k_nearest_neighbor.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "k-nearest-neighbor.ipynb",
      "provenance": [],
      "authorship_tag": "ABX9TyMzS6cb9WZ5rCmWwt6SyB5b",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/nykolai-d/k-nearest-neighbor_1/blob/main/k_nearest_neighbor.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "_47cHB6301Vw"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "%matplotlib inline"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Importing the data\n",
        "import io\n",
        "from google.colab import files\n",
        "\n",
        "uploaded = files.upload()"
      ],
      "metadata": {
        "colab": {
          "resources": {
            "http://localhost:8080/nbextensions/google.colab/files.js": {
              "data": 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              "ok": true,
              "headers": [
                [
                  "content-type",
                  "application/javascript"
                ]
              ],
              "status": 200,
              "status_text": "OK"
            }
          },
          "base_uri": "https://localhost:8080/",
          "height": 74
        },
        "id": "SFOoEy7C08nV",
        "outputId": "c28e4a97-d39e-4d5a-ef22-f7ca76b04ede"
      },
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-490b57fa-1d72-4701-b322-cecdb269704d\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-490b57fa-1d72-4701-b322-cecdb269704d\">\n",
              "      Upload widget is only available when the cell has been executed in the\n",
              "      current browser session. Please rerun this cell to enable.\n",
              "      </output>\n",
              "      <script src=\"/nbextensions/google.colab/files.js\"></script> "
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {}
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Saving classified_data.csv to classified_data.csv\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "raw_data = pd.read_csv('classified_data.csv')"
      ],
      "metadata": {
        "id": "_uKa-1_e1Kzt"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "raw_data.info()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "-ZgE2edW1jBF",
        "outputId": "9713f232-b950-4dad-a2b8-7cf67148a69d"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 1000 entries, 0 to 999\n",
            "Data columns (total 12 columns):\n",
            " #   Column        Non-Null Count  Dtype  \n",
            "---  ------        --------------  -----  \n",
            " 0   Unnamed: 0    1000 non-null   int64  \n",
            " 1   WTT           1000 non-null   float64\n",
            " 2   PTI           1000 non-null   float64\n",
            " 3   EQW           1000 non-null   float64\n",
            " 4   SBI           1000 non-null   float64\n",
            " 5   LQE           1000 non-null   float64\n",
            " 6   QWG           1000 non-null   float64\n",
            " 7   FDJ           1000 non-null   float64\n",
            " 8   PJF           1000 non-null   float64\n",
            " 9   HQE           1000 non-null   float64\n",
            " 10  NXJ           1000 non-null   float64\n",
            " 11  TARGET CLASS  1000 non-null   int64  \n",
            "dtypes: float64(10), int64(2)\n",
            "memory usage: 93.9 KB\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "raw_data.columns"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BpaQh0qv1lv9",
        "outputId": "3fd42923-52a6-4a28-aa44-ee175deeb4e6"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['Unnamed: 0', 'WTT', 'PTI', 'EQW', 'SBI', 'LQE', 'QWG', 'FDJ', 'PJF',\n",
              "       'HQE', 'NXJ', 'TARGET CLASS'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "raw_data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "EJszNkbg1trc",
        "outputId": "d3edf86f-7524-4ba5-ca97-014a8e0051c9"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-76fd2c09-c7d3-4ae1-91fc-705b0af3b68e\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe thead th {\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Unnamed: 0</th>\n",
              "      <th>WTT</th>\n",
              "      <th>PTI</th>\n",
              "      <th>EQW</th>\n",
              "      <th>SBI</th>\n",
              "      <th>LQE</th>\n",
              "      <th>QWG</th>\n",
              "      <th>FDJ</th>\n",
              "      <th>PJF</th>\n",
              "      <th>HQE</th>\n",
              "      <th>NXJ</th>\n",
              "      <th>TARGET CLASS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.913917</td>\n",
