38_Clustering_K_Means.ipynb

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    "# 38 - Clustering: K-Means\n",
    "\n",
    "\n",
    "* En este Notebook vamos a ver como solucionar problemas de ***Clusterización con la técnica del K-Means*** y como se implementa.\n",
    "\n",
    "\n",
    "* Vamos a tratar los siguientes puntos:\n",
    "<span></span><br>\n",
    "    1. [Clustering](#M1)\n",
    "<span></span><br>\n",
    "    2. [K-Means](#M2)\n",
    "<span></span><br>\n",
    "    3. [Pseudocódigo del K-Means](#M3)\n",
    "<span></span><br>\n",
    "    4. [Implementación: K-Means](#M4)\n",
    "<span></span><br>\n",
    "    5. [Ejemplo de Clustering](#M5)\n",
    "<span></span><br>\n",
    "    6. [Resultados](#M6)\n",
    "\n",
    "\n",
    "<hr>\n",
    "\n",
    "\n",
    "\n",
    "# <a name=\"M1\">1. Clustering</a>\n",
    "\n",
    "\n",
    "* El ***Clustering*** es una ***tarea***; dentro del ***aprendizaje NO SUPERVISADO***, que consiste en ***agrupar un conjunto de objetos (no etiquetados) en subconjuntos de objetos llamados Clusters***.\n",
    "\n",
    "\n",
    "* ***Cada Cluster está formado por una colección de objetos que son similares (o se consideran similares) entre sí, pero que son distintos respecto a los objetos de otros Clusters***.\n",
    "\n",
    "\n",
    "<img src=\"./imgs/40_01_cl.png\" style=\"width: 500px;\"/>\n",
    "\n",
    "\n",
    "* Para el ***Clustering, solo disponemos de un conjunto de datos de entrada (aprendizaje NO SUPEERVISADO)***, sobre los que ***debemos obtener información sobre la estructura del dominio de salida***, que es una información de la cual no se dispone.\n",
    "\n",
    "\n",
    "* En el Clustering definimos:\n",
    "<span></span><br><br>\n",
    "    + **<span style=\"font-size:18px\">Cluster</span>**: Conjunto de objetos que son similares entre sí.\n",
    "<span></span><br><br>  \n",
    "    + **<span style=\"font-size:18px\">Clustering</span>**: Tarea de dividir un conjunto de objetos en subconjuntos de objetos (Clusters) similares entre sí.\n",
    "\n",
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M2\">2. K-Means</a>\n",
    "\n",
    "\n",
    "* El ***K-Means es un método de Clustering que separa <span style=\"color:red\">‘K’ grupos de objetos</span> (Clusters) de similar varianza, minimizando un concepto conocido como inercia.***\n",
    "\n",
    "\n",
    "<img src=\"./imgs/40_02_cl.png\" style=\"width: 700px;\"/>\n",
    "\n",
    "\n",
    "* La ***Inercia es la suma de las distancias al cuadrado de cada objeto del Cluster a un punto ‘μ’ conocido como <span style=\"color:red\">Centroide</span>*** (punto medio de todos los objetos del Cluster).\n",
    "\n",
    "<span style=\"font-size:20px\">$$Inercia = \\sum_{i=0}^{N} \\left \\| x_i - \\mu  \\right \\|^{2}$$</span>\n",
    "\n",
    "\n",
    "* El algoritmo del K-Means tiene como objetivo ***elegir ‘K’ centroides que reduzcan al mínimo la inercia***:\n",
    "\n",
    "<span style=\"font-size:20px\">$$\\underset{K}{argmin} \\sum_{j=1}^{k}\\sum_{x_i \\in  c_j}\\left \\| x_i - \\mu  \\right \\|^{2}$$</span>\n",
    "\n",
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M3\">3. Pseudocódigo del K-Means</a>\n",
    "\n",
    "\n",
    "* El algoritmo del K-Means funciona de la siguiente manera:\n",
    "\n",
    "    1. ***Inicialización***: Elige un centroide para cada uno de los ‘k’ Cluster. Lo puede elegir bien de forma aleatoria, eligiendo ‘k’ puntos del dataset al azar, etc.\n",
    "<span></span><br><br>\n",
    "    2. ***Loop***: Asignación-Actualización hasta converger:\n",
    "<span></span><br><br>\n",
    "        * ***Asignación***: Se asigna cada objeto del dataset al Cluster más cercano, aplicando alguna medida de distancia (como por ejemplo la distancia euclídea) entre el objeto y el centroide del Cluster.\n",
    "<span></span><br><br>\n",
    "        <span style=\"font-size:20px\">$$d_e(X,\\mu ) = \\sqrt{\\sum_{i=1}^{n} (x_i - \\mu_i)^2}$$</span>\n",
    "<span></span><br><br>\n",
    "        * ***Actualización***: Calcula los nuevos centroides, haciendo la media de los objetos que forman el Cluster.\n",
    "<span></span><br><br>\n",
    "        <span style=\"font-size:20px\">$$\\mu = \\frac{1}{N} \\sum_{j=1}^{N} x_j $$</span>\n",
    "\n",
    "\n",
    "\n",
    "* Un ejemplo visual de como se haría el Clustering para agrupar elementos definidos por dos variables (coordenadas), sería:\n",
    "\n",
    "<img src=\"./imgs/40_03_cl.png\" style=\"width: 900px;\"/>\n",
    "\n",
    "\n",
    "* Veamos a continuación el Pseudocódigo:\n",
