43_Clustering_Gaussian_Mixture_Models.ipynb

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    "# 43 - Clustering: Gaussian Mixture Models\n",
    "\n",
    "\n",
    "* En este Notebook vamos a ver como solucionar problemas de ***Clusterización con la técnica del Gaussian Mixture Models*** y como se implementa.\n",
    "\n",
    "\n",
    "* Vamos a tratar los siguientes puntos:\n",
    "<span></span><br>\n",
    "    1. [Gaussian Mixture Models](#M1)\n",
    "<span></span><br>\n",
    "    2. [Pseudocódigo del Gaussian Mixture Models](#M2)\n",
    "<span></span><br>\n",
    "    3. [Implementación: Gaussian Mixture Models](#M3)\n",
    "<span></span><br>\n",
    "    4. [Ejemplo de Clustering con Gaussian Mixture Models](#M4)\n",
    "<span></span><br>\n",
    "    5. [Resultados](#M5)\n",
    "\n",
    "\n",
    "<hr>\n",
    "\n",
    "\n",
    "\n",
    "# <a name=\"M1\">1. Gaussian Mixture Models</a>\n",
    "\n",
    "\n",
    "* El ***Gaussian Mixture Models (GMM) es un método estadístico de Clustering similar al K-means, pero con un enfoque probabilístico***. \n",
    "\n",
    "\n",
    "* ***Este método asume que todos los objetos (del dataset) han sido generados a partir de ‘k’ distribuciones de probabilidad*** de las cuales desconocemos a priori sus parámetros.\n",
    "\n",
    "\n",
    "* En la siguiente imagen de ejemplo, podemos ver como los ***dos grupos de objetos (Clusters) se generan de acuerdo a dos distribuciones de probabilidad; por ejemplo dos distribuciones normales*** (gaussianas) p(x|μ,σ) definidas por su media (μ) y su desviación típica (σ):\n",
    "\n",
    "\n",
    "<img src=\"./imgs/45_01_gmm.png\" style=\"width: 300px;\"/>\n",
    "\n",
    "\n",
    "* El ***Gaussian Mixture Models (GMM) es la implementación del algoritmo Expectation-Maximization (EM)*** se usa en estadística para encontrar estimadores de máxima verosimilitud de parámetros en modelos probabilísticos que dependen de variables no observables; asumiendo que estos modelos probabilísticos son distribuciones normales de ahí el nombre de Gaussian Mixture Models (Mezcla de Modelos Gausianos, en Español).\n",
    "\n",
    "\n",
    "* El problema a resolver es por tanto el calcular la probabilidad de pertenencia de un elemento a cada uno de los Cluster. Para ello tenemos lo siguiente:\n",
    "\n",
    "<span style=\"font-size:16px\">$$P(X,C | \\pi, \\overrightarrow{\\mu}, \\overrightarrow{\\sigma}) = P(X | C, \\overrightarrow{\\mu}, \\overrightarrow{\\sigma}) \\cdot P(C|\\pi); \\; donde\\;\n",
    "\\left\\{\\begin{matrix}\n",
    "\\pi = Probabilidad\\;de\\;pertenecer\\;a\\;un\\;Cluster\\\\ \n",
    "C = Clusters\\\\ \n",
    "X = Elemento\\\\ \n",
    "\\mu = Media\\;de\\;los\\;elementos\\;del\\;Cluster\\\\ \n",
    "\\sigma = Desviación\\;típica\\;de\\;los\\;elementos\\;del\\;Cluster\n",
    "\\end{matrix}\\right.$$</span>\n",
    "\n",
    "\n",
    "* En notación **\"plate-notation\"** seria lo siguiente:\n",
    "\n",
    "\n",
    "<img src=\"./imgs/45_02_gmm.png\" style=\"width: 400px;\"/>\n",
    "\n",
    "\n",
    "* Lo que nos interesa saber es la ***probabilidad de pertenencia de un elemento a cada uno de los Clusters***:\n",
    "\n",
    "<span style=\"font-size:20px\">$$P(X | C, \\overrightarrow{\\mu}, \\overrightarrow{\\sigma})$$</span>\n",
    "\n",
    "\n",
    "* Tenemos por otro lado que $𝑃(𝐶│\\pi)$ es un valor constante ( $𝑃\\;(𝑐=1│\\pi_1 ), 𝑃\\;(𝑐=2│\\pi_2 ), …, 𝑃\\;(𝑐=𝑘│\\pi_𝑘 )$ ), cosa que nos ayuda a la hora de realizar el cálculo de probabilidades quedando de la siguiente manera:\n",
    "\n",
    "<span style=\"font-size:16px\">$$P(X | C, \\overrightarrow{\\mu}, \\overrightarrow{\\sigma}) = \\sum_{k=1}^{K} P(X,C=k | \\pi, \\overrightarrow{\\mu}, \\overrightarrow{\\sigma}) = \\sum_{k=1}^{K} \\pi_k \\cdot  P(X| \\overrightarrow{\\mu}, \\overrightarrow{\\sigma})$$</span>\n",
    "    \n",
    "    \n",
