{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IUM 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Installation of packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: kaggle in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (1.6.6)\n",
      "Requirement already satisfied: six>=1.10 in c:\\users\\skype\\appdata\\roaming\\python\\python312\\site-packages (from kaggle) (1.16.0)\n",
      "Requirement already satisfied: certifi in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from kaggle) (2024.2.2)\n",
      "Requirement already satisfied: python-dateutil in c:\\users\\skype\\appdata\\roaming\\python\\python312\\site-packages (from kaggle) (2.9.0.post0)\n",
      "Requirement already satisfied: requests in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from kaggle) (2.31.0)\n",
      "Requirement already satisfied: tqdm in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from kaggle) (4.66.2)\n",
      "Requirement already satisfied: python-slugify in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from kaggle) (8.0.4)\n",
      "Requirement already satisfied: urllib3 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from kaggle) (2.2.1)\n",
      "Requirement already satisfied: bleach in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from kaggle) (6.1.0)\n",
      "Requirement already satisfied: webencodings in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from bleach->kaggle) (0.5.1)\n",
      "Requirement already satisfied: text-unidecode>=1.3 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from python-slugify->kaggle) (1.3)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from requests->kaggle) (3.3.2)\n",
      "Requirement already satisfied: idna<4,>=2.5 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from requests->kaggle) (3.6)\n",
      "Requirement already satisfied: colorama in c:\\users\\skype\\appdata\\roaming\\python\\python312\\site-packages (from tqdm->kaggle) (0.4.6)\n",
      "Note: you may need to restart the kernel to use updated packages.\n",
      "Requirement already satisfied: pandas in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (2.2.1)\n",
      "Requirement already satisfied: numpy<2,>=1.26.0 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from pandas) (1.26.3)\n",
      "Requirement already satisfied: python-dateutil>=2.8.2 in c:\\users\\skype\\appdata\\roaming\\python\\python312\\site-packages (from pandas) (2.9.0.post0)\n",
      "Requirement already satisfied: pytz>=2020.1 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from pandas) (2024.1)\n",
      "Requirement already satisfied: tzdata>=2022.7 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from pandas) (2024.1)\n",
      "Requirement already satisfied: six>=1.5 in c:\\users\\skype\\appdata\\roaming\\python\\python312\\site-packages (from python-dateutil>=2.8.2->pandas) (1.16.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n",
      "Requirement already satisfied: numpy in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (1.26.3)\n",
      "Note: you may need to restart the kernel to use updated packages.\n",
      "Requirement already satisfied: scikit-learn in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (1.4.1.post1)\n",
      "Requirement already satisfied: numpy<2.0,>=1.19.5 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from scikit-learn) (1.26.3)\n",
      "Requirement already satisfied: scipy>=1.6.0 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from scikit-learn) (1.12.0)\n",
      "Requirement already satisfied: joblib>=1.2.0 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from scikit-learn) (1.3.2)\n",
      "Requirement already satisfied: threadpoolctl>=2.0.0 in c:\\users\\skype\\appdata\\local\\programs\\python\\python312\\lib\\site-packages (from scikit-learn) (3.3.0)\n",
      "Note: you may need to restart the kernel to use updated packages.\n"
     ]
    }
   ],
   "source": [
    "%pip install kaggle\n",
    "%pip install pandas\n",
    "%pip install numpy\n",
    "%pip install scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importing libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# To preprocess the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "# To split the data\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Downloading a dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "creditcardfraud.zip: Skipping, found more recently modified local copy (use --force to force download)\n"
     ]
    }
   ],
   "source": [
    "!kaggle datasets download -d mlg-ulb/creditcardfraud"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uncompress a file"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Archive:  creditcardfraud.zip\n",
      "  inflating: creditcard.csv          \n"
     ]
    }
   ],
   "source": [
    "!unzip -o creditcardfraud.zip"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv('creditcard.csv')\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Check missing values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Time      0\n",
       "V1        0\n",
       "V2        0\n",
       "V3        0\n",
       "V4        0\n",
       "V5        0\n",
       "V6        0\n",
       "V7        0\n",
       "V8        0\n",
       "V9        0\n",
       "V10       0\n",
       "V11       0\n",
       "V12       0\n",
       "V13       0\n",
       "V14       0\n",
       "V15       0\n",
       "V16       0\n",
       "V17       0\n",
       "V18       0\n",
       "V19       0\n",
       "V20       0\n",
       "V21       0\n",
       "V22       0\n",
       "V23       0\n",
       "V24       0\n",
       "V25       0\n",
       "V26       0\n",
       "V27       0\n",
       "V28       0\n",
       "Amount    0\n",
       "Class     0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Size of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 284807 entries, 0 to 284806\n",
      "Data columns (total 31 columns):\n",
      " #   Column  Non-Null Count   Dtype  \n",
      "---  ------  --------------   -----  \n",
      " 0   Time    284807 non-null  float64\n",
      " 1   V1      284807 non-null  float64\n",
      " 2   V2      284807 non-null  float64\n",
      " 3   V3      284807 non-null  float64\n",
      " 4   V4      284807 non-null  float64\n",
      " 5   V5      284807 non-null  float64\n",
      " 6   V6      284807 non-null  float64\n",
      " 7   V7      284807 non-null  float64\n",
      " 8   V8      284807 non-null  float64\n",
      " 9   V9      284807 non-null  float64\n",
      " 10  V10     284807 non-null  float64\n",
      " 11  V11     284807 non-null  float64\n",
      " 12  V12     284807 non-null  float64\n",
      " 13  V13     284807 non-null  float64\n",
      " 14  V14     284807 non-null  float64\n",
      " 15  V15     284807 non-null  float64\n",
      " 16  V16     284807 non-null  float64\n",
      " 17  V17     284807 non-null  float64\n",
      " 18  V18     284807 non-null  float64\n",
      " 19  V19     284807 non-null  float64\n",
      " 20  V20     284807 non-null  float64\n",
      " 21  V21     284807 non-null  float64\n",
      " 22  V22     284807 non-null  float64\n",
      " 23  V23     284807 non-null  float64\n",
      " 24  V24     284807 non-null  float64\n",
      " 25  V25     284807 non-null  float64\n",
      " 26  V26     284807 non-null  float64\n",
      " 27  V27     284807 non-null  float64\n",
      " 28  V28     284807 non-null  float64\n",
      " 29  Amount  284807 non-null  float64\n",
      " 30  Class   284807 non-null  int64  \n",
      "dtypes: float64(30), int64(1)\n",
      "memory usage: 67.4 MB\n"
     ]
    }
   ],
   "source": [
    "df.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normalising the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "\n",
    "df['Amount'] = scaler.fit_transform(df['Amount'].values.reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>V10</th>\n",
       "      <th>V11</th>\n",
       "      <th>V12</th>\n",
       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
       "      <th>V15</th>\n",
       "      <th>V16</th>\n",
       "      <th>V17</th>\n",
       "      <th>V18</th>\n",
       "      <th>V19</th>\n",
       "      <th>V20</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>284807.000000</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>2.848070e+05</td>\n",
       "      <td>284807.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>94813.859575</td>\n",
       "      <td>1.168375e-15</td>\n",
       "      <td>3.416908e-16</td>\n",
       "      <td>-1.379537e-15</td>\n",
       "      <td>2.074095e-15</td>\n",
       "      <td>9.604066e-16</td>\n",
       "      <td>1.487313e-15</td>\n",
       "      <td>-5.556467e-16</td>\n",
       "      <td>1.213481e-16</td>\n",
       "      <td>-2.406331e-15</td>\n",
       "      <td>2.239053e-15</td>\n",
       "      <td>1.673327e-15</td>\n",
       "      <td>-1.247012e-15</td>\n",
       "      <td>8.190001e-16</td>\n",
       "      <td>1.207294e-15</td>\n",
       "      <td>4.887456e-15</td>\n",
       "      <td>1.437716e-15</td>\n",
       "      <td>-3.772171e-16</td>\n",
       "      <td>9.564149e-16</td>\n",
