ML_FINAL.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "ATHARVA AGIWAL "
      ],
      "metadata": {
        "id": "n8SWlvPauiE4"
      },
      "id": "n8SWlvPauiE4"
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **MACHINE LEARNING ASSIGNMENT 1**"
      ],
      "metadata": {
        "id": "brpeO8-5u2vd"
      },
      "id": "brpeO8-5u2vd"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "scrolled": false,
        "id": "Z5OK1Xsyt5je"
      },
      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "id": "Z5OK1Xsyt5je"
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.read_csv('ML_dataset.csv')\n",
        "display(df)"
      ],
      "metadata": {
        "id": "sIQiPPigt5jf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 505
        },
        "outputId": "8c60dbb4-1e4c-4316-91b2-30b215c136cf"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "           id diagnosis  radius_mean  texture_mean  perimeter_mean  area_mean  \\\n",
              "0      842302         M        17.99         10.38          122.80     1001.0   \n",
              "1      842517         M        20.57         17.77          132.90     1326.0   \n",
              "2    84300903         M        19.69         21.25          130.00     1203.0   \n",
              "3    84348301         M        11.42         20.38           77.58      386.1   \n",
              "4    84358402         M        20.29         14.34          135.10     1297.0   \n",
              "..        ...       ...          ...           ...             ...        ...   \n",
              "564    926424         M        21.56         22.39          142.00     1479.0   \n",
              "565    926682         M        20.13         28.25          131.20     1261.0   \n",
              "566    926954         M        16.60         28.08          108.30      858.1   \n",
              "567    927241         M        20.60         29.33          140.10     1265.0   \n",
              "568     92751         B         7.76         24.54           47.92      181.0   \n",
              "\n",
              "     smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \\\n",
              "0            0.11840           0.27760         0.30010              0.14710   \n",
              "1            0.08474           0.07864         0.08690              0.07017   \n",
              "2            0.10960           0.15990         0.19740              0.12790   \n",
              "3            0.14250           0.28390         0.24140              0.10520   \n",
              "4            0.10030           0.13280         0.19800              0.10430   \n",
              "..               ...               ...             ...                  ...   \n",
              "564          0.11100           0.11590         0.24390              0.13890   \n",
              "565          0.09780           0.10340         0.14400              0.09791   \n",
              "566          0.08455           0.10230         0.09251              0.05302   \n",
              "567          0.11780           0.27700         0.35140              0.15200   \n",
              "568          0.05263           0.04362         0.00000              0.00000   \n",
              "\n",
              "     ...  radius_worst  texture_worst  perimeter_worst  area_worst  \\\n",
              "0    ...        25.380          17.33           184.60      2019.0   \n",
              "1    ...        24.990          23.41           158.80      1956.0   \n",
              "2    ...        23.570          25.53           152.50      1709.0   \n",
              "3    ...        14.910          26.50            98.87       567.7   \n",
              "4    ...        22.540          16.67           152.20      1575.0   \n",
              "..   ...           ...            ...              ...         ...   \n",
              "564  ...        25.450          26.40           166.10      2027.0   \n",
              "565  ...        23.690          38.25           155.00      1731.0   \n",
              "566  ...        18.980          34.12           126.70      1124.0   \n",
              "567  ...        25.740          39.42           184.60      1821.0   \n",
              "568  ...         9.456          30.37            59.16       268.6   \n",
              "\n",
              "     smoothness_worst  compactness_worst  concavity_worst  \\\n",
              "0             0.16220            0.66560           0.7119   \n",
              "1             0.12380            0.18660           0.2416   \n",
              "2             0.14440            0.42450           0.4504   \n",
              "3             0.20980            0.86630           0.6869   \n",
              "4             0.13740            0.20500           0.4000   \n",
              "..                ...                ...              ...   \n",
              "564           0.14100            0.21130           0.4107   \n",
              "565           0.11660            0.19220           0.3215   \n",
              "566           0.11390            0.30940           0.3403   \n",
              "567           0.16500            0.86810           0.9387   \n",
              "568           0.08996            0.06444           0.0000   \n",
              "\n",
              "     concave points_worst  symmetry_worst  fractal_dimension_worst  \n",
              "0                  0.2654          0.4601                  0.11890  \n",
              "1                  0.1860          0.2750                  0.08902  \n",
              "2                  0.2430          0.3613                  0.08758  \n",
              "3                  0.2575          0.6638                  0.17300  \n",
              "4                  0.1625          0.2364                  0.07678  \n",
              "..                    ...             ...                      ...  \n",
              "564                0.2216          0.2060                  0.07115  \n",
              "565                0.1628          0.2572                  0.06637  \n",
              "566                0.1418          0.2218                  0.07820  \n",
              "567                0.2650          0.4087                  0.12400  \n",
              "568                0.0000          0.2871                  0.07039  \n",
              "\n",
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              "      <th></th>\n",
              "      <th>id</th>\n",
              "      <th>diagnosis</th>\n",
              "      <th>radius_mean</th>\n",
              "      <th>texture_mean</th>\n",
              "      <th>perimeter_mean</th>\n",
              "      <th>area_mean</th>\n",
              "      <th>smoothness_mean</th>\n",
              "      <th>compactness_mean</th>\n",
              "      <th>concavity_mean</th>\n",
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              "      <th>texture_worst</th>\n",
              "      <th>perimeter_worst</th>\n",
              "      <th>area_worst</th>\n",
              "      <th>smoothness_worst</th>\n",
              "      <th>compactness_worst</th>\n",
              "      <th>concavity_worst</th>\n",
              "      <th>concave points_worst</th>\n",
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              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>842302</td>\n",
              "      <td>M</td>\n",
              "      <td>17.99</td>\n",
              "      <td>10.38</td>\n",
              "      <td>122.80</td>\n",
              "      <td>1001.0</td>\n",
              "      <td>0.11840</td>\n",
              "      <td>0.27760</td>\n",
              "      <td>0.30010</td>\n",
              "      <td>0.14710</td>\n",
              "      <td>...</td>\n",
              "      <td>25.380</td>\n",
              "      <td>17.33</td>\n",
              "      <td>184.60</td>\n",
              "      <td>2019.0</td>\n",
              "      <td>0.16220</td>\n",
              "      <td>0.66560</td>\n",
              "      <td>0.7119</td>\n",
              "      <td>0.2654</td>\n",
              "      <td>0.4601</td>\n",
              "      <td>0.11890</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>842517</td>\n",
              "      <td>M</td>\n",
              "      <td>20.57</td>\n",
              "      <td>17.77</td>\n",
              "      <td>132.90</td>\n",
              "      <td>1326.0</td>\n",
              "      <td>0.08474</td>\n",
              "      <td>0.07864</td>\n",
              "      <td>0.08690</td>\n",
              "      <td>0.07017</td>\n",
              "      <td>...</td>\n",
              "      <td>24.990</td>\n",
              "      <td>23.41</td>\n",
              "      <td>158.80</td>\n",
              "      <td>1956.0</td>\n",
              "      <td>0.12380</td>\n",
              "      <td>0.18660</td>\n",
              "      <td>0.2416</td>\n",
              "      <td>0.1860</td>\n",
              "      <td>0.2750</td>\n",
              "      <td>0.08902</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>84300903</td>\n",
              "      <td>M</td>\n",
              "      <td>19.69</td>\n",
              "      <td>21.25</td>\n",
              "      <td>130.00</td>\n",
              "      <td>1203.0</td>\n",
              "      <td>0.10960</td>\n",
              "      <td>0.15990</td>\n",
              "      <td>0.19740</td>\n",
              "      <td>0.12790</td>\n",
              "      <td>...</td>\n",
              "      <td>23.570</td>\n",
              "      <td>25.53</td>\n",
              "      <td>152.50</td>\n",
              "      <td>1709.0</td>\n",
              "      <td>0.14440</td>\n",
              "      <td>0.42450</td>\n",
              "      <td>0.4504</td>\n",
              "      <td>0.2430</td>\n",
              "      <td>0.3613</td>\n",
              "      <td>0.08758</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>84348301</td>\n",
              "      <td>M</td>\n",
              "      <td>11.42</td>\n",
              "      <td>20.38</td>\n",
              "      <td>77.58</td>\n",
              "      <td>386.1</td>\n",
              "      <td>0.14250</td>\n",
              "      <td>0.28390</td>\n",
              "      <td>0.24140</td>\n",
              "      <td>0.10520</td>\n",
              "      <td>...</td>\n",
              "      <td>14.910</td>\n",
              "      <td>26.50</td>\n",
              "      <td>98.87</td>\n",
              "      <td>567.7</td>\n",
              "      <td>0.20980</td>\n",
              "      <td>0.86630</td>\n",
              "      <td>0.6869</td>\n",
              "      <td>0.2575</td>\n",
              "      <td>0.6638</td>\n",
              "      <td>0.17300</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>84358402</td>\n",
              "      <td>M</td>\n",
              "      <td>20.29</td>\n",
              "      <td>14.34</td>\n",
              "      <td>135.10</td>\n",
              "      <td>1297.0</td>\n",
              "      <td>0.10030</td>\n",
              "      <td>0.13280</td>\n",
              "      <td>0.19800</td>\n",
              "      <td>0.10430</td>\n",
              "      <td>...</td>\n",
              "      <td>22.540</td>\n",
              "      <td>16.67</td>\n",
              "      <td>152.20</td>\n",
              "      <td>1575.0</td>\n",
              "      <td>0.13740</td>\n",
              "      <td>0.20500</td>\n",
              "      <td>0.4000</td>\n",
              "      <td>0.1625</td>\n",
              "      <td>0.2364</td>\n",
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              "      <td>22.39</td>\n",
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              "      <td>1479.0</td>\n",
              "      <td>0.11100</td>\n",
              "      <td>0.11590</td>\n",
              "      <td>0.24390</td>\n",
              "      <td>0.13890</td>\n",
              "      <td>...</td>\n",
              "      <td>25.450</td>\n",
              "      <td>26.40</td>\n",
              "      <td>166.10</td>\n",
              "      <td>2027.0</td>\n",
              "      <td>0.14100</td>\n",
              "      <td>0.21130</td>\n",
              "      <td>0.4107</td>\n",
              "      <td>0.2216</td>\n",
              "      <td>0.2060</td>\n",
              "      <td>0.07115</td>\n",
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              "      <th>565</th>\n",
              "      <td>926682</td>\n",
              "      <td>M</td>\n",
              "      <td>20.13</td>\n",
              "      <td>28.25</td>\n",
              "      <td>131.20</td>\n",
              "      <td>1261.0</td>\n",
              "      <td>0.09780</td>\n",
              "      <td>0.10340</td>\n",
              "      <td>0.14400</td>\n",
              "      <td>0.09791</td>\n",
              "      <td>...</td>\n",
              "      <td>23.690</td>\n",
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              "      <td>155.00</td>\n",
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              "      <td>926954</td>\n",
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              "      <td>28.08</td>\n",
              "      <td>108.30</td>\n",
              "      <td>858.1</td>\n",
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              "      <td>0.05302</td>\n",
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              "      <td>18.980</td>\n",
              "      <td>34.12</td>\n",
              "      <td>126.70</td>\n",
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              "      <td>0.11390</td>\n",
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              "      <td>0.3403</td>\n",
              "      <td>0.1418</td>\n",
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              "      <td>29.33</td>\n",
              "      <td>140.10</td>\n",
