ClassicalMachineLearning.ipynb

classicalmachinelearning.ipynb

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      "name": "ClassicalMachineLearning.ipynb",
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      "name": "python3",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/Saroramath/4b1fafbc8d939ea04aad703d9f186c94/classicalmachinelearning.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4REcJBkjFq4s"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "import seaborn as sns"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gADiALEkF57w"
      },
      "source": [
        "### Linear regression."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YPoz4S98J6J7"
      },
      "source": [
        "We illustrate linear regression with the classical Boston house price dataset"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yKhJYO4SF9iu"
      },
      "source": [
        "from sklearn.datasets import load_boston\n",
        "\n",
        "# Load in the dataset\n",
        "ds = load_boston()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0MYZ1CNiKwXT"
      },
      "source": [
        "This will load in the data as a dictionary. The keys of the dictionary are as follows:\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "m9rttL4QLLA1",
        "outputId": "6b5163f9-923a-4f76-dcc9-f7c058ad675c"
      },
      "source": [
        "ds.keys()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_keys(['data', 'target', 'feature_names', 'DESCR', 'filename'])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DvEYmECDL1Qe"
      },
      "source": [
        "Description of the dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7b4nXGblLz0O",
        "outputId": "58fe37c5-74eb-46db-869f-2c932fde394d"
      },
      "source": [
        "print(ds.DESCR)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            ".. _boston_dataset:\n",
            "\n",
            "Boston house prices dataset\n",
            "---------------------------\n",
            "\n",
            "**Data Set Characteristics:**  \n",
            "\n",
            "    :Number of Instances: 506 \n",
            "\n",
            "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
            "\n",
            "    :Attribute Information (in order):\n",
            "        - CRIM     per capita crime rate by town\n",
            "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
            "        - INDUS    proportion of non-retail business acres per town\n",
            "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
            "        - NOX      nitric oxides concentration (parts per 10 million)\n",
            "        - RM       average number of rooms per dwelling\n",
            "        - AGE      proportion of owner-occupied units built prior to 1940\n",
            "        - DIS      weighted distances to five Boston employment centres\n",
            "        - RAD      index of accessibility to radial highways\n",
            "        - TAX      full-value property-tax rate per $10,000\n",
            "        - PTRATIO  pupil-teacher ratio by town\n",
            "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
            "        - LSTAT    % lower status of the population\n",
            "        - MEDV     Median value of owner-occupied homes in $1000's\n",
            "\n",
            "    :Missing Attribute Values: None\n",
            "\n",
            "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
            "\n",
            "This is a copy of UCI ML housing dataset.\n",
            "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
            "\n",
            "\n",
            "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
            "\n",
            "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
            "prices and the demand for clean air', J. Environ. Economics & Management,\n",
            "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
            "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
            "pages 244-261 of the latter.\n",
            "\n",
            "The Boston house-price data has been used in many machine learning papers that address regression\n",
            "problems.   \n",
            "     \n",
            ".. topic:: References\n",
            "\n",
            "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
            "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Q-w3wohNM91n"
      },
      "source": [
        "Now convert the data into a pandas DataFrame:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "0LsTuDpqMZAd",
        "outputId": "e13f35da-4a85-4478-bfef-dba22013c619"
      },
      "source": [
        "df = pd.DataFrame(ds.data)\n",
        "df.columns = ds.feature_names\n",
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CRIM</th>\n",
              "      <th>ZN</th>\n",
              "      <th>INDUS</th>\n",
              "      <th>CHAS</th>\n",
              "      <th>NOX</th>\n",
              "      <th>RM</th>\n",
              "      <th>AGE</th>\n",
              "      <th>DIS</th>\n",
              "      <th>RAD</th>\n",
              "      <th>TAX</th>\n",
              "      <th>PTRATIO</th>\n",
              "      <th>B</th>\n",
              "      <th>LSTAT</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1.0</td>\n",
              "      <td>296.0</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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            ],
            "text/plain": [
              "      CRIM    ZN  INDUS  CHAS    NOX  ...  RAD    TAX  PTRATIO       B  LSTAT\n",
