Clustering_no_jerarquico.ipynb

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  "metadata": {
    "colab": {
      "name": "Clustering_no_jerarquico.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyNm3nNkM7RL8pbYSDdrVlE2",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Bastian951/ClusteringPython/blob/master/Clustering_no_jerarquico.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NdN6FIorSUu2"
      },
      "source": [
        "#**Clustering no Jerárquico**\n",
        "\n",
        "El clustering jerárquico es bastante intuitivo y fácil de implementar. En este sentido la clase de métodos no jerárquicos son mas complejos y contra-intuitivos, ademas el número de cluster se debe elegir antes de aplicar el algoritmo. Hay dos ventajas de usar estos métodos\n",
        "\n",
        "- No requieren matriz de distancias. Lo cual ahorra tiempo y memoria, pues para $n$ grande trabajar con una matriz de $(n \\times n)$ es costoso. \n",
        "- En los métodos jerárquicos dos unidades que se separan en 2 clusters no pueden volver a ser unidas en los pasos siguientes. Por lo que los pasos dependen de los pasos anteriores. Lo cual contradice el pensamiento humano. \n",
        "\n",
        "## **K-means**\n",
        "\n",
        "K-means es uno de los algoritmos no jerarquicos mas usados. Puede ser usado cuando todas las variables son cuantitativas. Elige la mejor partición de $n$ unidades en $k$ clusters.  Para definir el concepto de la mejor partición  descomponemos la suma de cuadrados ($T$) en la suma de dos terminos. La suma de cuadrados dentro del cluster ($W$) y la suma de cuadrados entre los clusters ($B$).\n",
        "\n",
        "$$T = W+B$$\n",
        "\n",
        "- $\\displaystyle T = \\sum_{i=1}^n\\sum_{j=1}^{p} (x_{ij}-\\bar{x}_j)^2$\n",
        "- $\\displaystyle W = \\sum_{g=1}^k W_g$ con $\\displaystyle  W_g = \\sum_{i=1}^{n_g}\\sum_{j=1}^p(x_{ij}-\\bar{x}_{ij})^2$\n",
        "- $\\displaystyle B = \\sum_{g=1}^{k}n_g(\\bar{x}_{gj}-\\bar{x}_j)^2$\n",
        "\n",
        "$W$ permite evaluar la calidad de la partición, se sigue que la mejor partición se obtiene de \n",
        "\n",
        "$$\\min W$$ o de forma equivalente \n",
        "\n",
        "$$\\max B$$\n",
        "\n",
        "Se puede expresar de manera equivalente como un problema de optimización con restricciones.\n",
        "\n",
        "$$\\min_{\\mathbf{U,H}} \\sum_{i=1}^n\\sum_{g=1}^k\\sum_{j=1}^p u_{ig}(x_{ij}-h_{gj})^2= \\sum_{i=1}^n\\sum_{g=1}^k u_{ig}d^2(\\mathbf{x}_i, \\mathbf{h}_g)$$\n",
        "\n",
        "$$sa \\hspace{1cm} u_{ig} \\in \\{0,1 \\},\\hspace{1cm} i=1,2,\\cdots,n \\hspace{1cm} g = 1,2,\\cdots, k$$\n",
        "\n",
        "$$\\sum_{g=1}^k u_{ig} = 1,\\hspace{1cm} i=1,2,\\cdots,n $$\n",
        "\n",
        "Donde $U$ de orden $(n \\times k)$ es una matriz binaria donde cada fila suma 1. La fila \n",
        "$n$ toma el valor 1 en la columna $g$ si el valor $n-esimo$ pertenece al cluster $g$. La matriz $H$ es la matriz de centroides $(k \\times p)$ con filas $(h_{g1},\\cdots, h_{gp}), g=1,2,\\cdots,k$. \n",
        "\n",
        "La solución óptima se obtiene con el siguiente algoritmo iterativo\n",
        "\n",
        "1. Se eligen $k$ centroides (aleatoria o racionalmente). Es decir, se escoge la matriz de centroides $H$\n",
        "2. Dado $H$ se asigna a cada unidad el cluster que tiene distancia minima al centroide \n",
        "\n",
        "$$u_{ig} = \\left\\{\\begin{matrix}  \\displaystyle 1,& \\text{ si } g=arg\\min_{g'=1,\\cdots,k}\\, d^2(\\mathbf{x}_i, \\mathbf{h}_{g'}) \\\\ 0, &\\text{ otro caso }\\end{matrix}\\right.$$\n",
        "para $i=1,2,\\cdots, n$ y $g=1,2,\\cdots,k$.\n",
        "3. Dado $U$, calculamos los centroides\n",
        "\n",
        "$$h_g = \\frac{\\displaystyle \\sum_{i=1}^n u_{ig}\\mathbf{x}_i}{\\displaystyle \\sum_{i=1}^n u_{ig}}$$\n",
        "\n",
        "4. Repetimos los pasos 2 y 3 hasta que no haya cambios en 2 iteraciones. \n",
        "\n",
        "Podemos relajar el criterio de convergencia fijando un número máximo de iteraciones. Notemos que la convergencia no asegura que encontramos la partición que minimiza $W$, por lo que es común realizar el algoritmo mas de una vez con distintas matrices iniciales. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Xo45PB-TTj84"
      },
      "source": [
        "## **K-means en Sklearn**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T8hx2IZyw4LT"
      },
      "source": [
        "from sklearn.cluster import KMeans\n",
        "from sklearn.datasets import load_breast_cancer\n",
        "from sklearn.model_selection import train_test_split \n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.metrics import confusion_matrix\n",
        "from sklearn.metrics import accuracy_score\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "data = load_breast_cancer()\n",
        "X = data.data\n",
        "y = data.target\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.4, random_state=0)\n",
        "\n",
        "sc = StandardScaler()\n",
        "# Los datos son reescalado con respecto a los datos de entrenamiento\n",
