith(\".jpg\")]\n",
    "images.sort()\n",
    "print(f\"Images du dossier 'chiffres' : {images}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lecture des fichiers image avec openCV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((10, 28, 28), dtype('uint8'))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cv2\n",
    "# lecture des images -> matrices ndarray 28x28 \n",
    "input_data = [255-cv2.cvtColor(cv2.imread(image),cv2.COLOR_BGR2GRAY) for image in images]\n",
    "input_data = np.array(input_data)\n",
    "input_data.shape, input_data.dtype  # on doit avoir 4 matrices de 28 x 28 valeurs "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualistion des images :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1080x360 with 10 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(15,5))\n",
    "for i,M in enumerate(input_data):  \n",
    "    plt.subplot(1,12,i+1)\n",
    "    plt.imshow(input_data[i], cmap='binary', interpolation='none');\n",
    "    plt.xticks([]); plt.yticks([])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "transformation des matrices 28x28 en vecteurs de float normalisés :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [],
   "source": [
    "nb_images = input_data.shape[0]\n",
    "# mise 'à plat' des matrices sous forme de vecteurs de floats :\n",
    "x_photo = input_data.reshape(nb_images, 28*28).astype('float32')\n",
    "# normalisation des données :\n",
    "x_photo /= 255"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "prédiction du réseau entrainé, avec les images perso :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.565 0.003 0.332 0.004 0.001 0.083 0.000 0.005 0.000 0.006]\n",
      " [0.000 0.955 0.000 0.014 0.001 0.007 0.008 0.005 0.008 0.003]\n",
      " [0.000 0.000 0.944 0.018 0.000 0.008 0.000 0.000 0.029 0.000]\n",
      " [0.000 0.000 0.000 0.999 0.000 0.000 0.000 0.000 0.000 0.000]\n",
      " [0.000 0.000 0.000 0.000 0.992 0.001 0.006 0.000 0.000 0.000]\n",
      " [0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000]\n",
      " [0.004 0.001 0.083 0.000 0.002 0.329 0.348 0.000 0.233 0.000]\n",
      " [0.001 0.084 0.326 0.122 0.130 0.019 0.007 0.242 0.067 0.000]\n",
      " [0.049 0.007 0.040 0.222 0.012 0.048 0.113 0.000 0.507 0.001]\n",
      " [0.000 0.001 0.001 0.994 0.000 0.004 0.000 0.000 0.000 0.000]]\n"
     ]
    }
   ],
   "source": [
    "np.set_printoptions(formatter={'float': '{:0.3f}'.format})  # demander à numpy d'afficher 3 décimales\n",
    "\n",
    "rep = model.predict(x_photo)\n",
    "print(rep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 2, 8, 3]"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[r.argmax() for r in rep]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 avec la probablilité 0.565\n",
      "1 avec la probablilité 0.955\n",
      "2 avec la probablilité 0.944\n",
      "3 avec la probablilité 0.999\n",
      "4 avec la probablilité 0.992\n",
      "5 avec la probablilité 1.000\n",
      "6 avec la probablilité 0.348\n",
      "2 avec la probablilité 0.326\n",
      "8 avec la probablilité 0.507\n",
      "3 avec la probablilité 0.994\n"
     ]
    }
   ],
   "source": [
    "for r in rep:\n",
    "    print(f\"{r.argmax()} avec la probablilité {r.max():.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Le 7 et le 9 ont été vus respectivement comme un 2 et 3 ...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec le deuxième réseau dense :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.132 0.000 0.248 0.412 0.002 0.003 0.000 0.079 0.002 0.123]\n",
      " [0.000 0.852 0.000 0.009 0.000 0.000 0.001 0.000 0.137 0.000]\n",
      " [0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000]\n",
      " [0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 0.000]\n",
      " [0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000]\n",
      " [0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000]\n",
      " [0.000 0.000 0.007 0.000 0.000 0.039 0.541 0.000 0.412 0.000]\n",
      " [0.000 0.001 0.019 0.372 0.002 0.000 0.000 0.005 0.602 0.000]\n",
      " [0.074 0.001 0.006 0.001 0.000 0.000 0.278 0.000 0.641 0.000]\n",
      " [0.000 0.006 0.000 0.992 0.000 0.000 0.000 0.002 0.000 0.000]]\n"
     ]
    }
   ],
   "source": [
    "rep = model2.predict(x_photo)\n",
    "print(rep)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[3, 1, 2, 3, 4, 5, 6, 8, 8, 3]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[r.argmax() for r in rep]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 avec la probablilité 0.412\n",
      "1 avec la probablilité 0.852\n",
      "2 avec la probablilité 1.000\n",
      "3 avec la probablilité 1.000\n",
      "4 avec la probablilité 1.000\n",
      "5 avec la probablilité 1.000\n",
      "6 avec la probablilité 0.541\n",
      "8 avec la probablilité 0.602\n",
      "8 avec la probablilité 0.641\n",
      "3 avec la probablilité 0.992\n"
     ]
    }
   ],
   "source": [
    "for r in rep:\n",
    "    print(f\"{r.argmax()} avec la probablilité {r.max():.3f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pas beaucoup mieux ...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les résultats montrent :\n",
    "- que le réseau à 1 seule couche cachée et à 2 couches cachées donnent quasiment les mêmes performances pour les images MNIST,\n",
    "- que l'apprentissage d'un réseau dense reste assez sensible à la nature du jeu de données : les images de chiffres hors banque MNIST ne ressemblent pas tout à fait à celles de la banque MNIST, d'où des erreurs de classification avec un simple réseau dense."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Suite....\n",
    "\n",
    "Pour aller au-delà des 98% de reconnaissance des chiffres, il faut passer à une autre architecture de réseau plus adaptée au traitement des images : les réseaux **convolutionnels**, traités dans le prochain cahier IPython `TP_MNIS_Keras_convo.ipynb`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Autres ressources intéressantes... des vidéos :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=\"https://www.youtube.com/embed/trWrEWfhTVg\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<iframe src=\"https://www.youtube.com/embed/trWrEWfhTVg\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=\"https://www.youtube.com/embed/aircAruvnKk\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<iframe src=\"https://www.youtube.com/embed/aircAruvnKk\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=\"https://www.youtube.com/embed/IHZwWFHWa-w\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<iframe src=\"https://www.youtube.com/embed/IHZwWFHWa-w\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe src=\"https://www.youtube.com/embed/Ilg3gGewQ5U\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%HTML\n",
    "<iframe src=\"https://www.youtube.com/embed/Ilg3gGewQ5U\" width=\"800\" height=\"450\" frameborder=\"0\" allow=\"accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen></iframe>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}