    "\n",
    "\n",
    "```python\n",
    "num_clusters = N\n",
    "num_iteraciones = 100\n",
    "condicion_parada = False\n",
    "\n",
    "# Inicializamos los 'N' Clusters: por ejemplo asinando como centroides 'N' elementos seleccionados al azar\n",
    "centroides_clusters = random_list(num_clusters)\n",
    "\n",
    "it_counter\n",
    "while not condicion_parada and it_counter < num_iteraciones:\n",
    "    \n",
    "    # Creo una variable para guardar el estado de los Clusters Anteriores\n",
    "    centroides_old = centroides_clusters\n",
    "    \n",
    "    # Actualización\n",
    "    for elemento in dataset:\n",
    "        distancia_centroides = lista(num_clusters)\n",
    "        for index, centroide in centroides_old:\n",
    "            distancia_centroides[index] = distancia_euclidea(elemento, centroide)\n",
    "        elementos_clusters[argmin(distancia_centroides)].append(elemento)\n",
    "    \n",
    "    \n",
    "    # Asignacion\n",
    "    for index, centroide_cluster in centroides_clusters:\n",
    "        centroides_clusters = avg(elementos_clusters[index])\n",
    "        \n",
    "    it_counter+= 1\n",
    "\n",
    "```\n",
    "\n",
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M4\">4. Implementación: K-Means</a>\n",
    "\n",
    "\n",
    "* En el siguiente fragmento de código está implementado el ***K-Means***, siguiendo el Pseudocódigo mostrado anteriormente junto con alguna lógica programática adicional.\n",
    "\n"
   ]
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    "import numpy as np\n",
    "from scipy.spatial import distance\n",
    "\n",
    "def print_iteration_status(iteracion_num, centroides_clusters, elementos_clusters):\n",
    "    \"\"\"\n",
    "    Función que imprime por pantalla el estado de los Clsuters por iteracion\n",
    "        - iteracion_num: número del epoch.\n",
    "        - centroides_clusters: Valores de los centroides del Cluster\n",
    "        - elementos_clusters: Elementos que hay en cada Cluster\n",
    "    \"\"\"\n",
    "    print('\\nITERATION {}'.format(iteracion_num))\n",
    "    for index, elem in enumerate(centroides_clusters):\n",
    "        print('\\tCluster {}'.format(index + 1))\n",
    "        print('\\t\\tNúmero de elementos en el Cluster {}'.format(len(elementos_clusters[index])))\n",
    "        print('\\t\\tCentroide: {}'.format(elem))\n",
    "\n",
    "\n",
    "def k_means(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 centroides de los Clusters de forma aleatoria\n",
    "    centroides_clusters = np.array([X[i] for i in np.random.choice(X.shape[0], 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",
    "        centroides_clusters_old = centroides_clusters.copy()\n",
    "\n",
    "        # Asignacion\n",
    "        for elem in X:\n",
    "            distancia_centroides = np.zeros(len(centroides_clusters_old))\n",
    "            for index, centroide in enumerate(centroides_clusters_old):\n",
    "                distancia_centroides[index] = distance.euclidean(elem, centroide)\n",
    "            elementos_clusters[np.argmin(distancia_centroides)].append(elem)\n",
    "\n",
    "        # Actualización\n",
    "        for index, centroide in enumerate(centroides_clusters_old):\n",
    "            centroides_clusters[index] = np.asarray([sum(i) for i in zip(*elementos_clusters[index])]) / len(\n",
    "                elementos_clusters[index])\n",
    "\n",
    "        # Condición de parada, si los Nuevos centroides son iguales que los anteriores\n",
    "        converge = [np.array_equal(centroides_clusters[index], centroides_clusters_old[index])\n",
    "                    for index, elem in enumerate(centroides_clusters)].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, centroides_clusters, elementos_clusters)\n",
    "    \n",
    "    return centroides_clusters, elementos_clusters"
   ]
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    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M5\">5. Ejemplo de Clustering</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",
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       "           X1        X2\n",
       "462  1.987217  2.075017\n",
       "160  1.579107  1.683219\n",
       "651  1.729299  3.057628\n",
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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)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "* Representando estos datos en una gráfica de dispersión, podemos distinguir 3 grupos (clusters) de puntos."