       "      <td>1.039917e-15</td>\n",
       "      <td>6.406204e-16</td>\n",
       "      <td>1.654067e-16</td>\n",
       "      <td>-3.568593e-16</td>\n",
       "      <td>2.578648e-16</td>\n",
       "      <td>4.473266e-15</td>\n",
       "      <td>5.340915e-16</td>\n",
       "      <td>1.683437e-15</td>\n",
       "      <td>-3.660091e-16</td>\n",
       "      <td>-1.227390e-16</td>\n",
       "      <td>2.913952e-17</td>\n",
       "      <td>0.001727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>47488.145955</td>\n",
       "      <td>1.958696e+00</td>\n",
       "      <td>1.651309e+00</td>\n",
       "      <td>1.516255e+00</td>\n",
       "      <td>1.415869e+00</td>\n",
       "      <td>1.380247e+00</td>\n",
       "      <td>1.332271e+00</td>\n",
       "      <td>1.237094e+00</td>\n",
       "      <td>1.194353e+00</td>\n",
       "      <td>1.098632e+00</td>\n",
       "      <td>1.088850e+00</td>\n",
       "      <td>1.020713e+00</td>\n",
       "      <td>9.992014e-01</td>\n",
       "      <td>9.952742e-01</td>\n",
       "      <td>9.585956e-01</td>\n",
       "      <td>9.153160e-01</td>\n",
       "      <td>8.762529e-01</td>\n",
       "      <td>8.493371e-01</td>\n",
       "      <td>8.381762e-01</td>\n",
       "      <td>8.140405e-01</td>\n",
       "      <td>7.709250e-01</td>\n",
       "      <td>7.345240e-01</td>\n",
       "      <td>7.257016e-01</td>\n",
       "      <td>6.244603e-01</td>\n",
       "      <td>6.056471e-01</td>\n",
       "      <td>5.212781e-01</td>\n",
       "      <td>4.822270e-01</td>\n",
       "      <td>4.036325e-01</td>\n",
       "      <td>3.300833e-01</td>\n",
       "      <td>1.000002e+00</td>\n",
       "      <td>0.041527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-5.640751e+01</td>\n",
       "      <td>-7.271573e+01</td>\n",
       "      <td>-4.832559e+01</td>\n",
       "      <td>-5.683171e+00</td>\n",
       "      <td>-1.137433e+02</td>\n",
       "      <td>-2.616051e+01</td>\n",
       "      <td>-4.355724e+01</td>\n",
       "      <td>-7.321672e+01</td>\n",
       "      <td>-1.343407e+01</td>\n",
       "      <td>-2.458826e+01</td>\n",
       "      <td>-4.797473e+00</td>\n",
       "      <td>-1.868371e+01</td>\n",
       "      <td>-5.791881e+00</td>\n",
       "      <td>-1.921433e+01</td>\n",
       "      <td>-4.498945e+00</td>\n",
       "      <td>-1.412985e+01</td>\n",
       "      <td>-2.516280e+01</td>\n",
       "      <td>-9.498746e+00</td>\n",
       "      <td>-7.213527e+00</td>\n",
       "      <td>-5.449772e+01</td>\n",
       "      <td>-3.483038e+01</td>\n",
       "      <td>-1.093314e+01</td>\n",
       "      <td>-4.480774e+01</td>\n",
       "      <td>-2.836627e+00</td>\n",
       "      <td>-1.029540e+01</td>\n",
       "      <td>-2.604551e+00</td>\n",
       "      <td>-2.256568e+01</td>\n",
       "      <td>-1.543008e+01</td>\n",
       "      <td>-3.532294e-01</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>54201.500000</td>\n",
       "      <td>-9.203734e-01</td>\n",
       "      <td>-5.985499e-01</td>\n",
       "      <td>-8.903648e-01</td>\n",
       "      <td>-8.486401e-01</td>\n",
       "      <td>-6.915971e-01</td>\n",
       "      <td>-7.682956e-01</td>\n",
       "      <td>-5.540759e-01</td>\n",
       "      <td>-2.086297e-01</td>\n",
       "      <td>-6.430976e-01</td>\n",
       "      <td>-5.354257e-01</td>\n",
       "      <td>-7.624942e-01</td>\n",
       "      <td>-4.055715e-01</td>\n",
       "      <td>-6.485393e-01</td>\n",
       "      <td>-4.255740e-01</td>\n",
       "      <td>-5.828843e-01</td>\n",
       "      <td>-4.680368e-01</td>\n",
       "      <td>-4.837483e-01</td>\n",
       "      <td>-4.988498e-01</td>\n",
       "      <td>-4.562989e-01</td>\n",
       "      <td>-2.117214e-01</td>\n",
       "      <td>-2.283949e-01</td>\n",
       "      <td>-5.423504e-01</td>\n",
       "      <td>-1.618463e-01</td>\n",
       "      <td>-3.545861e-01</td>\n",
       "      <td>-3.171451e-01</td>\n",
       "      <td>-3.269839e-01</td>\n",
       "      <td>-7.083953e-02</td>\n",
       "      <td>-5.295979e-02</td>\n",
       "      <td>-3.308401e-01</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>84692.000000</td>\n",
       "      <td>1.810880e-02</td>\n",
       "      <td>6.548556e-02</td>\n",
       "      <td>1.798463e-01</td>\n",
       "      <td>-1.984653e-02</td>\n",
       "      <td>-5.433583e-02</td>\n",
       "      <td>-2.741871e-01</td>\n",
       "      <td>4.010308e-02</td>\n",
       "      <td>2.235804e-02</td>\n",
       "      <td>-5.142873e-02</td>\n",
       "      <td>-9.291738e-02</td>\n",
       "      <td>-3.275735e-02</td>\n",
       "      <td>1.400326e-01</td>\n",
       "      <td>-1.356806e-02</td>\n",
       "      <td>5.060132e-02</td>\n",
       "      <td>4.807155e-02</td>\n",
       "      <td>6.641332e-02</td>\n",
       "      <td>-6.567575e-02</td>\n",
       "      <td>-3.636312e-03</td>\n",
       "      <td>3.734823e-03</td>\n",
       "      <td>-6.248109e-02</td>\n",
       "      <td>-2.945017e-02</td>\n",
       "      <td>6.781943e-03</td>\n",
       "      <td>-1.119293e-02</td>\n",
       "      <td>4.097606e-02</td>\n",
       "      <td>1.659350e-02</td>\n",
       "      <td>-5.213911e-02</td>\n",
       "      <td>1.342146e-03</td>\n",
       "      <td>1.124383e-02</td>\n",
       "      <td>-2.652715e-01</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>139320.500000</td>\n",
       "      <td>1.315642e+00</td>\n",
       "      <td>8.037239e-01</td>\n",
       "      <td>1.027196e+00</td>\n",
       "      <td>7.433413e-01</td>\n",
       "      <td>6.119264e-01</td>\n",
       "      <td>3.985649e-01</td>\n",
       "      <td>5.704361e-01</td>\n",
       "      <td>3.273459e-01</td>\n",
       "      <td>5.971390e-01</td>\n",
       "      <td>4.539234e-01</td>\n",
       "      <td>7.395934e-01</td>\n",
       "      <td>6.182380e-01</td>\n",
       "      <td>6.625050e-01</td>\n",
       "      <td>4.931498e-01</td>\n",
       "      <td>6.488208e-01</td>\n",
       "      <td>5.232963e-01</td>\n",
       "      <td>3.996750e-01</td>\n",
       "      <td>5.008067e-01</td>\n",
       "      <td>4.589494e-01</td>\n",
       "      <td>1.330408e-01</td>\n",
       "      <td>1.863772e-01</td>\n",
       "      <td>5.285536e-01</td>\n",
       "      <td>1.476421e-01</td>\n",
       "      <td>4.395266e-01</td>\n",
       "      <td>3.507156e-01</td>\n",
       "      <td>2.409522e-01</td>\n",
       "      <td>9.104512e-02</td>\n",
       "      <td>7.827995e-02</td>\n",
       "      <td>-4.471707e-02</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>172792.000000</td>\n",
       "      <td>2.454930e+00</td>\n",
       "      <td>2.205773e+01</td>\n",
       "      <td>9.382558e+00</td>\n",
       "      <td>1.687534e+01</td>\n",
       "      <td>3.480167e+01</td>\n",
       "      <td>7.330163e+01</td>\n",
       "      <td>1.205895e+02</td>\n",
       "      <td>2.000721e+01</td>\n",
       "      <td>1.559499e+01</td>\n",
       "      <td>2.374514e+01</td>\n",
       "      <td>1.201891e+01</td>\n",
       "      <td>7.848392e+00</td>\n",
       "      <td>7.126883e+00</td>\n",
       "      <td>1.052677e+01</td>\n",
       "      <td>8.877742e+00</td>\n",
       "      <td>1.731511e+01</td>\n",
       "      <td>9.253526e+00</td>\n",
       "      <td>5.041069e+00</td>\n",
       "      <td>5.591971e+00</td>\n",
       "      <td>3.942090e+01</td>\n",
       "      <td>2.720284e+01</td>\n",
       "      <td>1.050309e+01</td>\n",
       "      <td>2.252841e+01</td>\n",
       "      <td>4.584549e+00</td>\n",
       "      <td>7.519589e+00</td>\n",
       "      <td>3.517346e+00</td>\n",
       "      <td>3.161220e+01</td>\n",
       "      <td>3.384781e+01</td>\n",
       "      <td>1.023622e+02</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time            V1            V2            V3            V4  \\\n",
       "count  284807.000000  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean    94813.859575  1.168375e-15  3.416908e-16 -1.379537e-15  2.074095e-15   \n",
       "std     47488.145955  1.958696e+00  1.651309e+00  1.516255e+00  1.415869e+00   \n",
       "min         0.000000 -5.640751e+01 -7.271573e+01 -4.832559e+01 -5.683171e+00   \n",
       "25%     54201.500000 -9.203734e-01 -5.985499e-01 -8.903648e-01 -8.486401e-01   \n",
       "50%     84692.000000  1.810880e-02  6.548556e-02  1.798463e-01 -1.984653e-02   \n",
       "75%    139320.500000  1.315642e+00  8.037239e-01  1.027196e+00  7.433413e-01   \n",
       "max    172792.000000  2.454930e+00  2.205773e+01  9.382558e+00  1.687534e+01   \n",
       "\n",
       "                 V5            V6            V7            V8            V9  \\\n",
       "count  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean   9.604066e-16  1.487313e-15 -5.556467e-16  1.213481e-16 -2.406331e-15   \n",
       "std    1.380247e+00  1.332271e+00  1.237094e+00  1.194353e+00  1.098632e+00   \n",
       "min   -1.137433e+02 -2.616051e+01 -4.355724e+01 -7.321672e+01 -1.343407e+01   \n",
       "25%   -6.915971e-01 -7.682956e-01 -5.540759e-01 -2.086297e-01 -6.430976e-01   \n",