              "      <td>1265.0</td>\n",
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              "      <td>0.27700</td>\n",
              "      <td>0.35140</td>\n",
              "      <td>0.15200</td>\n",
              "      <td>...</td>\n",
              "      <td>25.740</td>\n",
              "      <td>39.42</td>\n",
              "      <td>184.60</td>\n",
              "      <td>1821.0</td>\n",
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              "      <td>59.16</td>\n",
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              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-5d63d6dc-6cea-4b3f-884f-f62bc2aec91d');\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",
              "  "
            ]
          },
          "metadata": {}
        }
      ],
      "id": "sIQiPPigt5jf"
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Feature Engineering Task 1**"
      ],
      "metadata": {
        "id": "mGd2uOCVO0EG"
      },
      "id": "mGd2uOCVO0EG"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "890d8578",
      "metadata": {
        "id": "890d8578",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "276069a6-36f7-4d58-84c5-8cda06008435"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['radius_mean', 'texture_mean', 'perimeter_mean', 'area_mean',\n",
              "       'smoothness_mean', 'compactness_mean', 'concavity_mean',\n",
              "       'concave points_mean', 'symmetry_mean', 'fractal_dimension_mean',\n",
              "       'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se',\n",
              "       'compactness_se', 'concavity_se', 'concave points_se', 'symmetry_se',\n",
              "       'fractal_dimension_se', 'radius_worst', 'texture_worst',\n",
              "       'perimeter_worst', 'area_worst', 'smoothness_worst',\n",
              "       'compactness_worst', 'concavity_worst', 'concave points_worst',\n",
              "       'symmetry_worst', 'fractal_dimension_worst'],\n",
              "      dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "cols = df.columns\n",
        "num_cols = df._get_numeric_data().columns[1:]\n",
        "#identifying which column contains continuous numeric data\n",
        "num_cols"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "2d31a4f6",
      "metadata": {
        "id": "2d31a4f6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c87be69e-d725-4a8d-bcb2-094770bc900a"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "['id', 'diagnosis']"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ],
      "source": [
        "categorical_cols = list(set(cols)-set(num_cols))\n",
        "categorical_cols\n",
        "#columns with categorical data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "352b24b0",
      "metadata": {
        "scrolled": true,
        "id": "352b24b0"
      },
      "outputs": [],
      "source": [
        "#finding missing total missing values in each column\n",
        "missing_values = sum(list(df.isna().sum()))\n",
        "#print(missing_values)\n",
        "#there were 7 missing values initially"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "1ace76ce",
      "metadata": {
        "id": "1ace76ce"
      },
      "outputs": [],
      "source": [
        "for col in df:\n",
        "    if col not in ['id','diagnosis']:\n",
        "        mean_value = df[col].mean()\n",
        "        #calculating the mean value\n",
        "        df[col].fillna(value=mean_value,inplace=True)\n",
        "        #replacing empty cell with the mean value calculated as mentioned in task 1"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Feature Engineering Task 2**"
      ],
      "metadata": {
        "id": "PkCKvyw_KkgJ"
      },
      "id": "PkCKvyw_KkgJ"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "dfdb2565",
      "metadata": {
        "id": "dfdb2565",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 505
        },
        "outputId": "f6b9f652-0503-48b8-8bcc-175c608b9699"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           id diagnosis  radius_mean  texture_mean  perimeter_mean  area_mean  \\\n",
              "0      842302         M     1.102422     -2.071512        1.268389   0.983510   \n",
              "1      842517         M     1.836635     -0.353322        1.684639   1.907030   \n",
              "2    84300903         M     1.586206      0.455786        1.565122   1.557513   \n",
              "3    84348301         M    -0.767260      0.253509       -0.595257  -0.763792   \n",
              "4    84358402         M     1.756953     -1.150804        1.775308   1.824624   \n",
              "..        ...       ...          ...           ...             ...        ...   \n",
              "564    926424         M     2.118368      0.720838        2.059677   2.341795   \n",
              "565    926682         M     1.711420      2.083301        1.614577   1.722326   \n",
              "566    926954         M     0.706858      2.043775        0.670803   0.577445   \n",
              "567    927241         M     1.845172      2.334403        1.981372   1.733693   \n",
              "568     92751         B    -1.808817      1.220718       -1.817631  -1.346604   \n",
              "\n",
              "     smoothness_mean  compactness_mean  concavity_mean  concave points_mean  \\\n",
              "0           1.567087          3.280628        2.650837             2.530249   \n",
              "1          -0.826235         -0.486643       -0.025417             0.547662   \n",
              "2           0.941382          1.052000        1.361666             2.035440   \n",
              "3           3.280667          3.399917        1.913989             1.450431   \n",
              "4           0.280125          0.538866        1.369198             1.427237   \n",
              "..               ...               ...             ...                  ...   \n",
              "564         1.040926          0.218868        1.945370             2.318924   \n",
              "565         0.102368         -0.017817        0.691347             1.262558   \n",
              "566        -0.839745         -0.038646        0.045004             0.105684   \n",
              "567         1.524426          3.269267        3.294795             2.656528   \n",
              "568        -3.109349         -1.149741       -1.116254            -1.260710   \n",
              "\n",
              "     ...  radius_worst  texture_worst  perimeter_worst  area_worst  \\\n",
              "0    ...      1.885031      -1.358098         2.301575    1.998658   \n",
              "1    ...      1.804340      -0.368879         1.533776    1.887973   \n",
              "2    ...      1.510541      -0.023953         1.346291    1.454016   \n",
              "3    ...     -0.281217       0.133866        -0.249720   -0.551147   \n",
              "4    ...      1.297434      -1.465481         1.337363    1.218589   \n",
              "..   ...           ...            ...              ...         ...   \n",
              "564  ...      1.899514       0.117596         1.751022    2.012713   \n",
              "565  ...      1.535369       2.045599         1.420690    1.492668   \n",
              "566  ...      0.560868       1.373645         0.578492    0.426222   \n",
              "567  ...      1.959515       2.235958         2.301575    1.650790   \n",
              "568  ...     -1.409652       0.763518        -1.431475   -1.076640   \n",
              "\n",
              "     smoothness_worst  compactness_worst  concavity_worst  \\\n",
              "0            1.306537           2.614365         2.107374   \n",
              "1           -0.375282          -0.430066        -0.147968   \n",
              "2            0.526944           1.081980         0.853340   \n",
              "3            3.391291           3.889975         1.987485   \n",
              "4            0.220362          -0.313119         0.611645   \n",
              "..                ...                ...              ...   \n",
              "564          0.378033          -0.273077         0.662958   \n",
              "565         -0.690623          -0.394473         0.235195   \n",
              "566         -0.808876           0.350427         0.325352   \n",
              "567          1.429169           3.901415         3.195002   \n",
              "568         -1.857384          -1.206491        -1.306570   \n",
              "\n",
              "     concave points_worst  symmetry_worst  fractal_dimension_worst  \n",
              "0                2.294058        2.748204                 1.935312  \n",
              "1                1.086129       -0.243675                 0.280943  \n",
              "2                1.953282        1.151242                 0.201214  \n",
              "3                2.173873        6.040726                 4.930672  \n",
              "4                0.728618       -0.867590                -0.396751  \n",
              "..                    ...             ...                      ...  \n",
              "564              1.627719       -1.358963                -0.708467  \n",
              "565              0.733182       -0.531387                -0.973122  \n",
              "566              0.413705       -1.103578                -0.318129  \n",
              "567              2.287972        1.917396                 2.217684  \n",
              "568             -1.743529       -0.048096                -0.750546  \n",
              "\n",
              "[569 rows x 32 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-51cf5ee2-f188-4671-8826-b1eb4e600b8e\">\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>id</th>\n",
              "      <th>diagnosis</th>\n",
              "      <th>radius_mean</th>\n",
              "      <th>texture_mean</th>\n",
              "      <th>perimeter_mean</th>\n",
              "      <th>area_mean</th>\n",
              "      <th>smoothness_mean</th>\n",
              "      <th>compactness_mean</th>\n",
              "      <th>concavity_mean</th>\n",
              "      <th>concave points_mean</th>\n",
              "      <th>...</th>\n",
              "      <th>radius_worst</th>\n",
              "      <th>texture_worst</th>\n",
              "      <th>perimeter_worst</th>\n",
              "      <th>area_worst</th>\n",
              "      <th>smoothness_worst</th>\n",
              "      <th>compactness_worst</th>\n",
              "      <th>concavity_worst</th>\n",
              "      <th>concave points_worst</th>\n",
              "      <th>symmetry_worst</th>\n",
              "      <th>fractal_dimension_worst</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>842302</td>\n",
              "      <td>M</td>\n",
              "      <td>1.102422</td>\n",
              "      <td>-2.071512</td>\n",
              "      <td>1.268389</td>\n",
              "      <td>0.983510</td>\n",
              "      <td>1.567087</td>\n",
              "      <td>3.280628</td>\n",
              "      <td>2.650837</td>\n",
              "      <td>2.530249</td>\n",
              "      <td>...</td>\n",
              "      <td>1.885031</td>\n",
              "      <td>-1.358098</td>\n",
              "      <td>2.301575</td>\n",
              "      <td>1.998658</td>\n",
              "      <td>1.306537</td>\n",
              "      <td>2.614365</td>\n",
              "      <td>2.107374</td>\n",
              "      <td>2.294058</td>\n",
              "      <td>2.748204</td>\n",
              "      <td>1.935312</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>842517</td>\n",
              "      <td>M</td>\n",
              "      <td>1.836635</td>\n",
              "      <td>-0.353322</td>\n",
              "      <td>1.684639</td>\n",
              "      <td>1.907030</td>\n",
              "      <td>-0.826235</td>\n",
              "      <td>-0.486643</td>\n",
              "      <td>-0.025417</td>\n",
              "      <td>0.547662</td>\n",
              "      <td>...</td>\n",
              "      <td>1.804340</td>\n",
              "      <td>-0.368879</td>\n",
              "      <td>1.533776</td>\n",
              "      <td>1.887973</td>\n",
              "      <td>-0.375282</td>\n",
              "      <td>-0.430066</td>\n",
              "      <td>-0.147968</td>\n",
              "      <td>1.086129</td>\n",
              "      <td>-0.243675</td>\n",
              "      <td>0.280943</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>84300903</td>\n",
              "      <td>M</td>\n",
              "      <td>1.586206</td>\n",
              "      <td>0.455786</td>\n",
              "      <td>1.565122</td>\n",
              "      <td>1.557513</td>\n",
              "      <td>0.941382</td>\n",
              "      <td>1.052000</td>\n",
              "      <td>1.361666</td>\n",
              "      <td>2.035440</td>\n",
              "      <td>...</td>\n",
              "      <td>1.510541</td>\n",
              "      <td>-0.023953</td>\n",
              "      <td>1.346291</td>\n",
              "      <td>1.454016</td>\n",
              "      <td>0.526944</td>\n",
              "      <td>1.081980</td>\n",
              "      <td>0.853340</td>\n",
              "      <td>1.953282</td>\n",
              "      <td>1.151242</td>\n",
              "      <td>0.201214</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>84348301</td>\n",
              "      <td>M</td>\n",
              "      <td>-0.767260</td>\n",
              "      <td>0.253509</td>\n",
              "      <td>-0.595257</td>\n",
              "      <td>-0.763792</td>\n",
              "      <td>3.280667</td>\n",
              "      <td>3.399917</td>\n",
              "      <td>1.913989</td>\n",
              "      <td>1.450431</td>\n",
              "      <td>...</td>\n",
              "      <td>-0.281217</td>\n",
              "      <td>0.133866</td>\n",