              "0  0.00632  18.0   2.31   0.0  0.538  ...  1.0  296.0     15.3  396.90   4.98\n",
              "1  0.02731   0.0   7.07   0.0  0.469  ...  2.0  242.0     17.8  396.90   9.14\n",
              "2  0.02729   0.0   7.07   0.0  0.469  ...  2.0  242.0     17.8  392.83   4.03\n",
              "3  0.03237   0.0   2.18   0.0  0.458  ...  3.0  222.0     18.7  394.63   2.94\n",
              "4  0.06905   0.0   2.18   0.0  0.458  ...  3.0  222.0     18.7  396.90   5.33\n",
              "\n",
              "[5 rows x 13 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mfru5XP2NUSL"
      },
      "source": [
        "As the price to be predicted is stored in the `ds.target` variable, we need to add it to our DataFrame:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "efZ7syThNjt6",
        "outputId": "78fdf5ea-de04-4d93-959d-d670a7bd8733"
      },
      "source": [
        "df['Price'] = ds.target\n",
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>CRIM</th>\n",
              "      <th>ZN</th>\n",
              "      <th>INDUS</th>\n",
              "      <th>CHAS</th>\n",
              "      <th>NOX</th>\n",
              "      <th>RM</th>\n",
              "      <th>AGE</th>\n",
              "      <th>DIS</th>\n",
              "      <th>RAD</th>\n",
              "      <th>TAX</th>\n",
              "      <th>PTRATIO</th>\n",
              "      <th>B</th>\n",
              "      <th>LSTAT</th>\n",
              "      <th>Price</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.00632</td>\n",
              "      <td>18.0</td>\n",
              "      <td>2.31</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.538</td>\n",
              "      <td>6.575</td>\n",
              "      <td>65.2</td>\n",
              "      <td>4.0900</td>\n",
              "      <td>1.0</td>\n",
              "      <td>296.0</td>\n",
              "      <td>15.3</td>\n",
              "      <td>396.90</td>\n",
              "      <td>4.98</td>\n",
              "      <td>24.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.02731</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>6.421</td>\n",
              "      <td>78.9</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>396.90</td>\n",
              "      <td>9.14</td>\n",
              "      <td>21.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.02729</td>\n",
              "      <td>0.0</td>\n",
              "      <td>7.07</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.469</td>\n",
              "      <td>7.185</td>\n",
              "      <td>61.1</td>\n",
              "      <td>4.9671</td>\n",
              "      <td>2.0</td>\n",
              "      <td>242.0</td>\n",
              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "      <td>34.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>0.03237</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>6.998</td>\n",
              "      <td>45.8</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>394.63</td>\n",
              "      <td>2.94</td>\n",
              "      <td>33.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>0.06905</td>\n",
              "      <td>0.0</td>\n",
              "      <td>2.18</td>\n",
              "      <td>0.0</td>\n",
              "      <td>0.458</td>\n",
              "      <td>7.147</td>\n",
              "      <td>54.2</td>\n",
              "      <td>6.0622</td>\n",
              "      <td>3.0</td>\n",
              "      <td>222.0</td>\n",
              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
              "      <td>36.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "      CRIM    ZN  INDUS  CHAS    NOX  ...    TAX  PTRATIO       B  LSTAT  Price\n",
              "0  0.00632  18.0   2.31   0.0  0.538  ...  296.0     15.3  396.90   4.98   24.0\n",
              "1  0.02731   0.0   7.07   0.0  0.469  ...  242.0     17.8  396.90   9.14   21.6\n",
              "2  0.02729   0.0   7.07   0.0  0.469  ...  242.0     17.8  392.83   4.03   34.7\n",
              "3  0.03237   0.0   2.18   0.0  0.458  ...  222.0     18.7  394.63   2.94   33.4\n",
              "4  0.06905   0.0   2.18   0.0  0.458  ...  222.0     18.7  396.90   5.33   36.2\n",
              "\n",
              "[5 rows x 14 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kVvS144gN9wW"
      },
      "source": [
        "Now lets plot a heat map of the data correlation:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "G6qNOaxVOCdf",
        "outputId": "c980c058-baa7-4e0d-a1c2-2cfc5917f53e"
      },
      "source": [
        "corr = df.corr()\n",
        "\n",
        "ax = sns.heatmap(\n",
        "    corr, \n",
        "    vmin=-1, vmax=1, center=0,\n",
        "    cmap=sns.diverging_palette(20, 220, n=200),\n",
        "    square=True\n",
        ")\n",
        "ax.set_xticklabels(\n",
        "    ax.get_xticklabels(),\n",
        "    rotation=45,\n",
        "    horizontalalignment='right'\n",
        ");"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1anGrCroPYlL"
      },
      "source": [
        "There is a quite strong positive correlation between the Nr. of rooms and the price of the house, so let's explore this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dMqdGWfQOWQX"
      },
      "source": [
        "rooms = df['RM']\n",
        "price = df['Price']"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "TMT7TrjvOwHb",
        "outputId": "835d3ba3-b881-4052-8d04-d92caa1a1685"
      },
      "source": [
        "plt.plot(rooms, price,'.')\n",
        "plt.xlabel('Average nr. of rooms')\n",
        "plt.ylabel('Price of house')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Price of house')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dld7wpRbPk92"
