W06.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "#import libraries\n",
    "import pandas as pd\n",
    "import numpy as np \n",
    "import matplotlib.pyplot as plt \n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "from sklearn.model_selection import cross_val_score\n",
    "from sklearn.metrics import classification_report\n",
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.metrics import make_scorer\n",
    "from sklearn.metrics import f1_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "\n",
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       "\n",
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       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LevelOfTrust</th>\n",
       "      <th>ScanTimeInSeconds</th>\n",
       "      <th>TotalBasketValue</th>\n",
       "      <th>ScannedProducts</th>\n",
       "      <th>CountOfVoidedScans</th>\n",
       "      <th>ActivateWithoutScan</th>\n",
       "      <th>ModifiedQuantities</th>\n",
       "      <th>Fraud</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>1401</td>\n",
       "      <td>58.83</td>\n",
       "      <td>17</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>655</td>\n",
       "      <td>57.20</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>770</td>\n",
       "      <td>36.00</td>\n",
       "      <td>28</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>272</td>\n",
       "      <td>89.76</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>1511</td>\n",
       "      <td>8.75</td>\n",
       "      <td>15</td>\n",
       "      <td>0</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "      <td>0</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299995</th>\n",
       "      <td>6</td>\n",
       "      <td>900</td>\n",
       "      <td>31.50</td>\n",
       "      <td>15</td>\n",
       "      <td>1</td>\n",
       "      <td>9</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299996</th>\n",
       "      <td>4</td>\n",
       "      <td>1395</td>\n",
       "      <td>23.02</td>\n",
       "      <td>11</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299997</th>\n",
       "      <td>4</td>\n",
       "      <td>131</td>\n",
       "      <td>87.75</td>\n",
       "      <td>27</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299998</th>\n",
       "      <td>2</td>\n",
       "      <td>1724</td>\n",
       "      <td>95.33</td>\n",
       "      <td>20</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299999</th>\n",
       "      <td>6</td>\n",
       "      <td>1206</td>\n",
       "      <td>11.49</td>\n",
       "      <td>22</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>300000 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        LevelOfTrust  ScanTimeInSeconds  TotalBasketValue  ScannedProducts  \\\n",
       "0                  2               1401             58.83               17   \n",
       "1                  2                655             57.20                6   \n",
       "2                  4                770             36.00               28   \n",
       "3                  5                272             89.76                1   \n",
       "4                  6               1511              8.75               15   \n",
       "...              ...                ...               ...              ...   \n",
       "299995             6                900             31.50               15   \n",
       "299996             4               1395             23.02               11   \n",
       "299997             4                131             87.75               27   \n",
       "299998             2               1724             95.33               20   \n",
       "299999             6               1206             11.49               22   \n",
       "\n",
       "        CountOfVoidedScans  ActivateWithoutScan  ModifiedQuantities  Fraud  \n",
       "0                        2                    7                   1      0  \n",
       "1                        7                    1                   4      0  \n",
       "2                       11                    3                   4      0  \n",
       "3                        4                    0                   2      0  \n",
       "4                        0                    7                   4      0  \n",
       "...                    ...                  ...                 ...    ...  \n",
       "299995                   1                    9                   2      0  \n",
       "299996                   1                    6                   0      0  \n",
       "299997                   1                    3                   0      0  \n",
       "299998                  10                    8                   3      0  \n",
       "299999                   8                    3                   3      0  \n",
       "\n",
       "[300000 rows x 8 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Import the data set \"W06_training.txt“\n",