       "50%   -5.433583e-02 -2.741871e-01  4.010308e-02  2.235804e-02 -5.142873e-02   \n",
       "75%    6.119264e-01  3.985649e-01  5.704361e-01  3.273459e-01  5.971390e-01   \n",
       "max    3.480167e+01  7.330163e+01  1.205895e+02  2.000721e+01  1.559499e+01   \n",
       "\n",
       "                V10           V11           V12           V13           V14  \\\n",
       "count  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean   2.239053e-15  1.673327e-15 -1.247012e-15  8.190001e-16  1.207294e-15   \n",
       "std    1.088850e+00  1.020713e+00  9.992014e-01  9.952742e-01  9.585956e-01   \n",
       "min   -2.458826e+01 -4.797473e+00 -1.868371e+01 -5.791881e+00 -1.921433e+01   \n",
       "25%   -5.354257e-01 -7.624942e-01 -4.055715e-01 -6.485393e-01 -4.255740e-01   \n",
       "50%   -9.291738e-02 -3.275735e-02  1.400326e-01 -1.356806e-02  5.060132e-02   \n",
       "75%    4.539234e-01  7.395934e-01  6.182380e-01  6.625050e-01  4.931498e-01   \n",
       "max    2.374514e+01  1.201891e+01  7.848392e+00  7.126883e+00  1.052677e+01   \n",
       "\n",
       "                V15           V16           V17           V18           V19  \\\n",
       "count  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean   4.887456e-15  1.437716e-15 -3.772171e-16  9.564149e-16  1.039917e-15   \n",
       "std    9.153160e-01  8.762529e-01  8.493371e-01  8.381762e-01  8.140405e-01   \n",
       "min   -4.498945e+00 -1.412985e+01 -2.516280e+01 -9.498746e+00 -7.213527e+00   \n",
       "25%   -5.828843e-01 -4.680368e-01 -4.837483e-01 -4.988498e-01 -4.562989e-01   \n",
       "50%    4.807155e-02  6.641332e-02 -6.567575e-02 -3.636312e-03  3.734823e-03   \n",
       "75%    6.488208e-01  5.232963e-01  3.996750e-01  5.008067e-01  4.589494e-01   \n",
       "max    8.877742e+00  1.731511e+01  9.253526e+00  5.041069e+00  5.591971e+00   \n",
       "\n",
       "                V20           V21           V22           V23           V24  \\\n",
       "count  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean   6.406204e-16  1.654067e-16 -3.568593e-16  2.578648e-16  4.473266e-15   \n",
       "std    7.709250e-01  7.345240e-01  7.257016e-01  6.244603e-01  6.056471e-01   \n",
       "min   -5.449772e+01 -3.483038e+01 -1.093314e+01 -4.480774e+01 -2.836627e+00   \n",
       "25%   -2.117214e-01 -2.283949e-01 -5.423504e-01 -1.618463e-01 -3.545861e-01   \n",
       "50%   -6.248109e-02 -2.945017e-02  6.781943e-03 -1.119293e-02  4.097606e-02   \n",
       "75%    1.330408e-01  1.863772e-01  5.285536e-01  1.476421e-01  4.395266e-01   \n",
       "max    3.942090e+01  2.720284e+01  1.050309e+01  2.252841e+01  4.584549e+00   \n",
       "\n",
       "                V25           V26           V27           V28        Amount  \\\n",
       "count  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05  2.848070e+05   \n",
       "mean   5.340915e-16  1.683437e-15 -3.660091e-16 -1.227390e-16  2.913952e-17   \n",
       "std    5.212781e-01  4.822270e-01  4.036325e-01  3.300833e-01  1.000002e+00   \n",
       "min   -1.029540e+01 -2.604551e+00 -2.256568e+01 -1.543008e+01 -3.532294e-01   \n",
       "25%   -3.171451e-01 -3.269839e-01 -7.083953e-02 -5.295979e-02 -3.308401e-01   \n",
       "50%    1.659350e-02 -5.213911e-02  1.342146e-03  1.124383e-02 -2.652715e-01   \n",
       "75%    3.507156e-01  2.409522e-01  9.104512e-02  7.827995e-02 -4.471707e-02   \n",
       "max    7.519589e+00  3.517346e+00  3.161220e+01  3.384781e+01  1.023622e+02   \n",
       "\n",
       "               Class  \n",
       "count  284807.000000  \n",
       "mean        0.001727  \n",
       "std         0.041527  \n",
       "min         0.000000  \n",
       "25%         0.000000  \n",
       "50%         0.000000  \n",
       "75%         0.000000  \n",
       "max         1.000000  "
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of legitimate and fraudulent transactions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Class\n",
       "0    284315\n",
       "1       492\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Class'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Undersampling the data\n",
    "We will employ undersampling as one class significantly dominates the other."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Determine the number of instances in the minority class\n",
    "fraud_count = len(df[df.Class == 1])\n",
    "fraud_indices = np.array(df[df.Class == 1].index)\n",
    "\n",
    "# Select indices corresponding to majority class instances\n",
    "normal_indices = df[df.Class == 0].index\n",
    "\n",
    "# Randomly sample the same number of instances from the majority class\n",
    "random_normal_indices = np.random.choice(normal_indices, fraud_count, replace=False)\n",
    "random_normal_indices = np.array(random_normal_indices)\n",
    "\n",
    "# Combine indices of both classes\n",
    "undersample_indice = np.concatenate([fraud_indices, random_normal_indices])\n",
    "\n",
    "# Undersample dataset\n",
    "undersample_data = df.iloc[undersample_indice, :]\n",
    "\n",
    "X_undersample = undersample_data.iloc[:, undersample_data.columns != 'Class']\n",
    "y_undersample = undersample_data.iloc[:, undersample_data.columns == 'Class']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Size of undersampled dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 984 entries, 541 to 141412\n",
      "Data columns (total 31 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   Time    984 non-null    float64\n",
      " 1   V1      984 non-null    float64\n",
      " 2   V2      984 non-null    float64\n",
      " 3   V3      984 non-null    float64\n",
      " 4   V4      984 non-null    float64\n",
      " 5   V5      984 non-null    float64\n",
      " 6   V6      984 non-null    float64\n",
      " 7   V7      984 non-null    float64\n",
      " 8   V8      984 non-null    float64\n",
      " 9   V9      984 non-null    float64\n",
      " 10  V10     984 non-null    float64\n",
      " 11  V11     984 non-null    float64\n",
      " 12  V12     984 non-null    float64\n",
      " 13  V13     984 non-null    float64\n",
      " 14  V14     984 non-null    float64\n",
      " 15  V15     984 non-null    float64\n",
      " 16  V16     984 non-null    float64\n",
      " 17  V17     984 non-null    float64\n",
      " 18  V18     984 non-null    float64\n",
      " 19  V19     984 non-null    float64\n",
      " 20  V20     984 non-null    float64\n",
      " 21  V21     984 non-null    float64\n",
      " 22  V22     984 non-null    float64\n",
      " 23  V23     984 non-null    float64\n",
      " 24  V24     984 non-null    float64\n",
      " 25  V25     984 non-null    float64\n",
      " 26  V26     984 non-null    float64\n",
      " 27  V27     984 non-null    float64\n",
      " 28  V28     984 non-null    float64\n",
      " 29  Amount  984 non-null    float64\n",
      " 30  Class   984 non-null    int64  \n",
      "dtypes: float64(30), int64(1)\n",
      "memory usage: 246.0 KB\n"
     ]
    }
   ],
   "source": [
    "undersample_data.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Summary statistics of the undersampled dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "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",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>V10</th>\n",
       "      <th>V11</th>\n",
       "      <th>V12</th>\n",
       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
       "      <th>V15</th>\n",
       "      <th>V16</th>\n",
       "      <th>V17</th>\n",
       "      <th>V18</th>\n",
       "      <th>V19</th>\n",
       "      <th>V20</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "      <td>984.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>88501.498984</td>\n",
       "      <td>-2.445079</td>\n",
       "      <td>1.781022</td>\n",
       "      <td>-3.509406</td>\n",
       "      <td>2.214004</td>\n",
       "      <td>-1.477993</td>\n",
       "      <td>-0.713150</td>\n",
       "      <td>-2.787427</td>\n",
       "      <td>0.279073</td>\n",
       "      <td>-1.253108</td>\n",
       "      <td>-2.841500</td>\n",
       "      <td>1.930697</td>\n",
       "      <td>-3.124120</td>\n",
       "      <td>-0.026229</td>\n",
       "      <td>-3.502384</td>\n",
       "      <td>-0.039494</td>\n",
       "      <td>-2.097294</td>\n",
       "      <td>-3.304208</td>\n",
       "      <td>-1.128950</td>\n",
       "      <td>0.343668</td>\n",
       "      <td>0.175905</td>\n",
       "      <td>0.331911</td>\n",
       "      <td>0.049631</td>\n",
       "      <td>-0.031264</td>\n",
       "      <td>-0.037389</td>\n",
       "      <td>0.022812</td>\n",
       "      <td>0.027632</td>\n",
       "      <td>0.086286</td>\n",
       "      <td>0.046738</td>\n",
       "      <td>0.039676</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>48996.269445</td>\n",
       "      <td>5.512352</td>\n",
       "      <td>3.713232</td>\n",
       "      <td>6.223001</td>\n",
       "      <td>3.231076</td>\n",
       "      <td>4.274632</td>\n",
       "      <td>1.789350</td>\n",
       "      <td>5.856197</td>\n",
       "      <td>4.857643</td>\n",