    "* Aplicando la función de densidad de una distribución normal, tenemos que la suma de todas las probabilidades de pertenencia de un elemento a los Clusters es:\n",
    "\n",
    "<span style=\"font-size:16px\">$$P(X | C, \\overrightarrow{\\mu}, \\overrightarrow{\\sigma}) = \\sum_{k=1}^{K} \\pi_k \\cdot  \\frac{1}{\\sigma_k \\sqrt{2\\pi}} \\cdot e^{-\\frac{1}{2}(\\frac{x-\\mu_k}{\\sigma_k})^2}$$</span>\n",
    "\n",
    "\n",
    "* Podemos simplificar esta probabilidad ya que $\\frac{1}{\\sqrt{2\\pi}}$ es una constante, quedando:\n",
    "\n",
    "<span style=\"font-size:16px\">$$P(X | C, \\overrightarrow{\\mu}, \\overrightarrow{\\sigma}) = \\sum_{k=1}^{K} \\pi_k \\cdot  \\frac{e^{-\\frac{1}{2}(\\frac{x-\\mu_k}{\\sigma_k})^2}}{\\sigma_k}\n",
    "$$</span>\n",
    "    \n",
    "    \n",
    "* Esto último lo podemos hacer ya que lo que ***nos interesa es asignar el elemento al Cluster con mayor probabilidad***; es decir:\n",
    "\n",
    "<span style=\"font-size:20px\">$$argmax \\sum_{k=1}^{K} \\pi_k \\cdot  \\frac{e^{-\\frac{1}{2}(\\frac{x-\\mu_k}{\\sigma_k})^2}}{\\sigma_k}$$</span>\n",
    "\n",
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M2\">2. Pseudocódigo del Gaussian Mixture Models</a>\n",
    "\n",
    "\n",
    "* El algoritmo del Gaussian Mixture Models funciona de la siguiente manera:\n",
    "\n",
    "    1. ***Inicialización***: Comienza inicializando los parámetros de las distribuciones de probabilidad $(\\mu,\\sigma)$ y probabilidades de pertenencia a los Clusters $\\pi$\n",
    "<span></span><br><br>    \n",
    "    2. ***Expectation-Maximization***, hasta converger o hasta que se cumpla una condición de parada:\n",
    " <span></span><br><br>   \n",
    "        + ***Expectation (Esperanza)***: Con los parámetros conocidos de las distribuciones normales y la probabilidad $\\pi$ de pertenencia a un Cluster, asignar cada elemento al Cluster con el mayor valor de probabilidad de pertenencia:\n",
    "<span></span><br><br>  \n",
    "$$argmax \\sum_{k=1}^{K} \\pi_k \\cdot  \\frac{e^{-\\frac{1}{2}(\\frac{x-\\mu_k}{\\sigma_k})^2}}{\\sigma_k}$$\n",
    "<span></span><br><br>       \n",
    "        + ***Maximization (Maximización)***: Calcular para cada Cluster; con los ***'n'*** elementos asignados a cada Cluster, el valor de los parámetros $\\pi_k, \\mu_k, \\sigma_k$ de la siguiente manera:\n",
    "<span></span><br><br>       \n",
    "            * $$\\pi_k = \\frac{Elementos\\;en\\;el\\;Cluster}{Total\\;Elementos\\;Dataset}$$\n",
    "<span></span><br><br>\n",
    "            * $$\\mu_k = \\frac{1}{n} \\sum_{i=1}^{n} x_i$$\n",
    "<span></span><br><br>\n",
    "            * $$\\sigma_k = \\sqrt{\\frac{1}{n-1} \\cdot \\sum_{n=1}^{n} (x_i-\\mu_i)^2}$$ \n",
    "\n",
    "* Veamos a continuación el Pseudocódigo:\n",
    "\n",
    "\n",
    "\n",
    "```python\n",
    "num_clusters = N\n",
    "num_iteraciones = 100\n",
    "condicion_parada = False\n",
    "\n",
    "# Inicializamos los 'N' Clusters\n",
    "clusters_new = num_cluster * {mean: random, std: 1, prob: 1/num_clusters}\n",
    "\n",
    "it_counter\n",
    "while not condicion_parada and it_counter < num_iteraciones:\n",
    "    \n",
    "    # Inicializamos una lista de los elementos que formarán el Cluster\n",
    "    elementos_clusters = [[] for i in range(num_clusters)]\n",
    "    \n",
    "    # Creo una variable para guardar el estado de los Clusters Anteriores\n",
    "    clusters_old = clusters_new\n",
    "    \n",
    "    # Expectation\n",
    "    for elemento in dataset:\n",
    "        probs_clusters = lista(num_clusters)\n",
    "        for index, cluster in clusters_old:\n",
    "            probs_clusters[index] = cluster.prob * \n",
    "                                    SUM(e ^ (-1 / 2 * ((x(i) - cluster.mean) ^ 2 / cluster.std ^ 2)) \n",
    "                                                        / cluster.std)\n",
    "        elementos_clusters[argmax(probs_clusters)].append(elemento)\n",
    "    \n",
    "    \n",
    "    # Maximization\n",