      },
      "source": [
        "Let's do simple univariate linear regression on this:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8PVzYZfiRWhr"
      },
      "source": [
        "from sklearn import linear_model\n",
        "from sklearn.metrics import mean_squared_error, r2_score\n",
        "from sklearn.model_selection import train_test_split"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xePElVp1SxTX"
      },
      "source": [
        "`LinearRegression` expects two-dimensional inputs (i.e. regression with more than one feature), that is, we have to add one extra dimension to our data:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X4pkUvEsS9Et"
      },
      "source": [
        "rooms = np.expand_dims(rooms, axis=1)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "od2FGY7VR9r0"
      },
      "source": [
        "First we have to split the data into training and test data (e.g. 80% to 20%):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VGvXtTtnSDc9"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(rooms, price, test_size=0.2)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1ocQXCyjRcz3",
        "outputId": "99db1de1-94b3-40b0-c525-851b0da3d58a"
      },
      "source": [
        "# This is the linear regression object\n",
        "univariate_linear_model = linear_model.LinearRegression() \n",
        "\n",
        "# Train the model \n",
        "univariate_linear_model.fit(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "A5TaDkaJTHcc"
      },
      "source": [
        "Now we can evaluate the model on the test data and make predictions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XgdEnCAtTeJa",
        "outputId": "dc8dd74f-ae34-463e-fb11-fb3b1ff40c58"
      },
      "source": [
        "# Make predictions and evaluate the scores\n",
        "y_pred = univariate_linear_model.predict(X_test)\n",
        "\n",
        "# The mean squared error\n",
        "print('Mean squared error: %.2f'\n",
        "      % mean_squared_error(y_test, y_pred))\n",
        "# The coefficient of determination: 1 is perfect prediction\n",
        "print('Coefficient of determination: %.2f'\n",
        "      % r2_score(y_test, y_pred))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean squared error: 37.72\n",
            "Coefficient of determination: 0.55\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LS3bsf4oT2-X"
      },
      "source": [
        "And plot the results:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "RgqeY6y0T4R6",
        "outputId": "f254dc8f-5ae3-4c29-807d-7e9b35316865"
      },
      "source": [
        "plt.plot(X_test, y_test, '.')\n",
        "plt.plot(X_test, y_pred, color='k', linewidth=1)\n",
        "plt.xlabel('Average nr. of rooms')\n",
        "plt.ylabel('Price of house')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Price of house')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ceY89YpyURUI"
      },
      "source": [
        "### Logistic regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JP0CXHChUX5s"
      },
      "source": [
        "Here we illustrate basic logistic regression using the `sklearn` handwritten digit dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E8BSrdkrHrSV"
      },
      "source": [
        "from sklearn.datasets import load_digits\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "from sklearn.metrics import accuracy_score"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gzUdQ8x4Ijai"
      },
      "source": [
        "There are ten classes (digits 0 through 9), but for the sake of illustration, we only load in two digits here to do standard binary classification using logistic regression."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "udTZF18jHlD-"
      },
      "source": [
        "X, y = load_digits(n_class=2, return_X_y=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "y50YPj-VKMCO"
      },
      "source": [
        "Each image is 8x8 pixels stacked as a 64-dimensional feature vector:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "M-d27aGMI7L-",
        "outputId": "3419b0bb-650c-4f39-f2f7-b9e5bb3b62f2"
      },
      "source": [
        "print(X.shape)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(360, 64)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "_jKgaNSqBI9W",
        "outputId": "00f4bf64-4951-4d66-c615-f855c4dde423"
      },
      "source": [
        "X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 0.,  0.,  5., ...,  0.,  0.,  0.],\n",
              "       [ 0.,  0.,  0., ..., 10.,  0.,  0.],\n",
              "       [ 0.,  0.,  1., ...,  3.,  0.,  0.],\n",
              "       ...,\n",
              "       [ 0.,  0.,  5., ...,  8.,  1.,  0.],\n",
              "       [ 0.,  0.,  6., ...,  4.,  0.,  0.],\n",
              "       [ 0.,  0.,  6., ...,  6.,  0.,  0.]])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 591
        },
        "id": "XC-HJqpUI0UX",
        "outputId": "b894225c-8532-4b6b-b968-f4986dcca35b"
      },
      "source": [
        "# Plot some elements of the dataset\n",
        "plt.figure(figsize=(10,10))\n",
        "for i in range(1,17):\n",
        "  plt.subplot(4,4,i)\n",
        "  X_im = np.reshape(X[i,],[8,8])\n",
        "  plt.imshow(X_im, cmap=plt.cm.gray_r)\n",
        "  plt.axis('off')\n",
        "  plt.title('Label: {}'.format(y[i]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 16 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c8d4TX9pKi3g"
      },
      "source": [
        "We again split the dataset into training and test subsets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "u54nPPAnKS9v"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, \n",