       "      <td>2.371055</td>\n",
       "      <td>4.563067</td>\n",
       "      <td>2.764745</td>\n",
       "      <td>4.595103</td>\n",
       "      <td>1.054377</td>\n",
       "      <td>4.653202</td>\n",
       "      <td>1.002911</td>\n",
       "      <td>3.465619</td>\n",
       "      <td>5.990033</td>\n",
       "      <td>2.412032</td>\n",
       "      <td>1.290973</td>\n",
       "      <td>1.126258</td>\n",
       "      <td>2.787884</td>\n",
       "      <td>1.167097</td>\n",
       "      <td>1.177562</td>\n",
       "      <td>0.551518</td>\n",
       "      <td>0.677541</td>\n",
       "      <td>0.476480</td>\n",
       "      <td>1.023332</td>\n",
       "      <td>0.479168</td>\n",
       "      <td>0.851800</td>\n",
       "      <td>0.500254</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>60.000000</td>\n",
       "      <td>-30.552380</td>\n",
       "      <td>-15.799625</td>\n",
       "      <td>-31.103685</td>\n",
       "      <td>-3.863126</td>\n",
       "      <td>-22.105532</td>\n",
       "      <td>-10.261990</td>\n",
       "      <td>-43.557242</td>\n",
       "      <td>-41.044261</td>\n",
       "      <td>-13.434066</td>\n",
       "      <td>-24.588262</td>\n",
       "      <td>-2.613374</td>\n",
       "      <td>-18.683715</td>\n",
       "      <td>-3.223045</td>\n",
       "      <td>-19.214325</td>\n",
       "      <td>-4.498945</td>\n",
       "      <td>-14.129855</td>\n",
       "      <td>-25.162799</td>\n",
       "      <td>-9.498746</td>\n",
       "      <td>-3.681904</td>\n",
       "      <td>-7.242879</td>\n",
       "      <td>-22.797604</td>\n",
       "      <td>-8.887017</td>\n",
       "      <td>-19.254328</td>\n",
       "      <td>-2.028024</td>\n",
       "      <td>-4.781606</td>\n",
       "      <td>-1.214960</td>\n",
       "      <td>-7.263482</td>\n",
       "      <td>-2.735623</td>\n",
       "      <td>-0.353229</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>45531.000000</td>\n",
       "      <td>-2.867222</td>\n",
       "      <td>-0.155438</td>\n",
       "      <td>-5.084967</td>\n",
       "      <td>-0.172018</td>\n",
       "      <td>-1.700260</td>\n",
       "      <td>-1.619179</td>\n",
       "      <td>-3.066415</td>\n",
       "      <td>-0.204192</td>\n",
       "      <td>-2.279453</td>\n",
       "      <td>-4.572043</td>\n",
       "      <td>-0.187147</td>\n",
       "      <td>-5.495221</td>\n",
       "      <td>-0.784589</td>\n",
       "      <td>-6.721799</td>\n",
       "      <td>-0.627097</td>\n",
       "      <td>-3.543426</td>\n",
       "      <td>-5.302111</td>\n",
       "      <td>-1.809496</td>\n",
       "      <td>-0.412430</td>\n",
       "      <td>-0.187708</td>\n",
       "      <td>-0.157259</td>\n",
       "      <td>-0.509376</td>\n",
       "      <td>-0.240064</td>\n",
       "      <td>-0.379825</td>\n",
       "      <td>-0.321251</td>\n",
       "      <td>-0.281187</td>\n",
       "      <td>-0.061809</td>\n",
       "      <td>-0.050194</td>\n",
       "      <td>-0.347302</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>83076.500000</td>\n",
       "      <td>-0.823244</td>\n",
       "      <td>0.957399</td>\n",
       "      <td>-1.381998</td>\n",
       "      <td>1.287041</td>\n",
       "      <td>-0.394605</td>\n",
       "      <td>-0.689473</td>\n",
       "      <td>-0.668321</td>\n",
       "      <td>0.147397</td>\n",
       "      <td>-0.694910</td>\n",
       "      <td>-0.948441</td>\n",
       "      <td>1.170286</td>\n",
       "      <td>-0.858094</td>\n",
       "      <td>-0.000686</td>\n",
       "      <td>-1.110717</td>\n",
       "      <td>-0.006070</td>\n",
       "      <td>-0.677801</td>\n",
       "      <td>-0.513640</td>\n",
       "      <td>-0.383038</td>\n",
       "      <td>0.221049</td>\n",
       "      <td>0.040630</td>\n",
       "      <td>0.155404</td>\n",
       "      <td>0.080270</td>\n",
       "      <td>-0.030318</td>\n",
       "      <td>0.009379</td>\n",
       "      <td>0.049923</td>\n",
       "      <td>-0.007475</td>\n",
       "      <td>0.063100</td>\n",
       "      <td>0.039464</td>\n",
       "      <td>-0.280984</td>\n",
       "      <td>0.500000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>135051.500000</td>\n",
       "      <td>0.919444</td>\n",
       "      <td>2.791569</td>\n",
       "      <td>0.356911</td>\n",
       "      <td>4.175332</td>\n",
       "      <td>0.616305</td>\n",
       "      <td>0.069620</td>\n",
       "      <td>0.265089</td>\n",
       "      <td>0.877002</td>\n",
       "      <td>0.134399</td>\n",
       "      <td>-0.016047</td>\n",
       "      <td>3.586502</td>\n",
       "      <td>0.190356</td>\n",
       "      <td>0.683977</td>\n",
       "      <td>0.110541</td>\n",
       "      <td>0.672903</td>\n",
       "      <td>0.250353</td>\n",
       "      <td>0.313841</td>\n",
       "      <td>0.334927</td>\n",
       "      <td>0.978754</td>\n",
       "      <td>0.445616</td>\n",
       "      <td>0.642724</td>\n",
       "      <td>0.624948</td>\n",
       "      <td>0.180735</td>\n",
       "      <td>0.365624</td>\n",
       "      <td>0.395001</td>\n",
       "      <td>0.324059</td>\n",
       "      <td>0.457194</td>\n",
       "      <td>0.226492</td>\n",
       "      <td>0.046539</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>172733.000000</td>\n",
       "      <td>2.335833</td>\n",
       "      <td>22.057729</td>\n",
       "      <td>3.476268</td>\n",
       "      <td>12.114672</td>\n",
       "      <td>14.103918</td>\n",
       "      <td>6.474115</td>\n",
       "      <td>5.802537</td>\n",
       "      <td>20.007208</td>\n",
       "      <td>6.816732</td>\n",
       "      <td>11.732926</td>\n",
       "      <td>12.018913</td>\n",
       "      <td>2.534876</td>\n",
       "      <td>3.091328</td>\n",
       "      <td>3.442422</td>\n",
       "      <td>2.471358</td>\n",
       "      <td>3.139656</td>\n",
       "      <td>6.739384</td>\n",
       "      <td>3.790316</td>\n",
       "      <td>5.228342</td>\n",
       "      <td>11.059004</td>\n",
       "      <td>27.202839</td>\n",
       "      <td>8.361985</td>\n",
       "      <td>5.466230</td>\n",
       "      <td>1.208141</td>\n",
       "      <td>2.208209</td>\n",
       "      <td>2.745261</td>\n",
       "      <td>3.052358</td>\n",
       "      <td>4.975792</td>\n",
       "      <td>8.146182</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time          V1          V2          V3          V4  \\\n",
       "count     984.000000  984.000000  984.000000  984.000000  984.000000   \n",
       "mean    88501.498984   -2.445079    1.781022   -3.509406    2.214004   \n",
       "std     48996.269445    5.512352    3.713232    6.223001    3.231076   \n",
       "min        60.000000  -30.552380  -15.799625  -31.103685   -3.863126   \n",
       "25%     45531.000000   -2.867222   -0.155438   -5.084967   -0.172018   \n",
       "50%     83076.500000   -0.823244    0.957399   -1.381998    1.287041   \n",
       "75%    135051.500000    0.919444    2.791569    0.356911    4.175332   \n",
       "max    172733.000000    2.335833   22.057729    3.476268   12.114672   \n",
       "\n",
       "               V5          V6          V7          V8          V9         V10  \\\n",
       "count  984.000000  984.000000  984.000000  984.000000  984.000000  984.000000   \n",
       "mean    -1.477993   -0.713150   -2.787427    0.279073   -1.253108   -2.841500   \n",
       "std      4.274632    1.789350    5.856197    4.857643    2.371055    4.563067   \n",
       "min    -22.105532  -10.261990  -43.557242  -41.044261  -13.434066  -24.588262   \n",
       "25%     -1.700260   -1.619179   -3.066415   -0.204192   -2.279453   -4.572043   \n",
       "50%     -0.394605   -0.689473   -0.668321    0.147397   -0.694910   -0.948441   \n",
       "75%      0.616305    0.069620    0.265089    0.877002    0.134399   -0.016047   \n",
       "max     14.103918    6.474115    5.802537   20.007208    6.816732   11.732926   \n",
       "\n",
       "              V11         V12         V13         V14         V15         V16  \\\n",
       "count  984.000000  984.000000  984.000000  984.000000  984.000000  984.000000   \n",
       "mean     1.930697   -3.124120   -0.026229   -3.502384   -0.039494   -2.097294   \n",
       "std      2.764745    4.595103    1.054377    4.653202    1.002911    3.465619   \n",
       "min     -2.613374  -18.683715   -3.223045  -19.214325   -4.498945  -14.129855   \n",
       "25%     -0.187147   -5.495221   -0.784589   -6.721799   -0.627097   -3.543426   \n",
       "50%      1.170286   -0.858094   -0.000686   -1.110717   -0.006070   -0.677801   \n",
       "75%      3.586502    0.190356    0.683977    0.110541    0.672903    0.250353   \n",
       "max     12.018913    2.534876    3.091328    3.442422    2.471358    3.139656   \n",
       "\n",
       "              V17         V18         V19         V20         V21         V22  \\\n",
       "count  984.000000  984.000000  984.000000  984.000000  984.000000  984.000000   \n",
       "mean    -3.304208   -1.128950    0.343668    0.175905    0.331911    0.049631   \n",