        "sc.fit(X_train) \n",
        "# Tanto el conjunto de entrenamiento como el de test son reescalados\n",
        "Z_train = sc.transform(X_train)\n",
        "Z_test = sc.transform(X_test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "G_kx-eXWT-da"
      },
      "source": [
        "kmeans = KMeans(n_clusters=2, random_state=0).fit(Z_train)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3tVLoLYUUUJt"
      },
      "source": [
        "y_pred = kmeans.predict(Z_test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Gy79NtjIUYOJ",
        "outputId": "78d8900d-c54c-48d1-a30b-faa5fdb97a1b"
      },
      "source": [
        "print(\"accuracy train\",round(accuracy_score(y_train,kmeans.predict(Z_train)),3))\n",
        "print(\"accuracy test\",round(accuracy_score(y_test, y_pred),3))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "accuracy train 0.909\n",
            "accuracy test 0.904\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vKFi07CfUmKp",
        "outputId": "5f5de83e-7922-49a4-e73f-da13868c8d73"
      },
      "source": [
        "confusion_matrix(y_test, y_pred)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 68,  15],\n",
              "       [  7, 138]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rW-IGTuhWK17"
      },
      "source": [
        "# **Elegir número de clusters**\n",
        "Este método utiliza los valores de la inercia obtenidos tras aplicar el K-means a diferente número de Clusters (desde 1 a N Clusters), siendo la inercia la suma de las distancias al cuadrado de cada objeto del Cluster a su centroide.\n",
        "\n",
        "En esta gráfica se debería de apreciar un cambio brusco en la evolución de la inercia, teniendo la línea representada una forma similar a la de un brazo y su codo. El punto en el que se observa ese cambio brusco en la inercia nos dirá el número óptimo de Clusters a seleccionar para ese data set; o dicho de otra manera: el punto que representaría al codo del brazo será el número óptimo de Clusters para ese data set. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "VsZqne56U01p",
        "outputId": "4bcda6fc-84a4-4a12-a028-86922c29a36c"
      },
      "source": [
        "Nc = range(1, 20)\n",
        "kmeans = [KMeans(n_clusters=i) for i in Nc]\n",
        "score = [kmeans[i].fit(Z_train).inertia_ for i in range(len(kmeans))]\n",
        "plt.plot(Nc,score)\n",
        "plt.xlabel('Number of Clusters')\n",
        "plt.ylabel('Score')\n",
        "plt.title('Regla del codo')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LbjZg6RSYHLP"
      },
      "source": [
        "## **K-medoids**"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aYOc7EABY7Hh"
      },
      "source": [
        "#pip install scikit-learn-extra\n",
        "#conda install -c conda-forge scikit-learn-extra"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2S02EPuLYYca"
      },
      "source": [
        "from sklearn_extra.cluster import KMedoids"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yZPN1DcvY1aM"
      },
      "source": [
        "kmedoids = KMedoids(n_clusters=2, random_state=0).fit(Z_train)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qIk04fwTZEJr"
      },
      "source": [
        "y_pred_medoids = kmedoids.predict(Z_test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TYEAxinVZLfk",
        "outputId": "67a36f71-8eb0-4918-8445-85ff3db4dcb5"
      },
      "source": [
        "print(\"accuracy train\",round(accuracy_score(y_train,kmedoids.predict(Z_train)),3))\n",
        "print(\"accuracy test\",round(accuracy_score(y_test, y_pred_medoids),3))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "accuracy train 0.941\n",
            "accuracy test 0.899\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "chSdGrVrZSYr",
        "outputId": "7a6109a9-87c7-4722-fc4e-7c2a88769536"
      },
      "source": [
        "confusion_matrix(y_test, y_pred_medoids)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 69,  14],\n",
              "       [  9, 136]])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tmMUjkGrZlk3"
      },
      "source": [
        "# **Scatter plot**\n",
        "\n",
        "Para graficar los puntos y colorear por cluster podemos utilizar PCA y plotear las dos primeras componentes principales. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o3LAFIZwZVp2"
      },
      "source": [
        "from sklearn.decomposition import PCA\n",
        "import pandas as pd\n",
        "\n",
        "pca = PCA(n_components=2)\n",
        "df_fit = pca.fit(X_train)\n",
        "pca_train = df_fit.transform(X_train)\n",
        "pca_train = pd.DataFrame(pca_train)\n",
        "pca_train.columns = ['P1', 'P2']"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "EIeGI0hPZnrL",
        "outputId": "cca2abc5-5279-4661-cb8b-f0c73ddff842"
      },
      "source": [
        "plt.scatter(pca_train['P1'], pca_train['P2'], c = kmeans.predict(Z_train), cmap ='rainbow')\n",
        "plt.title(\"Scatter Plot - K-means\")\n",
        "plt.show() "
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wqcv6pRdZua0"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}