Laboratorio06-Incertidumbre.ipynb

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   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Laboratorio 06: Incertidumbre\n",
    "\n",
    "## Reconocimiento de género en imágenes de caras"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Problema \n",
    "\n",
    "Se desea reconocer si una cara pertenece a un hombre o una mujer dada una imagen de una cara. La implementación del clasificador se debe realizar utilizando el material de probabilidades visto en clases.\n",
    "\n",
    "### Base de datos\n",
    "\n",
    "https://www.kaggle.com/cashutosh/gender-classification-dataset\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Objetivo General\n",
    "* Clasificar imágenes de rostros como hombre o mujeres.\n",
    "\n",
    "## Objetivos Específicos\n",
    "1. Acondicionar las imágenes para su uso.\n",
    "2. Transformar las imágenes a un conjunto de características discriminantes utilizando PCA y LDA.\n",
    "3. Implementar las funciones de densidad de probabilidades para cada género.\n",
    "4. Utilizar el teorema de bayes para clasificar las caras."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Cargar imágenes y sus etiquetas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(25, 25)\n"
     ]
    }
   ],
   "source": [
    "from os import listdir\n",
    "from os.path import isfile, join\n",
    "import re\n",
    "from PIL import Image, ImageOps\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# Cargar base de datos hombres y mujeres\n",
    "def load_database_gender(mypath, label=0, grayscale=False, scale=None, flatten=False):\n",
    "    files = [join(mypath, f) for f in listdir(mypath) if isfile(join(mypath, f))]\n",
    "    X = []\n",
    "    y = []\n",
    "    for file in files:\n",
    "        y.append(label)\n",
    "        with Image.open(file) as img:\n",
    "            if grayscale:\n",
    "                img = ImageOps.grayscale(img)\n",
    "            if scale is not None:\n",
    "                img = img.resize(scale) \n",
    "                # Transformo las imágenes a vectores numpy\n",
    "            if flatten:\n",
    "                img = np.array(img).flatten()\n",
    "            else: # Transformo solo a matrix numpy\n",
    "                img = np.array(img)\n",
    "            X.append(img)\n",
    "    \n",
    "    return X, y\n",
    "        \n",
    "# path donde se encuentran las imágenes de hombres\n",
    "mypath = 'database/Training/male' \n",
    "\n",
    "#X_male_train, y_male_train = load_database_gender(mypath, label=0, grayscale=True)\n",
    "#plt.imshow(X_male_train[10])\n",
    "\n",
    "X_male_train, y_male_train = load_database_gender(mypath, label=0, grayscale=True, scale=(25,25), flatten=False)\n",
    "print(X_male_train[0].shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Cargar el conjunto de entrenamiento y de validación\n",
    "\n",
    "Escriba el código para cargar el conjunto de entrenamiento (mujeres y hombres) y el de validación (mujeres y hombres).\n",
    "\n",
    "La imagen debe ser de $25\\times25$. Se utilizará la etiqueta **0 para hombre** y **1 para mujeres**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "# Escriba el código aquí"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fed789ee990>"
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     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Escriba el código aquí\n",
    "mypath = 'database/Training/male' \n",
    "X_male_train, y_male_train = load_database_gender(mypath, label=0, grayscale=True, scale=(25,25))\n",
    "plt.imshow(X_male_train[10], cmap='gray', vmin=0, vmax=255)\n",
    "\n",
    "mypath = 'database/Training/female' \n",
    "X_female_train, y_female_train = load_database_gender(mypath, label=1, grayscale=True, scale=(25,25))\n",
    "plt.imshow(X_female_train[0], cmap='gray', vmin=0, vmax=255)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fed78405e10>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Imágenes de hombres\n",
    "plt.imshow(X_male_train[1], cmap='gray', vmin=0, vmax=255)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Imágenes de mujeres\n",
    "plt.imshow(X_female_train[1], cmap='gray', vmin=0, vmax=255)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Transformar las imágenes a un nuevo conjunto de características discriminantes\n",
    "\n",
    "### PCA (_Principal Component Analysis_)\n",
    "\n",
    "En estadística, el análisis de componentes principales (en español ACP, en inglés, PCA) es una técnica utilizada para describir un conjunto de datos en términos de nuevas variables («componentes») no correlacionadas. Los componentes se ordenan por la cantidad de varianza original que describen, por lo que la técnica es útil para reducir la dimensionalidad de un conjunto de datos. \n",
    "\n",
    "https://es.wikipedia.org/wiki/An%C3%A1lisis_de_componentes_principales"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Transformar los datos a formato sklearn\n",
    "\n",
    "Convertir la lista de vectores `numpy` a una matriz `numpy`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Largo de la lista: 23766\n",
      "Forma de matriz: (23766, 625)\n"
     ]
    }
   ],
   "source": [
    "mypath = 'database/Training/male' \n",
    "X_male_train, y_male_train = load_database_gender(mypath, label=0, grayscale=True, scale=(25,25), flatten=True)\n",
    "print(f'Largo de la lista: {len(X_male_train)}')\n",
    "X_male_train = np.vstack(X_male_train)\n",
    "print(f'Forma de matriz: {X_male_train.shape}')\n",
    "\n",