    "df = pd.read_csv('W06_training.txt', delimiter=\";\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LevelOfTrust</th>\n",
       "      <th>ScanTimeInSeconds</th>\n",
       "      <th>TotalBasketValue</th>\n",
       "      <th>ScannedProducts</th>\n",
       "      <th>CountOfVoidedScans</th>\n",
       "      <th>ActivateWithoutScan</th>\n",
       "      <th>ModifiedQuantities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>1401</td>\n",
       "      <td>58.83</td>\n",
       "      <td>17</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>655</td>\n",
       "      <td>57.20</td>\n",
       "      <td>6</td>\n",
       "      <td>7</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>770</td>\n",
       "      <td>36.00</td>\n",
       "      <td>28</td>\n",
       "      <td>11</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>272</td>\n",
       "      <td>89.76</td>\n",
       "      <td>1</td>\n",
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       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>1511</td>\n",
       "      <td>8.75</td>\n",
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       "      <td>4</td>\n",
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       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299995</th>\n",
       "      <td>6</td>\n",
       "      <td>900</td>\n",
       "      <td>31.50</td>\n",
       "      <td>15</td>\n",
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       "      <td>9</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>299996</th>\n",
       "      <td>4</td>\n",
       "      <td>1395</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>299997</th>\n",
       "      <td>4</td>\n",
       "      <td>131</td>\n",
       "      <td>87.75</td>\n",
       "      <td>27</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299998</th>\n",
       "      <td>2</td>\n",
       "      <td>1724</td>\n",
       "      <td>95.33</td>\n",
       "      <td>20</td>\n",
       "      <td>10</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299999</th>\n",
       "      <td>6</td>\n",
       "      <td>1206</td>\n",
       "      <td>11.49</td>\n",
       "      <td>22</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>300000 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        LevelOfTrust  ScanTimeInSeconds  TotalBasketValue  ScannedProducts  \\\n",
       "0                  2               1401             58.83               17   \n",
       "1                  2                655             57.20                6   \n",
       "2                  4                770             36.00               28   \n",
       "3                  5                272             89.76                1   \n",
       "4                  6               1511              8.75               15   \n",
       "...              ...                ...               ...              ...   \n",
       "299995             6                900             31.50               15   \n",
       "299996             4               1395             23.02               11   \n",
       "299997             4                131             87.75               27   \n",
       "299998             2               1724             95.33               20   \n",
       "299999             6               1206             11.49               22   \n",
       "\n",
       "        CountOfVoidedScans  ActivateWithoutScan  ModifiedQuantities  \n",
       "0                        2                    7                   1  \n",
       "1                        7                    1                   4  \n",
       "2                       11                    3                   4  \n",
       "3                        4                    0                   2  \n",
       "4                        0                    7                   4  \n",
       "...                    ...                  ...                 ...  \n",
       "299995                   1                    9                   2  \n",
       "299996                   1                    6                   0  \n",
       "299997                   1                    3                   0  \n",
       "299998                  10                    8                   3  \n",
       "299999                   8                    3                   3  \n",
       "\n",
       "[300000 rows x 7 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Use only the first 7 columns (i.e. ignore the „Fraud“ column for now)\n",
    "y = df['Fraud']\n",
    "df = df.drop(columns='Fraud')\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LevelOfTrust</th>\n",
       "      <th>ScanTimeInSeconds</th>\n",
       "      <th>TotalBasketValue</th>\n",
       "      <th>ScannedProducts</th>\n",
       "      <th>CountOfVoidedScans</th>\n",
       "      <th>ActivateWithoutScan</th>\n",
       "      <th>ModifiedQuantities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.729308</td>\n",