              "      <td>-0.249720</td>\n",
              "      <td>-0.551147</td>\n",
              "      <td>3.391291</td>\n",
              "      <td>3.889975</td>\n",
              "      <td>1.987485</td>\n",
              "      <td>2.173873</td>\n",
              "      <td>6.040726</td>\n",
              "      <td>4.930672</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>84358402</td>\n",
              "      <td>M</td>\n",
              "      <td>1.756953</td>\n",
              "      <td>-1.150804</td>\n",
              "      <td>1.775308</td>\n",
              "      <td>1.824624</td>\n",
              "      <td>0.280125</td>\n",
              "      <td>0.538866</td>\n",
              "      <td>1.369198</td>\n",
              "      <td>1.427237</td>\n",
              "      <td>...</td>\n",
              "      <td>1.297434</td>\n",
              "      <td>-1.465481</td>\n",
              "      <td>1.337363</td>\n",
              "      <td>1.218589</td>\n",
              "      <td>0.220362</td>\n",
              "      <td>-0.313119</td>\n",
              "      <td>0.611645</td>\n",
              "      <td>0.728618</td>\n",
              "      <td>-0.867590</td>\n",
              "      <td>-0.396751</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",
              "      <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>564</th>\n",
              "      <td>926424</td>\n",
              "      <td>M</td>\n",
              "      <td>2.118368</td>\n",
              "      <td>0.720838</td>\n",
              "      <td>2.059677</td>\n",
              "      <td>2.341795</td>\n",
              "      <td>1.040926</td>\n",
              "      <td>0.218868</td>\n",
              "      <td>1.945370</td>\n",
              "      <td>2.318924</td>\n",
              "      <td>...</td>\n",
              "      <td>1.899514</td>\n",
              "      <td>0.117596</td>\n",
              "      <td>1.751022</td>\n",
              "      <td>2.012713</td>\n",
              "      <td>0.378033</td>\n",
              "      <td>-0.273077</td>\n",
              "      <td>0.662958</td>\n",
              "      <td>1.627719</td>\n",
              "      <td>-1.358963</td>\n",
              "      <td>-0.708467</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>565</th>\n",
              "      <td>926682</td>\n",
              "      <td>M</td>\n",
              "      <td>1.711420</td>\n",
              "      <td>2.083301</td>\n",
              "      <td>1.614577</td>\n",
              "      <td>1.722326</td>\n",
              "      <td>0.102368</td>\n",
              "      <td>-0.017817</td>\n",
              "      <td>0.691347</td>\n",
              "      <td>1.262558</td>\n",
              "      <td>...</td>\n",
              "      <td>1.535369</td>\n",
              "      <td>2.045599</td>\n",
              "      <td>1.420690</td>\n",
              "      <td>1.492668</td>\n",
              "      <td>-0.690623</td>\n",
              "      <td>-0.394473</td>\n",
              "      <td>0.235195</td>\n",
              "      <td>0.733182</td>\n",
              "      <td>-0.531387</td>\n",
              "      <td>-0.973122</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>566</th>\n",
              "      <td>926954</td>\n",
              "      <td>M</td>\n",
              "      <td>0.706858</td>\n",
              "      <td>2.043775</td>\n",
              "      <td>0.670803</td>\n",
              "      <td>0.577445</td>\n",
              "      <td>-0.839745</td>\n",
              "      <td>-0.038646</td>\n",
              "      <td>0.045004</td>\n",
              "      <td>0.105684</td>\n",
              "      <td>...</td>\n",
              "      <td>0.560868</td>\n",
              "      <td>1.373645</td>\n",
              "      <td>0.578492</td>\n",
              "      <td>0.426222</td>\n",
              "      <td>-0.808876</td>\n",
              "      <td>0.350427</td>\n",
              "      <td>0.325352</td>\n",
              "      <td>0.413705</td>\n",
              "      <td>-1.103578</td>\n",
              "      <td>-0.318129</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>567</th>\n",
              "      <td>927241</td>\n",
              "      <td>M</td>\n",
              "      <td>1.845172</td>\n",
              "      <td>2.334403</td>\n",
              "      <td>1.981372</td>\n",
              "      <td>1.733693</td>\n",
              "      <td>1.524426</td>\n",
              "      <td>3.269267</td>\n",
              "      <td>3.294795</td>\n",
              "      <td>2.656528</td>\n",
              "      <td>...</td>\n",
              "      <td>1.959515</td>\n",
              "      <td>2.235958</td>\n",
              "      <td>2.301575</td>\n",
              "      <td>1.650790</td>\n",
              "      <td>1.429169</td>\n",
              "      <td>3.901415</td>\n",
              "      <td>3.195002</td>\n",
              "      <td>2.287972</td>\n",
              "      <td>1.917396</td>\n",
              "      <td>2.217684</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>568</th>\n",
              "      <td>92751</td>\n",
              "      <td>B</td>\n",
              "      <td>-1.808817</td>\n",
              "      <td>1.220718</td>\n",
              "      <td>-1.817631</td>\n",
              "      <td>-1.346604</td>\n",
              "      <td>-3.109349</td>\n",
              "      <td>-1.149741</td>\n",
              "      <td>-1.116254</td>\n",
              "      <td>-1.260710</td>\n",
              "      <td>...</td>\n",
              "      <td>-1.409652</td>\n",
              "      <td>0.763518</td>\n",
              "      <td>-1.431475</td>\n",
              "      <td>-1.076640</td>\n",
              "      <td>-1.857384</td>\n",
              "      <td>-1.206491</td>\n",
              "      <td>-1.306570</td>\n",
              "      <td>-1.743529</td>\n",
              "      <td>-0.048096</td>\n",
              "      <td>-0.750546</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>569 rows × 32 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-51cf5ee2-f188-4671-8826-b1eb4e600b8e')\"\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",
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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",
              "      cursor: pointer;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "      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",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-51cf5ee2-f188-4671-8826-b1eb4e600b8e 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-51cf5ee2-f188-4671-8826-b1eb4e600b8e');\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",
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              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "df_norm = df\n",
        "#here I created a dummy dataframe and normalized it as mentioned in task 2\n",
        "for col in df_norm:\n",
        "    if col not in ['id','diagnosis']:\n",
        "        df_norm[col] = (df_norm[col] - df_norm[col].mean()) / df_norm[col].std()\n",
        "df_norm"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "6989fb7a",
      "metadata": {
        "id": "6989fb7a",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "910281a6-f40f-40bd-b0cd-90b37dfdf139"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0 0\n"
          ]
        }
      ],
      "source": [
        "missing_value1 = df['diagnosis'].isna().sum()\n",
        "missing_value2 = df['id'].isna().sum()\n",
        "#finding missing value in our categorical data\n",
        "#here there was no missing value in both\n",
        "# print(missing_value1,missing_value2)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df['diagnosis'].value_counts()"
      ],
      "metadata": {
        "id": "RlYjtK_vzSFk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6a0747b1-3a2d-497a-b561-b232fbfdcd17"
      },
      "id": "RlYjtK_vzSFk",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "B    357\n",
              "M    212\n",
              "Name: diagnosis, dtype: int64"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Perceptron Learning Algorithm**"
      ],
      "metadata": {
        "id": "cXahyuMQPZsw"
      },
      "id": "cXahyuMQPZsw"
    },
    {
      "cell_type": "code",
      "source": [
        "#task 2 was accomplished\n",
        "\n",
        "class Perceptron:\n",
        "    \n",
        "    def __init__(self, learning_rate = 0.001, epochs = 1000):\n",
        "        self.weights = None\n",
        "        self.bias = None\n",
        "        self.learning_rate = learning_rate\n",
        "        self.epochs = epochs\n",
        "\n",
        "    def activation(self, z):\n",
        "        return np.heaviside(z, 0)\n",
        "    \n",
        "#                       0   if x1 < 0\n",
        "# heaviside(x1, x2) =  x2   if x1 == 0\n",
        "# here x2 = 0\n",
        "#                       1   if x1 > 0\n",
        "\n",
        "    def fit(self, X, y):\n",
        "        columns = X.shape[1]\n",
        "        # This will give the number of columns is 2-d array \n",
        "        # Initializing weights and bias with zeros\n",
        "        self.weights = np.zeros((columns))\n",
        "        self.bias = 0\n",
        "        \n",
        "        # Iterating until the number of epochs\n",
        "        for epoch in range(self.epochs):\n",
        "            \n",
        "            # Traversing through the entire training set\n",
        "            for i in range(len(X)):\n",
        "                z = np.dot(X, self.weights) + self.bias # Finding the dot product and adding the bias\n",
        "                y_pred = self.activation(z) # Passing through an activation function\n",
        "                \n",
        "                # old_weight = self.weights \n",
        "                #Updating weights and bias\n",
        "                self.weights = self.weights + self.learning_rate * (y[i] - y_pred[i]) * X[i]\n",
        "                self.bias = self.bias + self.learning_rate * (y[i] - y_pred[i])\n",
        "                \n",
        "                # if((old_weight==self.weights).all()):\n",
        "                  # print(\"Weights are unchanged from the previous iteration\")\n",
        "                # else:\n",
        "                  # print(self.weights)\n",
        "        return self.weights, self.bias\n",
        "    \n",
        "    def predict(self, X):\n",
        "        z = np.dot(X, self.weights) + self.bias\n",
        "        return self.activation(z)"
      ],
      "metadata": {
        "id": "tPi25n07PW2Y"
      },
      "id": "tPi25n07PW2Y",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **PM1**"
      ],
      "metadata": {
        "id": "0nrxz7jCO-sT"
      },
      "id": "0nrxz7jCO-sT"
    },
    {
      "cell_type": "code",
      "source": [
        "\n",
        "X = df.iloc[:, 2:].values\n",
        "y = np.where(df.iloc[:, 1].values == 'M', 1, 0)\n",
        "  #create a numpy array and put value where the cancer is malignant to 1 if not then 0\n",
        "  #above function is a compact form of the below function\n",
        "\n",
        "  # li = []\n",
        "  # for i in df.iloc[:,1].values:\n",
        "  #     if i == 'M':\n",
        "  #         li.append(1)\n",
        "  #     else:\n",
        "  #         li.append(-1)\n",
        "  # y = np.array(li)\n",
        "\n",
        "  # set a random seed for reproducibility\n",
        "# np.random.seed(1)\n",
        "  # shuffle the indices of the samples\n",
        "indices = np.arange(len(X))\n",
        "  #The np.arange() function is used to create an array of indices \n",
        "      #corresponding to the number of samples in the dataset\n",
        "np.random.shuffle(indices)\n",
        "\n",
        "  # split the indices into training and testing sets as ***mentioned by Bhanu Sir***\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "\n",
        "  # create the training and testing feature and target arrays\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]\n",
        "\n",
        "\n",
        "\n",
        " "
      ],
      "metadata": {
        "id": "PrswV6LhGAsf"
      },
      "id": "PrswV6LhGAsf",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "043724a4",
      "metadata": {
        "id": "043724a4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5f7acf03-1ea4-4062-80be-a814b291f4b2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 96.84210526315789 %\n"
          ]
        }
      ],
      "source": [
        "perceptron = Perceptron()\n",
        "\n",
        "perceptron.fit(X_train, y_train)\n",
        "\n",
        "# Make predictions on the testing dataset\n",
        "y_pred = perceptron.predict(X_test)\n",
        "\n",
        "# Calculate the accuracy of the model on the testing dataset\n",
        "accuracy = np.sum(y_pred == y_test)/len(y_test) * 100\n",
        "print(f\"Accuracy: {accuracy} %\")"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **PM2**"
      ],
      "metadata": {
        "id": "esmjREX4Pq-o"
      },
      "id": "esmjREX4Pq-o"
    },
    {
      "cell_type": "code",
      "source": [
        "X = df.iloc[:, 2:].values\n",
        "# Get Malignant cancer datapoints and label them as 1, and begnign as 0\n",
        "y = np.where(df.iloc[:, 1].values == 'M', 1, 0)\n",
        "  #create a numpy array and put value where the cancer is malignant to 1 if not then 0\n",
        "  #above function is a compact form of the below function\n",
        "\n",
        "  # li = []\n",
        "  # for i in df.iloc[:,1].values:\n",
        "  #     if i == 'M':\n",
        "  #         li.append(1)\n",
        "  #     else:\n",
        "  #         li.append(-1)\n",
        "  # y = np.array(li)\n",
        "\n",
        "  # set a random seed for reproducibility\n",