        "                                                    shuffle=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cxIQsLZwOC6v"
      },
      "source": [
        "Now scale the features to be in the range [0,1]:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qpFfAZupOAkU"
      },
      "source": [
        "scaler = MinMaxScaler()\n",
        "X_train = scaler.fit_transform(X_train)\n",
        "X_test = scaler.transform(X_test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5OSFI4_dL5Rn"
      },
      "source": [
        "Now create the classifier and fit it on the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OxE-GIlaL88j",
        "outputId": "7272fbef-1141-4f8b-889f-b09b91270975"
      },
      "source": [
        "logistic_regression = LogisticRegression()\n",
        "logistic_regression.fit(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
              "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
              "                   multi_class='auto', n_jobs=None, penalty='l2',\n",
              "                   random_state=None, solver='lbfgs', tol=0.0001, verbose=0,\n",
              "                   warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AHPFFmMHMHn6"
      },
      "source": [
        "Predict on the test data and evaluate accuracy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8wI3wp1wMFfo",
        "outputId": "2de931f1-603a-44c1-9752-13cf7cc53e98"
      },
      "source": [
        "y_pred = logistic_regression.predict(X_test)\n",
        "acc = accuracy_score(y_test, y_pred)\n",
        "print('Accuracy on the test dataset: {}'.format(acc))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy on the test dataset: 1.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gK7_RE_XO-37"
      },
      "source": [
        "### Support vector machines"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "39VMQOTsjdmM"
      },
      "source": [
        "Support vector machines can also be used for multi-class classification. Here one implements either a *one-vs-one* approach where a total of `n_classes * (n_classes - 1)/2` classifiers are constructed and each one trained on data from two classes; or one implements a *one-vs-the-rest* strategy, in which case `n_classes` models have to be trained.\n",
        "\n",
        "Sklearn implements one-vs-one in `svm.SVC` and `svm.NuSVC` and one-vs-rest in `svm.LinearSVC`.\n",
        "\n",
        "In practice, the one-vs-the-rest strategy is usually preferred as the results are similar but the runtime is significantly less for large number of classes.\n",
        "\n",
        "We illustrate this multi-class SVM classification here."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ItjWbSzHkEgl"
      },
      "source": [
        "from sklearn import svm\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "from sklearn.metrics import accuracy_score"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ACnrlMO-xOxA"
      },
      "source": [
        "As an example we work with the iris dataset, which consists of three different flower types of irises' (Setosa, Versicolour, and Virginica) petal and sepal length."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YYeGIrHqygZB"
      },
      "source": [
        "from sklearn.datasets import load_iris"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1SZxGJFIyrU3"
      },
      "source": [
        "iris = load_iris()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SZiB_QVPzOhE"
      },
      "source": [
        "This will load in the data as a dictionary. The keys of the dictionary are as follows:\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P9_IlYREyx5E",
        "outputId": "8dfff23b-85b4-4ead-978a-d62c74afed28"
      },
      "source": [
        "iris.keys()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "dict_keys(['data', 'target', 'target_names', 'DESCR', 'feature_names', 'filename'])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ccLt3OtQzSz1"
      },
      "source": [
        "The features are as follows:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4HM57slezUp3",
        "outputId": "1d0eada7-c410-45b4-e82b-927791fc95c9"
      },
      "source": [
        "print(iris.DESCR)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            ".. _iris_dataset:\n",
            "\n",
            "Iris plants dataset\n",
            "--------------------\n",
            "\n",
            "**Data Set Characteristics:**\n",
            "\n",
            "    :Number of Instances: 150 (50 in each of three classes)\n",
            "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
            "    :Attribute Information:\n",
            "        - sepal length in cm\n",
            "        - sepal width in cm\n",
            "        - petal length in cm\n",
            "        - petal width in cm\n",
            "        - class:\n",
            "                - Iris-Setosa\n",
            "                - Iris-Versicolour\n",
            "                - Iris-Virginica\n",
            "                \n",
            "    :Summary Statistics:\n",
            "\n",
            "    ============== ==== ==== ======= ===== ====================\n",
            "                    Min  Max   Mean    SD   Class Correlation\n",
            "    ============== ==== ==== ======= ===== ====================\n",
            "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
            "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
            "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
            "    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\n",
