cap07/C07_E1_Ejemplo-CNN-MNIST-Keras.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; clear: both;\">\n",
    "<div style=\"float: left; width: 50%;\">\n",
    "<img src=\"http://www.uoc.edu/portal/_resources/common/imatges/marca_UOC/UOC_Masterbrand.jpg\", align=\"left\">\n",
    "</div>\n",
    "<div style=\"float: right; width: 50%;\">\n",
    "<p style=\"margin: 0; padding-top: 22px; text-align:right;\"><a href=\"https://www.editorialuoc.cat/deep-learning\" target=\"_blank\\\">Deep learning: Principios y fundamentos</a></p>\n",
    "<p style=\"margin: 0; text-align:right;\">Estudios de Informática, Multimedia y Telecomunicación</p>\n",
    "<p style=\"margin: 0; text-align:right; padding-button: 100px;\">Universitat Oberta de Catalunya (UOC)</p>\n",
    "</div>\n",
    "</div>\n",
    "<div style=\"width:100%;\">&nbsp;</div>\n",
    "\n",
    "\n",
    "# Capítulo 7: Ejemplo de Redes Neuronales Convolucionales (CNN) con MNIST y Keras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este ejemplo veremos la implementación de una red neuronal convolucional (CNN) para reconocer los dígitos del conjunto de datos de referencia MNIST. Se utilizará la librería Keras para la implementación, compilación y entrenamiento del modelo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Carga de datos"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El siguiente código carga los paquetes necesarios para el ejercicio y, además, lee los datos que utilizaremos para entrenar la red neuronal. El Dataset [MNIST](https://en.wikipedia.org/wiki/MNIST_database) corresponde a imágenes de digitos del 0 al 9 de tamaño 28x28 píxeles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import keras\n",
    "# En caso de emplear TF 2.x, usar:\n",
    "# from tensorflow import keras\n",
    "from keras.datasets import mnist\n",
    "from keras.utils import to_categorical\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Conv2D, Flatten\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deshabilitamos la aparición de *warnings*. \n",
    "\n",
    "<u>Nota</u>: No se recomienda este paso cuando se está desarrollando el código."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Descarga de el dataset MNIST y hace la partición train/test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Descarga de el dataset MNIST y hace la partición train/test\n",
    "(x_train_orig, y_train_orig), (x_test_orig, y_test_orig) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizamos la primera imagen del dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/EBThB4Ii/EBQ/weCC5r/92q6mAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0bf54080b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualizamos la primera imagen del dataset\n",
    "first_image = x_train_orig[0]\n",
    "first_image = np.array(first_image, dtype='float')\n",
    "pixels = first_image.reshape((28, 28))\n",
    "plt.imshow(pixels, cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28, 28)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Comprobación del tamaño de la imagen\n",
    "x_train_orig[0].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación implementaremos una red neuronal convolucional de una capa y haremos el entrenamiento y test sobre el dataset MNIST. Tenemos 60.000 imágenes para entrenar y 10.000 para testear. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Pre-procesado de datos\n",
    "\n",
    "El primer paso para entrenar una red neuronal consiste en pre-procesar los datos de entrenamiento y test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tamaño de los datos originales de train: (60000, 28, 28)\n",
      "Tamaño de los datos originales de test : (10000, 28, 28)\n"
     ]
    }
   ],
   "source": [
    "# Tamaño de los datos originales\n",
    "print(\"Tamaño de los datos originales de train: {}\".format(x_train_orig.shape))\n",
    "print(\"Tamaño de los datos originales de test : {}\".format(x_test_orig.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Seguidamente, aplicaremos una simple normalización de los datos para que queden comprendidos entre el rango 0 y 1. Aunque existen clases para aplicar la normalización, aquí emplearemos el método más simple, que es dividir los valores por el máximo para obtener valores en el rango entre 0 y 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Los valores del primer registro son: [[  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   3  18  18  18 126 136\n",
      "  175  26 166 255 247 127   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0  30  36  94 154 170 253 253 253 253 253\n",
      "  225 172 253 242 195  64   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0  49 238 253 253 253 253 253 253 253 253 251\n",