       "std      5.990033    2.412032    1.290973    1.126258    2.787884    1.167097   \n",
       "min    -25.162799   -9.498746   -3.681904   -7.242879  -22.797604   -8.887017   \n",
       "25%     -5.302111   -1.809496   -0.412430   -0.187708   -0.157259   -0.509376   \n",
       "50%     -0.513640   -0.383038    0.221049    0.040630    0.155404    0.080270   \n",
       "75%      0.313841    0.334927    0.978754    0.445616    0.642724    0.624948   \n",
       "max      6.739384    3.790316    5.228342   11.059004   27.202839    8.361985   \n",
       "\n",
       "              V23         V24         V25         V26         V27         V28  \\\n",
       "count  984.000000  984.000000  984.000000  984.000000  984.000000  984.000000   \n",
       "mean    -0.031264   -0.037389    0.022812    0.027632    0.086286    0.046738   \n",
       "std      1.177562    0.551518    0.677541    0.476480    1.023332    0.479168   \n",
       "min    -19.254328   -2.028024   -4.781606   -1.214960   -7.263482   -2.735623   \n",
       "25%     -0.240064   -0.379825   -0.321251   -0.281187   -0.061809   -0.050194   \n",
       "50%     -0.030318    0.009379    0.049923   -0.007475    0.063100    0.039464   \n",
       "75%      0.180735    0.365624    0.395001    0.324059    0.457194    0.226492   \n",
       "max      5.466230    1.208141    2.208209    2.745261    3.052358    4.975792   \n",
       "\n",
       "           Amount       Class  \n",
       "count  984.000000  984.000000  \n",
       "mean     0.039676    0.500000  \n",
       "std      0.851800    0.500254  \n",
       "min     -0.353229    0.000000  \n",
       "25%     -0.347302    0.000000  \n",
       "50%     -0.280984    0.500000  \n",
       "75%      0.046539    1.000000  \n",
       "max      8.146182    1.000000  "
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "undersample_data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of legitimate and fraudulent transactions in an undersampled dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Class\n",
       "1    492\n",
       "0    492\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "undersample_data['Class'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Splitting whole data into training and test datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df.iloc[:, df.columns != 'Class']\n",
    "y = df.iloc[:, df.columns == 'Class']\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical measures of the training dataset of whole data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 199364 entries, 161145 to 117952\n",
      "Data columns (total 31 columns):\n",
      " #   Column  Non-Null Count   Dtype  \n",
      "---  ------  --------------   -----  \n",
      " 0   Time    199364 non-null  float64\n",
      " 1   V1      199364 non-null  float64\n",
      " 2   V2      199364 non-null  float64\n",
      " 3   V3      199364 non-null  float64\n",
      " 4   V4      199364 non-null  float64\n",
      " 5   V5      199364 non-null  float64\n",
      " 6   V6      199364 non-null  float64\n",
      " 7   V7      199364 non-null  float64\n",
      " 8   V8      199364 non-null  float64\n",
      " 9   V9      199364 non-null  float64\n",
      " 10  V10     199364 non-null  float64\n",
      " 11  V11     199364 non-null  float64\n",
      " 12  V12     199364 non-null  float64\n",
      " 13  V13     199364 non-null  float64\n",
      " 14  V14     199364 non-null  float64\n",
      " 15  V15     199364 non-null  float64\n",
      " 16  V16     199364 non-null  float64\n",
      " 17  V17     199364 non-null  float64\n",
      " 18  V18     199364 non-null  float64\n",
      " 19  V19     199364 non-null  float64\n",
      " 20  V20     199364 non-null  float64\n",
      " 21  V21     199364 non-null  float64\n",
      " 22  V22     199364 non-null  float64\n",
      " 23  V23     199364 non-null  float64\n",
      " 24  V24     199364 non-null  float64\n",
      " 25  V25     199364 non-null  float64\n",
      " 26  V26     199364 non-null  float64\n",
      " 27  V27     199364 non-null  float64\n",
      " 28  V28     199364 non-null  float64\n",
      " 29  Amount  199364 non-null  float64\n",
      " 30  Class   199364 non-null  int64  \n",
      "dtypes: float64(30), int64(1)\n",
      "memory usage: 48.7 MB\n"
     ]
    }
   ],
   "source": [
    "pd.concat([X_train, y_train], axis=1).info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>V10</th>\n",
       "      <th>V11</th>\n",
       "      <th>V12</th>\n",
       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
       "      <th>V15</th>\n",
       "      <th>V16</th>\n",
       "      <th>V17</th>\n",
       "      <th>V18</th>\n",
       "      <th>V19</th>\n",
       "      <th>V20</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "      <td>199364.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>94799.493936</td>\n",
       "      <td>0.000315</td>\n",
       "      <td>-0.002690</td>\n",
       "      <td>-0.001532</td>\n",
       "      <td>0.000721</td>\n",
       "      <td>-0.001494</td>\n",
       "      <td>-0.000210</td>\n",
       "      <td>-0.000870</td>\n",
       "      <td>-0.001980</td>\n",
       "      <td>0.000212</td>\n",
       "      <td>0.001357</td>\n",
       "      <td>-0.001039</td>\n",
       "      <td>-0.001565</td>\n",
       "      <td>0.000693</td>\n",
       "      <td>0.000137</td>\n",
       "      <td>0.000322</td>\n",
       "      <td>0.000084</td>\n",
       "      <td>0.000292</td>\n",
       "      <td>-0.000134</td>\n",
       "      <td>0.000490</td>\n",
       "      <td>0.000430</td>\n",
       "      <td>-0.000014</td>\n",
       "      <td>-0.000022</td>\n",
       "      <td>-0.000258</td>\n",
       "      <td>0.000362</td>\n",
       "      <td>0.000395</td>\n",
       "      <td>-0.000094</td>\n",
       "      <td>-0.000027</td>\n",
       "      <td>0.000015</td>\n",
       "      <td>0.001271</td>\n",
       "      <td>0.001731</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>47499.835491</td>\n",
       "      <td>1.963554</td>\n",
       "      <td>1.657379</td>\n",
       "      <td>1.516716</td>\n",
       "      <td>1.417138</td>\n",
       "      <td>1.368744</td>\n",
       "      <td>1.328673</td>\n",
       "      <td>1.226018</td>\n",
       "      <td>1.212338</td>\n",
       "      <td>1.102021</td>\n",
       "      <td>1.092801</td>\n",
       "      <td>1.020027</td>\n",
       "      <td>0.996526</td>\n",
       "      <td>0.997718</td>\n",
       "      <td>0.956938</td>\n",
       "      <td>0.916143</td>\n",
       "      <td>0.876131</td>\n",
       "      <td>0.852181</td>\n",
       "      <td>0.837556</td>\n",
       "      <td>0.814506</td>\n",
       "      <td>0.770257</td>\n",
       "      <td>0.743450</td>\n",
       "      <td>0.727625</td>\n",
       "      <td>0.629145</td>\n",
       "      <td>0.605298</td>\n",
       "      <td>0.521175</td>\n",
       "      <td>0.481842</td>\n",
       "      <td>0.401042</td>\n",
       "      <td>0.324849</td>\n",
       "      <td>0.983948</td>\n",
       "      <td>0.041563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-46.855047</td>\n",
       "      <td>-63.344698</td>\n",
       "      <td>-33.680984</td>\n",
       "      <td>-5.560118</td>\n",
       "      <td>-42.147898</td>\n",
       "      <td>-23.496714</td>\n",
       "      <td>-43.557242</td>\n",
       "      <td>-73.216718</td>\n",
       "      <td>-13.434066</td>\n",
       "      <td>-24.588262</td>\n",
       "      <td>-4.797473</td>\n",
       "      <td>-17.769143</td>\n",
       "      <td>-5.791881</td>\n",
       "      <td>-19.214325</td>\n",
       "      <td>-4.498945</td>\n",
       "      <td>-14.129855</td>\n",
       "      <td>-25.162799</td>\n",
       "      <td>-9.498746</td>\n",
       "      <td>-7.213527</td>\n",
       "      <td>-23.646890</td>\n",
       "      <td>-34.830382</td>\n",
       "      <td>-10.933144</td>\n",
       "      <td>-44.807735</td>\n",
       "      <td>-2.822684</td>\n",
       "      <td>-10.295397</td>\n",
       "      <td>-2.534330</td>\n",
       "      <td>-22.565679</td>\n",
       "      <td>-11.710896</td>\n",
       "      <td>-0.353229</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>54126.000000</td>\n",
       "      <td>-0.921539</td>\n",
       "      <td>-0.601213</td>\n",
       "      <td>-0.892838</td>\n",
       "      <td>-0.848835</td>\n",
       "      <td>-0.692874</td>\n",
       "      <td>-0.769177</td>\n",
       "      <td>-0.554220</td>\n",
       "      <td>-0.209086</td>\n",
       "      <td>-0.644753</td>\n",
       "      <td>-0.535493</td>\n",
       "      <td>-0.762852</td>\n",
       "      <td>-0.407660</td>\n",
       "      <td>-0.648456</td>\n",
       "      <td>-0.425122</td>\n",
       "      <td>-0.583616</td>\n",
       "      <td>-0.467945</td>\n",
       "      <td>-0.484055</td>\n",
       "      <td>-0.498850</td>\n",
       "      <td>-0.456800</td>\n",
       "      <td>-0.211662</td>\n",
       "      <td>-0.229272</td>\n",
       "      <td>-0.544345</td>\n",
       "      <td>-0.162021</td>\n",
       "      <td>-0.354179</td>\n",