            "    ============== ==== ==== ======= ===== ====================\n",
            "\n",
            "    :Missing Attribute Values: None\n",
            "    :Class Distribution: 33.3% for each of 3 classes.\n",
            "    :Creator: R.A. Fisher\n",
            "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
            "    :Date: July, 1988\n",
            "\n",
            "The famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\n",
            "from Fisher's paper. Note that it's the same as in R, but not as in the UCI\n",
            "Machine Learning Repository, which has two wrong data points.\n",
            "\n",
            "This is perhaps the best known database to be found in the\n",
            "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
            "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
            "data set contains 3 classes of 50 instances each, where each class refers to a\n",
            "type of iris plant.  One class is linearly separable from the other 2; the\n",
            "latter are NOT linearly separable from each other.\n",
            "\n",
            ".. topic:: References\n",
            "\n",
            "   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\n",
            "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
            "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
            "   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\n",
            "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
            "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
            "     Structure and Classification Rule for Recognition in Partially Exposed\n",
            "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
            "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
            "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
            "     on Information Theory, May 1972, 431-433.\n",
            "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
            "     conceptual clustering system finds 3 classes in the data.\n",
            "   - Many, many more ...\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "V0oRY8MFzlk7"
      },
      "source": [
        "We extract the data for the SVM classifier:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OFDFZSjHzkEt"
      },
      "source": [
        "X = iris.data \n",
        "y = iris.target"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZbiAj0mpzkx-"
      },
      "source": [
        "We again convert the data into a pandas DataFrame to get some initial statistics:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SEE_PTQKz7Si"
      },
      "source": [
        "df = pd.DataFrame(X)\n",
        "df.columns = iris.feature_names"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "DY_fsX5m0Djy",
        "outputId": "5e6abda9-c73b-40fd-80d7-8db12d091523"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
              "0                5.1               3.5                1.4               0.2\n",
              "1                4.9               3.0                1.4               0.2\n",
              "2                4.7               3.2                1.3               0.2\n",
              "3                4.6               3.1                1.5               0.2\n",
              "4                5.0               3.6                1.4               0.2"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ds_IXB9p0GyP"
      },
      "source": [
        "df['label'] = iris.target"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "7pGt6ArX0Mh8",
        "outputId": "634693ee-d74b-4c95-c405-f902c7828d78"
      },
      "source": [
        "df.head()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>4.6</td>\n",
              "      <td>3.1</td>\n",
              "      <td>1.5</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>5.0</td>\n",
              "      <td>3.6</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   sepal length (cm)  sepal width (cm)  ...  petal width (cm)  label\n",
              "0                5.1               3.5  ...               0.2      0\n",
              "1                4.9               3.0  ...               0.2      0\n",
              "2                4.7               3.2  ...               0.2      0\n",
              "3                4.6               3.1  ...               0.2      0\n",
              "4                5.0               3.6  ...               0.2      0\n",
              "\n",
              "[5 rows x 5 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 328
        },
        "id": "Hu5NJAda0PUP",
        "outputId": "9f92b340-0e11-4fae-b172-638a2fa0f398"
      },
      "source": [
        "corr = df.corr()\n",
        "\n",
        "ax = sns.heatmap(\n",
        "    corr, \n",
        "    vmin=-1, vmax=1, center=0,\n",
        "    cmap=sns.diverging_palette(20, 220, n=200),\n",
        "    square=True\n",
        ")\n",
        "ax.set_xticklabels(\n",
        "    ax.get_xticklabels(),\n",
        "    rotation=45,\n",
        "    horizontalalignment='right'\n",
        ");"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        },
        "id": "uT9bbvsT0nqu",
        "outputId": "a1c1456a-5b2c-4e8e-ca10-a3a8734b320e"
      },
      "source": [
        "corr"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>sepal length (cm)</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.117570</td>\n",
              "      <td>0.871754</td>\n",
              "      <td>0.817941</td>\n",
              "      <td>0.782561</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <td>-0.117570</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.428440</td>\n",
