k_means_1.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/anirudh-bukka/DataAnalysis-SupervisedML/blob/main/k_means_1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "nmHNAyl7QT4-"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "import numpy as np\n",
        "import seaborn as sns\n",
        "from sklearn.cluster import KMeans\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "XTWhIaCaQT5B",
        "outputId": "7591dfaa-016d-4007-c47c-8f23af97dc83"
      },
      "outputs": [
        {
          "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>Name</th>\n",
              "      <th>Age</th>\n",
              "      <th>Income($)</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Rob</td>\n",
              "      <td>27</td>\n",
              "      <td>70000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Michael</td>\n",
              "      <td>29</td>\n",
              "      <td>90000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Mohan</td>\n",
              "      <td>29</td>\n",
              "      <td>61000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Ismail</td>\n",
              "      <td>28</td>\n",
              "      <td>60000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Kory</td>\n",
              "      <td>42</td>\n",
              "      <td>150000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Gautam</td>\n",
              "      <td>39</td>\n",
              "      <td>155000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>David</td>\n",
              "      <td>41</td>\n",
              "      <td>160000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Andrea</td>\n",
              "      <td>38</td>\n",
              "      <td>162000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Brad</td>\n",
              "      <td>36</td>\n",
              "      <td>156000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Angelina</td>\n",
              "      <td>35</td>\n",
              "      <td>130000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Donald</td>\n",
              "      <td>37</td>\n",
              "      <td>137000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Tom</td>\n",
              "      <td>26</td>\n",
              "      <td>45000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Arnold</td>\n",
              "      <td>27</td>\n",
              "      <td>48000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Jared</td>\n",
              "      <td>28</td>\n",
              "      <td>51000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Stark</td>\n",
              "      <td>29</td>\n",
              "      <td>49500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Ranbir</td>\n",
              "      <td>32</td>\n",
              "      <td>53000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Dipika</td>\n",
              "      <td>40</td>\n",
              "      <td>65000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Priyanka</td>\n",
              "      <td>41</td>\n",
              "      <td>63000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Nick</td>\n",
              "      <td>43</td>\n",
              "      <td>64000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Alia</td>\n",
              "      <td>39</td>\n",
              "      <td>80000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>Sid</td>\n",
              "      <td>41</td>\n",
              "      <td>82000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>Abdul</td>\n",
              "      <td>39</td>\n",
              "      <td>58000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Name  Age  Income($)\n",
              "0        Rob   27      70000\n",
              "1    Michael   29      90000\n",
              "2      Mohan   29      61000\n",
              "3     Ismail   28      60000\n",
              "4       Kory   42     150000\n",
              "5     Gautam   39     155000\n",
              "6      David   41     160000\n",
              "7     Andrea   38     162000\n",
              "8       Brad   36     156000\n",
              "9   Angelina   35     130000\n",
              "10    Donald   37     137000\n",
              "11       Tom   26      45000\n",
              "12    Arnold   27      48000\n",
              "13     Jared   28      51000\n",
              "14     Stark   29      49500\n",
              "15    Ranbir   32      53000\n",
              "16    Dipika   40      65000\n",
              "17  Priyanka   41      63000\n",
              "18      Nick   43      64000\n",
              "19      Alia   39      80000\n",
              "20       Sid   41      82000\n",
              "21     Abdul   39      58000"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df = pd.read_csv(\"/Users/DELL/Documents/Files_from_d/PROGRAMMING/PYTHON/ML_DS/DATASETS/income.csv\")\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JepnEQoRQT5C"
      },
      "source": [
        "### Scatter plot of Age v/s Income"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ajeq6HE1QT5E",
        "outputId": "205cc140-5b60-4b61-84a6-b3aabda99a68"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Income')"
            ]
          },
          "execution_count": 11,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.scatter(df.Age, df['Income($)'])\n",
        "plt.xlabel(\"Age\")\n",
        "plt.ylabel(\"Income\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "DyTzrJ3JQT5F"
      },
      "source": [
        "# KMeans classifier"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-ZS887RMQT5F"
      },
      "source": [
        "Classifying the data points into 3 groups/clusters, by running the KMeans Algorithm."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "Ktk7IDz3QT5F",