        "np.random.seed(1)\n",
        "  # shuffle the indices of the samples\n",
        "indices = np.arange(len(X))\n",
        "  #The np.arange() function is used to create an array of indices \n",
        "      #corresponding to the number of samples in the dataset\n",
        "np.random.shuffle(indices)\n",
        "\n",
        "  # split the indices into training and testing sets as ***mentioned by Bhanu Sir***\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "\n",
        "# Shuffle the train_indices\n",
        "np.random.shuffle(train_indices)\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "\n",
        "X_test, y_test = X[test_indices], y[test_indices]\n",
        "print(X_test)"
      ],
      "metadata": {
        "id": "-rLSHvl_PyHI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d9a61812-f471-487d-bd64-c1bb0b23161d"
      },
      "id": "-rLSHvl_PyHI",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1.71142018  2.08330086  1.61457747 ...  0.73318211 -0.53138705\n",
            "  -0.97312203]\n",
            " [ 1.5833598   0.55576183  1.56100073 ...  1.68705047  1.84950885\n",
            "  -0.26386948]\n",
            " [ 1.29024384 -0.39284689  1.30548091 ...  1.87417297  1.45188469\n",
            "   0.43763168]\n",
            " ...\n",
            " [ 0.87760486  1.21606789  0.91395861 ...  1.14546014  0.66633451\n",
            "   2.76581825]\n",
            " [-0.02450933  0.45578591 -0.09204765 ... -0.53210068 -1.09064705\n",
            "  -0.43052445]\n",
            " [-0.30908794 -0.20219513 -0.38795608 ... -0.98089041 -1.47695671\n",
            "  -1.23224006]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "perceptron = Perceptron()\n",
        "perceptron.fit(X_train, y_train)\n",
        "y_pred = perceptron.predict(X_test)\n",
        "accuracy = np.sum(y_pred == y_test)/len(y_test) * 100\n",
        "print(f\"Accuracy: {accuracy} %\")\n",
        "\n",
        "#accuracy of PM2 matches with accuracy of PM1"
      ],
      "metadata": {
        "id": "QD3qCao1QQKK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9e5e088e-18d8-4d11-d73d-00f9e313768e"
      },
      "id": "QD3qCao1QQKK",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 97.89473684210527 %\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **PM3**"
      ],
      "metadata": {
        "id": "kfvo3wcfSFoC"
      },
      "id": "kfvo3wcfSFoC"
    },
    {
      "cell_type": "code",
      "source": [
        "X = df_norm.iloc[:, 2:].values\n",
        "y = np.where(df_norm.iloc[:, 1].values == 'M', 1, 0)\n",
        "\n",
        "\n",
        "# np.random.seed(1)\n",
        "indices = np.arange(len(X))\n",
        "np.random.shuffle(indices)\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]\n",
        "perceptron = Perceptron()\n",
        "perceptron.fit(X_train, y_train)\n",
        "y_pred = perceptron.predict(X_test)\n",
        "accuracy = np.sum(y_pred == y_test)/len(y_test) * 100\n",
        "print(f\"Accuracy: {accuracy} %\")\n"
      ],
      "metadata": {
        "id": "yGCf5t5DSOE6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f07fdc78-ed74-4819-ec6b-296c535229e8"
      },
      "id": "yGCf5t5DSOE6",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 94.21052631578948 %\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **PM4**"
      ],
      "metadata": {
        "id": "ogJ7KPXq4vSW"
      },
      "id": "ogJ7KPXq4vSW"
    },
    {
      "cell_type": "code",
      "source": [
        "shuffled_cols = df.iloc[:, 2:].sample(frac=1, axis=1)\n",
        "df2 = pd.concat([df.iloc[:, :2], shuffled_cols], axis=1)\n",
        "X = df2.iloc[:, 2:].values\n",
        "y = np.where(df2.iloc[:, 1].values == 'M', 1, 0)\n",
        "# np.random.seed(1)\n",
        "indices = np.arange(len(X))\n",
        "np.random.shuffle(indices)\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]"
      ],
      "metadata": {
        "id": "qsrqhKPz6Rlr"
      },
      "id": "qsrqhKPz6Rlr",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "perceptron = Perceptron()\n",
        "perceptron.fit(X_train, y_train)\n",
        "y_pred = perceptron.predict(X_test)\n",
        "accuracy = np.sum(y_pred == y_test)/len(y_test) * 100\n",
        "print(f\"Accuracy: {accuracy} %\")\n",
        "\n",
        "#accuracy of PM2 matches with accuracy of PM1"
      ],
      "metadata": {
        "id": "NJ04iPsxDeCB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "aa4699dc-46bb-42ca-f4ed-04ea44d75f23"
      },
      "id": "NJ04iPsxDeCB",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Accuracy: 97.36842105263158 %\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Fisher’s Linear Discriminant Analysis**\n"
      ],
      "metadata": {
        "id": "mlMeeu186TuP"
      },
      "id": "mlMeeu186TuP"
    },
    {
      "cell_type": "code",
      "source": [
        "# Imports\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from numpy.linalg import inv as inv\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm as norm\n"
      ],
      "metadata": {
        "id": "ntuXl2Zc6WU0"
      },
      "id": "ntuXl2Zc6WU0",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def find_predictions(X_test, W, threshold):\n",
        "    \n",
        "    # Project the Test data onto W\n",
        "    proj_testdata = np.dot(W, X_test.transpose()).reshape(X_test.shape[0],1)\n",
        "    \n",
        "    # Compare with threshold\n",
        "    predictions = (proj_testdata >= threshold).astype(int).reshape(X_test.shape[0],1)\n",
        "    \n",
        "    return proj_testdata, predictions"
      ],
      "metadata": {
        "id": "z8X4kdFf60qb"
      },
      "id": "z8X4kdFf60qb",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_projections(projections, y_test, threshold):\n",
        "    proj_pred_data = pd.DataFrame(np.concatenate((projections, y_test.reshape(-1, 1)), axis=1))\n",
        "    \n",
        "\n",
        "    proj1_pred = proj_pred_data.loc[proj_pred_data[1] == 1][[0]]\n",
        "    proj2_pred = proj_pred_data.loc[proj_pred_data[1] == 0][[0]]    \n",
        "    plt.figure(figsize=(8, 5))\n",
        "    plt.plot(proj1_pred, np.ones(proj1_pred.shape), '.', color='b', label='Malignant (value 1)')\n",
        "    plt.plot(proj2_pred, np.ones(proj2_pred.shape), '.', color='r',label='Benign (value 0)')\n",
        "    plt.plot([threshold], [1], '.', color='g',label='Threshold')\n",
        "    plt.legend(loc = 'upper right')\n",
        "    plt.title('Projections onto W vector. Threshold = '+ str(threshold))\n",
        "    plt.show()\n"
      ],
      "metadata": {
        "id": "Jagpx-xN83p_"
      },
      "id": "Jagpx-xN83p_",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def find_w_cordinates(X_train1, X_train2):\n",
        "    # X_train1 is the positive class and X_train2 is the negative class\n",
        "    \n",
        "    # 1. Find M1, M2, Cov1, Cov2\n",
        "    Mean1 = np.mean(X_train1,axis=0)\n",
        "    Mean2 = np.mean(X_train2,axis=0)\n",
        "    Mean_difference = np.subtract(Mean1,Mean2)\n",
        "\n",
        "    Cov1 = np.cov(np.transpose(X_train1))\n",
        "    Cov2 = np.cov(np.transpose(X_train2))\n",
        "\n",
        "    # 2. Within class spread Sw = Cov1 + Cov2  \n",
        "    Sw_inv = np.linalg.inv(np.add(Cov1,Cov2))\n",
        "    \n",
        "    # 3. W = (Sw_inv).(M1-M2)\n",
        "    W = np.dot(Sw_inv,Mean_difference)\n",
        "    \n",
        "    # 4. Normalise W\n",
        "    W_norm = W / np.linalg.norm(W)\n",
        "    \n",
        "    # Note:\n",
        "    # change X limits for pdf plot to -30 to 30 if W is used\n",
        "    # change X limits for pdf plot to -3 to 3 if normalised W is used\n",
        "    \n",
        "    return W_norm"
      ],
      "metadata": {
        "id": "8JBxuR8_6YFj"
      },
      "id": "8JBxuR8_6YFj",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def solve_pdfs(pdf_mean_1, pdf_mean_2, pdf_std_1, pdf_std_2):\n",
        "    coeff1 = 1/(2*pdf_std_1**2) - 1/(2*pdf_std_2**2)\n",
        "    coeff2 = pdf_mean_2/(pdf_std_2**2) - pdf_mean_1/(pdf_std_1**2)\n",
        "    coeff3 = pdf_mean_1**2 /(2*pdf_std_1**2) - pdf_mean_2**2 / (2*pdf_std_2**2) - np.log(pdf_std_2/pdf_std_1)\n",
        "\n",
        "    coeffs = [coeff1, coeff2, coeff3]\n",
        "    roots_of_eq = np.roots(coeffs)\n",
        "    threshold = roots_of_eq[1]\n",
        "    #found by experimenting\n",
        "    #take[1] when using normalized value\n",
        "    #else take[0] as [1] gives negative solution or the other incorrect solution\n",
        "    return threshold"
      ],
      "metadata": {
        "id": "FD7LYrDn6w5h"
      },
      "id": "FD7LYrDn6w5h",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def plot_pdfs(mean1, mean2, std1, std2, threshold):\n",
        "    # change X limits for pdf plot to -3 to 3 if normalised W is used. Otherwise set it to -30 to 30 \n",
        "    X_axis = np.linspace(-1,1,100000)\n",
        "    plt.plot(X_axis, norm.pdf(X_axis, mean1, std1),'-', color='b',label='Malignant (value 1)')    \n",
        "    plt.plot(X_axis, norm.pdf(X_axis, mean2, std2),'-', color='r',label='Benign (value 0)')\n",
        "    plt.plot([threshold], norm.pdf([threshold], mean1, std1), '*', color='g',label='Threshold')\n",
        "    plt.legend(loc = 'upper right')\n",
        "    plt.title('Normal distributions. Threshold = '+ str(threshold))\n",
        "    plt.show()\n",
        "    print('\\n')"
      ],
      "metadata": {
        "id": "9ZnBW_iW7Ses"
      },
      "id": "9ZnBW_iW7Ses",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def find_threshold(X_train1, X_train2, W):\n",
        "    # Threshold = point of intersection of the (probability density functions)\n",
        "    \n",
        "    # 1. Find Projections on the line W\n",
        "    Proj1 = np.dot(W,X_train1.transpose())\n",
        "    Proj2 = np.dot(W,X_train2.transpose())\n",
        "    \n",
        "    # 2. Find Means of the projected data for positive and negative classes\n",
        "    proj_mean1 = np.mean(Proj1)\n",
        "    proj_mean2 = np.mean(Proj2)\n",
        "    print('malignant_mean',proj_mean1,' benign_mean2',proj_mean2)\n",
        "    # 3. Find Std deviations of the projected data for positive and negative classes\n",
        "    proj_std1 = np.std(Proj1)\n",
        "    proj_std2 = np.std(Proj2)\n",
        "    print('malignant_std',proj_std1,' benign_std2',proj_std2)\n",
        "    # 4. Solve the equations\n",
        "\n",
        "    threshold = solve_pdfs(proj_mean1, proj_mean2, proj_std1, proj_std2)\n",
        "    print(\"threshold\",threshold)\n",
        "    print('\\n')\n",
        "    # Plot the pdfs\n",
        "    plot_pdfs(proj_mean1, proj_mean2, proj_std1, proj_std2, threshold)\n",
        "    return threshold\n"
      ],
      "metadata": {
        "id": "nEJ0pfAh7H4P"
      },
      "id": "nEJ0pfAh7H4P",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "vr4DGeMcdHzS"
      },
      "id": "vr4DGeMcdHzS"
    },
    {
      "cell_type": "markdown",
      "source": [
        "**“TP” = true positive; “FN” = false negative; “FP” = false positive; “TN” = true negative.**"
      ],
      "metadata": {
        "id": "wVzZ2XV0dopD"
      },
      "id": "wVzZ2XV0dopD"
    },
    {
      "cell_type": "code",
      "source": [
        "def matrix(y_test , y_predicted):\n",
        "  li1 = []\n",
        "  for i in y_test:\n",
        "          li1.append(i)\n",
        "  li = []\n",
        "  for i in y_predicted:\n",
        "          li.append(i[0])\n",
        "  \n",
        "  TP = 0\n",
        "  TN = 0\n",
        "  FP = 0\n",
        "  FN = 0\n",
        "  for i in range(len(li)):\n",
        "    if li[i]==li1[i]:\n",
        "      if li[i]==1:\n",
        "        TP += 1\n",
        "      else:\n",
        "        TN += 1\n",
        "    else:\n",
        "        if li[i]==1:\n",
        "          FP += 1\n",
        "        else:\n",
        "          FN += 1\n",
        "  return TP,TN,FP,FN"
      ],
      "metadata": {
        "id": "kRU3Bh4Z8Kfe"
      },
      "id": "kRU3Bh4Z8Kfe",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def accuracy(y_test , y_predicted):\n",
        "    TP,TN,FP,FN = matrix(y_test , y_predicted)\n",
        "    return (TP + TN)/(TP + TN + FP + FN)\n",
        "    # Accuracy = (TP + TN)/(TP + TN + FP + FN)\n"
      ],
      "metadata": {
        "id": "8eSG0Ey77Y2k"
      },
      "id": "8eSG0Ey77Y2k",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def precision(y_test , y_predicted):\n",
        "    # Precision = (TP)/(TP + FP) = True pos out of the actual results\n",
        "    TP,TN,FP,FN = matrix(y_test , y_predicted)\n",
        "    return TP/(TP + FP)"
      ],
      "metadata": {
        "id": "HFf12S6VcYaX"
      },
      "id": "HFf12S6VcYaX",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def recall(y_test , y_predicted):\n",
        "    # Recall = (TP)/(TP + FN) = True pos out of the predicted results\n",
        "    TP,TN,FP,FN = matrix(y_test , y_predicted)\n",
        "    return TP/(TP + FN)"
      ],
      "metadata": {
        "id": "BLEjePH8cch9"
      },
      "id": "BLEjePH8cch9",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def f_score(y_test , y_predicted):\n",
        "    # F_Score = 2PR/(P+R)\n",
        "    P = precision(y_test , y_predicted)\n",
        "    R = recall(y_test , y_predicted)\n",
        "    return 2*P*R/(P + R)"
      ],
      "metadata": {
        "id": "Oou5HKeVclMn"
      },
      "id": "Oou5HKeVclMn",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def fisher(X_train1, X_train2, X_test, y_test):\n",
        "    \n",
        "    # 1. Find Projection Line\n",
        "    W = find_w_cordinates(X_train1, X_train2)\n",
        "    \n",
        "    # 2. Find Threshold\n",
        "    threshold = find_threshold(X_train1, X_train2, W)\n",
        "    \n",