    "    for index, cluster in clusters_old:\n",
    "        clusters_new[index].mean = cluster.mean\n",
    "        clusters_new[index].std = cluster.std\n",
    "        clusters_new[index].prob = len(cluster) / Total Elementos\n",
    "        \n",
    "        \n",
    "    it_counter+= 1\n",
    "\n",
    "```\n",
    "\n",
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M3\">3. Implementación: Gaussian Mixture Models</a>\n",
    "\n",
    "\n",
    "* En el siguiente fragmento de código está implementado el ***Gaussian Mixture Models***, siguiendo el Pseudocódigo mostrado anteriormente junto con alguna lógica programática adicional.\n",
    "\n"
   ]
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   "cell_type": "code",
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   "source": [
    "import numpy as np\n",
    "import copy\n",
    "import math\n",
    "\n",
    "\n",
    "def print_iteration_status(iteracion_num, clusters, elementos_clusters):\n",
    "    \"\"\"\n",
    "    Función que imprime por pantalla el estado de los Clsuters por iteracion\n",
    "        - iteracion_num: número del epoch.\n",
    "        - clusters: Valores de las distribuciones de los Clusters\n",
    "        - elementos_clusters: Elementos que hay en cada Cluster\n",
    "    \"\"\"\n",
    "    print('\\nITERATION {}'.format(iteracion_num))\n",
    "    for index, elem in enumerate(clusters):\n",
    "        print('\\n  Cluster {}'.format(index + 1))\n",
    "        print('    Número de elementos en el Cluster {}'.format(len(elementos_clusters[index])))\n",
    "        print('      Distribución: {}'.format(elem))\n",
    "    print('--------------------------------------------------------------------------------')\n",
    "\n",
    "\n",
    "def gaussian_mixture_models(X, num_clusters, num_iteraciones, verbose=False):\n",
    "    \"\"\"\n",
    "    Función que devuelve el modelo o hipótesis de la Clusterización (estado final de los Clusters),\n",
    "    recibiendo como parámetros:\n",
    "        - X: Elementos\n",
    "        - num_clusters: Número de Clusters\n",
    "        - num_iteraciones: Número de Iteraciones máximas a ejecutar\n",
    "        - verbose: Boolean para indicar si queremos imprimir por pantalla el estado de la iteracion\n",
    "    \"\"\"\n",
    "    # Inicializamos los parámetros de los clusters\n",
    "    clusters_new = [{'mean': X[np.random.choice(X.shape[0])],\n",
    "                     'std': np.ones(X.shape[1]),\n",
    "                     'prob': 1 / num_clusters,\n",
    "                     'converge': False} for i in range(num_clusters)]\n",
    "\n",
    "    converge = False\n",
    "    it_counter = 0\n",
    "    while (not converge) and (it_counter < num_iteraciones):\n",
    "\n",
    "        # Inicializamos una lista de los elementos que formarán el Cluster\n",
    "        elementos_clusters = [[] for i in range(num_clusters)]\n",
    "\n",
    "        # Creamos una copia de los centroides de la iteración anterior\n",
    "        clusters_old = copy.deepcopy(clusters_new)\n",
    "\n",
    "        # Expectation (Asignación)\n",
    "        for elem in X:\n",
    "            # prob * SUM(e ^ (-1 / 2 * ((x(i) - mean) ^ 2 / std ^ 2)) / std)\n",
    "            probs_clusters = np.zeros(len(clusters_old))\n",
    "            for index, cluster in enumerate(clusters_old):\n",
    "                prob = 1.0\n",
    "                for i, e in enumerate(elem):\n",
    "                    prob *= (math.exp(-0.5 * (math.pow((e - clusters_old[index]['mean'][i]), 2) /\n",
    "                                              math.pow(clusters_old[index]['std'][i], 2))) / \n",
    "                                                       clusters_old[index]['std'][i])\n",
    "                probs_clusters[index] = prob * clusters_old[index]['prob']\n",
    "            elementos_clusters[np.argmax(probs_clusters)].append(elem)\n",
    "\n",
    "        # Maximization (Actualización)\n",