        "outputId": "6139f5cf-ebc8-4873-80c8-0edf4e5d60db"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1],\n",
              "      dtype=int32)"
            ]
          },
          "execution_count": 15,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# Instantiate the KMeans object.\n",
        "km = KMeans(n_clusters = 3)\n",
        "\n",
        "y_predicted = km.fit_predict(df[['Age', 'Income($)']])\n",
        "y_predicted"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TJcgtVldQT5G"
      },
      "source": [
        "Append the `'cluster'` column to the dataframe."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ZpjuFA_uQT5H",
        "outputId": "1015503f-fddb-48f8-bc92-222de9dd190e"
      },
      "outputs": [
        {
          "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>Name</th>\n",
              "      <th>Age</th>\n",
              "      <th>Income($)</th>\n",
              "      <th>cluster</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Rob</td>\n",
              "      <td>27</td>\n",
              "      <td>70000</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Michael</td>\n",
              "      <td>29</td>\n",
              "      <td>90000</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Mohan</td>\n",
              "      <td>29</td>\n",
              "      <td>61000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Ismail</td>\n",
              "      <td>28</td>\n",
              "      <td>60000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Kory</td>\n",
              "      <td>42</td>\n",
              "      <td>150000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Gautam</td>\n",
              "      <td>39</td>\n",
              "      <td>155000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>David</td>\n",
              "      <td>41</td>\n",
              "      <td>160000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Andrea</td>\n",
              "      <td>38</td>\n",
              "      <td>162000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Brad</td>\n",
              "      <td>36</td>\n",
              "      <td>156000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Angelina</td>\n",
              "      <td>35</td>\n",
              "      <td>130000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Donald</td>\n",
              "      <td>37</td>\n",
              "      <td>137000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Tom</td>\n",
              "      <td>26</td>\n",
              "      <td>45000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Arnold</td>\n",
              "      <td>27</td>\n",
              "      <td>48000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Jared</td>\n",
              "      <td>28</td>\n",
              "      <td>51000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Stark</td>\n",
              "      <td>29</td>\n",
              "      <td>49500</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Ranbir</td>\n",
              "      <td>32</td>\n",
              "      <td>53000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Dipika</td>\n",
              "      <td>40</td>\n",
              "      <td>65000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Priyanka</td>\n",
              "      <td>41</td>\n",
              "      <td>63000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Nick</td>\n",
              "      <td>43</td>\n",
              "      <td>64000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Alia</td>\n",
              "      <td>39</td>\n",
              "      <td>80000</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>Sid</td>\n",
              "      <td>41</td>\n",
              "      <td>82000</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>Abdul</td>\n",
              "      <td>39</td>\n",
              "      <td>58000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Name  Age  Income($)  cluster\n",
              "0        Rob   27      70000        2\n",
              "1    Michael   29      90000        2\n",
              "2      Mohan   29      61000        0\n",
              "3     Ismail   28      60000        0\n",
              "4       Kory   42     150000        1\n",
              "5     Gautam   39     155000        1\n",
              "6      David   41     160000        1\n",
              "7     Andrea   38     162000        1\n",
              "8       Brad   36     156000        1\n",
              "9   Angelina   35     130000        1\n",
              "10    Donald   37     137000        1\n",
              "11       Tom   26      45000        0\n",
              "12    Arnold   27      48000        0\n",
              "13     Jared   28      51000        0\n",
              "14     Stark   29      49500        0\n",
              "15    Ranbir   32      53000        0\n",
              "16    Dipika   40      65000        0\n",
              "17  Priyanka   41      63000        0\n",
              "18      Nick   43      64000        0\n",
              "19      Alia   39      80000        2\n",
              "20       Sid   41      82000        2\n",
              "21     Abdul   39      58000        0"
            ]
          },
          "execution_count": 13,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df['cluster'] = y_predicted\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MBph_TJzQT5H"
      },
      "source": [
        "### Scatter plot categorizing data points based on the clusters"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JVxV0sd_QT5I"
      },
      "source": [
        "#### `.cluster_centers_`:\n",
        "\n",