              "      <td>1.162073</td>\n",
              "      <td>0.567946</td>\n",
              "      <td>0.755464</td>\n",
              "      <td>0.780862</td>\n",
              "      <td>0.352608</td>\n",
              "      <td>0.759697</td>\n",
              "      <td>0.643798</td>\n",
              "      <td>0.879422</td>\n",
              "      <td>1.231409</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.635632</td>\n",
              "      <td>1.003722</td>\n",
              "      <td>0.535342</td>\n",
              "      <td>0.825645</td>\n",
              "      <td>0.924109</td>\n",
              "      <td>0.648450</td>\n",
              "      <td>0.675334</td>\n",
              "      <td>1.013546</td>\n",
              "      <td>0.621552</td>\n",
              "      <td>1.492702</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.721360</td>\n",
              "      <td>1.201493</td>\n",
              "      <td>0.921990</td>\n",
              "      <td>0.855595</td>\n",
              "      <td>1.526629</td>\n",
              "      <td>0.720781</td>\n",
              "      <td>1.626351</td>\n",
              "      <td>1.154483</td>\n",
              "      <td>0.957877</td>\n",
              "      <td>1.285597</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>1.234204</td>\n",
              "      <td>1.386726</td>\n",
              "      <td>0.653046</td>\n",
              "      <td>0.825624</td>\n",
              "      <td>1.142504</td>\n",
              "      <td>0.875128</td>\n",
              "      <td>1.409708</td>\n",
              "      <td>1.380003</td>\n",
              "      <td>1.522692</td>\n",
              "      <td>1.153093</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>1.279491</td>\n",
              "      <td>0.949750</td>\n",
              "      <td>0.627280</td>\n",
              "      <td>0.668976</td>\n",
              "      <td>1.232537</td>\n",
              "      <td>0.703727</td>\n",
              "      <td>1.115596</td>\n",
              "      <td>0.646691</td>\n",
              "      <td>1.463812</td>\n",
              "      <td>1.419167</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>995</th>\n",
              "      <td>995</td>\n",
              "      <td>1.010953</td>\n",
              "      <td>1.034006</td>\n",
              "      <td>0.853116</td>\n",
              "      <td>0.622460</td>\n",
              "      <td>1.036610</td>\n",
              "      <td>0.586240</td>\n",
              "      <td>0.746811</td>\n",
              "      <td>0.319752</td>\n",
              "      <td>1.117340</td>\n",
              "      <td>1.348517</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>996</th>\n",
              "      <td>996</td>\n",
              "      <td>0.575529</td>\n",
              "      <td>0.955786</td>\n",
              "      <td>0.941835</td>\n",
              "      <td>0.792882</td>\n",
              "      <td>1.414277</td>\n",
              "      <td>1.269540</td>\n",
              "      <td>1.055928</td>\n",
              "      <td>0.713193</td>\n",
              "      <td>0.958684</td>\n",
              "      <td>1.663489</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>997</th>\n",
              "      <td>997</td>\n",
              "      <td>1.135470</td>\n",
              "      <td>0.982462</td>\n",
              "      <td>0.781905</td>\n",
              "      <td>0.916738</td>\n",
              "      <td>0.901031</td>\n",
              "      <td>0.884738</td>\n",
              "      <td>0.386802</td>\n",
              "      <td>0.389584</td>\n",
              "      <td>0.919191</td>\n",
              "      <td>1.385504</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>998</th>\n",
              "      <td>998</td>\n",
              "      <td>1.084894</td>\n",
              "      <td>0.861769</td>\n",
              "      <td>0.407158</td>\n",
              "      <td>0.665696</td>\n",
              "      <td>1.608612</td>\n",
              "      <td>0.943859</td>\n",
              "      <td>0.855806</td>\n",
              "      <td>1.061338</td>\n",
              "      <td>1.277456</td>\n",
              "      <td>1.188063</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>999</th>\n",
              "      <td>999</td>\n",
              "      <td>0.837460</td>\n",
              "      <td>0.961184</td>\n",
              "      <td>0.417006</td>\n",
              "      <td>0.799784</td>\n",
              "      <td>0.934399</td>\n",
              "      <td>0.424762</td>\n",