       "      <td>0.560713</td>\n",
       "      <td>0.566667</td>\n",
       "      <td>0.181818</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.2</td>\n",
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       "      <th>1</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.340968</td>\n",
       "      <td>0.545177</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>0.636364</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.8</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.400833</td>\n",
       "      <td>0.343119</td>\n",
       "      <td>0.933333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.141593</td>\n",
       "      <td>0.855509</td>\n",
       "      <td>0.033333</td>\n",
       "      <td>0.363636</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.786569</td>\n",
       "      <td>0.083397</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>299995</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.468506</td>\n",
       "      <td>0.300229</td>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.090909</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299996</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.726184</td>\n",
       "      <td>0.219405</td>\n",
       "      <td>0.366667</td>\n",
       "      <td>0.090909</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299997</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.068194</td>\n",
       "      <td>0.836352</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>0.090909</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299998</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.897449</td>\n",
       "      <td>0.908597</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.909091</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>299999</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.627798</td>\n",
       "      <td>0.109512</td>\n",
       "      <td>0.733333</td>\n",
       "      <td>0.727273</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>300000 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        LevelOfTrust  ScanTimeInSeconds  TotalBasketValue  ScannedProducts  \\\n",
       "0           0.333333           0.729308          0.560713         0.566667   \n",
       "1           0.333333           0.340968          0.545177         0.200000   \n",
       "2           0.666667           0.400833          0.343119         0.933333   \n",
       "3           0.833333           0.141593          0.855509         0.033333   \n",
       "4           1.000000           0.786569          0.083397         0.500000   \n",
       "...              ...                ...               ...              ...   \n",
       "299995      1.000000           0.468506          0.300229         0.500000   \n",
       "299996      0.666667           0.726184          0.219405         0.366667   \n",
       "299997      0.666667           0.068194          0.836352         0.900000   \n",
       "299998      0.333333           0.897449          0.908597         0.666667   \n",
       "299999      1.000000           0.627798          0.109512         0.733333   \n",
       "\n",
       "        CountOfVoidedScans  ActivateWithoutScan  ModifiedQuantities  \n",
       "0                 0.181818                  0.7                 0.2  \n",
       "1                 0.636364                  0.1                 0.8  \n",
       "2                 1.000000                  0.3                 0.8  \n",
       "3                 0.363636                  0.0                 0.4  \n",
       "4                 0.000000                  0.7                 0.8  \n",
       "...                    ...                  ...                 ...  \n",
       "299995            0.090909                  0.9                 0.4  \n",
       "299996            0.090909                  0.6                 0.0  \n",
       "299997            0.090909                  0.3                 0.0  \n",
       "299998            0.909091                  0.8                 0.6  \n",
       "299999            0.727273                  0.3                 0.6  \n",
       "\n",
       "[300000 rows x 7 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Divide each column by its maximum value, so that each each column is scaled between 0 and 1\n",
    "df_scaled = df.apply(lambda x: x / x.max())\n",
    "df_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Perform a principal component analysis. Report the explained variance ratio and \n",
    "#the components of the first two principal components\n",
    "\n",
    "pca = PCA()\n",
    "pca.fit(df_scaled)\n",
    "evr = pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Explained variance ratio</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1st</th>\n",
       "      <td>0.184881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2nd</th>\n",
       "      <td>0.158641</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Explained variance ratio\n",