        "`.cluster_centers_`, is the arithmetic mean of all the points belonging to the cluster."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "vt_8WREQQT5I",
        "outputId": "27c00d9b-2d61-45be-ab6c-b8781dddbe0a"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([[3.82857143e+01, 1.50000000e+05],\n",
              "       [3.29090909e+01, 5.61363636e+04],\n",
              "       [3.40000000e+01, 8.05000000e+04]])"
            ]
          },
          "execution_count": 32,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "km.cluster_centers_"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "-k5jV6j7QT5I",
        "outputId": "ec5278e3-02bf-4deb-9cb5-efb77e43a482"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "df0 = df[df['cluster'] == 0]\n",
        "df1 = df[df['cluster'] == 1]\n",
        "df2 = df[df['cluster'] == 2]\n",
        "\n",
        "plt.scatter(df0.Age, df0['Income($)'], color = 'green', label='cluster 0')\n",
        "plt.scatter(df1.Age, df1['Income($)'], color = 'blue', label='cluster 1')\n",
        "plt.scatter(df2.Age, df2['Income($)'], color = 'red', label='cluster 2')\n",
        "\n",
        "plt.scatter(km.cluster_centers_[:,0],km.cluster_centers_[:,1],color='purple',marker='*',label='centroid')\n",
        "\n",
        "plt.xlabel(\"Age\")\n",
        "plt.ylabel(\"Income($)\")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4V-LQ9V6QT5J"
      },
      "source": [
        "In the above scatter plot, the red and green clusters seem incorrect. <br>\n",
        "<br>\n",
        "Probably because the scaling might not be right. <br>\n",
        "- The range of values on y-axis is very high.\n",
        "- But the range of values on x-axis is very narrow. <br>\n",
        "<br>\n",
        "Hence, we normalize the data."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "DdWAK-P-QT5J",
        "outputId": "04371aee-fa0c-4316-e625-71ce24c41d66"
      },
      "outputs": [
        {
          "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>Name</th>\n",
              "      <th>Age</th>\n",
              "      <th>Income($)</th>\n",
              "      <th>cluster</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Rob</td>\n",
              "      <td>0.058824</td>\n",
              "      <td>0.213675</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Michael</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.384615</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Mohan</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.136752</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Ismail</td>\n",
              "      <td>0.117647</td>\n",
              "      <td>0.128205</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Kory</td>\n",
              "      <td>0.941176</td>\n",
              "      <td>0.897436</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Gautam</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.940171</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>David</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.982906</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Andrea</td>\n",
              "      <td>0.705882</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Brad</td>\n",
              "      <td>0.588235</td>\n",
              "      <td>0.948718</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Angelina</td>\n",
              "      <td>0.529412</td>\n",
              "      <td>0.726496</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Donald</td>\n",
              "      <td>0.647059</td>\n",
              "      <td>0.786325</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Tom</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Arnold</td>\n",
              "      <td>0.058824</td>\n",
              "      <td>0.025641</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Jared</td>\n",
              "      <td>0.117647</td>\n",
              "      <td>0.051282</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Stark</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.038462</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Ranbir</td>\n",
              "      <td>0.352941</td>\n",
              "      <td>0.068376</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Dipika</td>\n",
              "      <td>0.823529</td>\n",
              "      <td>0.170940</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Priyanka</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.153846</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Nick</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.162393</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Alia</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.299145</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>Sid</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.316239</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>Abdul</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.111111</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Name       Age  Income($)  cluster\n",
              "0        Rob  0.058824   0.213675        2\n",
              "1    Michael  0.176471   0.384615        2\n",
              "2      Mohan  0.176471   0.136752        0\n",
              "3     Ismail  0.117647   0.128205        0\n",
              "4       Kory  0.941176   0.897436        1\n",
              "5     Gautam  0.764706   0.940171        1\n",
              "6      David  0.882353   0.982906        1\n",
              "7     Andrea  0.705882   1.000000        1\n",
              "8       Brad  0.588235   0.948718        1\n",
              "9   Angelina  0.529412   0.726496        1\n",
              "10    Donald  0.647059   0.786325        1\n",
              "11       Tom  0.000000   0.000000        0\n",