       "      <td>-0.316088</td>\n",
       "      <td>-0.327327</td>\n",
       "      <td>-0.070864</td>\n",
       "      <td>-0.052907</td>\n",
       "      <td>-0.330640</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>84633.500000</td>\n",
       "      <td>0.019705</td>\n",
       "      <td>0.063784</td>\n",
       "      <td>0.177888</td>\n",
       "      <td>-0.017852</td>\n",
       "      <td>-0.055832</td>\n",
       "      <td>-0.274397</td>\n",
       "      <td>0.039228</td>\n",
       "      <td>0.021803</td>\n",
       "      <td>-0.049633</td>\n",
       "      <td>-0.092069</td>\n",
       "      <td>-0.034135</td>\n",
       "      <td>0.137912</td>\n",
       "      <td>-0.013416</td>\n",
       "      <td>0.051179</td>\n",
       "      <td>0.049289</td>\n",
       "      <td>0.067772</td>\n",
       "      <td>-0.065113</td>\n",
       "      <td>-0.003217</td>\n",
       "      <td>0.004422</td>\n",
       "      <td>-0.062889</td>\n",
       "      <td>-0.029045</td>\n",
       "      <td>0.006744</td>\n",
       "      <td>-0.010915</td>\n",
       "      <td>0.040974</td>\n",
       "      <td>0.018014</td>\n",
       "      <td>-0.052287</td>\n",
       "      <td>0.001064</td>\n",
       "      <td>0.011119</td>\n",
       "      <td>-0.265271</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>139334.250000</td>\n",
       "      <td>1.316707</td>\n",
       "      <td>0.802437</td>\n",
       "      <td>1.025529</td>\n",
       "      <td>0.745566</td>\n",
       "      <td>0.609349</td>\n",
       "      <td>0.397928</td>\n",
       "      <td>0.569638</td>\n",
       "      <td>0.327023</td>\n",
       "      <td>0.597096</td>\n",
       "      <td>0.458129</td>\n",
       "      <td>0.738143</td>\n",
       "      <td>0.617393</td>\n",
       "      <td>0.664148</td>\n",
       "      <td>0.493925</td>\n",
       "      <td>0.649589</td>\n",
       "      <td>0.523095</td>\n",
       "      <td>0.401034</td>\n",
       "      <td>0.500436</td>\n",
       "      <td>0.460367</td>\n",
       "      <td>0.132834</td>\n",
       "      <td>0.187095</td>\n",
       "      <td>0.531017</td>\n",
       "      <td>0.147503</td>\n",
       "      <td>0.438953</td>\n",
       "      <td>0.350802</td>\n",
       "      <td>0.241082</td>\n",
       "      <td>0.090491</td>\n",
       "      <td>0.077989</td>\n",
       "      <td>-0.043058</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>172792.000000</td>\n",
       "      <td>2.451888</td>\n",
       "      <td>22.057729</td>\n",
       "      <td>9.382558</td>\n",
       "      <td>16.715537</td>\n",
       "      <td>34.099309</td>\n",
       "      <td>23.917837</td>\n",
       "      <td>44.054461</td>\n",
       "      <td>20.007208</td>\n",
       "      <td>15.594995</td>\n",
       "      <td>23.745136</td>\n",
       "      <td>12.018913</td>\n",
       "      <td>7.848392</td>\n",
       "      <td>4.569009</td>\n",
       "      <td>10.526766</td>\n",
       "      <td>5.825654</td>\n",
       "      <td>7.059132</td>\n",
       "      <td>9.207059</td>\n",
       "      <td>5.041069</td>\n",
       "      <td>5.572113</td>\n",
       "      <td>39.420904</td>\n",
       "      <td>27.202839</td>\n",
       "      <td>10.503090</td>\n",
       "      <td>22.528412</td>\n",
       "      <td>4.022866</td>\n",
       "      <td>7.519589</td>\n",
       "      <td>3.463246</td>\n",
       "      <td>12.152401</td>\n",
       "      <td>22.620072</td>\n",
       "      <td>78.235272</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time             V1             V2             V3  \\\n",
       "count  199364.000000  199364.000000  199364.000000  199364.000000   \n",
       "mean    94799.493936       0.000315      -0.002690      -0.001532   \n",
       "std     47499.835491       1.963554       1.657379       1.516716   \n",
       "min         0.000000     -46.855047     -63.344698     -33.680984   \n",
       "25%     54126.000000      -0.921539      -0.601213      -0.892838   \n",
       "50%     84633.500000       0.019705       0.063784       0.177888   \n",
       "75%    139334.250000       1.316707       0.802437       1.025529   \n",
       "max    172792.000000       2.451888      22.057729       9.382558   \n",
       "\n",
       "                  V4             V5             V6             V7  \\\n",
       "count  199364.000000  199364.000000  199364.000000  199364.000000   \n",
       "mean        0.000721      -0.001494      -0.000210      -0.000870   \n",
       "std         1.417138       1.368744       1.328673       1.226018   \n",
       "min        -5.560118     -42.147898     -23.496714     -43.557242   \n",
       "25%        -0.848835      -0.692874      -0.769177      -0.554220   \n",
       "50%        -0.017852      -0.055832      -0.274397       0.039228   \n",
       "75%         0.745566       0.609349       0.397928       0.569638   \n",
       "max        16.715537      34.099309      23.917837      44.054461   \n",
       "\n",
       "                  V8             V9            V10            V11  \\\n",
       "count  199364.000000  199364.000000  199364.000000  199364.000000   \n",
       "mean       -0.001980       0.000212       0.001357      -0.001039   \n",
       "std         1.212338       1.102021       1.092801       1.020027   \n",
       "min       -73.216718     -13.434066     -24.588262      -4.797473   \n",
       "25%        -0.209086      -0.644753      -0.535493      -0.762852   \n",
       "50%         0.021803      -0.049633      -0.092069      -0.034135   \n",
       "75%         0.327023       0.597096       0.458129       0.738143   \n",
       "max        20.007208      15.594995      23.745136      12.018913   \n",
       "\n",
       "                 V12            V13            V14            V15  \\\n",
       "count  199364.000000  199364.000000  199364.000000  199364.000000   \n",
       "mean       -0.001565       0.000693       0.000137       0.000322   \n",
       "std         0.996526       0.997718       0.956938       0.916143   \n",
       "min       -17.769143      -5.791881     -19.214325      -4.498945   \n",
       "25%        -0.407660      -0.648456      -0.425122      -0.583616   \n",
       "50%         0.137912      -0.013416       0.051179       0.049289   \n",
       "75%         0.617393       0.664148       0.493925       0.649589   \n",
       "max         7.848392       4.569009      10.526766       5.825654   \n",
       "\n",
       "                 V16            V17            V18            V19  \\\n",
       "count  199364.000000  199364.000000  199364.000000  199364.000000   \n",
       "mean        0.000084       0.000292      -0.000134       0.000490   \n",
       "std         0.876131       0.852181       0.837556       0.814506   \n",
       "min       -14.129855     -25.162799      -9.498746      -7.213527   \n",
       "25%        -0.467945      -0.484055      -0.498850      -0.456800   \n",
       "50%         0.067772      -0.065113      -0.003217       0.004422   \n",
       "75%         0.523095       0.401034       0.500436       0.460367   \n",
       "max         7.059132       9.207059       5.041069       5.572113   \n",
       "\n",
       "                 V20            V21            V22            V23  \\\n",
       "count  199364.000000  199364.000000  199364.000000  199364.000000   \n",
       "mean        0.000430      -0.000014      -0.000022      -0.000258   \n",
       "std         0.770257       0.743450       0.727625       0.629145   \n",
       "min       -23.646890     -34.830382     -10.933144     -44.807735   \n",
       "25%        -0.211662      -0.229272      -0.544345      -0.162021   \n",
       "50%        -0.062889      -0.029045       0.006744      -0.010915   \n",
       "75%         0.132834       0.187095       0.531017       0.147503   \n",
       "max        39.420904      27.202839      10.503090      22.528412   \n",
       "\n",
       "                 V24            V25            V26            V27  \\\n",
       "count  199364.000000  199364.000000  199364.000000  199364.000000   \n",
       "mean        0.000362       0.000395      -0.000094      -0.000027   \n",
       "std         0.605298       0.521175       0.481842       0.401042   \n",
       "min        -2.822684     -10.295397      -2.534330     -22.565679   \n",
       "25%        -0.354179      -0.316088      -0.327327      -0.070864   \n",
       "50%         0.040974       0.018014      -0.052287       0.001064   \n",
       "75%         0.438953       0.350802       0.241082       0.090491   \n",
       "max         4.022866       7.519589       3.463246      12.152401   \n",
       "\n",
       "                 V28         Amount          Class  \n",
       "count  199364.000000  199364.000000  199364.000000  \n",
       "mean        0.000015       0.001271       0.001731  \n",
       "std         0.324849       0.983948       0.041563  \n",
       "min       -11.710896      -0.353229       0.000000  \n",
       "25%        -0.052907      -0.330640       0.000000  \n",
       "50%         0.011119      -0.265271       0.000000  \n",