        "    # 3. Find Predictions for the Test Data by Projecting onto W and comparing to the threshold\n",
        "    projections, y_predicted = find_predictions(X_test, W, threshold)\n",
        "    \n",
        "    # Plot the projections\n",
        "    plot_projections(projections, y_test, threshold)\n",
        "    print('\\n')\n",
        "    print('W:\\n',W)\n",
        "    print('\\n')\n",
        "    print('Threshold:',threshold)\n",
        "    print('accuracy:',accuracy(y_test , y_predicted))\n",
        "    \n",
        "    print(\"precision:\",precision(y_test , y_predicted))\n",
        "    print(\"recall:\",recall(y_test , y_predicted))\n",
        "    print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "KHDVtT097bHH"
      },
      "id": "KHDVtT097bHH",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **FLDM1**"
      ],
      "metadata": {
        "id": "Jh5w1tOBt6s8"
      },
      "id": "Jh5w1tOBt6s8"
    },
    {
      "cell_type": "code",
      "source": [
        "df_norm = df\n",
        "#here I created a dummy dataframe and normalized it as mentioned in task 2\n",
        "for col in df_norm:\n",
        "    if col not in ['id','diagnosis']:\n",
        "        df_norm[col] = (df_norm[col] - df_norm[col].mean()) / df_norm[col].std()\n",
        "        \n",
        "X = df_norm.iloc[:, 2:].values\n",
        "y = np.where(df_norm.iloc[:, 1].values == 'M', 1, 0)\n",
        "\n",
        "  #create a numpy array and put value where the cancer is malignant to 1 if not then 0\n",
        "  #above function is a compact form of the below function\n",
        "\n",
        "  # li = []\n",
        "  # for i in df.iloc[:,1].values:\n",
        "  #     if i == 'M':\n",
        "  #         li.append(1)\n",
        "  #     else:\n",
        "  #         li.append(-1)\n",
        "  # y = np.array(li)\n",
        "\n",
        "  # set a random seed for reproducibility\n",
        "np.random.seed(13123)\n",
        "  # shuffle the indices of the samples\n",
        "indices = np.arange(len(X))\n",
        "  #The np.arange() function is used to create an array of indices \n",
        "      #corresponding to the number of samples in the dataset\n",
        "np.random.shuffle(indices)\n",
        "\n",
        "  # split the indices into training and testing sets as ***mentioned by Bhanu Sir***\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "\n",
        "  # create the training and testing feature and target arrays\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]\n",
        "\n",
        "# X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.6)\n",
        "\n",
        "\n",
        "X_train1 = X_train[y_train == 1]\n",
        "X_train2 =  X_train[y_train == 0]"
      ],
      "metadata": {
        "id": "CDEUNIY0t42u"
      },
      "id": "CDEUNIY0t42u",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fisher(X_train1, X_train2, X_test, y_test)"
      ],
      "metadata": {
        "id": "ea30qGmp-0WS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 982
        },
        "outputId": "ee9fdcbb-a9a2-40d6-f7d3-018a17ddb16a"
      },
      "id": "ea30qGmp-0WS",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "malignant_mean 0.5759037768593619  benign_mean2 -0.33495743395722954\n",
            "malignant_std 0.275229610164177  benign_std2 0.22324542339513603\n",
            "threshold 0.0870530650206827\n",
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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BzdxgHjXy1Hcwn4vxzyN8hQ9Ch4fSXgJuCg33wj/MtQP4L9ArlNYSH5g+C9bv60DfuHk9SPDwXIJ6nIa/OrUjWDc5obS5wTrYCvwvth6CtGHBdMVBm74A9AylW7C+Yg+j3U3FJ9fb4W+nFeP3MVeG0n6HP7j8KkibSOi/JIJ1VhDUeQUV/+tlNv5qSXHo81Io/XD8We9XQftfHNceA/D3l4vxB20DQmkd8Ze1NwXL9P+ATkHawKAfbY+b94C4ZS4lbp98IH5iT7tKLQsu7ZYBHZxzn9R1fUREJJp06bvudMf/O8GnVWUUEZFDlwJ1HTCz8/GXjK53zu2q6/qIiEh06dK3iIhIhOmMWkREJMIUqEVERCIscm/PadWqlcvJyanraoiIiNSaBQsWfO6ca50oLXKBOicnh8LCwrquhoiISK0xs6Q/n6tL3yIiIhGmQC0iIhJhCtQiIiIRFrl71CIiB4uSkhLWrl3Lzp0767oqEhENGzYkOzubzMzMlKdRoBYRqSFr166ladOm5OTkUPHNmXIocs6xadMm1q5dS8eOHVOeTpe+RURqyM6dO2nZsqWCtABgZrRs2bLaV1gUqEVEapCCtITtS39QoBYROYiZGZdcckn5cGlpKa1bt+b73/9+pdMVFBSU53n22We58847a7SeYYsWLeLFF19Mmr5w4UIuv/zyfSp78uTJjB8/fl+rVsHNN99M+/btadKkSYXxf/rTn5g0aVJa5gEK1CIiB7XGjRuzdOlSduzYAcCrr75Ku3btqlXGueeeyw033FAT1UuoqkD9m9/8hquvvrrW6pPMOeecw/z58/caP2bMGP74xz+mbT4K1CIiB7lBgwbxwgsvADB16lRGjBhRnjZ//nz69+9Pr169+Na3vsWKFSv2mj58FvrBBx9w0kkn0aNHD375y1+Wn00WFBSQn5/PBRdcQOfOnRk5ciSxtzNOnDiRE088ke7duzNu3Ljy8fn5+Vx//fX07duX4447jrlz57Jr1y5uvfVWpk+fTm5uLtOnT69Ql23btrF48WJOOOEEdu/eTU5ODps3by5P79SpExs3buS5556jX79+9OrVi9NOO42NGzfutVyjR49mxowZ5cPhM+N77rmHE088kZ49e3LbbbclbNeTTjqJNm3a7DX+G9/4Bjk5OQmD+L5QoBYRiZB58+C3v/V/0+Wiiy5i2rRp7Ny5k8WLF9OvX7/ytM6dOzN37lwWLlzIxIkTuemmmyot65prruGaa65hyZIlZGdnV0hbuHAh9913H8uXL+fDDz/kjTfeAGD8+PG888475Wf2zz//fPk0paWlzJ8/n/vuu4/bb7+drKwsJk6cyPDhw1m0aBHDhw+vMI/CwkK6d+8OQL169Rg8eDBPP/00AG+//TYdOnTgyCOP5Dvf+Q5vvfUWCxcu5KKLLuLuu+9Oub1eeeUVVq5cyfz581m0aBELFixgzpw5KU8PkJeXx9y5c6s1TTIK1CIiETFvHpx6Ktxyi/+brmDds2dPVq9ezdSpUxk0aFCFtC1btjBs2DC6d+/Oz372M5YtW1ZFHecxbNgwAC6++OIKaX379iU7O5t69eqRm5vL6tWrAZg9ezb9+vWjR48evPbaaxXmMXToUAD69OlTnr8yGzZsoHXrPe+uGD58ePlZ97Rp08oD+9q1aznjjDPo0aMH99xzT5XLFfbKK6/wyiuv0KtXL3r37s17773HypUrU54e4IgjjmD9+vXVmiYZBWoRkYgoKIBdu6CszP8tKEhf2eeeey7XXntthcveALfccgsnn3wyS5cu5bnnntuvH2dp0KBB+feMjAxKS0vZuXMnP/7xj5kxYwZLlixh7NixFeYRmyaWvyqNGjWqMH3//v1ZtWoVRUVFPPPMM+WB/yc/+Qnjx49nyZIlPPjggwmXq379+uzevRuA3bt3s2vXLsD/v/ONN97IokWLWLRoEatWrar2w2s7d+6kUaNG1ZomGQVqEZGIyM+HrCzIyPB/8/PTV/aYMWO47bbb6NGjR4XxW7ZsKX+4bPLkyVWWc9JJJ/Hkk08C/gy2KrEA2apVK4qLiyvcE06madOmbNu2LWFaly5dWLVqVfmwmTFkyBB+/vOf06VLF1q2bAlUXK5HH300YVk5OTksWLAA8E+2l5SUAHDGGWcwadIkiouLAVi3bh2fffZZlfUOe//998sv0e8vBWoRkYjo3x9mzYJf/cr/7d8/fWVnZ2cnfFL6uuuu48Ybb6RXr14pndHed9993HvvvfTs2ZNVq1Zx2GGHVZq/efPmjB07lu7du3PGGWdw4oknVjmPk08+meXLlyd8mKxz585s2bKlQiAfPnw4jz32WIX72RMmTGDYsGH06dOHVq1aJZzP2LFj+c9//sMJJ5zAvHnzaNy4MQCnn346F198Mf3796dHjx5ccMEFCQ8crrvuOrKzs9m+fTvZ2dlMmDChPO2NN97ge9/7XpXLmgqLPX0XFXl5eU7voxaRg8G7775Lly5d6roaabV9+3YaNWqEmTFt2jSmTp3KzJkza7UOv//972natClXXHFFrc43VQsXLuTee+/lH//4R8L0RP3CzBY45/IS5ddvfYuISMoWLFjA+PHjcc7RvHnztP6wR6p+9KMf8a9//avW55uqzz//nF/96ldpK0+BWkREUjZgwAD+97//1WkdGjZsyKWXXlqndahMui55x+getYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iMhBLCMjg9zcXE444QR69+7Nm2++uc9l3Xrrrfz73/9OS72cc5xyyils3bp1n6aPf7Xkvvr6668ZPnw4xx57LP369Sv/GdMlS5YwevTotMxjf+mpbxGRg1ijRo1YtGgRAC+//DI33ngj//nPf/aprIkTJ6atXi+++CInnHACzZo1S1uZ++KRRx6hRYsWrFq1imnTpnH99dczffp0evTowdq1a/nkk084+uij67SOOqMWETlEbN26lRYtWpQPJ3qV4+rVq+nSpQtjx46lW7dunH766eXvsg6/FvLFF1+kc+fO9OnTh6uvvprvf//7gP9FsDFjxpCfn88xxxzD/fffn7Aujz/+OIMHDwbghhtu4M9//nN52oQJE/jd735HcXExp556Kr1796ZHjx4Jf1iloKCgfN7g39QV+ynUBQsWMHDgQPr06cMZZ5zBhg0b9pp+5syZXHbZZQBccMEFzJo1q/w1nOecc05KP5Na0xSoRUSiJM3vudyxYwe5ubl07tyZK664gltuuQWo/FWOK1eu5KqrrmLZsmU0b968/Le9Y3bu3MmVV17JSy+9xIIFCygqKqqQ/t577/Hyyy8zf/58br/99vLf0A5744036NOnD+B/AvSJJ54oT3viiScYPnw4DRs25Omnn+a///0vs2fP5he/+AWp/ppmSUkJP/nJT5gxYwYLFixgzJgx3HzzzXvlW7duHe3btwf8SzoOO+wwNm3aBKT3VZX7Q5e+RUSiIvaey127/Fs50vCD3+FL3/PmzWPUqFEsXbq0wqscAYqLi1m5ciVHH300HTt2JDc3F0j8+sn33nuPY445ho4dOwIwYsQIHnroofL0s88+mwYNGtCgQQOOOOIINm7cuNe7q7/44guaNm0KQK9evfjss89Yv349RUVFtGjRgvbt21NSUsJNN93EnDlzqFevHuvWrWPjxo0cddRRVS73ihUrWLp0afmPj5SVldGmTZtqtV06X1W5PxSoRUSiItF7LtP4Zo7+/fvz+eefU1RUVP4qxyuvvLJCntWrV+/1usrYpe9UJXrdZbzYKybr1fMXdocNG8aMGTP49NNPy1+u8fjjj1NUVMSCBQvIzMwkJydnr9dVhl9VCXve1uWco1u3bsyr4spEu3btWLNmDdnZ2ZSWlrJly5byN3Cl81WV+0OXvkVEoqIm33OJPxMuKyujZcuW+/Uqx+OPP54PP/yw/Ew7/g1X1SkjZvjw4UybNo0ZM2YwbNgwwL+q8ogjjiAzM5PZs2fz8ccf71VOhw4dWL58OV9//TWbN29m1qxZ5eUXFRWVB+qSkhKWLVu21/Tnnntu+WswZ8yYwSmnnIKZAel9VeX+0Bm1iEhUxN5zWVDgg3QazqZj96jBn2U++uijZGRkcPrpp/Puu+/SP5hHkyZNeOyxx8jIyKiyzEaNGvGXv/yFM888k8aNG6f06sp4Z599NgUFBRx77LEAdOvWjW3bttGuXbvyS9QjR47knHPOoUePHuTl5dG5c+e9ymnfvj0XXngh3bt3p2PHjuWX8rOyspgxYwZXX301W7ZsobS0lJ/+9Kd069atwvSXX345l156KcceeyyHH354hYfHZs+ezdlnn13tZUs3veZSRKSGHIyvuYwpLi6mSZMmOOe46qqr6NSpEz/72c9Snn7Dhg2MGjWKV199tQZrue++/vprBg4cyOuvv079+uk9p63uay6rvPRtZpPM7DMzW5ok3czsfjNbZWaLzax3XHozM1trZn+qxnKIiEiEPfzww+Tm5tKtWze2bNmy173uqrRp04axY8fu8w+e1LRPPvmEO++8M+1Bel9UeUZtZt8FioEpzrm9Ltab2SDgJ8AgoB/wB+dcv1D6H4DWwBfOufFVVUhn1CJysDiYz6hl36X9jNo5Nwf4opIsg/FB3Dnn3gKam1mbYMZ9gCOBV1Ksv4iIiISk46nvdsCa0PBaoJ2Z1QP+L3BtGuYhIiJySKrJf8/6MfCic25tVRnNbJyZFZpZYfwv3IiIiBzK0nGXfB3QPjScHYzrDwwwsx8DTYAsMyt2zt0QX4Bz7iHgIfD3qNNQJxERkYNCOs6onwVGBU9/nwRscc5tcM6NdM4d7ZzLwV/+npIoSIuISM3YtGkTubm55ObmctRRR9GuXTtyc3Np3rw5Xbt2Tfv8Yi/TqI5kr6sMvwDkUFflGbWZTQXygVZmtha4DcgEcM49ALyIf+J7FbAd+EFNVVZERFLXsmXL8t/5njBhAk2aNOHaa69l9erVFd44lUxpaWkk/j3pUJfKU98jnHNtnHOZzrls59wjzrkHgiBN8LT3Vc65bzrnejjn9vrfKufc5FT+NUtERGpHWVlZwldZ5ufn89Of/pS8vDz+8Ic/JH1V5P3330/Xrl3p2bMnF110UXm5y5cvT/iKy3vvvZfu3bvTvXt37rvvvr3q45xj/PjxHH/88Zx22mkp/5zpoUCHSiIiETJvzTwKVheQn5NP//bpeyFHvJUrVzJ16lQefvhhLrzwQp588kkuueQSAHbt2kVhYSElJSUMHDiQmTNn0rp1a6ZPn87NN9/MpEmTuPPOO/noo49o0KABmzdvLi/3vffeY/bs2Wzbto3jjz+eH/3oRyxevJi///3vvP322zjn6NevHwMHDiz/uU+Ap59+mhUrVrB8+XI2btxI165dGTNmTI0t/4FEgVpEJCLmrZnHqVNOZVfZLrIyspg1alaNBevKXmUZe3tVZa+K7NmzJyNHjuS8887jvPPOK5820SsuX3/9dYYMGULjxo0BGDp0KHPnzq0QqOfMmcOIESPIyMigbdu2nHLKKTWy3AciBWoRkYgoWF3ArrJdlLkydpXtomB1QY0F6speZRkLqJW9KvKFF15gzpw5PPfcc9xxxx0sWbIkYbmJXnEp1aPXXIqIRER+Tj5ZGVlkWAZZGVnk5+TXaX2SvSpy9+7drFmzhpNPPpm77rqLLVu2lL8uM5EBAwbwzDPPsH37dr766iuefvppBgwYUCHPd7/7XaZPn05ZWRkbNmxg9uzZNbpsBxKdUYuIRET/9v2ZNWpWrdyjTkWyV0Ued9xxXHLJJWzZsgXnHFdffTXNmzdPWk7v3r0ZPXo0ffv2BeCKK66ocNkbYMiQIbz22mt07dqVo48+uvz1m6LXXIqI1Bi9lEMSSftLOURERKTuKFCLiIhEmAK1iIhIhClQi4jUoKg9ByR1a1/6gwK1iEgNadiwIZs2bVKwFsAH6U2bNtGwYcNqTad/zxIRqSHZ2dmsXbuWoqKiuq6KRETDhg3Jzs6u1jQK1CIiNSQzM5OOHTvWdTXkAKdL3yIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYVUGajObZGafmdnSJOlmZveb2SozW2xmvYPxuWY2z8yWBeOHp7vyIiIiB7tUzqgnA2dWkn4W0Cn4jAP+GozfDoxyznULpr/PzJrvc01FREQOQfWryuCcm2NmOZVkGQxMcc454C0za25mbZxz74fKWG9mnwGtgc37WWcREZFDRjruUbcD1oSG1wbjyplZXyAL+CBRAWY2zswKzaywqKgoDVUSERE5ONT4w2Rm1gb4B/AD59zuRHmccw855/Kcc3mtW7eu6SqJiIgcMNIRqNcB7UPD2cE4zKwZ8AJws3PurTTMS0RE5JCSjkD9LDAqePr7JGCLc26DmWUBT+PvX89Iw3xEREQOOVU+TGZmU4F8oJWZrQVuAzIBnHMPAC8Cg4BV+Ce9fxBMeiHwXaClmY0Oxo12zi1KX/VFREQObqk89T2iinQHXJVg/GPAY/teNREREdEvk4mIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhFUZqM1skpl9ZmZLk6Sbmd1vZqvMbLGZ9Q6lXWZmK4PPZemsuIiIyKEglTPqycCZlaSfBXQKPuOAvwKY2eHAbUA/oC9wm5m12J/KioiIHGrqV5XBOTfHzHIqyTIYmOKcc8BbZtbczNoA+cCrzrkvAMzsVXzAn7rfta6OefOgoADy86F///Tlrcm6xOcLD0P10qZM8eObNfNpbdvCddfBM8/AP/8JxxwDI0fCwoXw6ac+71FHQa9e8NJL8P770KoVHH54xfErVkBJCRQVQUYGNG0KHTrsydesGSxaBGvWwKpVfvjyy2HrVj+Pbdtg5kzYsQOysqBJE/jyS3AOmjeHbt32lLVtG7z9NvTrB1995ctt1AjOOcfXL374rbd8vsaN4aST4LjjfJ7cXD//f/8b1q/3bdG9u6/P6tWwbh0cdpif7+WXQ48evs1atvTLvH69b9utW/e0VWzazz+Hiy+Gu+5i3jxYOWUep386haO+WA47d1YsL7aubrgBPvgARo5kyTfPo+SRKbRpC22uG7V3/6ik78xbM4+C1QXk5+TTv71PW/LQvMrLq6LLJfPQQ/Dkk3D++RUXJzZNrMuFu9Ko6i1OwnwtW/ouCr4Lxr6PGuX/xvJs2rTnb6JNJDyv66/fexOIlRlennTuEmLlbd4Mzz0HZnDNNTBuXPK8lS1HKnnC5d19t+/Gl1/u5xnOv2TJnnWbSn32Z/mT1a8md7+pSqUetV5X51yVHyAHWJok7XngO6HhWUAecC3wy9D4W4Brq5pXnz59XNq8+aZzjRo5l5Hh/775Znry1mRd4vM9+OCe4QYNnMvKSpyWleXTw2lZWc750FfxY5Z4vD4VP/XrO1evXrWmWTPyOjcw6023gwZuN7jd4fTMzD3rKiOjfPxucLuoV56/NDOrYv+opO+8+cmbrtGvG7mM2zNco183cm9+8qZb/GDF+e9V3j52zQcfrLi4scWJTfPmm74LxjdLgwYpL07CelW2CjIzfXPG8sS6dr16e28i4Xldd13yMmP1TfcuIVZeos3vwQcrXyeJliOVPOHyMjMrzvO66/bkr1+/evXZl7aorIya3v2mo47VybMvgELnEsfFSDxMZmbjzKzQzAqLiorSV3BBAezaBWVl/m9BQXry1mRd4vM9+WTF4ZKSxGklJXtPV1KSeB7OpXfZDlalpbB7d7Um+cZLT/HtkgIy2YUBFk6MrbvY35AMdpfnt5KSiv2jkr5TsLqAXWW7KHNl7CrbRcHqAjY9WXH+e5UXJ9Wu+eSTFYfDXbGgYE858eLLrO6mUNkqKCnxn1ieWNfevTvx5hOb11NPJS8zfnnStUuIlZdo84tv26p2A4nql2xZY+XF7w6eempP/tLS6tVnX9qisjJqevebjjpWJ0+6pSNQrwPah4azg3HJxu/FOfeQcy7POZfXunXrNFQpkJ/vL6tmZPi/sUuO+5u3JusSn+/88ysOZ2YmTsvM3Hu6zMzE8zBLPF4qql8f6lVvE9l+1lDeyMynhCwcUGGfHFt3sb8hZdQrz+8yMyv2j0r6Tn5OPlkZWWRYBlkZWeTn5NPy/Irz36u8OKl2zfPPrzgc7or5+XvKiRdfZnU3hcpWQWam/8TyhP8m2nxi8xo6NHmZ8cuTrl1CZcsT37ZV7QYS1S/ZssbKi98dDB26J3/9uJugVdVnX9qisjJqevebjjpWJ0+6mUvh7Cq4R/28c657grSzgfHAIPyDY/c75/oGD5MtAGJPgf8X6OOCe9bJ5OXlucLCwmotRKV0j9qP1z1q3aOuhO5R6x617lGnXo+aqKuZLXDO5SVMqypQm9lU/INhrYCN+Ce5MwGccw+YmQF/wj8oth34gXOuMJh2DHBTUNQdzrm/V1XZtAdqERGRiKssUKfy1PeIKtIdcFWStEnApFQqKSIiInuLxMNkIiIikpgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEmAK1iIhIhClQi4iIRJgCtYiISIQpUIuIiESYArWIiEiEKVCLiIhEWEqB2szONLMVZrbKzG5IkN7BzGaZ2WIzKzCz7FDa3Wa2zMzeNbP7zczSuQAiIiIHsyoDtZllAH8GzgK6AiPMrGtctt8BU5xzPYGJwG+Dab8FfBvoCXQHTgQGpq32IiIiB7lUzqj7Aquccx8653YB04DBcXm6Aq8F32eH0h3QEMgCGgCZwMb9rbSIiMihIpVA3Q5YExpeG4wL+x8wNPg+BGhqZi2dc/PwgXtD8HnZOfdu/AzMbJyZFZpZYVFRUXWXQURE5KCVrofJrgUGmtlC/KXtdUCZmR0LdAGy8cH9FDMbED+xc+4h51yecy6vdevWaaqSiIjIga9+CnnWAe1Dw9nBuHLOufUEZ9Rm1gQ43zm32czGAm8554qDtJeA/sDcNNRdRETkoJfKGfU7QCcz62hmWcBFwLPhDGbWysxiZd0ITAq+f4I/065vZpn4s+29Ln2LiIhIYlUGaudcKTAeeBkfZJ9wzi0zs4lmdm6QLR9YYWbvA0cCdwTjZwAfAEvw97H/55x7Lr2LICIicvAy51xd16GCvLw8V1hYWNfVEBERqTVmtsA5l5coTb9MJiIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRllKgNrMzzWyFma0ysxsSpHcws1lmttjMCswsO5R2tJm9YmbvmtlyM8tJY/1FREQOalUGajPLAP4MnAV0BUaYWde4bL8DpjjnegITgd+G0qYA9zjnugB9gc/SUXEREZFDQSpn1H2BVc65D51zu4BpwOC4PF2B14Lvs2PpQUCv75x7FcA5V+yc256WmouIiBwCUgnU7YA1oeG1wbiw/wFDg+9DgKZm1hI4DthsZk+Z2UIzuyc4QxcREZEUpOthsmuBgWa2EBgIrAPKgPrAgCD9ROAYYHT8xGY2zswKzaywqKgoTVUSERE58KUSqNcB7UPD2cG4cs659c65oc65XsDNwbjN+LPvRcFl81LgGaB3/Ayccw855/Kcc3mtW7fepwURERE5GKUSqN8BOplZRzPLAi4Cng1nMLNWZhYr60ZgUmja5mYWi76nAMv3v9oiIiKHhioDdXAmPB54GXgXeMI5t8zMJprZuUG2fGCFmb0PHAncEUxbhr/sPcvMlgAGPJz2pRARETlImXOurutQQV5enissLKzraoiIiNQaM1vgnMtLlKZfJhMREYkwBWoREZEIU6AWERGJMAVqERGRCFOgFhERiTAFahERkQhToBYREYkwBWoREZEIU6AWERGJMAVqERGRCFOgFhERiTAFahERkQhToBYREYkwBWoREZEIU6AWERGJMAVqERGRCFOgFhERiTAFahERkQhToBYREYkwBWoREZEIU6AWERGJMAVqERGRCFOgFhERiTAFahERkQhToBYREYkwBWoREZEIU6AWERGJMAVqERGRCFOgFhERiTAFahERkQhToBYREYkwBWoREZEIM+dcXdehAjMrAj6uxVm2Aj6vxfkdrNSO6aF2TA+1Y3qoHdMjlXbs4JxrnSghcoG6tplZoXMur67rcaBTO6aH2jE91I7poXZMj/1tR136FhERiTAFahERkQhToIaH6roCBwm1Y3qoHdND7Zgeasf02K92POTvUYuIiESZzqhFREQi7JAL1GY2zMyWmdluM0v6FJ6ZnWlmK8xslZndUJt1PBCY2eFm9qqZrQz+tkiSr8zMFgWfZ2u7nlFVVf8yswZmNj1If9vMcuqgmpGXQjuONrOiUB+8oi7qGWVmNsnMPjOzpUnSzczuD9p4sZn1ru06HghSaMd8M9sS6ou3plr2IReogaXAUGBOsgxmlgH8GTgL6AqMMLOutVO9A8YNwCznXCdgVjCcyA7nXG7wObf2qhddKfavy4EvnXPHAr8H7qrdWkZfNbbT6aE++LdareSBYTJwZiXpZwGdgs844K+1UKcD0WQqb0eAuaG+ODHVgg+5QO2ce9c5t6KKbH2BVc65D51zu4BpwOCar90BZTDwaPD9UeC8uqvKASeV/hVu3xnAqWZmtVjHA4G20zRwzs0Bvqgky2BgivPeApqbWZvaqd2BI4V23GeHXKBOUTtgTWh4bTBO9jjSObch+P4pcGSSfA3NrNDM3jKz82qnapGXSv8qz+OcKwW2AC1rpXYHjlS30/ODS7YzzKx97VTtoKL9Yfr0N7P/mdlLZtYt1Ynq12SN6oqZ/Rs4KkHSzc65mbVdnwNVZe0YHnDOOTNL9u8DHZxz68zsGOA1M1vinPsg3XUVSeI5YKpz7mszuxJ/leKUOq6THJr+i98fFpvZIOAZ/O2EKh2Ugdo5d9p+FrEOCB95ZwfjDimVtaOZbTSzNs65DcFlsM+SlLEu+PuhmRUAvYBDPVCn0r9iedaaWX3gMGBT7VTvgFFlOzrnwm32N+DuWqjXwUb7wzRwzm0NfX/RzP5iZq2cc1X+lroufSf2DtDJzDqaWRZwEaAnlit6Frgs+H4ZsNeVCjNrYWYNgu+tgG8Dy2uthtGVSv8Kt+8FwGtOP3oQr8p2jLuXei7wbi3W72DxLDAqePr7JGBL6LaXpMjMjoo9Z2JmffHxN6WD74PyjLoyZjYE+CPQGnjBzBY5584ws7bA35xzg5xzpWY2HngZyAAmOeeW1WG1o+hO4Akzuxz/trMLAYJ/efuhc+4KoAvwoJntxnfKO51zh3ygTta/zGwiUOicexZ4BPiHma3CP6ByUd3VOJpSbMerzexcoBTfjqPrrMIRZWZTgXyglZmtBW4DMgGccw8ALwKDgFXAduAHdVPTaEuhHS8AfmRmpcAO4KJUD771y2QiIiIRpkvfIiIiEaZALSIiEmEK1CIiIhGmQC0iIhJhCtQiIiIRpkAtIiISYQrUIiIiEaZALSIiEmH/H0W5P4my/Vu7AAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "W:\n",