    "mypath = 'database/Training/female' \n",
    "X_female_train, y_female_train = load_database_gender(mypath, label=1, grayscale=True, scale=(25,25), flatten=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Aplicar PCA con sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(47009, 625)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "PCA(n_components=2)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# Concateno las matrices de hombres y mujeres\n",
    "X = np.vstack((X_male_train, X_female_train))\n",
    "print(X.shape)\n",
    "pca = PCA(n_components=2)\n",
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Visualizar PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(23243, 2)\n"
     ]
    }
   ],
   "source": [
    "pca_male_train = pca.transform(X_male_train)\n",
    "pca_female_train = pca.transform(X_female_train)\n",
    "\n",
    "print(pca_female_train.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Graficar ambos PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fed743c1510>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(pca_male_train[:, 0], pca_male_train[:, 1], label='Hombres')\n",
    "plt.scatter(pca_female_train[:, 0], pca_female_train[:, 1], label='Mujeres')\n",
    "plt.xlabel('PCA 1')\n",
    "plt.ylabel('PCA 2')\n",
    "plt.title('Proyección PCA y su clase')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Proyección LDA (_Linear Discriminant Analysis_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearDiscriminantAnalysis()"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "X = np.vstack((X_male_train, X_female_train))\n",
    "y = y_male_train + y_female_train\n",
    "clf = LinearDiscriminantAnalysis()\n",
    "clf.fit(X, y)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Visualizar LDA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(23766, 1)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fed74195e50>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lda_male = clf.transform(X_male_train)\n",
    "print(lda_male.shape)\n",
    "lda_female = clf.transform(X_female_train)\n",
    "\n",
    "\n",
    "plt.hist(lda_male, bins=60, alpha=1, edgecolor = 'black',  linewidth=1, label='Hombres')\n",
    "plt.hist(lda_female, bins=60, alpha=1, edgecolor = 'black',  linewidth=1, label='Mujeres')\n",
    "\n",
    "\n",
    "plt.xlabel('LDA')\n",
    "plt.ylabel('frecuencia')\n",
    "plt.title('Histogramas de componente LDA dado el género')\n",
    "plt.grid(False)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Laboratorio:\n",
    "\n",
    "* Construir las funciones de densidad de probabilidad para $P(X|Male)$ y $P(X|Female)$.\n",
    "* Clasificar una imagen utilizando el Teorema de Bayes $P(Male|X)$\n",
    "* Pruebe los siguientes modelos:\n",
    "  * Aplique a las imágenes LDA y construya y pruebe el clasificador.\n",
    "  * Aplique a las imágenes PCA y retenga 50 características, luego aplique LDA. Construya y pruebe el clasificador.\n",
    "  * Aplique a las imágenes PCA y retenga 100 características, luego aplique LDA. Construya y pruebe el clasificador.\n",
    "  * Aplique a las imágenes PCA y retenga 150 características, luego aplique LDA. Construya y pruebe el clasificador.\n",
    "  \n",
    "¿Qué clasificador tiene mejor rendimiento?\n",
    "\n",
    "**Entrega: 15 de Enero hasta las 23:00 horas.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Matemáticas\n",
    "\n",
    "Aplicaremos el teorema de bayes para construir el clasificador:\n",
    "\n",
    "La regla se Bayes:\n",
    "\n",
    "\\begin{equation}\n",
    "p(X_1 \\mid X_2) = \\frac{p(X_2 \\mid X_1)p(X_1)}{\\sum_{x_1} p(X_2 \\mid x_1)p(x_1)}\n",
    "\\end{equation}\n",
    "\n",
    "Se puede obtener, combinando las definiciones de **probabilidad condicional** y **marginalización**\n",
    "\n",
    "\\begin{equation}\n",
    "p(X_1 \\mid X_2) = \\frac{p(X_1,X_2)}{p(X_2)} = \\frac{p(X_2 \\mid X_1)p(X_1)}{\\sum_{x_1} p(X_2 \\mid x_1)p(x_1)}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Matemáticas\n",
    "\n",
    "En nuestro caso, las variables aleatorias LDA y G (Género). La variable aleatoria LDA puede tomar los valores  ($\\alpha_{LDA}$) y que representan los atributos de entrada. La variable G tiene valores discretos como etiquetas de salida hombre (0) y mujer (1).\n",
    "\n",
    "Desde la base de datos podemos obtener las funciones de densidad $f(LDA|G=hombre)$ y $f(LDA|G=Mujer)$. Tanto, $f(LDA|G=hombre)$ como $f(LDA|G=Mujer)$ pueden ser aproximadas a una función gaussiana o normal ($\\mathcal{N}(\\mu_{LDA|G}, \\sigma_{LDA|G})$).\n",
    "\n",
    "Para nuestro caso la función de densidad normal se define:\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "f_{\\mu,\\sigma^2}(x) = \\frac{1}{\\sigma\\sqrt{2\\pi}}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}, \\; x \\in \\mathbb{R}\n",
    "\\end{equation}\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Matemáticas\n",
    "\n",
    "Adaptamos el teorema de bayes a nuestro problema\n",
    "\n",
    "\\begin{equation}\n",
    "F(G \\mid LDA) = \\frac{F(LDA \\mid G)p(G)}{\\sum_{x \\in (hombre, mujer)} p(LDA \\mid x)p(x)}\n",
    "\\end{equation}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Referencias\n",
    "* Revisiting Linear Discriminant Techniques in Gender Recognition.  Juan Bekios-Calfa, José M. Buenaposada, Luis Baumela. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI. [PDF](http://www.dia.fi.upm.es/%7Epcr/publications/pami2011.pdf), [info](https://ieeexplore.ieee.org/document/5661777?arnumber=5661777)"
   ]
  }
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