    "        for index, centroide in enumerate(clusters_old):\n",
    "            clusters_new[index]['mean'] = np.mean(elementos_clusters[index], axis=0)\n",
    "            clusters_new[index]['std'] = np.std(elementos_clusters[index], axis=0)\n",
    "            clusters_new[index]['prob'] = len(elementos_clusters[index]) / float(len(X))\n",
    "            clusters_new[index]['converge'] = np.array_equal(clusters_new[index]['mean'], clusters_old[index]['mean'])\n",
    "\n",
    "        # Condición de parada, si los Nuevos centroides son iguales que los anteriores\n",
    "        converge = [clusters_new[index]['converge'] for index, elem in enumerate(clusters_new)].count(False) == 0\n",
    "\n",
    "        # Incremento Iteracion\n",
    "        it_counter += 1\n",
    "\n",
    "        # Imprimimos por pantalla el estado de los Clusters\n",
    "        if verbose:\n",
    "            print_iteration_status(it_counter, clusters_new, elementos_clusters)\n",
    "        \n",
    "    return clusters_new, elementos_clusters"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M4\">4. Ejemplo de Clustering con Gaussian Mixture Models</a>\n",
    "\n",
    "\n",
    "\n",
    "* Dado un ***conjunto de datos*** que tiene dos variables numéricas, vamos a agruparlas en 3 grupos o Clusters.\n",
    "\n",
    "\n",
    "* Este conjunto de datos se encuentra en: ***'./data/DS_3Clusters_999Puntos.txt'***\n",
    "\n",
    "\n",
    "* En primer lugar vamos a cargar los datos.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
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       "      <th>68</th>\n",
       "      <td>2.357526</td>\n",
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       "      <th>24</th>\n",
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       "      <td>5.602543</td>\n",
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       "           X1        X2\n",
       "68   2.357526  3.760249\n",
       "24   1.971106  3.980642\n",
       "484  2.052296  3.907201\n",
       "189  5.602543  2.760227"
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   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_table('./data/DS_3Clusters_999Puntos.txt', sep='::', header=None, names=['X1', 'X2'], engine='python')\n",
    "df.sample(4)"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "* Dado que el Gaussian Mixture Models es un algoritmo probabilístico, vamos a representar las distribuciones de cada una de las variables en un histograma.\n",
    "\n",
    "\n",
    "* Se puede apreciar como los datos no sigue una distribución normal (gaussiana) y dividiendo los datos en grupos, estos podrían seguir distribuciones normales independientes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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    {
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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# importamos las librerías\n",
    "import warnings\n",
    "warnings.filterwarnings(\"ignore\")\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline \n",
    "\n",
    "\n",
    "# Dibujamos las distribuciones de las 2 variables\n",
    "f, axes = plt.subplots(1, 2, figsize=(10, 5), sharex=True)\n",
    "sns.kdeplot(df['X1'], shade=True, ax=axes[0])\n",
    "sns.kdeplot(df['X2'], shade=True, ax=axes[1])\n",
    "axes[0].title.set_text('Distribución de X1')\n",
    "axes[1].title.set_text('Distribución de X2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Vamos a ejecutar el K-Means para obtener los centroides de los clusters pasandole los siguientes parámetros:\n",
    "    + ***Número de Clusters*** = 3\n",
    "    + ***Número Máximo de Iteracciones*** = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "ITERATION 1\n",
      "\n",
      "  Cluster 1\n",
      "    Número de elementos en el Cluster 561\n",
      "      Distribución: {'mean': array([1.968402  , 2.15292836]), 'std': array([0.32843928, 0.56185994]), 'prob': 0.5615615615615616, 'converge': False}\n",