            " [-0.07020747  0.02349569  0.07979575 -0.02800129 -0.0076535  -0.20505715\n",
            "  0.08392987  0.10266201  0.01025452 -0.04157101  0.18381503 -0.00984625\n",
            " -0.03162539 -0.07722896  0.03107518  0.04152803 -0.15272481  0.10168187\n",
            "  0.00956984 -0.0291826   0.69699245  0.05711523  0.08870868 -0.56022095\n",
            "  0.06068807 -0.02479384  0.1322392   0.00177734  0.04686823  0.1137293 ]\n",
            "\n",
            "\n",
            "Threshold: 0.0870530650206827\n",
            "accuracy: 0.9789473684210527\n",
            "precision: 0.9583333333333334\n",
            "recall: 0.9583333333333334\n",
            "f score: 0.9583333333333334\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **FLDM2**"
      ],
      "metadata": {
        "id": "VBYF7cKBAyRJ"
      },
      "id": "VBYF7cKBAyRJ"
    },
    {
      "cell_type": "code",
      "source": [
        "shuffled_cols = df.iloc[:, 2:].sample(frac=1, axis=1)\n",
        "df2 = pd.concat([df.iloc[:, :2], shuffled_cols], axis=1)\n",
        "X = df2.iloc[:, 2:].values\n",
        "y = np.where(df2.iloc[:, 1].values == 'M', 1, 0)\n",
        "np.random.seed(13123)\n",
        "indices = np.arange(len(X))\n",
        "np.random.shuffle(indices)\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]\n",
        "\n",
        "X_train1 = X_train[y_train == 1]\n",
        "X_train2 =  X_train[y_train == 0]"
      ],
      "metadata": {
        "id": "dRpLYzirA2eL"
      },
      "id": "dRpLYzirA2eL",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "fisher(X_train1, X_train2, X_test, y_test)"
      ],
      "metadata": {
        "id": "4tjyRRvdBNcc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 982
        },
        "outputId": "df61c5bb-c7cf-4b62-d0da-1e2645915cff"
      },
      "id": "4tjyRRvdBNcc",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "malignant_mean 0.5759037768593805  benign_mean2 -0.33495743395724026\n",
            "malignant_std 0.275229610164186  benign_std2 0.223245423395143\n",
            "threshold 0.08705306502068533\n",
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "\n",
            "W:\n",
            " [ 0.10266201  0.04686823  0.06068807  0.1137293  -0.56022095 -0.07020747\n",
            "  0.01025452 -0.20505715 -0.0076535   0.10168187  0.03107518  0.00177734\n",
            "  0.08870868  0.69699245  0.00956984  0.1322392   0.08392987  0.02349569\n",
            "  0.05711523 -0.0291826   0.18381503  0.04152803 -0.00984625 -0.02800129\n",
            "  0.07979575 -0.15272481 -0.02479384 -0.03162539 -0.07722896 -0.04157101]\n",
            "\n",
            "\n",
            "Threshold: 0.08705306502068533\n",
            "accuracy: 0.9789473684210527\n",
            "precision: 0.9583333333333334\n",
            "recall: 0.9583333333333334\n",
            "f score: 0.9583333333333334\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Logistic Regression**"
      ],
      "metadata": {
        "id": "Pb4FUhwF9YnA"
      },
      "id": "Pb4FUhwF9YnA"
    },
    {
      "cell_type": "code",
      "source": [
        "#importing the required libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n"
      ],
      "metadata": {
        "id": "cHiiK7g-9au9"
      },
      "id": "cHiiK7g-9au9",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**corrected**"
      ],
      "metadata": {
        "id": "VKflAoGAwlab"
      },
      "id": "VKflAoGAwlab"
    },
    {
      "cell_type": "markdown",
      "source": [
        "![image.png](data:image/png;base64,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)"
      ],
      "metadata": {
        "id": "Qx4pUse7d6a0"
      },
      "id": "Qx4pUse7d6a0"
    },
    {
      "cell_type": "markdown",
      "source": [
        "**“TP” = true positive; “FN” = false negative; “FP” = false positive; “TN” = true negative.**"
      ],
      "metadata": {
        "id": "QIpiANE2eCF2"
      },
      "id": "QIpiANE2eCF2"
    },
    {
      "cell_type": "code",
      "source": [
        "#function to calculate sigmoid\n",
        "def sigmoid(x):\n",
        "    return 1/(1 + np.exp(-x))  #changes made -x to x\n",
        "#hypothesis for logistic regression\n",
        "def hypothesis(X,theta):\n",
        "    return sigmoid(np.dot(X, theta))\n",
        "#binary cross entropy cost function, i.e derivative which we have to minimize\n",
        "def cost(X_train,y_train,theta):\n",
        "  h = hypothesis(X_train,theta)\n",
        "  h = np.clip(h, 1e-7, 1-1e-7) #done to avoid zero in log warning as value coming close to zero\n",
        "                                  #may be interpreted as 0\n",
        "  arr = []\n",
        "  for i in range(len(h)):\n",
        "    arr.append(h[i][0])\n",
        "  h = np.array(arr)\n",
        "  return (-1/len(y_train))*(np.sum((y_train * np.log(h)) + (1-y_train)*np.log(1-h)))"
      ],
      "metadata": {
        "id": "8KQSyJY--mYj"
      },
      "id": "8KQSyJY--mYj",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#function to predict the class of a test data point\n",
        "def predict(X, theta, threshold=0.5):\n",
        "    return (hypothesis(X, theta) >= threshold).astype(int)"
      ],
      "metadata": {
        "id": "NZXJjcbax1dk"
      },
      "id": "NZXJjcbax1dk",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def matrix(y_test , y_predicted):\n",
        "  li1 = []\n",
        "  for i in y_test:\n",
        "          li1.append(i)\n",
        "  li = []\n",
        "  for i in y_predicted:\n",
        "          li.append(i[0])\n",
        "  TP = 0\n",
        "  TN = 0\n",
        "  FP = 0\n",
        "  FN = 0\n",
        "  for i in range(len(li)):\n",
        "    if li[i]==li1[i]:\n",
        "      if li[i]==1:\n",
        "        TP += 1\n",
        "      else:\n",
        "        TN += 1\n",
        "    else:\n",
        "        if li[i]==1:\n",
        "          FP += 1\n",
        "        else:\n",
        "          FN += 1\n",
        "  return TP,TN,FP,FN\n",
        "\n",
        "\n",
        "def accuracy(y_test , y_predicted):\n",
        "    TP,TN,FP,FN = matrix(y_test , y_predicted)\n",
        "    return (TP + TN)/(TP + TN + FP + FN)\n",
        "    # Accuracy = (TP + TN)/(TP + TN + FP + FN)\n",
        "\n",
        "def recall(y_test , y_predicted):\n",
        "    # Recall = (TP)/(TP + FN) = True pos out of the predicted results\n",
        "    TP,TN,FP,FN = matrix(y_test , y_predicted)\n",
        "    return TP/(TP + FN)\n",
        "\n",
        "#function to calculate precision of the classifier\n",
        "def precision(y_test , y_predicted):\n",
        "    # Precision = (TP)/(TP + FP) = True pos out of the actual results\n",
        "    TP,TN,FP,FN = matrix(y_test , y_predicted)\n",
        "    return TP/(TP + FP)\n",
        "\n",
        "def f_score(y_test , y_predicted):\n",
        "    # F_Score = 2PR/(P+R)\n",
        "    P = precision(y_test , y_predicted)\n",
        "    R = recall(y_test , y_predicted)\n",
        "    return 2*P*R/(P + R)"
      ],
      "metadata": {
        "id": "GHPsTUHD9hS9"
      },
      "id": "GHPsTUHD9hS9",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **LR1**"
      ],
      "metadata": {
        "id": "BczLL55KgSRa"
      },
      "id": "BczLL55KgSRa"
    },
    {
      "cell_type": "code",
      "source": [
        "def batch_gradient_descent(X,y,theta,learning_rate,iterations):\n",
        "    cost_history=np.zeros(iterations)\n",
        "    m=len(y)\n",
        "    for i in range(iterations):\n",
        "        li1 = []\n",
        "        for j in hypothesis(X,theta):\n",
        "          li1.append(j[0])\n",
        "          a = np.array(li1)\n",
        "        gradient = (1/m)* np.dot(X.T, (a - y).reshape(379, 1))\n",
        "        #w=w-ita*gradient\n",
        "        theta = theta - learning_rate*gradient\n",
        "        cost_history[i] = cost(X, y, theta)\n",
        "    plt.title('Learning curve (Cost Function vs Iterations), Weights = normal, LR = {} , itr = {}'.format(learning_rate, iterations))\n",
        "    plt.plot(list(range(iterations)), cost_history, '-r')\n",
        "        \n",
        "    return theta,cost_history"
      ],
      "metadata": {
        "id": "doQo0tyxyH83"
      },
      "id": "doQo0tyxyH83",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "**2/3 Training and rest 1/3 for Testing as told by sir**"
      ],
      "metadata": {
        "id": "ejyUAzLpqp-e"
      },
      "id": "ejyUAzLpqp-e"
    },
    {
      "cell_type": "code",
      "source": [
        "# Without feature engineering the result are as follows:\n",
        "cols = df.columns\n",
        "num_cols = df._get_numeric_data().columns[1:]\n",
        "categorical_cols = list(set(cols)-set(num_cols))\n",
        "\n",
        "#finding missing total missing values in each column\n",
        "missing_values = sum(list(df.isna().sum()))\n",
        "#print(missing_values)\n",
        "#there were 7 missing values initially\n",
        "\n",
        "for col in df:\n",
        "    if col not in ['id','diagnosis']:\n",
        "        mean_value = df[col].mean()\n",
        "        #calculating the mean value\n",
        "        df[col].fillna(value=mean_value,inplace=True)\n",
        "        #replacing empty cell with the mean value calculated as mentioned in task 1\n",
        "        \n",
        "X = df.iloc[:, 2:].values\n",
        "y = np.where(df.iloc[:, 1].values == 'M', 1, 0)\n",
        "\n",
        "  #concatenate a columns of ones (to accomodate the bias)\n",
        "ones=np.ones((X.shape[0],1))\n",
        "X=np.concatenate((ones,X),axis=1) \n",
        "\n",
        "  #gaussian weight initialisations can be tried:\n",
        "  #theta=np.random.randn(X.shape[1],1)\n",
        "  #1. initialise weights to zeroes\n",
        "theta1=np.zeros((X.shape[1],1))\n",
        "  #split the data into training and testing data, change the test split here\n",
        "np.random.seed(1)\n",
        "indices = np.arange(len(X))\n",
        "np.random.shuffle(indices)\n",
        "  # split the indices into training and testing sets as ***mentioned by Bhanu Sir***\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "\n",
        "  # create the training and testing feature and target arrays\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]"
      ],
      "metadata": {
        "id": "b7zpEPhq-bkH"
      },
      "id": "b7zpEPhq-bkH",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.01,1000)\n",
        "y_predicted = predict(X_test,theta[0]) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "kbUnUaROUiQZ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "outputId": "566a7d9c-3617-43f6-8997-e1287e5b8209"
      },
      "id": "kbUnUaROUiQZ",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9842105263157894\n",
            "precision: 1.0\n",
            "recall: 0.958904109589041\n",
            "f score: 0.9790209790209791\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Q) What happens to testing accuracy when you vary the decision probability threshold from 0.5 to 0.3, 0.4, 0.6 and 0.7."
      ],
      "metadata": {
        "id": "ivFNrsO4gZ26"
      },
      "id": "ivFNrsO4gZ26"
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.3"
      ],
      "metadata": {
        "id": "PHp241pzzgMI"
      },
      "id": "PHp241pzzgMI"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.3) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "gxiIi7n1g80o",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e96277c0-ce94-4c42-c6f3-97f3d536b358"
      },
      "id": "gxiIi7n1g80o",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9736842105263158\n",
            "precision: 0.9594594594594594\n",
            "recall: 0.9726027397260274\n",
            "f score: 0.9659863945578231\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.4) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "mFSTgzLFg1lT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "00c752bb-5049-447a-d6c5-79e36eb29f1e"
      },
      "id": "mFSTgzLFg1lT",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9894736842105263\n",
            "precision: 1.0\n",
            "recall: 0.9726027397260274\n",
            "f score: 0.9861111111111112\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.6) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "8fKMKGcLmbX5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9d063f15-b91d-48dd-a5ac-62e293bb819b"
      },
      "id": "8fKMKGcLmbX5",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.968421052631579\n",
            "precision: 1.0\n",
            "recall: 0.9178082191780822\n",
            "f score: 0.9571428571428571\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.7) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "THh2NSammcvu",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eabacc76-22c7-4eee-e716-a072e43affd6"
      },
      "id": "THh2NSammcvu",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9473684210526315\n",