      "   93  82  82  56  39   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0  18 219 253 253 253 253 253 198 182 247 241\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0  80 156 107 253 253 205  11   0  43 154\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0  14   1 154 253  90   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0 139 253 190   2   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0  11 190 253  70   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0  35 241 225 160 108   1\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0  81 240 253 253 119\n",
      "   25   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0  45 186 253 253\n",
      "  150  27   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0  16  93 252\n",
      "  253 187   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0 249\n",
      "  253 249  64   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0  46 130 183 253\n",
      "  253 207   2   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0  39 148 229 253 253 253\n",
      "  250 182   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0  24 114 221 253 253 253 253 201\n",
      "   78   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0  23  66 213 253 253 253 253 198  81   2\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0  18 171 219 253 253 253 253 195  80   9   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0  55 172 226 253 253 253 253 244 133  11   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0 136 253 253 253 212 135 132  16   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]\n",
      " [  0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "    0   0   0   0   0   0   0   0   0   0]]\n",
      "Los valores mínimo y máximo son 0 y 255.\n",
      "Los valores del primer registro después de la normalización son: [[0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
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      "  0.         0.         0.         0.        ]\n",
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      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.01176471 0.07058824 0.07058824 0.07058824 0.49411765 0.53333333\n",
      "  0.68627451 0.10196078 0.65098039 1.         0.96862745 0.49803922\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.11764706 0.14117647 0.36862745 0.60392157\n",
      "  0.66666667 0.99215686 0.99215686 0.99215686 0.99215686 0.99215686\n",
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      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
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      "  0.99215686 0.99215686 0.99215686 0.99215686 0.99215686 0.98431373\n",
      "  0.36470588 0.32156863 0.32156863 0.21960784 0.15294118 0.\n",
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      "  0.74509804 0.99215686 0.2745098  0.         0.         0.\n",
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      "  0.1372549  0.94509804 0.88235294 0.62745098 0.42352941 0.00392157\n",
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      "  0.         0.         0.         0.         0.         0.\n",
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      "  0.09803922 0.         0.         0.         0.         0.\n",
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      "  0.         0.         0.17647059 0.72941176 0.99215686 0.99215686\n",
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      "  0.         0.         0.         0.0627451  0.36470588 0.98823529\n",
      "  0.99215686 0.73333333 0.         0.         0.         0.\n",
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      "  0.         0.         0.         0.         0.         0.97647059\n",
      "  0.99215686 0.97647059 0.25098039 0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
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      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.18039216 0.50980392 0.71764706 0.99215686\n",
      "  0.99215686 0.81176471 0.00784314 0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.15294118 0.58039216 0.89803922 0.99215686 0.99215686 0.99215686\n",
      "  0.98039216 0.71372549 0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.09411765 0.44705882\n",
      "  0.86666667 0.99215686 0.99215686 0.99215686 0.99215686 0.78823529\n",
      "  0.30588235 0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.09019608 0.25882353 0.83529412 0.99215686\n",
      "  0.99215686 0.99215686 0.99215686 0.77647059 0.31764706 0.00784314\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.07058824 0.67058824 0.85882353 0.99215686 0.99215686 0.99215686\n",
      "  0.99215686 0.76470588 0.31372549 0.03529412 0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.21568627 0.6745098\n",
      "  0.88627451 0.99215686 0.99215686 0.99215686 0.99215686 0.95686275\n",
      "  0.52156863 0.04313725 0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.53333333 0.99215686\n",
      "  0.99215686 0.99215686 0.83137255 0.52941176 0.51764706 0.0627451\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]\n",