       "75%         0.077989      -0.043058       0.000000  \n",
       "max        22.620072      78.235272       1.000000  "
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_train, y_train], axis=1).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Class\n",
       "0    199019\n",
       "1       345\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_train, y_train], axis=1)['Class'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical measures of the test dataset of whole data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 85443 entries, 183484 to 240913\n",
      "Data columns (total 31 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   Time    85443 non-null  float64\n",
      " 1   V1      85443 non-null  float64\n",
      " 2   V2      85443 non-null  float64\n",
      " 3   V3      85443 non-null  float64\n",
      " 4   V4      85443 non-null  float64\n",
      " 5   V5      85443 non-null  float64\n",
      " 6   V6      85443 non-null  float64\n",
      " 7   V7      85443 non-null  float64\n",
      " 8   V8      85443 non-null  float64\n",
      " 9   V9      85443 non-null  float64\n",
      " 10  V10     85443 non-null  float64\n",
      " 11  V11     85443 non-null  float64\n",
      " 12  V12     85443 non-null  float64\n",
      " 13  V13     85443 non-null  float64\n",
      " 14  V14     85443 non-null  float64\n",
      " 15  V15     85443 non-null  float64\n",
      " 16  V16     85443 non-null  float64\n",
      " 17  V17     85443 non-null  float64\n",
      " 18  V18     85443 non-null  float64\n",
      " 19  V19     85443 non-null  float64\n",
      " 20  V20     85443 non-null  float64\n",
      " 21  V21     85443 non-null  float64\n",
      " 22  V22     85443 non-null  float64\n",
      " 23  V23     85443 non-null  float64\n",
      " 24  V24     85443 non-null  float64\n",
      " 25  V25     85443 non-null  float64\n",
      " 26  V26     85443 non-null  float64\n",
      " 27  V27     85443 non-null  float64\n",
      " 28  V28     85443 non-null  float64\n",
      " 29  Amount  85443 non-null  float64\n",
      " 30  Class   85443 non-null  int64  \n",
      "dtypes: float64(30), int64(1)\n",
      "memory usage: 20.9 MB\n"
     ]
    }
   ],
   "source": [
    "pd.concat([X_test, y_test], axis=1).info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\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>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>V10</th>\n",
       "      <th>V11</th>\n",
       "      <th>V12</th>\n",
       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
       "      <th>V15</th>\n",
       "      <th>V16</th>\n",
       "      <th>V17</th>\n",
       "      <th>V18</th>\n",
       "      <th>V19</th>\n",
       "      <th>V20</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "      <td>85443.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>94847.378896</td>\n",
       "      <td>-0.000734</td>\n",
       "      <td>0.006277</td>\n",
       "      <td>0.003574</td>\n",
       "      <td>-0.001682</td>\n",
       "      <td>0.003486</td>\n",
       "      <td>0.000489</td>\n",
       "      <td>0.002030</td>\n",
       "      <td>0.004620</td>\n",
       "      <td>-0.000495</td>\n",
       "      <td>-0.003167</td>\n",
       "      <td>0.002424</td>\n",
       "      <td>0.003652</td>\n",
       "      <td>-0.001616</td>\n",
       "      <td>-0.000319</td>\n",
       "      <td>-0.000751</td>\n",
       "      <td>-0.000195</td>\n",
       "      <td>-0.000682</td>\n",
       "      <td>0.000312</td>\n",
       "      <td>-0.001144</td>\n",
       "      <td>-0.001004</td>\n",
       "      <td>0.000033</td>\n",
       "      <td>0.000052</td>\n",
       "      <td>0.000602</td>\n",
       "      <td>-0.000845</td>\n",
       "      <td>-0.000922</td>\n",
       "      <td>0.000220</td>\n",
       "      <td>0.000062</td>\n",
       "      <td>-0.000036</td>\n",
       "      <td>-0.002966</td>\n",
       "      <td>0.001720</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>47461.120548</td>\n",
       "      <td>1.947325</td>\n",
       "      <td>1.637050</td>\n",
       "      <td>1.515182</td>\n",
       "      <td>1.412908</td>\n",
       "      <td>1.406722</td>\n",
       "      <td>1.340636</td>\n",
       "      <td>1.262562</td>\n",
       "      <td>1.151291</td>\n",
       "      <td>1.090691</td>\n",
       "      <td>1.079574</td>\n",
       "      <td>1.022315</td>\n",
       "      <td>1.005413</td>\n",
       "      <td>0.989553</td>\n",
       "      <td>0.962457</td>\n",
       "      <td>0.913388</td>\n",
       "      <td>0.876542</td>\n",
       "      <td>0.842669</td>\n",
       "      <td>0.839626</td>\n",
       "      <td>0.812957</td>\n",
       "      <td>0.772484</td>\n",
       "      <td>0.713266</td>\n",
       "      <td>0.721198</td>\n",
       "      <td>0.613394</td>\n",
       "      <td>0.606464</td>\n",
       "      <td>0.521520</td>\n",
       "      <td>0.483126</td>\n",
       "      <td>0.409616</td>\n",
       "      <td>0.341987</td>\n",
       "      <td>1.036492</td>\n",
       "      <td>0.041443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>-56.407510</td>\n",
       "      <td>-72.715728</td>\n",
       "      <td>-48.325589</td>\n",
       "      <td>-5.683171</td>\n",
       "      <td>-113.743307</td>\n",
       "      <td>-26.160506</td>\n",
       "      <td>-28.215112</td>\n",
       "      <td>-50.943369</td>\n",
       "      <td>-9.481456</td>\n",
       "      <td>-20.949192</td>\n",
       "      <td>-4.568390</td>\n",
       "      <td>-18.683715</td>\n",
       "      <td>-3.888606</td>\n",
       "      <td>-18.493773</td>\n",
       "      <td>-4.391307</td>\n",
       "      <td>-13.303888</td>\n",
       "      <td>-22.883999</td>\n",
       "      <td>-9.287832</td>\n",
       "      <td>-6.938297</td>\n",
       "      <td>-54.497720</td>\n",
       "      <td>-22.665685</td>\n",
       "      <td>-9.499423</td>\n",
       "      <td>-32.828995</td>\n",
       "      <td>-2.836627</td>\n",
       "      <td>-8.696627</td>\n",
       "      <td>-2.604551</td>\n",
       "      <td>-9.793568</td>\n",
       "      <td>-15.430084</td>\n",
       "      <td>-0.353229</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>54354.000000</td>\n",
       "      <td>-0.916858</td>\n",
       "      <td>-0.591858</td>\n",
       "      <td>-0.883828</td>\n",
       "      <td>-0.848202</td>\n",
       "      <td>-0.688280</td>\n",
       "      <td>-0.766664</td>\n",
       "      <td>-0.553479</td>\n",
       "      <td>-0.207216</td>\n",
       "      <td>-0.638926</td>\n",
       "      <td>-0.535400</td>\n",
       "      <td>-0.761716</td>\n",
       "      <td>-0.400087</td>\n",
       "      <td>-0.648761</td>\n",
       "      <td>-0.426516</td>\n",
       "      <td>-0.581015</td>\n",
       "      <td>-0.468312</td>\n",
       "      <td>-0.483139</td>\n",
       "      <td>-0.498660</td>\n",
       "      <td>-0.455027</td>\n",
       "      <td>-0.211881</td>\n",
       "      <td>-0.226184</td>\n",
       "      <td>-0.537704</td>\n",
       "      <td>-0.161490</td>\n",
       "      <td>-0.355671</td>\n",
       "      <td>-0.319736</td>\n",
       "      <td>-0.326068</td>\n",
       "      <td>-0.070797</td>\n",
       "      <td>-0.053129</td>\n",
       "      <td>-0.331280</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>84850.000000</td>\n",
       "      <td>0.013238</td>\n",
       "      <td>0.070185</td>\n",
       "      <td>0.185047</td>\n",
       "      <td>-0.024109</td>\n",
       "      <td>-0.051627</td>\n",
       "      <td>-0.273686</td>\n",
       "      <td>0.042343</td>\n",
       "      <td>0.023782</td>\n",
       "      <td>-0.053821</td>\n",
       "      <td>-0.094949</td>\n",
       "      <td>-0.029129</td>\n",
       "      <td>0.144948</td>\n",
       "      <td>-0.013803</td>\n",
       "      <td>0.049248</td>\n",
       "      <td>0.045291</td>\n",
       "      <td>0.062957</td>\n",
       "      <td>-0.066955</td>\n",
       "      <td>-0.004245</td>\n",
       "      <td>0.002229</td>\n",
       "      <td>-0.061529</td>\n",
       "      <td>-0.030687</td>\n",
       "      <td>0.006971</td>\n",
       "      <td>-0.011789</td>\n",
       "      <td>0.040976</td>\n",
       "      <td>0.013508</td>\n",
       "      <td>-0.051695</td>\n",
       "      <td>0.001984</td>\n",
       "      <td>0.011561</td>\n",
       "      <td>-0.265271</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>139277.500000</td>\n",
       "      <td>1.313257</td>\n",
       "      <td>0.806615</td>\n",
       "      <td>1.031155</td>\n",
       "      <td>0.737784</td>\n",
       "      <td>0.618067</td>\n",
       "      <td>0.399864</td>\n",
       "      <td>0.572423</td>\n",
       "      <td>0.328337</td>\n",
       "      <td>0.597388</td>\n",
       "      <td>0.443126</td>\n",
       "      <td>0.743511</td>\n",
       "      <td>0.620694</td>\n",
       "      <td>0.657826</td>\n",
       "      <td>0.491916</td>\n",
       "      <td>0.647117</td>\n",
       "      <td>0.523608</td>\n",
       "      <td>0.396799</td>\n",
       "      <td>0.501455</td>\n",