              "      <td>0.778234</td>\n",
              "      <td>0.907962</td>\n",
              "      <td>1.257190</td>\n",
              "      <td>1.364837</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1000 rows × 12 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-76fd2c09-c7d3-4ae1-91fc-705b0af3b68e')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-76fd2c09-c7d3-4ae1-91fc-705b0af3b68e button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-76fd2c09-c7d3-4ae1-91fc-705b0af3b68e');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "     Unnamed: 0       WTT       PTI  ...       HQE       NXJ  TARGET CLASS\n",
              "0             0  0.913917  1.162073  ...  0.879422  1.231409             1\n",
              "1             1  0.635632  1.003722  ...  0.621552  1.492702             0\n",
              "2             2  0.721360  1.201493  ...  0.957877  1.285597             0\n",
              "3             3  1.234204  1.386726  ...  1.522692  1.153093             1\n",
              "4             4  1.279491  0.949750  ...  1.463812  1.419167             1\n",
              "..          ...       ...       ...  ...       ...       ...           ...\n",
              "995         995  1.010953  1.034006  ...  1.117340  1.348517             1\n",
              "996         996  0.575529  0.955786  ...  0.958684  1.663489             0\n",
              "997         997  1.135470  0.982462  ...  0.919191  1.385504             1\n",
              "998         998  1.084894  0.861769  ...  1.277456  1.188063             1\n",
              "999         999  0.837460  0.961184  ...  1.257190  1.364837             1\n",
              "\n",
              "[1000 rows x 12 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Fixing the unnamed column at the left\n",
        "raw_data = pd.read_csv('classified_data.csv', index_col = 0)"
      ],
      "metadata": {
        "id": "opV6F3ZO1yr8"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "raw_data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 424
        },
        "id": "ikv__jWS19RF",
        "outputId": "ca0178e2-3fd1-4f5f-c15e-92d6fa8d3e8e"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "\n",
              "  <div id=\"df-1127da0b-5979-4b50-897f-37ff44b3f6fe\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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>WTT</th>\n",
              "      <th>PTI</th>\n",
              "      <th>EQW</th>\n",
              "      <th>SBI</th>\n",
              "      <th>LQE</th>\n",
              "      <th>QWG</th>\n",
              "      <th>FDJ</th>\n",
              "      <th>PJF</th>\n",
              "      <th>HQE</th>\n",
              "      <th>NXJ</th>\n",
              "      <th>TARGET CLASS</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0.913917</td>\n",
              "      <td>1.162073</td>\n",
              "      <td>0.567946</td>\n",
              "      <td>0.755464</td>\n",
              "      <td>0.780862</td>\n",
              "      <td>0.352608</td>\n",
              "      <td>0.759697</td>\n",
              "      <td>0.643798</td>\n",
              "      <td>0.879422</td>\n",
              "      <td>1.231409</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.635632</td>\n",
              "      <td>1.003722</td>\n",
              "      <td>0.535342</td>\n",
              "      <td>0.825645</td>\n",
              "      <td>0.924109</td>\n",
              "      <td>0.648450</td>\n",
              "      <td>0.675334</td>\n",
              "      <td>1.013546</td>\n",
              "      <td>0.621552</td>\n",
              "      <td>1.492702</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0.721360</td>\n",
              "      <td>1.201493</td>\n",
              "      <td>0.921990</td>\n",
              "      <td>0.855595</td>\n",
              "      <td>1.526629</td>\n",
              "      <td>0.720781</td>\n",
              "      <td>1.626351</td>\n",
              "      <td>1.154483</td>\n",
              "      <td>0.957877</td>\n",
              "      <td>1.285597</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.234204</td>\n",
              "      <td>1.386726</td>\n",
              "      <td>0.653046</td>\n",
              "      <td>0.825624</td>\n",
              "      <td>1.142504</td>\n",
              "      <td>0.875128</td>\n",
              "      <td>1.409708</td>\n",
              "      <td>1.380003</td>\n",
              "      <td>1.522692</td>\n",
              "      <td>1.153093</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>1.279491</td>\n",