      " [0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.         0.         0.\n",
      "  0.         0.         0.         0.        ]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Los valores del primer registro son: {}\".format(x_train_orig[0,:,:]))\n",
    "\n",
    "# Determinar valores mínimo y máximo para la normalización\n",
    "v_min = np.min(x_train_orig)\n",
    "v_max = np.max(x_train_orig)\n",
    "print(\"Los valores mínimo y máximo son {} y {}.\".format(v_min, v_max))\n",
    "\n",
    "# Normalización entre 0 y 1\n",
    "x_train_orig = (x_train_orig - v_min) / (v_max - v_min)\n",
    "x_test_orig = (x_test_orig - v_min) / (v_max - v_min)\n",
    "\n",
    "print(\"Los valores del primer registro después de la normalización son: {}\".format(x_train_orig[0,:,:]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación, ajustaremos el tamaño de los datos de entrenamiento y test utilizando 4 dimensiones, ya que la última dimensión debe ser 1 para indicar que las imágenes están en escala de grises."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tamaño de los datos de train: (60000, 28, 28, 1)\n",
      "Tamaño de los datos de test : (10000, 28, 28, 1)\n"
     ]
    }
   ],
   "source": [
    "x_train = x_train_orig.reshape(60000,28,28,1)\n",
    "x_test = x_test_orig.reshape(10000,28,28,1)\n",
    "\n",
    "print(\"Tamaño de los datos de train: {}\".format(x_train.shape))\n",
    "print(\"Tamaño de los datos de test : {}\".format(x_test.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finalemte, codificaremos los valores de las etiquetas de salida en un vector `one-hot`. El objetivo de esta acción es convertir los datos al mismo formato que tendrá la salida de la red neuronal. Por ejemplo, el vector de salida para una imagen que contiene un 5 sería: [0., 0., 0., 0., 0., 1., 0., 0., 0., 0.]. \n",
    "\n",
    "Para realizar esta tarea de forma sencilla, se puede utilizar la función `to_categorical` de `Keras.utils`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "El tamaño de y_train_orig es (60000,) y el valor de y_train_orig[0] es 5\n",
      "El tamaño de y_train es (60000, 10) y el valor de y_train[0] es [0. 0. 0. 0. 0. 1. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "y_train = to_categorical(y_train_orig)\n",
    "y_test = to_categorical(y_test_orig)\n",
    "\n",
    "print(\"El tamaño de y_train_orig es {} y el valor de y_train_orig[0] es {}\".format(y_train_orig.shape, y_train_orig[0]))\n",
    "print(\"El tamaño de y_train es {} y el valor de y_train[0] es {}\".format(y_train.shape, y_train[0]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Creación del modelo\n",
    "\n",
    "Vamos a usar un modelo `Secuencial` de Keras, ya que es muy intuitivo y fácil de utilizar. Este tipo de modelos nos permiten construir el modelo capa a capa. En concreto:\n",
    "\n",
    "- La primera capa que añadiremos será una capa convolucional con las siguientes propiedades: \n",
    "    - Número de kernels (neuronas) primera capa: 64 neuronas\n",
    "    - Tamaño de los kernels: 3x3\n",
    "    - Activacion de los kernels: ReLU\n",
    "- A continuación añadiremos una capa *Flatten* para conectar la salida de la capa convolucional con la entrada de una capa densa.\n",
    "- Por último, añadiremos una capa densa de salida, y por lo tanto tendrá tantas neuronas como clases queremos predecir. La activación de esta última capa sera *Softmax*. La predicción final del modelo será entonces la clase que tenga una probabilidad más alta. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El siguiente código implementa el modelo anterior, teniendo en cuenta que la salida de la red neuronal será un vector de probabilidades de las 10 clases anteriormente comentadas, i.e. 0...9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Número de clases\n",
    "num_classes = 10\n",
    "\n",
    "model = Sequential()\n",
    "\n",
    "# Añadir las capas indicadas\n",
    "model.add(Conv2D(64, kernel_size=3, activation=\"relu\", input_shape=(28,28,1)))\n",
    "model.add(Flatten())\n",
    "model.add(Dense(num_classes, activation=\"softmax\"))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Compilación el modelo\n",
    "\n",
    "Una vez definido el modelo, se debe compilar de forma previa al proceso de entrenamiento. Para ello vamos a utilizar el algoritmo de optimización `Adam`, la función de coste `categorical_crossentropy` y la métrica `accuracy`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "model.compile(optimizer='adam', loss='categorical_crossentropy', metrics=['accuracy'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Entrenamiento del modelo\n",
    "\n",
    "En este punto ya podemos entrenar el modelo. Haremos que el modelo vea cada imagen 10 veces diferentes (es decir, `epochs`=10), fijaremos un valor de `bacth` igual a 128 y utilizaremos el conjunto de test para la validación del proceso."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 60000 samples, validate on 10000 samples\n",