       "1st                  0.184881\n",
       "2nd                  0.158641"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(evr[:2], columns=['Explained variance ratio'], index=['1st', '2nd'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cum_explained = np.cumsum(pca.explained_variance_ratio_)\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.plot(range(1,len(pca.explained_variance_ratio_)+1),cum_explained)\n",
    "plt.xlabel(\"Number of principal components\")\n",
    "plt.ylabel(\"Share of explained variance\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Components of the first two principal components\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LevelOfTrust</th>\n",
       "      <th>ScanTimeInSeconds</th>\n",
       "      <th>TotalBasketValue</th>\n",
       "      <th>ScannedProducts</th>\n",
       "      <th>CountOfVoidedScans</th>\n",
       "      <th>ActivateWithoutScan</th>\n",
       "      <th>ModifiedQuantities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1st</th>\n",
       "      <td>-0.001364</td>\n",
       "      <td>0.000306</td>\n",
       "      <td>0.00272</td>\n",
       "      <td>-0.010662</td>\n",
       "      <td>0.002007</td>\n",
       "      <td>0.011759</td>\n",
       "      <td>0.999867</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2nd</th>\n",
       "      <td>-0.013057</td>\n",
       "      <td>0.001897</td>\n",
       "      <td>-0.00708</td>\n",
       "      <td>0.018096</td>\n",
       "      <td>-0.168284</td>\n",
       "      <td>-0.985384</td>\n",
       "      <td>0.012120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     LevelOfTrust  ScanTimeInSeconds  TotalBasketValue  ScannedProducts  \\\n",
       "1st     -0.001364           0.000306           0.00272        -0.010662   \n",
       "2nd     -0.013057           0.001897          -0.00708         0.018096   \n",
       "\n",
       "     CountOfVoidedScans  ActivateWithoutScan  ModifiedQuantities  \n",
       "1st            0.002007             0.011759            0.999867  \n",
       "2nd           -0.168284            -0.985384            0.012120  "
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Components of the first two principal components')\n",
    "pd.DataFrame(pca.components_[:2], columns=df.columns, index=['1st', '2nd'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 0 ... 2 1 0]\n"
     ]
    }
   ],
   "source": [
    "#Perform a k-means cluster analysis to derive a solution with 3 clusters. \n",
    "#For comparison use KMeans(n_clusters=3, random_state=100) to always get the same results.\n",
    "#Report the components of the cluster centers and the size of the clusters \n",
    "#(i.e. the number of data points assigned to each cluster)\n",
    "\n",
    "model = KMeans(n_clusters=3, random_state=100)\n",
    "model.fit(df_scaled)\n",
    "labels = model.predict(df_scaled)\n",
    "print(labels)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster centers\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LevelOfTrust</th>\n",
       "      <th>ScanTimeInSeconds</th>\n",
       "      <th>TotalBasketValue</th>\n",
       "      <th>ScannedProducts</th>\n",
       "      <th>CountOfVoidedScans</th>\n",
       "      <th>ActivateWithoutScan</th>\n",
       "      <th>ModifiedQuantities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.583484</td>\n",
       "      <td>0.476233</td>\n",
       "      <td>0.476842</td>\n",
       "      <td>0.514624</td>\n",
       "      <td>0.503496</td>\n",
       "      <td>0.502306</td>\n",
       "      <td>0.846643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.585983</td>\n",
       "      <td>0.476453</td>\n",
       "      <td>0.476744</td>\n",
       "      <td>0.516873</td>\n",
       "      <td>0.521093</td>\n",
       "      <td>0.791409</td>\n",
       "      <td>0.260811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.582773</td>\n",
       "      <td>0.476715</td>\n",
       "      <td>0.476150</td>\n",
       "      <td>0.516977</td>\n",
       "      <td>0.472939</td>\n",
       "      <td>0.207929</td>\n",
       "      <td>0.265392</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   LevelOfTrust  ScanTimeInSeconds  TotalBasketValue  ScannedProducts  \\\n",
       "0      0.583484           0.476233          0.476842         0.514624   \n",
       "1      0.585983           0.476453          0.476744         0.516873   \n",
       "2      0.582773           0.476715          0.476150         0.516977   \n",
       "\n",
       "   CountOfVoidedScans  ActivateWithoutScan  ModifiedQuantities  \n",
       "0            0.503496             0.502306            0.846643  \n",
       "1            0.521093             0.791409            0.260811  \n",
       "2            0.472939             0.207929            0.265392  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centroids = model.cluster_centers_\n",
    "print('Cluster centers')\n",