              "      <td>0.949750</td>\n",
              "      <td>0.627280</td>\n",
              "      <td>0.668976</td>\n",
              "      <td>1.232537</td>\n",
              "      <td>0.703727</td>\n",
              "      <td>1.115596</td>\n",
              "      <td>0.646691</td>\n",
              "      <td>1.463812</td>\n",
              "      <td>1.419167</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>995</th>\n",
              "      <td>1.010953</td>\n",
              "      <td>1.034006</td>\n",
              "      <td>0.853116</td>\n",
              "      <td>0.622460</td>\n",
              "      <td>1.036610</td>\n",
              "      <td>0.586240</td>\n",
              "      <td>0.746811</td>\n",
              "      <td>0.319752</td>\n",
              "      <td>1.117340</td>\n",
              "      <td>1.348517</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>996</th>\n",
              "      <td>0.575529</td>\n",
              "      <td>0.955786</td>\n",
              "      <td>0.941835</td>\n",
              "      <td>0.792882</td>\n",
              "      <td>1.414277</td>\n",
              "      <td>1.269540</td>\n",
              "      <td>1.055928</td>\n",
              "      <td>0.713193</td>\n",
              "      <td>0.958684</td>\n",
              "      <td>1.663489</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>997</th>\n",
              "      <td>1.135470</td>\n",
              "      <td>0.982462</td>\n",
              "      <td>0.781905</td>\n",
              "      <td>0.916738</td>\n",
              "      <td>0.901031</td>\n",
              "      <td>0.884738</td>\n",
              "      <td>0.386802</td>\n",
              "      <td>0.389584</td>\n",
              "      <td>0.919191</td>\n",
              "      <td>1.385504</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>998</th>\n",
              "      <td>1.084894</td>\n",
              "      <td>0.861769</td>\n",
              "      <td>0.407158</td>\n",
              "      <td>0.665696</td>\n",
              "      <td>1.608612</td>\n",
              "      <td>0.943859</td>\n",
              "      <td>0.855806</td>\n",
              "      <td>1.061338</td>\n",
              "      <td>1.277456</td>\n",
              "      <td>1.188063</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>999</th>\n",
              "      <td>0.837460</td>\n",
              "      <td>0.961184</td>\n",
              "      <td>0.417006</td>\n",
              "      <td>0.799784</td>\n",
              "      <td>0.934399</td>\n",
              "      <td>0.424762</td>\n",
              "      <td>0.778234</td>\n",
              "      <td>0.907962</td>\n",
              "      <td>1.257190</td>\n",
              "      <td>1.364837</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>1000 rows × 11 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1127da0b-5979-4b50-897f-37ff44b3f6fe')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "      fill: #1967D2;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-1127da0b-5979-4b50-897f-37ff44b3f6fe button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-1127da0b-5979-4b50-897f-37ff44b3f6fe');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ],
            "text/plain": [
              "          WTT       PTI       EQW  ...       HQE       NXJ  TARGET CLASS\n",
              "0    0.913917  1.162073  0.567946  ...  0.879422  1.231409             1\n",
              "1    0.635632  1.003722  0.535342  ...  0.621552  1.492702             0\n",
              "2    0.721360  1.201493  0.921990  ...  0.957877  1.285597             0\n",
              "3    1.234204  1.386726  0.653046  ...  1.522692  1.153093             1\n",
              "4    1.279491  0.949750  0.627280  ...  1.463812  1.419167             1\n",
              "..        ...       ...       ...  ...       ...       ...           ...\n",
              "995  1.010953  1.034006  0.853116  ...  1.117340  1.348517             1\n",
              "996  0.575529  0.955786  0.941835  ...  0.958684  1.663489             0\n",
              "997  1.135470  0.982462  0.781905  ...  0.919191  1.385504             1\n",
              "998  1.084894  0.861769  0.407158  ...  1.277456  1.188063             1\n",
              "999  0.837460  0.961184  0.417006  ...  1.257190  1.364837             1\n",
              "\n",
              "[1000 rows x 11 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "We standarize the data by adjusting every x value so that they are roughly on the same scale."