            "precision: 1.0\n",
            "recall: 0.863013698630137\n",
            "f score: 0.9264705882352942\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "You must implement the above two learning tasks using Batch Gradient Descent, Mini-batch Gradient Descent and Stochastic Gradient Descent using learning rates 0.01, 0.001 and 0.0001. Plot the learning curves (Cost Function vs Iterations) for the same."
      ],
      "metadata": {
        "id": "ILOE_09T5GOy"
      },
      "id": "ILOE_09T5GOy"
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Batch Gradient Descent**"
      ],
      "metadata": {
        "id": "3K7z6YIb04o5"
      },
      "id": "3K7z6YIb04o5"
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.01,1000)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "LfcC9E-Fzt_6",
        "outputId": "e4e4cf53-73de-4c44-efa9-c49175b882bd"
      },
      "id": "LfcC9E-Fzt_6",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.001,1000)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "IvMx1uK9zvFE",
        "outputId": "a88e20c7-0255-4d9d-ff81-1d5c99df6354"
      },
      "id": "IvMx1uK9zvFE",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.0001,1000)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "Ng6QZuYLzv6-",
        "outputId": "21aa40c7-7710-4656-e345-836b7853b90a"
      },
      "id": "Ng6QZuYLzv6-",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Explaination:**"
      ],
      "metadata": {
        "id": "iDwd1s310mMS"
      },
      "id": "iDwd1s310mMS"
    },
    {
      "cell_type": "markdown",
      "source": [
        "**The learning rate α determines how rapidly we update the parameters. If the learning rate is too large, we may \"overshoot\" the optimal value. Similarly, if it is too small, we will need too many iterations to converge to the best values. That's why it is crucial to use a well-tuned learning rate.**"
      ],
      "metadata": {
        "id": "mPjKhkuT0kjP"
      },
      "id": "mPjKhkuT0kjP"
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "pj0cZPRV0Wa4"
      },
      "id": "pj0cZPRV0Wa4"
    },
    {
      "cell_type": "markdown",
      "source": [
        "**If you have low learning rate means your cost function will decrease slowly but in case of large learning rate cost function will decrease very fast.**"
      ],
      "metadata": {
        "id": "wGkWnfIXUR0c"
      },
      "id": "wGkWnfIXUR0c"
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Graph of Batch, Stochastic, Mini-Batch***"
      ],
      "metadata": {
        "id": "uHkEErQ-J1Yg"
      },
      "id": "uHkEErQ-J1Yg"
    },
    {
      "cell_type": "markdown",
      "source": [
        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)"
      ],
      "metadata": {
        "id": "x0HXuzD2Jw_I"
      },
      "id": "x0HXuzD2Jw_I"
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **LR2**"
      ],
      "metadata": {
        "id": "VLB7ARFgKNQR"
      },
      "id": "VLB7ARFgKNQR"
    },
    {
      "cell_type": "markdown",
      "source": [
        "##**Applying Feature Engineering 1 to the dataset**\n",
        "\n"
      ],
      "metadata": {
        "id": "9QyVi57AovE2"
      },
      "id": "9QyVi57AovE2"
    },
    {
      "cell_type": "code",
      "source": [
        "cols = df.columns\n",
        "num_cols = df._get_numeric_data().columns[1:]\n",
        "categorical_cols = list(set(cols)-set(num_cols))\n",
        "categorical_cols\n",
        "#columns with categorical data\n",
        "print(\"The cols that contain categorical data are {}\".format(categorical_cols))\n",
        "\n",
        "#finding missing total missing values in each column\n",
        "missing_values = sum(list(df.isna().sum()))\n",
        "#print(missing_values)\n",
        "#there were 7 missing values initially\n",
        "\n",
        "for col in df:\n",
        "    if col not in ['id','diagnosis']:\n",
        "        mean_value = df[col].mean()\n",
        "        #calculating the mean value\n",
        "        df[col].fillna(value=mean_value,inplace=True)\n",
        "        #replacing empty cell with the mean value calculated as mentioned in task 1\n",
        "df_norm = df\n",
        "#here I created a dummy dataframe and normalized it as mentioned in task 2\n",
        "for col in df_norm:\n",
        "    if col not in ['id','diagnosis']:\n",
        "        df_norm[col] = (df_norm[col] - df_norm[col].mean()) / df_norm[col].std()"
      ],
      "metadata": {
        "id": "UBW6prP6pkUV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "01b32b85-89e7-4160-e33a-f062370e963f"
      },
      "id": "UBW6prP6pkUV",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The cols that contain categorical data are ['id', 'diagnosis']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating train and test splits\n",
        "X = df_norm.iloc[:, 2:].values\n",
        "y = np.where(df_norm.iloc[:, 1].values == 'M', 1, 0)\n",
        "\n",
        "#concatenate a columns of ones (to accomodate the bias)\n",
        "ones=np.ones((X.shape[0],1))\n",
        "X=np.concatenate((ones,X),axis=1) \n",
        "\n",
        "  #gaussian weight initialisations can be tried:\n",
        "  #theta=np.random.randn(X.shape[1],1)\n",
        "  #1. initialise weights to zeroes\n",
        "theta1=np.zeros((X.shape[1],1))\n",
        "  #split the data into training and testing data, change the test split here\n",
        "np.random.seed(1)\n",
        "indices = np.arange(len(X))\n",
        "np.random.shuffle(indices)\n",
        "  # split the indices into training and testing sets as ***mentioned by Bhanu Sir***\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "\n",
        "  # create the training and testing feature and target arrays\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]"
      ],
      "metadata": {
        "id": "KsV7ytNghXpx"
      },
      "id": "KsV7ytNghXpx",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Batch Gradient Descent**"
      ],
      "metadata": {
        "id": "tI_0PKarr4pQ"
      },
      "id": "tI_0PKarr4pQ"
    },
    {
      "cell_type": "code",
      "source": [
        "#function to predict the class of a test data point\n",
        "def predict(X, theta, threshold=0.5):\n",
        "    return (hypothesis(X, theta) >= threshold).astype(int)"
      ],
      "metadata": {
        "id": "Rpfi-c8SS-Aa"
      },
      "id": "Rpfi-c8SS-Aa",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.01,1000)\n",
        "y_predicted = predict(X_test,theta[0]) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "MzFqJuNvr4pQ",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "outputId": "488c6dad-43c4-47aa-ddcf-d163db7a2732"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9842105263157894\n",
            "precision: 1.0\n",
            "recall: 0.958904109589041\n",
            "f score: 0.9790209790209791\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "id": "MzFqJuNvr4pQ"
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.3"
      ],
      "metadata": {
        "id": "kC426tv7DMBI"
      },
      "id": "kC426tv7DMBI"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.3) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Qp_ib7RaC0XT",
        "outputId": "1672c8d0-d7fe-46ac-f7ee-f5b48575faa3"
      },
      "id": "Qp_ib7RaC0XT",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9736842105263158\n",
            "precision: 0.9594594594594594\n",
            "recall: 0.9726027397260274\n",
            "f score: 0.9659863945578231\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.4"
      ],
      "metadata": {
        "id": "PS9e6SgyDOIw"
      },
      "id": "PS9e6SgyDOIw"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.4) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "c0DiJzddr4pR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cee14228-85bf-4bf5-a2d2-27c36004a493"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9894736842105263\n",
            "precision: 1.0\n",
            "recall: 0.9726027397260274\n",
            "f score: 0.9861111111111112\n"
          ]
        }
      ],
      "id": "c0DiJzddr4pR"
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.6"
      ],
      "metadata": {
        "id": "WiNjjDL7DPdM"
      },
      "id": "WiNjjDL7DPdM"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.6) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qv9ZVx6FDA6O",
        "outputId": "e4efe419-8292-4471-f798-5bf3e06ac9c3"
      },
      "id": "qv9ZVx6FDA6O",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.968421052631579\n",
            "precision: 1.0\n",
            "recall: 0.9178082191780822\n",
            "f score: 0.9571428571428571\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.7"
      ],
      "metadata": {
        "id": "mv1lW36pDQnu"
      },
      "id": "mv1lW36pDQnu"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.7) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "vvxOc1PcDCHi",
        "outputId": "cffbc18c-c7c6-4c39-9a35-7bc2c942f06b"
      },
      "id": "vvxOc1PcDCHi",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9473684210526315\n",
            "precision: 1.0\n",
            "recall: 0.863013698630137\n",
            "f score: 0.9264705882352942\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.01,1000)"
      ],
      "metadata": {
        "id": "1nZdzy7Wr4pS",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "dfff8738-ccdc-4bca-cade-e17b7b4a4858"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "id": "1nZdzy7Wr4pS"
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.001,1000)"
      ],
      "metadata": {
        "id": "BZRMLTcyr4pT",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "50e50299-b7ac-488e-cfe4-778e1c9753ff"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "id": "BZRMLTcyr4pT"
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.0001,1000)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "id": "4YhIWiFwDZT1",
        "outputId": "e74125e5-1ace-450e-e9b3-5913833d3a4e"
      },
      "id": "4YhIWiFwDZT1",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**If you have low learning rate means your cost function will decrease slowly but in case of large learning rate cost function will decrease very fast.**"
      ],
      "metadata": {
        "id": "3YTfZqFMr4pT"
      },
      "id": "3YTfZqFMr4pT"
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Applying Feature Engineering 2 to normalise the dataset**"
      ],
      "metadata": {
        "id": "JV2EYh7VqG_c"
      },
      "id": "JV2EYh7VqG_c"
    },
    {
      "cell_type": "code",
      "source": [
        "df_norm = df\n",
        "#here I created a dummy dataframe and normalized it as mentioned in task 2\n",
        "for col in df_norm:\n",
        "    if col not in ['id','diagnosis']:\n",
        "        df_norm[col] = (df_norm[col] - df_norm[col].mean()) / df_norm[col].std()"
      ],
      "metadata": {
        "id": "kEKBixTxsg8h"
      },
      "id": "kEKBixTxsg8h",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Creating train and test splits\n",
        "X = df_norm.iloc[:, 2:].values\n",
        "y = np.where(df_norm.iloc[:, 1].values == 'M', 1, 0)\n",
        "\n",
        "#concatenate a columns of ones (to accomodate the bias)\n",
        "ones=np.ones((X.shape[0],1))\n",
        "X=np.concatenate((ones,X),axis=1) \n",
        "\n",
        "  #gaussian weight initialisations can be tried:\n",
        "  #theta=np.random.randn(X.shape[1],1)\n",
        "  #1. initialise weights to zeroes\n",
        "theta1=np.zeros((X.shape[1],1))\n",
        "  #split the data into training and testing data, change the test split here\n",
        "np.random.seed(1)\n",
        "indices = np.arange(len(X))\n",
        "np.random.shuffle(indices)\n",
        "  # split the indices into training and testing sets as ***mentioned by Bhanu Sir***\n",
        "n_train = int(len(X) * 2/3)\n",
        "train_indices, test_indices = indices[:n_train], indices[n_train:]\n",
        "\n",
        "  # create the training and testing feature and target arrays\n",
        "X_train, y_train = X[train_indices], y[train_indices]\n",
        "X_test, y_test = X[test_indices], y[test_indices]"
      ],
      "metadata": {
        "id": "XQwFuxhFs5xD"
      },
      "execution_count": null,
      "outputs": [],
      "id": "XQwFuxhFs5xD"
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Batch Gradient Descent**"
      ],
      "metadata": {
        "id": "U6VFDzXgs-3_"
      },
      "id": "U6VFDzXgs-3_"
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.01,1000)\n",
        "y_predicted = predict(X_test,theta[0]) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))\n"
      ],
      "metadata": {
        "id": "z5wTrLzBs-4A",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 350
        },
        "outputId": "02d2ae7d-7518-49bc-8356-b97058d3208f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9842105263157894\n",
            "precision: 1.0\n",
            "recall: 0.958904109589041\n",
            "f score: 0.9790209790209791\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "id": "z5wTrLzBs-4A"
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.3"
      ],
      "metadata": {
        "id": "eqg90i_PE1CW"
      },
      "id": "eqg90i_PE1CW"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.3) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "id": "utScvKiMs-4B",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1af72fae-4376-4cbe-f4b4-3d97be85a5d4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9736842105263158\n",
            "precision: 0.9594594594594594\n",
            "recall: 0.9726027397260274\n",
            "f score: 0.9659863945578231\n"
          ]
        }
      ],
      "id": "utScvKiMs-4B"
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.4"
      ],
      "metadata": {
        "id": "DJmDQWRCE2E5"
      },
      "id": "DJmDQWRCE2E5"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.4) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BQk8XYfZERcI",