              "      <td>-0.366126</td>\n",
              "      <td>-0.426658</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>petal length (cm)</th>\n",
              "      <td>0.871754</td>\n",
              "      <td>-0.428440</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.962865</td>\n",
              "      <td>0.949035</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>petal width (cm)</th>\n",
              "      <td>0.817941</td>\n",
              "      <td>-0.366126</td>\n",
              "      <td>0.962865</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.956547</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>label</th>\n",
              "      <td>0.782561</td>\n",
              "      <td>-0.426658</td>\n",
              "      <td>0.949035</td>\n",
              "      <td>0.956547</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                   sepal length (cm)  ...     label\n",
              "sepal length (cm)           1.000000  ...  0.782561\n",
              "sepal width (cm)           -0.117570  ... -0.426658\n",
              "petal length (cm)           0.871754  ...  0.949035\n",
              "petal width (cm)            0.817941  ...  0.956547\n",
              "label                       0.782561  ...  1.000000\n",
              "\n",
              "[5 rows x 5 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pJ3tlEsk02rB"
      },
      "source": [
        "So let us just pick *petal length* and *petal width* as features:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZAJ7C7Rj086c"
      },
      "source": [
        "features = X[:,2:]\n",
        "labels = iris.target"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E0mrDaaN2EA-"
      },
      "source": [
        "Plot the data:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 623
        },
        "id": "sCOeZ8EF2M88",
        "outputId": "8f9f447a-3d48-40bc-df0d-a879de2b3263"
      },
      "source": [
        "fig = plt.figure(figsize=(10,10))\n",
        "plt.scatter(features[:,0], features[:,1], c=labels, cmap=plt.cm.Set1)\n",
        "plt.xlabel('Petal length')\n",
        "plt.ylabel('Petal width')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Petal width')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XwJnmDU62uGr"
      },
      "source": [
        "Split into training and testing data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uyrZ0She2tfU"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(features, labels, test_size=0.2, \n",
        "                                                    shuffle=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gHLlSi8U25BW"
      },
      "source": [
        "Define and fit the SVM:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ejln2AAH26n9",
        "outputId": "fe00b71b-3945-4c8a-8af3-3a78a263cda4"
      },
      "source": [
        "svm_iris = svm.SVC(kernel='linear')\n",
        "svm_iris.fit(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "SVC(C=1.0, break_ties=False, cache_size=200, class_weight=None, coef0=0.0,\n",
              "    decision_function_shape='ovr', degree=3, gamma='scale', kernel='linear',\n",
              "    max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
              "    tol=0.001, verbose=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pRbe15SD5ipl"
      },
      "source": [
        "We can again evaluate the accuracy of the classifier:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "E9WKTs0I5l_D",
        "outputId": "9ddf06a9-5b45-48d0-f0f0-c0658ce87792"
      },
      "source": [
        "y_pred = svm_iris.predict(X_test)\n",
        "\n",
        "acc = accuracy_score(y_test, y_pred)\n",
        "print(\"Accuracy on the test dataset: {}\".format(acc))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy on the test dataset: 0.9666666666666667\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yeskyI4139sh"
      },
      "source": [
        "To plot the decision boundary, let's use the classifier for all 'grid points' of our feature domain:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "Euw6PI1q4LlV",
        "outputId": "b047042b-3651-4967-ec72-a9ffac37b2a6"
      },
      "source": [
        "# Cover our feature domain with artificial data samples\n",
        "x_min, x_max = features[:, 0].min() - 1, features[:, 0].max() + 1\n",
        "y_min, y_max = features[:, 1].min() - 1, features[:, 1].max() + 1\n",
        "feature1, feature2 = np.meshgrid(np.arange(x_min, x_max, 0.1),\n",
        "                     np.arange(y_min, y_max, 0.1))\n",
        "\n",
        "Z = svm_iris.predict(np.column_stack((feature1.flatten(), feature2.flatten())))\n",
        "Z = Z.reshape(feature1.shape)\n",
        "\n",
        "plt.contourf(feature1, feature2, Z, alpha=0.4)\n",
        "plt.scatter(features[:,0], features[:,1], c=labels, s=20)\n",
        "plt.xlabel('Petal length')\n",
        "plt.ylabel('Petal width')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Petal width')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 41
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LAvyw-wU_lOp"
      },
      "source": [
        "### Ensemble methods"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "De3kFrXX_nM9"
      },
      "source": [
        "Here we show how ensemble methods can boost the classification accuracy for linear SVM classification on the Fashion-MNIST dataset."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jd129Hi9_wqr"
      },
      "source": [
        "We first begin with the base case of a single classifier (see lecture notes):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "aLHBZBry_0IT"