      ],
      "metadata": {
        "id": "7em_kvlk2M2L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.preprocessing import StandardScaler"
      ],
      "metadata": {
        "id": "vcw3IqIY1-91"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "scaler = StandardScaler()\n",
        "scaler.fit(raw_data.drop('TARGET CLASS', axis=1))\n",
        "scaled_features = scaler.transform(raw_data.drop('TARGET CLASS', axis=1))\n",
        "scaled_data = pd.DataFrame(scaled_features, columns = raw_data.drop('TARGET CLASS', axis=1).columns)"
      ],
      "metadata": {
        "id": "BGjH1jPE2Tgl"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Splitting the data set into training and test data\n",
        "from sklearn.model_selection import train_test_split"
      ],
      "metadata": {
        "id": "qYab1HmV2nLl"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x = scaled_data\n",
        "\n",
        "y = raw_data['TARGET CLASS']"
      ],
      "metadata": {
        "id": "nY9AnJzH23Wt"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "x_training_data, x_test_data, y_training_data, y_test_data = train_test_split(x, y, test_size = 0.3)"
      ],
      "metadata": {
        "id": "jRMxKyNP29EE"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Training the model\n",
        "from sklearn.neighbors import KNeighborsClassifier"
      ],
      "metadata": {
        "id": "qU2HPfpP2_B0"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = KNeighborsClassifier(n_neighbors = 1)"
      ],
      "metadata": {
        "id": "H_xbUpHL3KDV"
      },
      "execution_count": 15,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model.fit(x_training_data, y_training_data)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "my4VD3EH3UTd",
        "outputId": "0f54da4f-dd31-479f-a599-77eb249021b8"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KNeighborsClassifier(n_neighbors=1)"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Making predictions\n",
        "predictions = model.predict(x_test_data)"
      ],
      "metadata": {
        "id": "DtpmV3eO3WUV"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Measuring the accuracy of the model\n",
        "\n",
        "from sklearn.metrics import classification_report\n",
        "\n",
        "from sklearn.metrics import confusion_matrix"
      ],
      "metadata": {
        "id": "zrz8VALf3rWt"
      },
      "execution_count": 18,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(classification_report(y_test_data, predictions))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "cRSXUC_T3zrN",
        "outputId": "ee02aa2b-3e9b-48ef-8b56-0a139c99da92"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "              precision    recall  f1-score   support\n",
            "\n",
            "           0       0.93      0.89      0.91       149\n",
            "           1       0.90      0.93      0.92       151\n",
            "\n",
            "    accuracy                           0.91       300\n",
            "   macro avg       0.91      0.91      0.91       300\n",
            "weighted avg       0.91      0.91      0.91       300\n",
            "\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(confusion_matrix(y_test_data, predictions))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CzRNHtwY310u",
        "outputId": "4c937873-0545-48b5-bb39-2b29329d537b"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[133  16]\n",
            " [ 10 141]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The model appears to be performant, but it can be improved by finding a better-suited value for $k$.<br/>\n",
        "To this end, the elbow method will be used. This methog involves iterating through different $k$ values and selecting the value with the lowest error rate when applied to the test data."
      ],
      "metadata": {
        "id": "0rNjsfsq4F5Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "error_rates = []"
      ],
      "metadata": {
        "id": "a1dv_qpR4FdZ"
      },
      "execution_count": 21,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "for i in np.arange(1, 101):\n",
        "\n",
        "    new_model = KNeighborsClassifier(n_neighbors = i)\n",
        "\n",
        "    new_model.fit(x_training_data, y_training_data)\n",
        "\n",
        "    new_predictions = new_model.predict(x_test_data)\n",
        "\n",
        "    error_rates.append(np.mean(new_predictions != y_test_data))"
      ],
      "metadata": {
        "id": "mRyRmX1q3_QN"
      },
      "execution_count": 22,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "error_rates"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CSnGA2tj4nqt",
        "outputId": "c1881164-3ee9-4a4c-f3ca-9847b52f26ce"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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          },
          "metadata": {},
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    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(error_rates)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 283
        },
        "id": "V7tIU9ui4u8E",
        "outputId": "65551b4a-2acd-46d3-bd30-36d5c0452dd3"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7fd18ef1b450>]"
            ]
          },
          "metadata": {},
          "execution_count": 24
        },
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Conclusion**: The error rates are minimized with $k=50$"
      ],
      "metadata": {
        "id": "CV4apXMd476G"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "**References**\n",
        "\n",
        "Nick McCullum https://nickmccullum.com/"
      ],
      "metadata": {
        "id": "y5IFB8ohOzHE"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "XAJzlr-YO97m"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}