      "\n",
      "  Cluster 2\n",
      "    Número de elementos en el Cluster 147\n",
      "      Distribución: {'mean': array([2.00243953, 4.09445674]), 'std': array([0.25188547, 0.18104223]), 'prob': 0.14714714714714713, 'converge': False}\n",
      "\n",
      "  Cluster 3\n",
      "    Número de elementos en el Cluster 291\n",
      "      Distribución: {'mean': array([4.68543947, 2.83052368]), 'std': array([1.18070924, 0.90093993]), 'prob': 0.2912912912912913, 'converge': False}\n",
      "--------------------------------------------------------------------------------\n",
      "\n",
      "ITERATION 2\n",
      "\n",
      "  Cluster 1\n",
      "    Número de elementos en el Cluster 566\n",
      "      Distribución: {'mean': array([2.01150177, 2.01695728]), 'std': array([0.36184712, 0.40250796]), 'prob': 0.5665665665665666, 'converge': False}\n",
      "\n",
      "  Cluster 2\n",
      "    Número de elementos en el Cluster 181\n",
      "      Distribución: {'mean': array([1.99744189, 4.03028592]), 'std': array([0.24722545, 0.21258328]), 'prob': 0.18118118118118118, 'converge': False}\n",
      "\n",
      "  Cluster 3\n",
      "    Número de elementos en el Cluster 252\n",
      "      Distribución: {'mean': array([5.00812713, 3.0249237 ]), 'std': array([0.9109103 , 0.81153239]), 'prob': 0.25225225225225223, 'converge': False}\n",
      "--------------------------------------------------------------------------------\n",
      "\n",
      "ITERATION 3\n",
      "\n",
      "  Cluster 1\n",
      "    Número de elementos en el Cluster 571\n",
      "      Distribución: {'mean': array([2.02788518, 2.0046025 ]), 'std': array([0.37849705, 0.38147472]), 'prob': 0.5715715715715716, 'converge': False}\n",
      "\n",
      "  Cluster 2\n",
      "    Número de elementos en el Cluster 186\n",
      "      Distribución: {'mean': array([1.99675985, 4.01852586]), 'std': array([0.25283376, 0.22137621]), 'prob': 0.18618618618618618, 'converge': False}\n",
      "\n",
      "  Cluster 3\n",
      "    Número de elementos en el Cluster 242\n",
      "      Distribución: {'mean': array([5.09411261, 3.0631674 ]), 'std': array([0.82251   , 0.79567349]), 'prob': 0.24224224224224225, 'converge': False}\n",
      "--------------------------------------------------------------------------------\n",
      "\n",
      "ITERATION 4\n",
      "\n",
      "  Cluster 1\n",
      "    Número de elementos en el Cluster 571\n",
      "      Distribución: {'mean': array([2.02788518, 2.0046025 ]), 'std': array([0.37849705, 0.38147472]), 'prob': 0.5715715715715716, 'converge': True}\n",
      "\n",
      "  Cluster 2\n",
      "    Número de elementos en el Cluster 186\n",
      "      Distribución: {'mean': array([1.99675985, 4.01852586]), 'std': array([0.25283376, 0.22137621]), 'prob': 0.18618618618618618, 'converge': True}\n",
      "\n",
      "  Cluster 3\n",
      "    Número de elementos en el Cluster 242\n",
      "      Distribución: {'mean': array([5.09411261, 3.0631674 ]), 'std': array([0.82251   , 0.79567349]), 'prob': 0.24224224224224225, 'converge': True}\n",
      "--------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "# Leemos los datos\n",
    "X = np.loadtxt('./data/DS_3Clusters_999Puntos.txt', delimiter='::')\n",
    "\n",
    "# Ejecutamos el k_means\n",
    "np.random.seed(1)\n",
    "clusters, elementos_cluster = gaussian_mixture_models(X=X, num_clusters=3, num_iteraciones=100, verbose=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Vamos a mostrar el estado final de los Clusters y el número de elementos que hay en cada uno de ellos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RESULTADO FINAL:\n",
      "\n",
      "ITERATION -\n",
      "\n",
      "  Cluster 1\n",
      "    Número de elementos en el Cluster 571\n",
      "      Distribución: {'mean': array([2.02788518, 2.0046025 ]), 'std': array([0.37849705, 0.38147472]), 'prob': 0.5715715715715716, 'converge': True}\n",