    "pd.DataFrame(centroids, columns=df.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Cluster Size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>121556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>89542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>88902</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Cluster Size\n",
       "0        121556\n",
       "2         89542\n",
       "1         88902"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.Series(labels).value_counts().to_frame('Cluster Size')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "14328"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Get an overview and understanding of the available data\n",
    "sum(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Only 14328 out of 300000 are fraud - that is 4.776%.\n",
    "We should get a similar percentage in the scoring data, assuming they have the same distibution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Clean the data if necessary and derive new “smart” variables\n",
    "#(e.g. scale the data or compute ratios of given variables) that can be used for the predictions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We use the scaled DataFrame from exercise 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_val, X_test, y_train_val, y_test = train_test_split(df_scaled, y, random_state=4, stratify=y, test_size=0.1)\n",
    "X_train, X_val, y_train, y_val = train_test_split(X_train_val, y_train_val, random_state=40, stratify=y_train_val)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Determine which characteristics are key characteristics as they are driving fraudulent behavior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "clf = DecisionTreeClassifier(random_state=40)\n",
    "clf.fit(X_train, y_train)\n",
    "plt.figure(figsize=(10,10))\n",
    "plt.barh(width=clf.feature_importances_,y=X_train_val.columns.values)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see, if we fit a Decision Tree Classifier, the features with more importance are: ScannedProducts, LevelOfTrust and ScanTimeInSeconds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Use the appropriate classification algorithms you are familiar with and make predictions. \n",
    "#If necessary, tune the parameters of the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We try two different models: Logistic Regression and Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set: 0.99108\n",
      "Accuracy on validation set: 0.99092\n",
      "f1 score on training set: 0.90503\n",
      "f1 score on validation set: 0.90305\n"
     ]
    }
   ],
   "source": [
    "logreg = LogisticRegression(max_iter=100)\n",
    "logreg.fit(X_train, y_train)\n",
    "print(\"Accuracy on training set: {:.5f}\".format(logreg.score(X_train, y_train)))\n",
    "print(\"Accuracy on validation set: {:.5f}\".format(logreg.score(X_val, y_val)))\n",
    "y_pred_train = logreg.predict(X_train)\n",
    "print(\"f1 score on training set: {:.5f}\".format(f1_score(y_train, y_pred_train)))\n",
    "y_pred_val = logreg.predict(X_val)\n",
    "print(\"f1 score on validation set: {:.5f}\".format(f1_score(y_val, y_pred_val)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.90299685 0.90616941 0.90539206 0.89561091 0.90702236]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.9034383182830974"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv_scores = cross_val_score(logreg, X_train_val, y_train_val, cv=5, scoring='f1')\n",
    "print(cv_scores)\n",
    "np.mean(cv_scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy on training set: 0.987\n",
      "Accuracy on test set: 0.987\n",
      "f1 score on training set: 0.86298\n",
      "f1 score on validation set: 0.86416\n"
     ]
    }
   ],
   "source": [
    "forest = RandomForestClassifier(n_estimators=50, max_depth=5, max_features=5, random_state=30, n_jobs=-1)\n",
    "forest.fit(X_train, y_train)\n",
    "print(\"Accuracy on training set: {:.3f}\".format(forest.score(X_train, y_train)))\n",
    "print(\"Accuracy on test set: {:.3f}\".format(forest.score(X_val, y_val)))\n",
    "y_pred_train = forest.predict(X_train)\n",
    "print(\"f1 score on training set: {:.5f}\".format(f1_score(y_train, y_pred_train)))\n",
    "y_pred_val = forest.predict(X_val)\n",
    "print(\"f1 score on validation set: {:.5f}\".format(f1_score(y_val, y_pred_val)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.84091841 0.84892086 0.85485855 0.84623281 0.84598349]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.8473828237050111"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv_scores = cross_val_score(forest, X_train_val, y_train_val, cv=5, scoring='f1')\n",
    "print(cv_scores)\n",
    "np.mean(cv_scores)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see that the Logistic Regression performs better, so we will do a gridsearch to find the best value for C, the inverse of regularization strength"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.e-05, 1.e-04, 1.e-03, 1.e-02, 1.e-01, 1.e+00, 1.e+01, 1.e+02,\n",