        "outputId": "61793da8-48e9-4223-eae2-13bb708f54f3"
      },
      "id": "BQk8XYfZERcI",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9894736842105263\n",
            "precision: 1.0\n",
            "recall: 0.9726027397260274\n",
            "f score: 0.9861111111111112\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.6"
      ],
      "metadata": {
        "id": "JZsFZrGNE3VP"
      },
      "id": "JZsFZrGNE3VP"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.6) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ySRHN8kTESU7",
        "outputId": "a5078f31-29be-40ad-9836-a91f11fa240c"
      },
      "id": "ySRHN8kTESU7",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.968421052631579\n",
            "precision: 1.0\n",
            "recall: 0.9178082191780822\n",
            "f score: 0.9571428571428571\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "0.7"
      ],
      "metadata": {
        "id": "KEh5WRQrE4hi"
      },
      "id": "KEh5WRQrE4hi"
    },
    {
      "cell_type": "code",
      "source": [
        "y_predicted = predict(X_test,theta[0],0.7) #we put inside it the respective threshold needed\n",
        "print(\"accuracy:\" , accuracy(y_test , y_predicted))\n",
        "print(\"precision:\",precision(y_test , y_predicted))\n",
        "print(\"recall:\",recall(y_test , y_predicted))\n",
        "print(\"f score:\",f_score(y_test , y_predicted))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o-jYyDxEJOaE",
        "outputId": "b64042ed-5dbc-4148-c7f0-934c80f167ab"
      },
      "id": "o-jYyDxEJOaE",
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "accuracy: 0.9473684210526315\n",
            "precision: 1.0\n",
            "recall: 0.863013698630137\n",
            "f score: 0.9264705882352942\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.01,1000)"
      ],
      "metadata": {
        "id": "qsorDXmes-4B",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "4d6ce094-b140-458b-840c-e89b892a90cc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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2X54e57mIcJDAy3H6HwmvvZ4WWiLPpXZ9NnTfghobKKYQPuByl0sInRAnE5oKNwJPETp75QpdSPhVNCtOKwt3v4fQsewRwpdy7rmL7Z//OOHL4mVCB6avxMd5hfAifBB4lQIdaYq4mfDB+7C7r06Mr299FZI75Cm3XP8idPg8DphvZmuB6wjbBnd/kPDheicheb6L2v303QhfausI22UNoakXwuFdoyw0Nd/dyGXM+TKh78J6QhP17tz/G4Qe6tMIvesvJ/Su30zoM/BErOm9yTu5+xpCa8HX43J8i3CkRnJdN1oMlU8SWiGSh0XtQ+gEu4GwW+QxEofx1uNhQopfbma5mr5NfC1a2IXxIPU3Cf+ccMTLasLr5N686VcR+t+ss8L9Wf6bEBznE163N9G4w+PaEcLHUsI2OYYQtHLOom6Hv0HU7srYRdyF8izhi+2lxKTHCZ0vp8b5NhK+6CbE515OeD10LPCYu/v+zncJ8If42jqD0HH8QUJ4ehK4xt0faeRjNYfLCIfkzSC8H56L45osrtcvEULYOkKr6eR67lLv9iTsNnsr71KolRHC58u34o+E5vJrQn+5Fwmvp3+QeD3GX/NHAXjo+3M+IVisJIT0ZD+XC2P9FxDC7VvU7QybNIja77OGFHr/t6Siy+GhT87phM/TdYTvm2TfrYsJu50XEj7ffuLu9zbyvgVZ4d1P2RF/5bxEOBRre0Pztxbxjfg8cLzvfgdKkWZlZqcBH3f3MxLjXiC8PtekWFebfH+3NvEX9b+Bgzx07pTIzC4k9GX5dYMzV7hMBgoz+w/CL/e9CL3Yd7r7h1MtSkSahd7fIq1TqzhTZgv4HKGZax5hn2ihzl0i0jbp/S3SCmWyhaIcYifEqwidYX7r7j/Om/4zwulMIfyS6uM6ZbWIiGSUAkUJYs//V4ATCWfZmwacFQ8bLTT/fwOHuvuny1eliIhI+bTmP5tpzcYAcz3+u2M8dHM84YiWQs5i10P/dtG7d28fOnRoc9UoIlIRnn322dXuXt3wnNKSFChKM4C6Zz5bTJFDQON5AIYRDicqNP084vHagwcPZvr06c1bqYhIxplZ/tlzJQVZ7ZTZmkwA7kicGrcOd7/O3Wvcvaa6WgFbRETaJgWK0iyh7il/B1L8pCcTqP3DKRERkUxSoCjNNGCEmQ2LJ4SZQIEz0MXTmfYknIFPREQksxQoShDPyDeR8G+Us4Hb3H2mmV1qZuMSs04Abinyb3giIiKZoU6ZJXL3KcT/0UiMuyhv+JJy1iQiIpIWtVCIiIhIkylQiIiISJMpUGTBrbfC1VenXYWIiFQwBYosuOsumDQp7SpERKSCKVBkQbdusGFD2lWIiEgFU6DIgm7d4I030q5CREQqmAJFFnTvDps3w/btaVciIiIVSoEiC7p1C9cbN6Zbh4iIVCwFiizIBQr1oxARkZQoUGSBAoWIiKRMgSILFChERCRlChRZoEAhIiIpU6DIAgUKERFJmQJFFnTvHq4VKEREJCUKFFmQa6HQya1ERCQlChRZ0LkzmKmFQkREUqNAkQXt2kHXrgoUIiKSGgWKrNAfhImISIoUKLJCgUJERFKkQJEVChQiIpIiBYqs6N5dgUJERFKjQJEVaqEQEZEUKVBkhQKFiIikSIEiK7p104mtREQkNQoUWdGtG2zaBDt2pF2JiIhUIAWKrND/eYiISIoUKEpkZmPNbI6ZzTWzC4rMc4aZzTKzmWZ2U4sW1KtXuF63rkWfRkREpJD2aRfQFplZFTAJOBFYDEwzs8nuPisxzwjgO8D73X2dmfVp0aIUKEREJEVqoSjNGGCuu893963ALcD4vHnOBSa5+zoAd1/ZohXlAsXatS36NCIiIoUoUJRmALAoMbw4jksaCYw0syfM7CkzG1vogczsPDObbmbTV61aVXpFPXuGawUKERFJgQJFy2kPjACOBc4CfmNmPfJncvfr3L3G3Wuqq6tLfza1UIiISIoUKEqzBBiUGB4YxyUtBia7+zZ3XwC8QggYLUMtFCIikiIFitJMA0aY2TAz6wBMACbnzXM3oXUCM+tN2AUyv8Uq6tgROndWoBARkVQoUJTA3bcDE4H7gNnAbe4+08wuNbNxcbb7gDVmNgt4BPimu69p0cJ69VKgEBGRVOiw0RK5+xRgSt64ixK3HfhavJSHAoWIiKRELRRZokAhIiIpUaDIEgUKERFJiQJFlvTsqTNliohIKhQosiTXQuGediUiIlJhFCiypFcv2LIF3nor7UpERKTCKFBkic6WKSIiKVGgyBIFChERSYkCRZbkAsWalj1/loiISD4FiizJ/bnY6tXp1iEiIhVHgSJL+vQJ1ytWpFuHiIhUHAWKLNl7bzCDlSvTrkRERCqMAkWWVFVB794KFCIiUnYKFFnTp492eYiISNkpUGRN375qoRARkbJToMiaPn0UKEREpOwUKLJGgUJERFKgQJE1ffrAhg3w9ttpVyIiIhVEgSJr+vYN12qlEBGRMlKgyJrcya0UKEREpIwUKLJGgUJERFKgQJE1Ov22iIikQIEiaxQoREQkBQoUWdOlC3TtCsuWpV2JiIhUEAWKLBowAJYsSbsKERGpIAoUWTRgACxenHYVIiJSQRQoskgtFCIiUmYKFCUys7FmNsfM5prZBQWmn2Nmq8zshXj5bNmKGzAg9KHYsaNsTykiIpWtfdoFtEVmVgVMAk4EFgPTzGyyu8/Km/VWd59Y9gIHDgxhYuVK6Nev7E8vIiKVRy0UpRkDzHX3+e6+FbgFGJ9yTbUGDAjX2u0hIiJlokBRmgHAosTw4jgu3+lmNsPM7jCzQYUeyMzOM7PpZjZ91apVzVSdAoWIiJSXAkXL+Rsw1N0PAh4A/lBoJne/zt1r3L2murq6eZ5ZgUJERMpMgaI0S4Bki8PAOO4d7r7G3bfEwd8C7ylTbeFsmVVVChQiIlI2ChSlmQaMMLNhZtYBmABMTs5gZsnekOOA2WWrrqoK+vdXoBARkbLRUR4lcPftZjYRuA+oAq5395lmdikw3d0nA18ys3HAdmAtcE5Zixw4EBYtang+ERGRZqBAUSJ3nwJMyRt3UeL2d4DvlLuudwwdCk89ldrTi4hIZdEuj6waNiy0UGzfnnYlIiJSARQosmro0BAm1I9CRETKQIEiq4YNC9evvZZqGSIiUhkUKLJq6NBwvWBBqmWIiEhlUKDIqsGDwUyBQkREykKBIqs6dAhnzNQuDxERKQMFiiwbNkwtFCIiUhYKFFk2dKgChYiIlIUCRZYNHw6LF8Nbb6VdiYiIZJwCRZaNHBmu585Ntw4REck8BYos22+/cD1nTrp1iIhI5ilQZNmIEeH6lVfSrUNERDJPgSLLunQJf2OuQCEiIi1MgSLr9ttPuzxERKTFKVBk3ciRaqEQEZEWp0CRdfvtB2vXwurVaVciIiIZpkCRdfvvH65nzUq3DhERyTQFiqw78MBwPWNGunWIiEimKVBkXf/+0KsXvPhi2pWIiEiGKVBknVlopVALhYiItCAFikpw4IHw0kuwc2falYiISEYpUFSCgw6CTZtg4cK0KxERkYxSoKgE6pgpIiItTIGiEhxwQLhWx0wREWkhChSVoEsX2HdfeOGFtCsREZGMUqCoFDU1MH162lWIiEhGKVCUyMzGmtkcM5trZhfUM9/pZuZmVlPO+nYxZkzolLliRapliIhINilQlMDMqoBJwMnAKOAsMxtVYL6uwJeBp8tbYQFjxoTradPSrUNERDJJgaI0Y4C57j7f3bcCtwDjC8z3A+By4O1yFlfQYYdBu3YKFCIi0iIUKEozAFiUGF4cx73DzA4DBrn7P+p7IDM7z8ymm9n0VatWNX+lOZ07w+jR8MwzLfccIiJSsRQoWoCZtQOuBL7e0Lzufp2717h7TXV1dcsWNmZMCBTuLfs8IiJScRQoSrMEGJQYHhjH5XQFDgAeNbPXgPcCk1tFx8y1a2HevFTLEBGR7FGgKM00YISZDTOzDsAEYHJuoru/4e693X2ouw8FngLGuXu6x22+733h+vHHUy1DRESyR4GiBO6+HZgI3AfMBm5z95lmdqmZjUu3unqMGgV77w2PPZZ2JSIikjHt0y6grXL3KcCUvHEXFZn32HLU1KB27eDoo2Hq1LQrERGRjFELRaU55hhYsAAWLWp4XhERkUZSoKg0xxwTrrXbQ0REmpECRaU58EDo0UOBQkREmpUCRaWpqoJjj4UHHtD5KEREpNkoUFSisWPDH4XNmZN2JSIikhEKFJVo7Nhwfc896dYhIiKZoUBRiYYMgf33h3vvTbsSERHJCAWKSjV2bOiYuXlz2pWIiEgGKFBUqpNPhi1b4MEH065EREQyQIGiUh1zTDh89M47065EREQyQIGiUnXoAOPHw+TJsHVr2tWIiEgbp0BRyU4/Hdavh4cfTrsSERFp4xQoKtmJJ0LXrtrtISIiTaZAUck6dYJTT4W//AW2b0+7GhERacMUKCrdmWfCmjU6J4WIiDSJAkWlO+UUqK6GG25IuxIREWnDFCgq3R57wNlnh6M91qxJuxoREWmjFCgEzjkHtm2Dm29OuxIREWmjFCgEDj4YDjkErr9ef2kuIiIlUaCQ4Nxz4fnn4amn0q5ERETaIAUKCT7xCejWDa6+Ou1KRESkDVKgkKBLF/j0p+H222Hp0rSrERGRNkaBQmp98YuwYwf86ldpVyIiIm2MAoXUGj4cTjsNJk2CjRvTrkZERNoQBQqp67vfhbVr4dpr065ERETaEAUKqWvMGDjpJPi//4PNm9OuRkRE2ggFihKZ2Vgzm2Nmc83sggLTzzezF83sBTP7p5mNSqPOklx4IaxcCdddl3YlIiLSRihQlMDMqoBJwMnAKOCsAoHhJnc/0N0PAa4ArixvlU1w1FFwzDFw+eWwaVPa1YiISBugQFGaMcBcd5/v7luBW4DxyRncfUNisDPQtk5B+aMfwfLlYdeHiIhIAxQoSjMAWJQYXhzH1WFmXzSzeYQWii8VeiAzO8/MppvZ9FWrVrVIsSU54gj4yEfgiitg2bK0qxERkVZOgaIFufskd38X8G3gwiLzXOfuNe5eU11dXd4CG/KjH4U/Dfve99KuREREWjkFitIsAQYlhgfGccXcAny4JQtqEe96F0ycGP40bNq0tKsREZFWTIGiNNOAEWY2zMw6ABOAyckZzGxEYvBDwKtlrK/5XHwx9OsH550H27enXY2IiLRSChQlcPftwETgPmA2cJu7zzSzS81sXJxtopnNNLMXgK8Bn0yn2ibq3h2uugpeeEF/HCYiIkWZe9s6+CDLampqfPr06WmXsSv3cEruRx+FGTNg333TrkhE5B1m9qy716RdR6VTC4U0zAyuuQaqqsLfnGvXh4iI5FGgkMYZPDiEiieeCCe8EhERSVCgkMb76EfhzDPhkkugNe6aERGR1ChQSOOZhX8h7dcvnPRqzZq0KxIRkVZCgUJ2T8+ecPvtsHRpaLHYsSPtikREpBVQoJDdd/jh8Mtfwv33w0UXpV2NiIi0Au3TLkDaqHPPhWeegR/+EEaOhE+2zdNsiIhI81CgkNJNmgQLFsBnPwv9+8OJJ6ZdkYiIpES7PKR0HTrAnXfC/vvD6aeHs2mKiEhFUqCQpuneHaZMCdcf/CDMmpV2RSIikgIFCmm6gQPhgQfCYaXHHQcvv5x2RSIiUmYKFNI83v1uePjh8L8fxx0Hc+akXZGIiJSRAoU0n1Gj4KGHwn99HHkkTJuWdkUiIlImChTSvA44AP75T+jSBT7wgbArREREMk+BQprfyJHhT8T23Rc+9CG48ca0KxIRkRamQCEto39/mDoV3v/+8Jfn3/ymTtMtIpJhChTScnr0CKfnnjgRfvpTOOUUWLcu7apERKQFKFBIy9pjD7j6avjNb+CRR6CmRp01RUQySIFCyuOzn4XHHgtHgLzvfaHFYufOtKsSEZFmokAh5XPEEeH03OPGhT4Vp5wCS5akXZWIiDQDBQopr5494Y474Fe/Cp02R4+G668PJ8QSEZE2S4FCys8MPvc5mDEDDjkEPvOZ8D8gr72WdmUiIlIiBQpJz/Dh4XTd11wDTz4ZzrR52WXw9ttpVyYiIrtJgULS1a4dfP7zMHNm6FPxve+FYPHXv2o3iIhIG6JAIa3D4MGhb8UDD0CnTvDhD4fdIM89l3ZlIiLSCAoUJTKzsWY2x8zmmtkFBaZ/zcxmmdkMM3vIzIakUWebc8IJ8O9/w5VXwrPPwnveA2eeCa+8knZlIiJSDwWKEphZFTAJOBkYBZxlZqPyZnseqHH3g4A7gCvKW2Ubtsce8NWvwvz5cOGF8Pe/h90g554bxomISKujQFGaMcBcd5/v7luBW4DxyRnc/RF33xwHnwIGlrnGtq97d/jBD0KI+MIX4I9/DH889rGPwUsvpV2diIgkKFCUZgCwKDG8OI4r5jPAPS1aUZb17Qu/+AUsWABf+QrcfTcceGDoZ/Gvf6nzpohIK6BA0cLM7GNADfCTItPPM7PpZjZ91apV5S2urenfP5yye+FCuOSS2n8zramBG27Q4aYiIilSoCjNEmBQYnhgHFeHmZ0AfBcY5+5bCj2Qu1/n7jXuXlNdXd0ixWbO3nvDxRfD66/DtdeGIPGpT8GgQfA//wOLFjX8GCIi0qwUKEozDRhhZsPMrAMwAZicnMHMDgV+TQgTK1OoMfu6dIHzzw/9KR56CI48Ei6/HIYMgbFj4dZb1WohIlImChQlcPftwETgPmA2cJu7zzSzS81sXJztJ0AX4HYze8HMJhd5OGkqMzjuOPjLX2DevHByrNmzYcKEsJtk4sRwCKr6WoiItBhzfci2GjU1NT59+vS0y8iGnTvDab2vvx7uugu2bIH99gvntDjzzHAYqohkgpk96+41addR6dRCIdnUrl04SdZNN8GyZeHfTfv3D4ehjh4djhK57DJ49dW0KxURyQS1ULQiaqEog2XLwim+b70VnngijDvgADjtNBg3DsaMCWFERNoMtVC0DgoUrYgCRZktWhTCxeTJ8PjjsGNHOOfFhz4UwsUJJ0DnzmlXKSINUKBoHRQoWhEFihStXQv33hvCxT33wIYN0KFDOM/FSSfBiSfCoYeq9UKkFVKgaB0UKFoRBYpWYuvWcNKse++F+++HF18M4/feO7RanHhiuB6i/3sTaQ0UKFqH9mkXINLqdOgQAsMJJ4Th5cvhwQfDX6vff3/ofwHhL9ePPjpcjjoqHEVill7dIiIpUgtFK6IWijbAHWbOhEcfDa0YU6fCihVhWnV1bbg48kg46KDwz6ki0qLUQtE6KFC0IgoUbZA7zJ1bGy6mToXXXgvTOnUK/S4OPzxcxoyBYcPUiiHSzBQoWgcFilZEgSIjFi2CJ5+Ep5+GZ54JZ+l8660wrbo6BIvDDw9h49BDw/kxFDJESqZA0TqoD4VIcxs0KFzOOCMMb9sW/m8kFzCefhqmTKk9FXjv3iFYHHJIuBx6KIwcCVVVaS2BiMhuUwtFK6IWigqycSPMmAHPPw8vvBCuX3opHGECsOeeoQ/GgQeGM3vmLv36qTVDJI9aKFoHBYpWRIGiwm3bFv7ULBcwnn8+HLK6dm3tPD16hGAxalTdoLHPPgoaUrEUKFoHBYpWRIFCduEOK1eGI0vyL+vW1c7Xo0c4bHXEiLC7JHcZMSL8zbtIhilQtA7qQyHSmpmF04H37Rv+oj3HPRyumgsXs2aFPzp77DH405/qPka/fruGjOHDYehQnVpcRJqNAoVIW2QWdnPssw8cf3zdaZs3h0NZX30VXnml9nL33bBqVd15+/QJh7LmX/bdN3Qs1Xk0RKSRFChEsmavvUKHzoMO2nXaunUhaMyfHy4LFoTLM8+EP0rbvr123nbtQqjIhYzBg2uPYMldtDtFRCIFCpFK0rNnOA/GmDG7Ttu+HZYsqQ0Zucv8+eF/TZYvrz3UNadHj11DRvIycGA4wZeIZJ4ChYgE7duHPzwbMgSOPXbX6Vu3wtKl4cRd+ZfXXw/n11izZtf79e4d+nH06xdO4pW7nT+s4CHSpilQiEjjdOgQOnIOHVp8ns2bYfHiumFj6dJwWbYsdB5dvrzurpWcHj3qBozc7X32CX09cpe999ZJv0RaIQUKEWk+e+1VezRJMTt3wurVIWDkgkb+7ccfD9e5E30lmYVWj2TIyF369t11XJcuOkeHSBkoUIhIebVrV/tlf/DBxedzDyf1WrEinIuj2OW558L1G28UfpxOnWpbNvIvvXsXHt+tm0KIyG5SoBCR1sms9gt+1KiG59+yJRwWWyx4rFkTLgsXhut163btZJrTvj306lV/+OjRI3RyzV337BmCSLt2zbkWRNoMBQoRyYaOHcNRJQMHNm7+HTtg/fraoJG7rF6967j582HatHB7y5bij2kG3bvvGjYKhY9C09QxVdowBQoRqUxVVbWtDY3lDm++GXbFrFsXAklD13Pm1N7evLn+x+/UKQSS7t1Da0fykj+uvuH2+miX8tOrTkSkscxCJ88uXcKJvnbX1q0Nh5A33oANG8LljTdg3ry6wzt3Nvw8e+7ZcADJLUeXLtC1a93h5Pg991R/EmkUBQoRkXLp0KG2Q2op3EMrRy5g5EJGfcO5cXPn1h23Y0fjnjMZooqFj/oCSe525851Lzr0N3MUKEpkZmOBq4Aq4Lfu/uO86UcDPwcOAia4+x1lL1JEssWs9gu5X7/SH8c99AXZtAk2bgzXyUv+uELzrFgRWk+S8zSm9SSnU6e6AeP222H06NKXSVKnQFECM6sCJgEnAouBaWY22d1nJWZ7HTgH+Eb5KxQRqYdZ+ELv1CkcvdIc3OHttwsHkY0bQ9+TYpdNm/S/MBmgQFGaMcBcd58PYGa3AOOBdwKFu78Wp+1GZBcRaaPMQn+LPfeE6uq0q5EU6IDp0gwAFiWGF8dxu83MzjOz6WY2fVX+X0uLiIi0EQoUKXP369y9xt1rqpXqRUSkjVKgKM0SYFBieGAcJyIiUpEUKEozDRhhZsPMrAMwAZicck0iIiKpUaAogbtvByYC9wGzgdvcfaaZXWpm4wDM7P+Z2WLgI8CvzWxmehWLiIi0LB3lUSJ3nwJMyRt3UeL2NMKuEBERkcxTC4WIiIg0mQKFiIiINJm5e9o1SGRmq4CFJd69N7C6GctpC7TMlUHLXBmassxD3F3H3adMgSIjzGy6u9ekXUc5aZkrg5a5MlTiMmeNdnmIiIhIkylQiIiISJMpUGTHdWkXkAItc2XQMleGSlzmTFEfChEREWkytVCIiIhIkylQiIiISJMpUGSAmY01szlmNtfMLki7nuZgZoPM7BEzm2VmM83sy3F8LzN7wMxejdc943gzs1/EdTDDzA5LdwlKZ2ZVZva8mf09Dg8zs6fjst0a/5AOM+sYh+fG6UNTLbxEZtbDzO4ws5fNbLaZHZH17WxmX42v65fM7GYz65S17Wxm15vZSjN7KTFut7ermX0yzv+qmX0yjWWRxlGgaOPMrAqYBJwMjALOMrNR6VbVLLYDX3f3UcB7gS/G5boAeMjdRwAPxWEIyz8iXs4Dri1/yc3my4Q/ncu5HPiZuw8H1gGfieM/A6yL438W52uLrgLudfd3AwcTlj2z29nMBgBfAmrc/QCgivCPxVnbzjcAY/PG7dZ2NbNewMXA4cAY4OJcCJHWR4Gi7RsDzHX3+e6+FbgFGJ9yTU3m7svc/bl4eyPhS2YAYdn+EGf7A/DheHs88EcPngJ6mFm/8lbddGY2EPgQ8Ns4bMBxwB1xlvxlzq2LO4Dj4/xthpl1B44Gfgfg7lvdfT0Z386EP2bc08zaA3sBy8jYdnb3qcDavNG7u10/CDzg7mvdfR3wALuGFGklFCjavgHAosTw4jguM2IT76HA00Bfd18WJy0H+sbbWVkPPwe+BeyMw3sD6919exxOLtc7yxynvxHnb0uGAauA38fdPL81s85keDu7+xLgp8DrhCDxBvAs2d7OObu7Xdv89q4kChTSqplZF+BO4CvuviE5zcMxz5k57tnMTgVWuvuzaddSRu2Bw4Br3f1Q4E1qm8GBTG7nnoRf5MOA/kBnKvBXd9a2qyhQZMESYFBieGAc1+aZ2R6EMPFnd78rjl6Ra+KO1yvj+Cysh/cD48zsNcKuq+MI/Qt6xKZxqLtc7yxznN4dWFPOgpvBYmCxuz8dh+8gBIwsb+cTgAXuvsrdtwF3EbZ9lrdzzu5u1yxs74qhQNH2TQNGxB7iHQiduyanXFOTxX3EvwNmu/uViUmTgVxP708Cf02M/0TsLf5e4I1E02qb4O7fcfeB7j6UsB0fdvezgUeA/4qz5S9zbl38V5y/Tf3ic/flwCIz2y+OOh6YRYa3M2FXx3vNbK/4Os8tc2a3c8Lubtf7gJPMrGds2TkpjpPWyN11aeMX4BTgFWAe8N2062mmZTqS0Bw6A3ghXk4h7Dt+CHgVeBDoFec3wtEu84AXCT3oU1+OJiz/scDf4+19gWeAucDtQMc4vlMcnhun75t23SUu6yHA9Lit7wZ6Zn07A98HXgZeAm4EOmZtOwM3E/qIbCO0RH2mlO0KfDou+1zgU2kvly7FLzr1toiIiDSZdnmIiIhIkylQiIiISJMpUIiIiEiTKVCIiIhIkylQiIiISJMpUIiIiEiTKVCIiIhIk/1/VcWJuX7XqW0AAAAASUVORK5CYII=\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "id": "qsorDXmes-4B"
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.001,1000)"
      ],
      "metadata": {
        "id": "3yry_OXns-4B",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "e1df4625-7f2e-4dab-9da2-8b1f5113f427"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "id": "3yry_OXns-4B"
    },
    {
      "cell_type": "code",
      "source": [
        "theta = batch_gradient_descent(X_train,y_train,theta1,0.001,1000)"
      ],
      "metadata": {
        "id": "aNb8n-ACs-4B",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "e0d69c20-f833-4abc-ac61-570ffce0eb18"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "id": "aNb8n-ACs-4B"
    },
    {
      "cell_type": "markdown",
      "source": [
        "**If you have low learning rate means your cost function will decrease slowly but in case of large learning rate cost function will decrease very fast.**"
      ],
      "metadata": {
        "id": "gr7KU-1ys-4B"
      },
      "id": "gr7KU-1ys-4B"
    }
  ],
  "metadata": {
    "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": "3.10.5"
    },
    "colab": {
      "provenance": [],
      "collapsed_sections": [
        "0nrxz7jCO-sT"
      ],
      "toc_visible": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}