   ]
  },
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   "cell_type": "code",
   "execution_count": 3,
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline \n",
    "\n",
    "sns.scatterplot(x=\"X1\", y=\"X2\", data = df)"
   ]
  },
  {
   "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",
      "\tCluster 1\n",
      "\t\tNúmero de elementos en el Cluster 561\n",
      "\t\tCentroide: [1.968402   2.15292836]\n",
      "\tCluster 2\n",
      "\t\tNúmero de elementos en el Cluster 147\n",
      "\t\tCentroide: [2.00243953 4.09445674]\n",
      "\tCluster 3\n",
      "\t\tNúmero de elementos en el Cluster 291\n",
      "\t\tCentroide: [4.68543947 2.83052368]\n",
      "\n",
      "ITERATION 2\n",
      "\tCluster 1\n",
      "\t\tNúmero de elementos en el Cluster 572\n",
      "\t\tCentroide: [2.03174321 2.0025339 ]\n",
      "\tCluster 2\n",
      "\t\tNúmero de elementos en el Cluster 187\n",
      "\t\tCentroide: [1.99921067 4.01443525]\n",
      "\tCluster 3\n",
      "\t\tNúmero de elementos en el Cluster 240\n",
      "\t\tCentroide: [5.10868962 3.07171485]\n",
      "\n",
      "ITERATION 3\n",
      "\tCluster 1\n",
      "\t\tNúmero de elementos en el Cluster 574\n",
      "\t\tCentroide: [2.04172578 1.99650307]\n",
      "\tCluster 2\n",
      "\t\tNúmero de elementos en el Cluster 191\n",
      "\t\tCentroide: [2.02022231 4.00032196]\n",
      "\tCluster 3\n",
      "\t\tNúmero de elementos en el Cluster 234\n",
      "\t\tCentroide: [5.14650411 3.09105165]\n",
      "\n",
      "ITERATION 4\n",
      "\tCluster 1\n",
      "\t\tNúmero de elementos en el Cluster 575\n",
      "\t\tCentroide: [2.04429024 1.99783017]\n",
      "\tCluster 2\n",
      "\t\tNúmero de elementos en el Cluster 191\n",
      "\t\tCentroide: [2.02022231 4.00032196]\n",
      "\tCluster 3\n",
      "\t\tNúmero de elementos en el Cluster 233\n",
      "\t\tCentroide: [5.15350073 3.09247426]\n",
      "\n",
      "ITERATION 5\n",
      "\tCluster 1\n",
      "\t\tNúmero de elementos en el Cluster 575\n",
      "\t\tCentroide: [2.04429024 1.99783017]\n",
      "\tCluster 2\n",
      "\t\tNúmero de elementos en el Cluster 191\n",
      "\t\tCentroide: [2.02022231 4.00032196]\n",
      "\tCluster 3\n",
      "\t\tNúmero de elementos en el Cluster 233\n",
      "\t\tCentroide: [5.15350073 3.09247426]\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",
    "centroides, elementos_cluster = k_means(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",
      "\tCluster 1\n",
      "\t\tNúmero de elementos en el Cluster 575\n",
      "\t\tCentroide: [2.04429024 1.99783017]\n",
      "\tCluster 2\n",
      "\t\tNúmero de elementos en el Cluster 191\n",
      "\t\tCentroide: [2.02022231 4.00032196]\n",
      "\tCluster 3\n",
      "\t\tNúmero de elementos en el Cluster 233\n",
      "\t\tCentroide: [5.15350073 3.09247426]\n"
     ]
    }
   ],
   "source": [
    "print('RESULTADO FINAL:')\n",
    "print_iteration_status(iteracion_num='-', centroides_clusters=centroides, elementos_clusters=elementos_cluster)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "\n",
    "# <a name=\"M6\">6. Resultados</a>\n",
    "\n",
    "\n",
    "* Podemos observar como el K-Means no ha agrupado los elementos que son similares entre sí en un mismo Cluster.\n",
    "    - Cluster 1: Rojo\n",
    "    - Cluster 2: Azul\n",
    "    - Cluster 3: Verde"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Creamos la gráfica\n",
    "fig, ax =  plt.subplots(figsize=(8, 6))\n",
    "ax.set_title('Clusters')\n",
    "ax.set_xlabel('X1')\n",
    "ax.set_ylabel('X2')\n",
    "\n",
    "# Dibujamos los elementos de cada Cluster\n",
    "plt.plot(np.array(elementos_cluster[0])[:, 0], np.array(elementos_cluster[0])[:, 1], linestyle='None', color='red', marker='.')\n",
    "plt.plot(np.array(elementos_cluster[1])[:, 0], np.array(elementos_cluster[1])[:, 1], linestyle='None', color='blue', marker='.')\n",
    "plt.plot(np.array(elementos_cluster[2])[:, 0], np.array(elementos_cluster[2])[:, 1], linestyle='None', color='green', marker='.')\n",
    "\n",
    "# Dibujamos los centroides\n",
    "plt.plot(np.array(centroides[:, 0]), np.array(centroides[:, 1]), 'o', color='black', markersize=10)\n",
    "plt.show()"
   ]
  },
  {
   "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",
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