      },
      "source": [
        "from sklearn.datasets import fetch_openml\n",
        "\n",
        "from sklearn.svm import SVC, LinearSVC\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import MinMaxScaler\n",
        "\n",
        "from sklearn.metrics import accuracy_score"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CkAvp_pCAKp-"
      },
      "source": [
        "Scikit-learn allows downloading of larger real-world datasets through their `fetch_` routines. Here we download the Fashion-MNIST dataset from the OpenML repository:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7KtkH759AJap"
      },
      "source": [
        "X, y = fetch_openml('Fashion-MNIST', return_X_y=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KumXKHbKBLk9"
      },
      "source": [
        "The original dataset has 70,000 samples, and it is customary to use 60,000 for training and 10,000 for testing:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2hG0OlxdBBa9"
      },
      "source": [
        "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=60000,\n",
        "                                                    test_size=10000)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Iz9B5OmdBBzI"
      },
      "source": [
        "Visualize some samples from the dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 574
        },
        "id": "lWfl0bI_BPpy",
        "outputId": "374e2dd9-73e0-4af8-9db4-6c87a4a14b62"
      },
      "source": [
        "# Visualize the dataset\n",
        "k=1\n",
        "fig = plt.figure(figsize=(10,10))\n",
        "for i in range(10):\n",
        "  ind = np.where(y_train==str(i))\n",
        "  for j in range(10):\n",
        "    plt.subplot(10,10,k)\n",
        "    plt.imshow(np.reshape(X_train[ind[0][j]],(28,28)), cmap=plt.cm.gray)\n",
        "    plt.axis('off')\n",
        "    k += 1"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 100 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MaEfvLc73EdT"
      },
      "source": [
        "Maximum pixel value is again 255, and the minimum pixel value is again 0"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BCM2SAMCBRnj",
        "outputId": "d39f019f-db31-4f3c-a762-1c9d865f934c"
      },
      "source": [
        "print(X_train.min(), X_train.max())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.0 255.0\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XyHB8QXMBKe6"
      },
      "source": [
        "As the pixel values of the images range from 0 to 255, we scale them to 0 to 1:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vCKRplGYBczT"
      },
      "source": [
        "scaler = MinMaxScaler()\n",
        "X_train = scaler.fit_transform(X_train)\n",
        "X_test = scaler.transform(X_test)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ez-X6EmcBjin"
      },
      "source": [
        "SVM as base classifier (we use `LinearSVC` as training on this dataset with `SVC` takes a long time):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "92uO946BBuCA",
        "outputId": "a0149d7f-b4a2-4cc8-b62c-70cd02d4e2f4"
      },
      "source": [
        "clf = LinearSVC(max_iter=100)\n",
        "clf.fit(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,\n",
              "          intercept_scaling=1, loss='squared_hinge', max_iter=100,\n",
              "          multi_class='ovr', penalty='l2', random_state=None, tol=0.0001,\n",
              "          verbose=0)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jfjDJ2PrB0gn"
      },
      "source": [
        "Get the accuracy of the classifier:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sg5lnUO5B39p",
        "outputId": "4c828a7e-5756-418b-92dd-2fb594a93d87"
      },
      "source": [
        "y_pred = clf.predict(X_test)\n",
        "acc = accuracy_score(y_test, y_pred)\n",
        "print('Accuracy on test data: {}'.format(acc))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy on test data: 0.8437\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nvIZsigXD9rd"
      },
      "source": [
        "We now compare this to a SVM-based bagging classifier:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JzHV0IpmEFJt"
      },
      "source": [
        "from sklearn.ensemble import BaggingClassifier"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eMS7WTrZB4BI"
      },
      "source": [
        "To keep the computational burden comparable, we train 10 estimators doing 10 optimization steps only (as we used a single classifier using 100 steps above as baseline):"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "zHZdFBcKEb0R",
        "outputId": "bf10d4a5-d36d-498f-f35f-8b85a997d840"
      },
      "source": [
        "bagging_clf = BaggingClassifier(base_estimator=LinearSVC(max_iter=10), \n",
        "                                n_estimators=10)\n",
        "bagging_clf.fit(X_train, y_train)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n",
            "/usr/local/lib/python3.6/dist-packages/sklearn/svm/_base.py:947: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
            "  \"the number of iterations.\", ConvergenceWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "BaggingClassifier(base_estimator=LinearSVC(C=1.0, class_weight=None, dual=True,\n",
              "                                           fit_intercept=True,\n",
              "                                           intercept_scaling=1,\n",
              "                                           loss='squared_hinge', max_iter=10,\n",
              "                                           multi_class='ovr', penalty='l2',\n",