       "       1.e+03, 1.e+04, 1.e+05])"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "c_space = np.logspace(-5, 5, 11)\n",
    "c_space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tuned Logistic Regression Parameters: {'C': 100.0}\n",
      "Best score is 0.9063409895170171\n"
     ]
    }
   ],
   "source": [
    "param_grid = {'C': c_space}\n",
    "logreg2 = LogisticRegression()\n",
    "logreg_cv = GridSearchCV(logreg2, param_grid, cv=5, scoring='f1')\n",
    "logreg_cv.fit(X_train_val, y_train_val)\n",
    "\n",
    "print(\"Tuned Logistic Regression Parameters: {}\".format(logreg_cv.best_params_)) \n",
    "print(\"Best score is {}\".format(logreg_cv.best_score_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "best_logreg = logreg_cv.best_estimator_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Measure the quality of the model or compare the quality of the models and choose a final model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's compare the confusion matrix for the Logistic Regression with the default value of C, and the one we found doing the gridsearch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion Matrix for the Logistic Regression with the default value of C (C=1)\n",
      "[[64032   244]\n",
      " [  369  2855]]\n"
     ]
    }
   ],
   "source": [
    "print('Confusion Matrix for the Logistic Regression with the default value of C (C=1)')\n",
    "print(confusion_matrix(y_val, logreg.predict(X_val)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Confusion Matrix for the Logistic Regression with the value of C from the gridsearch (C=100)\n",
      "[[64003   273]\n",
      " [  328  2896]]\n"
     ]
    }
   ],
   "source": [
    "print('Confusion Matrix for the Logistic Regression with the value of C from the gridsearch (C=100)')\n",
    "print(confusion_matrix(y_val, best_logreg.predict(X_val)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, although with C=100 we get a higher F1 score, in this particular case we are interested in minimizing the false positives, since they are penalized with a loss of 25 EUR for the supermarket. And we can see that with C=100 we get a higher number of false positives than with C=1. Therefore we're going to define our own metric, based on the gains and losses for each case and use gridsearch again to find the C that maximizes that metric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Use statistical key figures, but especially the total costs or the total revenue"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "def revenue(y_true, y_pred):\n",
    "    M = confusion_matrix(y_true, y_pred)\n",
    "    return (M[0,1]*(-25) + M[1,0]*(-5) + M[1,1]*(5))/(M[0,0] + M[0,1] + M[1,0] + M[1,1])\n",
    "\n",
    "revenue_scorer = make_scorer(revenue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "If we didn't make any prediction mistakes, the score with this new metric would be: 0.23879629629629628\n"
     ]
    }
   ],
   "source": [
    "print(\"If we didn't make any prediction mistakes, the score with this new metric would be:\", revenue(y_train_val, y_train_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Tuned Logistic Regression Parameters: {'C': 0.1}\n",
      "Best score is 0.10564814814814816\n"
     ]
    }
   ],
   "source": [
    "c_space = np.logspace(-5, 5, 11)\n",
    "param_grid = {'C': c_space}\n",
    "\n",
    "logreg3 = LogisticRegression()\n",
    "logreg_cv_custom = GridSearchCV(logreg3, param_grid, cv=5, scoring=revenue_scorer)\n",
    "logreg_cv_custom.fit(X_train_val, y_train_val)\n",
    "\n",
    "# Print the tuned parameters and score\n",
    "print(\"Tuned Logistic Regression Parameters: {}\".format(logreg_cv_custom.best_params_)) \n",
    "print(\"Best score is {}\".format(logreg_cv_custom.best_score_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [],
   "source": [
    "best_logreg_custom = logreg_cv_custom.best_estimator_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Results on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>C=100</th>\n",
       "      <th>C=0.1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>F1</th>\n",
       "      <td>0.911994</td>\n",
       "      <td>0.883234</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Revenue</th>\n",
       "      <td>0.106167</td>\n",
       "      <td>0.105333</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            C=100     C=0.1\n",
       "F1       0.911994  0.883234\n",
       "Revenue  0.106167  0.105333"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = [[f1_score(y_test, best_logreg.predict(X_test)), f1_score(y_test, best_logreg_custom.predict(X_test))],\n",
    "     [revenue(y_test, best_logreg.predict(X_test)), revenue(y_test, best_logreg_custom.predict(X_test))]]\n",
    "pd.DataFrame(M, columns=['C=100', 'C=0.1'], index=['F1', 'Revenue'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LevelOfTrust</th>\n",
       "      <th>ScanTimeInSeconds</th>\n",