              "12    Arnold  0.058824   0.025641        0\n",
              "13     Jared  0.117647   0.051282        0\n",
              "14     Stark  0.176471   0.038462        0\n",
              "15    Ranbir  0.352941   0.068376        0\n",
              "16    Dipika  0.823529   0.170940        0\n",
              "17  Priyanka  0.882353   0.153846        0\n",
              "18      Nick  1.000000   0.162393        0\n",
              "19      Alia  0.764706   0.299145        2\n",
              "20       Sid  0.882353   0.316239        2\n",
              "21     Abdul  0.764706   0.111111        0"
            ]
          },
          "execution_count": 31,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "from sklearn.preprocessing import MinMaxScaler\n",
        "scaler = MinMaxScaler()\n",
        "\n",
        "df['Income($)'] = scaler.fit_transform(df[['Income($)']])\n",
        "# df['Income($)'] = scaler.transform(df[['Income($)']])\n",
        "\n",
        "df['Age'] = scaler.fit_transform(df[['Age']])\n",
        "# df['Age'] = scaler.transform(df[['Age']])\n",
        "\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "T829-5XSQT5K"
      },
      "source": [
        "The above shows dataframe shows: <br>\n",
        "- `'Age'` column is scaled to values between 0 & 1, <br>\n",
        "- `'Income($)'` columns is scaled to values between 0 and 1.\n",
        "<br> \n",
        "Hence the values are now comparable."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8Kgmm-TnQT5K"
      },
      "source": [
        "### Apply KMeans function again\n",
        "To get a better classification result."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gYcDGOV_QT5K",
        "outputId": "581a5921-cea6-459c-f8f9-cdaa76ff7c10"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2],\n",
              "      dtype=int32)"
            ]
          },
          "execution_count": 33,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "km = KMeans(n_clusters=3)\n",
        "\n",
        "y_predicted = km.fit_predict(df[['Age', 'Income($)']])\n",
        "y_predicted"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mz0fbHEYQT5L"
      },
      "source": [
        "psst, compare this one with the first predicted clusters XD.<br>\n",
        "<br>\n",
        "Now replace the `'clusters'` column in the dataframe."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "s8Rkk6ZlQT5L",
        "outputId": "0b0008b8-9bbe-41f4-a459-e44f54488761"
      },
      "outputs": [
        {
          "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>Name</th>\n",
              "      <th>Age</th>\n",
              "      <th>Income($)</th>\n",
              "      <th>cluster</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Rob</td>\n",
              "      <td>0.058824</td>\n",
              "      <td>0.213675</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Michael</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.384615</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Mohan</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.136752</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Ismail</td>\n",
              "      <td>0.117647</td>\n",
              "      <td>0.128205</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Kory</td>\n",
              "      <td>0.941176</td>\n",
              "      <td>0.897436</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Gautam</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.940171</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>David</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.982906</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Andrea</td>\n",
              "      <td>0.705882</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Brad</td>\n",
              "      <td>0.588235</td>\n",
              "      <td>0.948718</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Angelina</td>\n",
              "      <td>0.529412</td>\n",
              "      <td>0.726496</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Donald</td>\n",
              "      <td>0.647059</td>\n",
              "      <td>0.786325</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Tom</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Arnold</td>\n",
              "      <td>0.058824</td>\n",
              "      <td>0.025641</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Jared</td>\n",
              "      <td>0.117647</td>\n",
              "      <td>0.051282</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Stark</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.038462</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Ranbir</td>\n",
              "      <td>0.352941</td>\n",
              "      <td>0.068376</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Dipika</td>\n",
              "      <td>0.823529</td>\n",
              "      <td>0.170940</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Priyanka</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.153846</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Nick</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.162393</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Alia</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.299145</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>Sid</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.316239</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>Abdul</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.111111</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Name       Age  Income($)  cluster\n",
              "0        Rob  0.058824   0.213675        1\n",
              "1    Michael  0.176471   0.384615        1\n",