              "                                           random_state=None, tol=0.0001,\n",
              "                                           verbose=0),\n",
              "                  bootstrap=True, bootstrap_features=False, max_features=1.0,\n",
              "                  max_samples=1.0, n_estimators=10, n_jobs=None,\n",
              "                  oob_score=False, random_state=None, verbose=0,\n",
              "                  warm_start=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sbbHKyPWF2b3",
        "outputId": "d45fa15f-209b-4611-ae4b-cb00bbcd06d7"
      },
      "source": [
        "y_pred = bagging_clf.predict(X_test)\n",
        "acc = accuracy_score(y_test, y_pred)\n",
        "print('Accuracy on test data: {}'.format(acc))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Accuracy on test data: 0.8421\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4BRG5N22kfHO"
      },
      "source": [
        "### Unsupervised learing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2eqo9cD6kiPF"
      },
      "source": [
        "Here we apply the k-means clustering algorithm to the iris data set."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6bSLojInkxQj"
      },
      "source": [
        "from sklearn.cluster import KMeans\n",
        "\n",
        "from sklearn.metrics import silhouette_score\n",
        "\n",
        "from sklearn.datasets import load_iris"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kTW2aL5bl4ho"
      },
      "source": [
        "X, y = load_iris(return_X_y=True)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O5RPlVMJl-7G"
      },
      "source": [
        "features = X[:,2:]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EkGthx_3mCQ3"
      },
      "source": [
        "We do not need the labels for the k-means clustering algorithm. To find the correct number of clusters, we use the silhouette score:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_DJ5GErBmaqc"
      },
      "source": [
        "score = []\n",
        "for k in range(2,8):\n",
        "  kmeans = KMeans(n_clusters=k)\n",
        "  y_pred = kmeans.fit_predict(features)\n",
        "  score.append(silhouette_score(features, kmeans.labels_))"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "nLKGB4YLmytk",
        "outputId": "909b3ca4-e65f-43f1-db6a-bbca35c6f4ca"
      },
      "source": [
        "plt.plot(np.arange(2,8), score,'o-')\n",
        "plt.xlabel('Nr. of clusters')\n",
        "plt.ylabel('Silhouette score')\n",
        "plt.grid()"
      ],
      "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": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l73GJZE6nq8k"
      },
      "source": [
        "Interestingly, the silhouette score is highest for 2 clusters! Let's plot the decision boundaries, along with the true labels of the dataset:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "0r6nO2yanHil",
        "outputId": "c5940d32-151d-4778-ab73-c992deb64b15"
      },
      "source": [
        "k = 2\n",
        "kmeans = KMeans(n_clusters=k)\n",
        "kmeans.fit(features)\n",
        "\n",
        "# Evaluate the algorihm at each point of the feature domain\n",
        "h = 0.02\n",
        "x_min, x_max = features[:,0].min() - 1, features[:,0].max() + 1\n",
        "y_min, y_max = features[:,1].min() - 1, features[:,1].max() + 1\n",
        "xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))\n",
        "\n",
        "# Obtain labels for each point in mesh. Use last trained model.\n",
        "Z = kmeans.predict(np.column_stack((xx.flatten(), yy.flatten())))\n",
        "\n",
        "# Put the result into a color plot\n",
        "Z = Z.reshape(xx.shape)\n",
        "plt.figure(1)\n",
        "plt.clf()\n",
        "plt.imshow(Z, interpolation='nearest',\n",
        "           extent=(xx.min(), xx.max(), yy.min(), yy.max()),\n",
        "           cmap=plt.cm.Paired,\n",
        "           aspect='auto', origin='lower')\n",
        "\n",
        "plt.scatter(features[:,0], features[:,1], c=y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f2a40a179e8>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 58
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "glFipxQ7mrg4"
      },
      "source": [
        "Besides the silhouette score, there is also the so-called *elbow method* to find the optimal number of clusters.\n",
        "\n",
        "Here one looks as the elbow of the performance measure of the optimizer as the point of diminishing returns, i.e. as the point where the additional cost is no longer worth it.\n",
        "\n",
        "For the k-means clustering method, this performance measure (besides the silhouette score) is the `inertia`, which is the sum of squared distances of samples to their closest cluster center."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ND_1bwDzrFIV"
      },
      "source": [
        "inertia = []\n",
        "for k in range(1,8):\n",
        "  kmeans = KMeans(n_clusters=k)\n",
        "  y_pred = kmeans.fit_predict(features)\n",
        "  inertia.append(kmeans.inertia_)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "_-FEHcvmrOhv",
        "outputId": "23072dc2-9207-455f-cb8f-e4988768caec"
      },
      "source": [
        "plt.plot(np.arange(1,8), inertia)\n",
        "plt.xlabel('Nr. of clusters')\n",
        "plt.ylabel('Inertia score')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Inertia score')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 60
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QevZAk9NsZOP"
      },
      "source": [
        "The elbow method does yield the optimal number of clusters to be k=3, which is where the elbow of the curve lies!"
      ]
    }
  ]
}