       "      <th>TotalBasketValue</th>\n",
       "      <th>ScannedProducts</th>\n",
       "      <th>CountOfVoidedScans</th>\n",
       "      <th>ActivateWithoutScan</th>\n",
       "      <th>ModifiedQuantities</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2</td>\n",
       "      <td>202</td>\n",
       "      <td>76.39</td>\n",
       "      <td>16</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>165</td>\n",
       "      <td>3.55</td>\n",
       "      <td>9</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>3</td>\n",
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       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>1601</td>\n",
       "      <td>57.11</td>\n",
       "      <td>6</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>571</td>\n",
       "      <td>22.73</td>\n",
       "      <td>14</td>\n",
       "      <td>4</td>\n",
       "      <td>7</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>288</td>\n",
       "      <td>53.36</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>99995</th>\n",
       "      <td>1</td>\n",
       "      <td>1142</td>\n",
       "      <td>2.36</td>\n",
       "      <td>11</td>\n",
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       "      <th>99996</th>\n",
       "      <td>5</td>\n",
       "      <td>1276</td>\n",
       "      <td>34.76</td>\n",
       "      <td>7</td>\n",
       "      <td>6</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
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       "    <tr>\n",
       "      <th>99997</th>\n",
       "      <td>4</td>\n",
       "      <td>540</td>\n",
       "      <td>52.79</td>\n",
       "      <td>12</td>\n",
       "      <td>10</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99998</th>\n",
       "      <td>3</td>\n",
       "      <td>1195</td>\n",
       "      <td>39.40</td>\n",
       "      <td>24</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
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       "    <tr>\n",
       "      <th>99999</th>\n",
       "      <td>6</td>\n",
       "      <td>462</td>\n",
       "      <td>72.60</td>\n",
       "      <td>19</td>\n",
       "      <td>11</td>\n",
       "      <td>10</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100000 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       LevelOfTrust  ScanTimeInSeconds  TotalBasketValue  ScannedProducts  \\\n",
       "0                 2                202             76.39               16   \n",
       "1                 3                165              3.55                9   \n",
       "2                 3               1601             57.11                6   \n",
       "3                 3                571             22.73               14   \n",
       "4                 6                288             53.36                3   \n",
       "...             ...                ...               ...              ...   \n",
       "99995             1               1142              2.36               11   \n",
       "99996             5               1276             34.76                7   \n",
       "99997             4                540             52.79               12   \n",
       "99998             3               1195             39.40               24   \n",
       "99999             6                462             72.60               19   \n",
       "\n",
       "       CountOfVoidedScans  ActivateWithoutScan  ModifiedQuantities  \n",
       "0                      10                    0                   5  \n",
       "1                       3                    8                   3  \n",
       "2                       1                    6                   4  \n",
       "3                       4                    7                   4  \n",
       "4                       5                    1                   3  \n",
       "...                   ...                  ...                 ...  \n",
       "99995                   3                    7                   1  \n",
       "99996                   6                    2                   4  \n",
       "99997                  10                    0                   5  \n",
       "99998                   0                    0                   2  \n",
       "99999                  11                   10                   1  \n",
       "\n",
       "[100000 rows x 7 columns]"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Hand-in your fraud predictions (0/1) for each of the 100,000 cases of the scoring dataset\n",
    "scoring = pd.read_csv('W06_scoring.txt', delimiter=\";\")\n",
    "scoring"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LevelOfTrust</th>\n",
       "      <th>ScanTimeInSeconds</th>\n",
       "      <th>TotalBasketValue</th>\n",
       "      <th>ScannedProducts</th>\n",
       "      <th>CountOfVoidedScans</th>\n",
       "      <th>ActivateWithoutScan</th>\n",
       "      <th>ModifiedQuantities</th>\n",