      "\n",
      "  Cluster 2\n",
      "    Número de elementos en el Cluster 186\n",
      "      Distribución: {'mean': array([1.99675985, 4.01852586]), 'std': array([0.25283376, 0.22137621]), 'prob': 0.18618618618618618, 'converge': True}\n",
      "\n",
      "  Cluster 3\n",
      "    Número de elementos en el Cluster 242\n",
      "      Distribución: {'mean': array([5.09411261, 3.0631674 ]), 'std': array([0.82251   , 0.79567349]), 'prob': 0.24224224224224225, 'converge': True}\n",
      "--------------------------------------------------------------------------------\n"
     ]
    }
   ],
   "source": [
    "print('RESULTADO FINAL:')\n",
    "print_iteration_status(iteracion_num='-', clusters=clusters, elementos_clusters=elementos_cluster)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M5\">5. Resultados</a>\n",
    "\n",
    "\n",
    "* Vamos a continuación a ver las distribuciones de cada una de las variables de los elementos asignados a cada Cluster para ver si el Gaussian Mixture Models ha conseguido extraer las diferentes distribuciones de los datos.\n",
    "\n",
    "\n",
    "* Para ellos vamos a ***asignar cada elemento del Dataset al Cluster que tiene mayor probabilidad de pertenencia usando el modelo generado*** por el Gaussian Mixture Models; es decir,\n",
    "    + Media del Cluster\n",
    "    + Desviación típica del Cluster\n",
    "    + Probabilidad de pertenencia al Cluster\n",
    "    \n",
    "    \n",
    "* Por último vamos a dibujar las distribuciones de los elementos de cada Cluster en el que se puede apreciar como se distinguen las 3 distribuciones normales de cada Cluster por variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Inicializamos una lista para guardar el cluster al que se asigna cada elemento\n",
    "labels = []\n",
    "\n",
    "# Recorremos la lista de elementos y los asignamos al cluster con mayor probabilidad\n",
    "for elem in X:\n",
    "    probs_clusters = np.zeros(len(clusters))\n",
    "    for index, cluster in enumerate(clusters):\n",
    "        prob = 1.0\n",
    "        for i, e in enumerate(elem):\n",
    "            prob *= (math.exp(-0.5 * (math.pow((e - clusters[index]['mean'][i]), 2) /\n",
    "                                      math.pow(clusters[index]['std'][i], 2))) / \n",
    "                                               clusters[index]['std'][i])\n",
    "            probs_clusters[index] = prob * clusters[index]['prob']\n",
    "    labels.append(np.argmax(probs_clusters))\n",
    " \n",
    " # Añadimos una nueva columna en el DataFrame para indicar la etiqueta de cada elemento\n",
    "df['label'] = labels\n",
    "df['label'] = df['label'].apply(lambda x: 'Cluster {}'.format(x+1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Una vez asignados los elementos a cada Cluster, procedemos a dibujar las distribuciones de las variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dibujamos las distribuciones de las 2 variables para cada uno de los Clusters\n",
    "f, axes = plt.subplots(1, 2, figsize=(10, 5), sharex=True)\n",
    "plt_position = [axes[0], axes[1]]\n",
    "for index, col in enumerate(df.columns.drop('label')):\n",
    "    for i in np.sort(df['label'].unique()):\n",
    "        df_plot = df[df['label'] == i][['label', col]] \n",
    "        sns.kdeplot(df_plot[col], shade=True, label=i, ax=plt_position[index])\n",
    "    plt_position[index].title.set_text('Distribución de {}'.format(col))\n",
    "    plt_position[index].set_xlabel('Valor {}'.format(col))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "*Este Notebook ha sido desarrollado por **Ricardo Moya García** y registrado en Safe Creative como ***Atribución-NoComercial-CompartirIgual***.*\n",
    "\n",
    "<img src=\"./imgs/CC_BY-NC-SA.png\" alt=\"CC BY-NC\">"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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