      "Epoch 1/10\n",
      "60000/60000 [==============================] - 21s 352us/step - loss: 0.2301 - acc: 0.9349 - val_loss: 0.0895 - val_acc: 0.9746\n",
      "Epoch 2/10\n",
      "60000/60000 [==============================] - 20s 340us/step - loss: 0.0745 - acc: 0.9789 - val_loss: 0.0666 - val_acc: 0.9788\n",
      "Epoch 3/10\n",
      "60000/60000 [==============================] - 20s 341us/step - loss: 0.0530 - acc: 0.9843 - val_loss: 0.0644 - val_acc: 0.9808\n",
      "Epoch 4/10\n",
      "60000/60000 [==============================] - 20s 337us/step - loss: 0.0398 - acc: 0.9884 - val_loss: 0.0590 - val_acc: 0.9815\n",
      "Epoch 5/10\n",
      "60000/60000 [==============================] - 20s 332us/step - loss: 0.0324 - acc: 0.9904 - val_loss: 0.0641 - val_acc: 0.9810\n",
      "Epoch 6/10\n",
      "60000/60000 [==============================] - 20s 334us/step - loss: 0.0253 - acc: 0.9927 - val_loss: 0.0599 - val_acc: 0.9822\n",
      "Epoch 7/10\n",
      "60000/60000 [==============================] - 20s 334us/step - loss: 0.0209 - acc: 0.9937 - val_loss: 0.0661 - val_acc: 0.9816\n",
      "Epoch 8/10\n",
      "60000/60000 [==============================] - 20s 335us/step - loss: 0.0167 - acc: 0.9951 - val_loss: 0.0656 - val_acc: 0.9806\n",
      "Epoch 9/10\n",
      "60000/60000 [==============================] - 20s 338us/step - loss: 0.0141 - acc: 0.9959 - val_loss: 0.0664 - val_acc: 0.9812\n",
      "Epoch 10/10\n",
      "60000/60000 [==============================] - 20s 331us/step - loss: 0.0111 - acc: 0.9970 - val_loss: 0.0690 - val_acc: 0.9822\n"
     ]
    }
   ],
   "source": [
    "# Entrenamiento del modelo\n",
    "n_epochs = 10\n",
    "mfit = model.fit(x_train, y_train, validation_data=(x_test, y_test), batch_size=128, epochs=n_epochs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. Evolución de la precisión"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación, vamos a crear una función que nos permitirá ver la evolución de la *accuracy* y el *loss* en el conjunto de entrenamiento y test en función de las diferentes épocas (*epochs*) del entrenamiento."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Plot del training loss y el accuracy\n",
    "def plot_prediction(n_epochs, mfit):\n",
    "    N = n_epochs\n",
    "    plt.style.use(\"ggplot\")\n",
    "    fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15,6))\n",
    "    fig.suptitle('Training Loss and Accuracy')\n",
    "    \n",
    "    ax1.plot(np.arange(0, N), mfit.history[\"acc\"], label=\"train\")\n",
    "    ax1.plot(np.arange(0, N), mfit.history[\"val_acc\"], label=\"val\")\n",
    "    ax1.set_title(\"Accuracy\")\n",
    "    ax1.set_xlabel(\"Epoch #\")\n",
    "    ax1.set_ylabel(\"Accuracy\")\n",
    "    ax1.legend(loc=\"lower right\")\n",
    "    \n",
    "    ax2.plot(np.arange(0, N), mfit.history[\"loss\"], label=\"train\")\n",
    "    ax2.plot(np.arange(0, N), mfit.history[\"val_loss\"], label=\"val\")\n",
    "    ax2.set_title(\"Loss\")\n",
    "    ax2.set_xlabel(\"Epoch #\")\n",
    "    ax2.set_ylabel(\"Loss\")\n",
    "    ax2.legend(loc=\"upper right\")\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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w1ycVklIgKRUrKprEpCRKS0tP+p4i0oVc2eBugIP7Ic0V6GpERILOkCFDqKmp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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0bd45142b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_prediction(n_epochs, mfit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7. Predicción\n",
    "\n",
    "Finalmente, podemos hacer la predicción para cuatro de las imágenes del conjunto de test y mirar si los resultados son o no correctos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[8.2632358e-15 1.7160427e-13 8.1686040e-11 1.2636316e-07 1.1634286e-14\n",
      "  1.2490455e-11 2.0120201e-21 9.9999988e-01 9.8667619e-10 2.8979748e-08]\n",
      " [2.1876938e-12 3.9645126e-10 1.0000000e+00 2.2406696e-10 5.2389698e-21\n",
      "  8.3534967e-12 5.0966094e-09 8.2585351e-24 4.5951576e-12 4.0705124e-18]\n",
      " [8.1125017e-07 9.9986017e-01 8.5136953e-06 7.8809576e-10 8.2128281e-05\n",
      "  1.7081739e-07 1.6878213e-08 2.0577497e-06 4.6190904e-05 1.9631039e-09]\n",
      " [9.9999964e-01 1.5076602e-10 5.8781914e-08 1.2309736e-11 4.1053865e-11\n",
      "  2.4673852e-09 3.2722198e-07 4.7614370e-09 3.4281467e-10 3.0139938e-10]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [1., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Hacemos la predicción para las 4 primeras imágenes del set de test\n",
    "print(model.predict(x_test[:4]))\n",
    "\n",
    "# Mostramos el ground truth para las primeras 4 imágenes\n",
    "y_test[:4]"
   ]
  }
 ],
 "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": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}