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       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>0.333333</td>\n",
       "      <td>0.105208</td>\n",
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       "      <td>0.909091</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.085938</td>\n",
       "      <td>0.033855</td>\n",
       "      <td>0.300000</td>\n",
       "      <td>0.272727</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.833854</td>\n",
       "      <td>0.544631</td>\n",
       "      <td>0.200000</td>\n",
       "      <td>0.090909</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.297396</td>\n",
       "      <td>0.216765</td>\n",
       "      <td>0.466667</td>\n",
       "      <td>0.363636</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.150000</td>\n",
       "      <td>0.508869</td>\n",
       "      <td>0.100000</td>\n",
       "      <td>0.454545</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.6</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99995</th>\n",
       "      <td>0.166667</td>\n",
       "      <td>0.594792</td>\n",
       "      <td>0.022506</td>\n",
       "      <td>0.366667</td>\n",
       "      <td>0.272727</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99996</th>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.664583</td>\n",
       "      <td>0.331490</td>\n",
       "      <td>0.233333</td>\n",
       "      <td>0.545455</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99997</th>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.281250</td>\n",
       "      <td>0.503433</td>\n",
       "      <td>0.400000</td>\n",
       "      <td>0.909091</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99998</th>\n",
       "      <td>0.500000</td>\n",
       "      <td>0.622396</td>\n",
       "      <td>0.375739</td>\n",
       "      <td>0.800000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>99999</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.240625</td>\n",
       "      <td>0.692352</td>\n",
       "      <td>0.633333</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>100000 rows × 7 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       LevelOfTrust  ScanTimeInSeconds  TotalBasketValue  ScannedProducts  \\\n",
       "0          0.333333           0.105208          0.728495         0.533333   \n",
       "1          0.500000           0.085938          0.033855         0.300000   \n",
       "2          0.500000           0.833854          0.544631         0.200000   \n",
       "3          0.500000           0.297396          0.216765         0.466667   \n",
       "4          1.000000           0.150000          0.508869         0.100000   \n",
       "...             ...                ...               ...              ...   \n",
       "99995      0.166667           0.594792          0.022506         0.366667   \n",
       "99996      0.833333           0.664583          0.331490         0.233333   \n",
       "99997      0.666667           0.281250          0.503433         0.400000   \n",
       "99998      0.500000           0.622396          0.375739         0.800000   \n",
       "99999      1.000000           0.240625          0.692352         0.633333   \n",
       "\n",
       "       CountOfVoidedScans  ActivateWithoutScan  ModifiedQuantities  \n",
       "0                0.909091                  0.0                 1.0  \n",
       "1                0.272727                  0.8                 0.6  \n",
       "2                0.090909                  0.6                 0.8  \n",
       "3                0.363636                  0.7                 0.8  \n",
       "4                0.454545                  0.1                 0.6  \n",
       "...                   ...                  ...                 ...  \n",
       "99995            0.272727                  0.7                 0.2  \n",
       "99996            0.545455                  0.2                 0.8  \n",
       "99997            0.909091                  0.0                 1.0  \n",
       "99998            0.000000                  0.0                 0.4  \n",
       "99999            1.000000                  1.0                 0.2  \n",
       "\n",
       "[100000 rows x 7 columns]"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scoring_scaled = scoring.apply(lambda x: x / x.max())\n",
    "scoring_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4194"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fraud_prediction = best_logreg_custom.predict(scoring_scaled)\n",
    "sum(fraud_prediction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Observation**: The number of incorrect labeled samples is probably a bit higher using C=0.1 than C=100, but we decided to optimize the revenue and not the F1 score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, ..., 0, 0, 0], dtype=int64)"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fraud_prediction"
   ]
  }
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