              "2      Mohan  0.176471   0.136752        1\n",
              "3     Ismail  0.117647   0.128205        1\n",
              "4       Kory  0.941176   0.897436        0\n",
              "5     Gautam  0.764706   0.940171        0\n",
              "6      David  0.882353   0.982906        0\n",
              "7     Andrea  0.705882   1.000000        0\n",
              "8       Brad  0.588235   0.948718        0\n",
              "9   Angelina  0.529412   0.726496        0\n",
              "10    Donald  0.647059   0.786325        0\n",
              "11       Tom  0.000000   0.000000        1\n",
              "12    Arnold  0.058824   0.025641        1\n",
              "13     Jared  0.117647   0.051282        1\n",
              "14     Stark  0.176471   0.038462        1\n",
              "15    Ranbir  0.352941   0.068376        1\n",
              "16    Dipika  0.823529   0.170940        2\n",
              "17  Priyanka  0.882353   0.153846        2\n",
              "18      Nick  1.000000   0.162393        2\n",
              "19      Alia  0.764706   0.299145        2\n",
              "20       Sid  0.882353   0.316239        2\n",
              "21     Abdul  0.764706   0.111111        2"
            ]
          },
          "execution_count": 35,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df['cluster'] = y_predicted\n",
        "df"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WsWACjnuQT5L"
      },
      "source": [
        "### Plot the scatter plot with data points in the new clusters."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "w-l7qouOQT5L",
        "outputId": "03dbaa75-838f-4728-fea8-d89bbce5e901"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "df0 = df[df['cluster'] == 0]\n",
        "df1 = df[df['cluster'] == 1]\n",
        "df2 = df[df['cluster'] == 2]\n",
        "\n",
        "plt.scatter(df0.Age, df0['Income($)'], color = 'green', label = 'cluster 0')\n",
        "plt.scatter(df1.Age, df1['Income($)'], color = 'blue', label = 'cluster 1')\n",
        "plt.scatter(df2.Age, df2['Income($)'], color = 'red', label = 'cluster 2')\n",
        "\n",
        "plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1], marker='*', color = 'purple', label = 'centroid')\n",
        "\n",
        "plt.xlabel(\"Age\")\n",
        "plt.ylabel(\"Income\")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "86H2bZvdQT5M"
      },
      "source": [
        "This scatter plot shows that the data points are clustered better."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hSiM7vv6QT5M",
        "outputId": "a7d432aa-74f8-4496-ea52-b0f05a7e3833"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "array([0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2],\n",
              "      dtype=int32)"
            ]
          },
          "execution_count": 44,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "km = KMeans(n_clusters=3)\n",
        "\n",
        "y_predicted = km.fit_predict(df[['Age', 'Income($)']])\n",
        "y_predicted"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "FLi995R-QT5M",
        "outputId": "32692098-dde6-4767-9615-8bc9bdca7380"
      },
      "outputs": [
        {
          "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>Name</th>\n",
              "      <th>Age</th>\n",
              "      <th>Income($)</th>\n",
              "      <th>cluster</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Rob</td>\n",
              "      <td>0.058824</td>\n",
              "      <td>0.213675</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>Michael</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.384615</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Mohan</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.136752</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Ismail</td>\n",
              "      <td>0.117647</td>\n",
              "      <td>0.128205</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Kory</td>\n",
              "      <td>0.941176</td>\n",
              "      <td>0.897436</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Gautam</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.940171</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>David</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.982906</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Andrea</td>\n",
              "      <td>0.705882</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Brad</td>\n",
              "      <td>0.588235</td>\n",
              "      <td>0.948718</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Angelina</td>\n",
              "      <td>0.529412</td>\n",
              "      <td>0.726496</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Donald</td>\n",
              "      <td>0.647059</td>\n",
              "      <td>0.786325</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>Tom</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Arnold</td>\n",
              "      <td>0.058824</td>\n",
              "      <td>0.025641</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>Jared</td>\n",
              "      <td>0.117647</td>\n",
              "      <td>0.051282</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>14</th>\n",
              "      <td>Stark</td>\n",
              "      <td>0.176471</td>\n",
              "      <td>0.038462</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>15</th>\n",
              "      <td>Ranbir</td>\n",
              "      <td>0.352941</td>\n",
              "      <td>0.068376</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>16</th>\n",
              "      <td>Dipika</td>\n",
              "      <td>0.823529</td>\n",
              "      <td>0.170940</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>17</th>\n",
              "      <td>Priyanka</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.153846</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>18</th>\n",
              "      <td>Nick</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.162393</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>19</th>\n",
              "      <td>Alia</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.299145</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>20</th>\n",
              "      <td>Sid</td>\n",
              "      <td>0.882353</td>\n",
              "      <td>0.316239</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>21</th>\n",
              "      <td>Abdul</td>\n",
              "      <td>0.764706</td>\n",
              "      <td>0.111111</td>\n",
              "      <td>2</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "        Name       Age  Income($)  cluster\n",
              "0        Rob  0.058824   0.213675        0\n",
              "1    Michael  0.176471   0.384615        0\n",
              "2      Mohan  0.176471   0.136752        0\n",
              "3     Ismail  0.117647   0.128205        0\n",
              "4       Kory  0.941176   0.897436        1\n",
              "5     Gautam  0.764706   0.940171        1\n",
              "6      David  0.882353   0.982906        1\n",
              "7     Andrea  0.705882   1.000000        1\n",
              "8       Brad  0.588235   0.948718        1\n",
              "9   Angelina  0.529412   0.726496        1\n",
              "10    Donald  0.647059   0.786325        1\n",
              "11       Tom  0.000000   0.000000        0\n",
              "12    Arnold  0.058824   0.025641        0\n",
              "13     Jared  0.117647   0.051282        0\n",
              "14     Stark  0.176471   0.038462        0\n",
              "15    Ranbir  0.352941   0.068376        0\n",
              "16    Dipika  0.823529   0.170940        2\n",
              "17  Priyanka  0.882353   0.153846        2\n",
              "18      Nick  1.000000   0.162393        2\n",
              "19      Alia  0.764706   0.299145        2\n",
              "20       Sid  0.882353   0.316239        2\n",
              "21     Abdul  0.764706   0.111111        2"
            ]
          },
          "execution_count": 45,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "df['cluster'] = y_predicted\n",
        "df"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bepBDKNxQT5M",
        "outputId": "6e916847-679d-4704-9d86-ba955712a665"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "df0 = df[df['cluster'] == 0]\n",
        "df1 = df[df['cluster'] == 1]\n",
        "df2 = df[df['cluster'] == 2]\n",
        "\n",
        "plt.scatter(df0.Age, df0['Income($)'], color = 'green', label = 'cluster 0')\n",
        "plt.scatter(df1.Age, df1['Income($)'], color = 'blue', label = 'cluster 1')\n",
        "plt.scatter(df2.Age, df2['Income($)'], color = 'red', label = 'cluster 2')\n",
        "\n",
        "plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1], marker='*', color = 'purple', label = 'centroid')\n",
        "\n",
        "plt.xlabel(\"Age\")\n",
        "plt.ylabel(\"Income\")\n",
        "plt.legend()\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F4BbvugIQT5M"
      },
      "source": [
        "**Now we see that the clustering does not change. Hence 3 is the best value for K**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gIelcQg9QT5N"
      },
      "source": [
        "## Calculate and Plot SSE\n",
        "SSE: Sum of Square Error"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cJWHzScNQT5N",
        "outputId": "a1a1c3fe-429a-44ca-c9e8-de89c0144835"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[5.434011511988177,\n",
              " 2.0911363886990766,\n",
              " 0.47507834985530945,\n",
              " 0.34910470944195643,\n",
              " 0.2621792762345213,\n",
              " 0.22020960864009395,\n",
              " 0.16858512236029755,\n",
              " 0.139888452061285,\n",
              " 0.10188787724979426]"
            ]
          },
          "execution_count": 53,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "# First create a range of integers in an interval. These integers are the 'k' values.\n",
        "k_range = range(1, 10)\n",
        "\n",
        "# Create an empty list that holds the SSE values for each 'k' value.\n",
        "sse = []\n",
        "for k in k_range:\n",
        "    km = KMeans(n_clusters=k)\n",
        "    km.fit(df[['Age', 'Income($)']])\n",
        "    sse.append(km.inertia_) # .inertia_ gives SSE value for each 'k' value.\n",
        "\n",
        "sse"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z2tIf1ErQT5N"
      },
      "source": [
        "## Plot SSE vs K values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "gAtnyNUJQT5N",
        "outputId": "37621d3f-d6d9-4bec-fb04-cdc45eaea69d"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x12fa378e0>]"
            ]
          },
          "execution_count": 54,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          },
          "output_type": "display_data"
        }
      ],
      "source": [
        "plt.xlabel('K')\n",
        "plt.ylabel('Sum of Squared Error')\n",
        "plt.plot(k_range, sse)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KAjC4XhaQT5N"
      },
      "source": [
        "**Here `k` = 3 is the elbow point, which is the best `'k'` value.**"
      ]
    }
  ],
  "metadata": {
    "interpreter": {
      "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
    },
    "kernelspec": {
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.9.12"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}