       "      <td>0.455249</td>\n",
       "      <td>0.133608</td>\n",
       "      <td>0.184846</td>\n",
       "      <td>0.523689</td>\n",
       "      <td>0.147923</td>\n",
       "      <td>0.441093</td>\n",
       "      <td>0.350617</td>\n",
       "      <td>0.240657</td>\n",
       "      <td>0.092224</td>\n",
       "      <td>0.078900</td>\n",
       "      <td>-0.047356</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>172788.000000</td>\n",
       "      <td>2.454930</td>\n",
       "      <td>15.876923</td>\n",
       "      <td>4.079168</td>\n",
       "      <td>16.875344</td>\n",
       "      <td>34.801666</td>\n",
       "      <td>73.301626</td>\n",
       "      <td>120.589494</td>\n",
       "      <td>18.748872</td>\n",
       "      <td>9.272376</td>\n",
       "      <td>15.331742</td>\n",
       "      <td>11.669205</td>\n",
       "      <td>4.406338</td>\n",
       "      <td>7.126883</td>\n",
       "      <td>7.439566</td>\n",
       "      <td>8.877742</td>\n",
       "      <td>17.315112</td>\n",
       "      <td>9.253526</td>\n",
       "      <td>4.712398</td>\n",
       "      <td>5.591971</td>\n",
       "      <td>38.117209</td>\n",
       "      <td>22.579714</td>\n",
       "      <td>7.220158</td>\n",
       "      <td>20.803344</td>\n",
       "      <td>4.584549</td>\n",
       "      <td>5.826159</td>\n",
       "      <td>3.517346</td>\n",
       "      <td>31.612198</td>\n",
       "      <td>33.847808</td>\n",
       "      <td>102.362243</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time            V1            V2            V3            V4  \\\n",
       "count   85443.000000  85443.000000  85443.000000  85443.000000  85443.000000   \n",
       "mean    94847.378896     -0.000734      0.006277      0.003574     -0.001682   \n",
       "std     47461.120548      1.947325      1.637050      1.515182      1.412908   \n",
       "min         0.000000    -56.407510    -72.715728    -48.325589     -5.683171   \n",
       "25%     54354.000000     -0.916858     -0.591858     -0.883828     -0.848202   \n",
       "50%     84850.000000      0.013238      0.070185      0.185047     -0.024109   \n",
       "75%    139277.500000      1.313257      0.806615      1.031155      0.737784   \n",
       "max    172788.000000      2.454930     15.876923      4.079168     16.875344   \n",
       "\n",
       "                 V5            V6            V7            V8            V9  \\\n",
       "count  85443.000000  85443.000000  85443.000000  85443.000000  85443.000000   \n",
       "mean       0.003486      0.000489      0.002030      0.004620     -0.000495   \n",
       "std        1.406722      1.340636      1.262562      1.151291      1.090691   \n",
       "min     -113.743307    -26.160506    -28.215112    -50.943369     -9.481456   \n",
       "25%       -0.688280     -0.766664     -0.553479     -0.207216     -0.638926   \n",
       "50%       -0.051627     -0.273686      0.042343      0.023782     -0.053821   \n",
       "75%        0.618067      0.399864      0.572423      0.328337      0.597388   \n",
       "max       34.801666     73.301626    120.589494     18.748872      9.272376   \n",
       "\n",
       "                V10           V11           V12           V13           V14  \\\n",
       "count  85443.000000  85443.000000  85443.000000  85443.000000  85443.000000   \n",
       "mean      -0.003167      0.002424      0.003652     -0.001616     -0.000319   \n",
       "std        1.079574      1.022315      1.005413      0.989553      0.962457   \n",
       "min      -20.949192     -4.568390    -18.683715     -3.888606    -18.493773   \n",
       "25%       -0.535400     -0.761716     -0.400087     -0.648761     -0.426516   \n",
       "50%       -0.094949     -0.029129      0.144948     -0.013803      0.049248   \n",
       "75%        0.443126      0.743511      0.620694      0.657826      0.491916   \n",
       "max       15.331742     11.669205      4.406338      7.126883      7.439566   \n",
       "\n",
       "                V15           V16           V17           V18           V19  \\\n",
       "count  85443.000000  85443.000000  85443.000000  85443.000000  85443.000000   \n",
       "mean      -0.000751     -0.000195     -0.000682      0.000312     -0.001144   \n",
       "std        0.913388      0.876542      0.842669      0.839626      0.812957   \n",
       "min       -4.391307    -13.303888    -22.883999     -9.287832     -6.938297   \n",
       "25%       -0.581015     -0.468312     -0.483139     -0.498660     -0.455027   \n",
       "50%        0.045291      0.062957     -0.066955     -0.004245      0.002229   \n",
       "75%        0.647117      0.523608      0.396799      0.501455      0.455249   \n",
       "max        8.877742     17.315112      9.253526      4.712398      5.591971   \n",
       "\n",
       "                V20           V21           V22           V23           V24  \\\n",
       "count  85443.000000  85443.000000  85443.000000  85443.000000  85443.000000   \n",
       "mean      -0.001004      0.000033      0.000052      0.000602     -0.000845   \n",
       "std        0.772484      0.713266      0.721198      0.613394      0.606464   \n",
       "min      -54.497720    -22.665685     -9.499423    -32.828995     -2.836627   \n",
       "25%       -0.211881     -0.226184     -0.537704     -0.161490     -0.355671   \n",
       "50%       -0.061529     -0.030687      0.006971     -0.011789      0.040976   \n",
       "75%        0.133608      0.184846      0.523689      0.147923      0.441093   \n",
       "max       38.117209     22.579714      7.220158     20.803344      4.584549   \n",
       "\n",
       "                V25           V26           V27           V28        Amount  \\\n",
       "count  85443.000000  85443.000000  85443.000000  85443.000000  85443.000000   \n",
       "mean      -0.000922      0.000220      0.000062     -0.000036     -0.002966   \n",
       "std        0.521520      0.483126      0.409616      0.341987      1.036492   \n",
       "min       -8.696627     -2.604551     -9.793568    -15.430084     -0.353229   \n",
       "25%       -0.319736     -0.326068     -0.070797     -0.053129     -0.331280   \n",
       "50%        0.013508     -0.051695      0.001984      0.011561     -0.265271   \n",
       "75%        0.350617      0.240657      0.092224      0.078900     -0.047356   \n",
       "max        5.826159      3.517346     31.612198     33.847808    102.362243   \n",
       "\n",
       "              Class  \n",
       "count  85443.000000  \n",
       "mean       0.001720  \n",
       "std        0.041443  \n",
       "min        0.000000  \n",
       "25%        0.000000  \n",
       "50%        0.000000  \n",
       "75%        0.000000  \n",
       "max        1.000000  "
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_test, y_test], axis=1).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Class\n",
       "0    85296\n",
       "1      147\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_test, y_test], axis=1)['Class'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Splitting undersampled data into training and test datasets"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_undersample, X_test_undersample, y_train_undersample, y_test_undersample = train_test_split(X_undersample, y_undersample, test_size = 0.3, random_state = 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical measures of the training dataset of undersampled data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 688 entries, 6870 to 208266\n",
      "Data columns (total 31 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   Time    688 non-null    float64\n",
      " 1   V1      688 non-null    float64\n",
      " 2   V2      688 non-null    float64\n",
      " 3   V3      688 non-null    float64\n",
      " 4   V4      688 non-null    float64\n",
      " 5   V5      688 non-null    float64\n",
      " 6   V6      688 non-null    float64\n",
      " 7   V7      688 non-null    float64\n",
      " 8   V8      688 non-null    float64\n",
      " 9   V9      688 non-null    float64\n",
      " 10  V10     688 non-null    float64\n",
      " 11  V11     688 non-null    float64\n",
      " 12  V12     688 non-null    float64\n",
      " 13  V13     688 non-null    float64\n",
      " 14  V14     688 non-null    float64\n",
      " 15  V15     688 non-null    float64\n",
      " 16  V16     688 non-null    float64\n",
      " 17  V17     688 non-null    float64\n",
      " 18  V18     688 non-null    float64\n",
      " 19  V19     688 non-null    float64\n",
      " 20  V20     688 non-null    float64\n",
      " 21  V21     688 non-null    float64\n",
      " 22  V22     688 non-null    float64\n",
      " 23  V23     688 non-null    float64\n",
      " 24  V24     688 non-null    float64\n",
      " 25  V25     688 non-null    float64\n",
      " 26  V26     688 non-null    float64\n",
      " 27  V27     688 non-null    float64\n",
      " 28  V28     688 non-null    float64\n",
      " 29  Amount  688 non-null    float64\n",
      " 30  Class   688 non-null    int64  \n",
      "dtypes: float64(30), int64(1)\n",
      "memory usage: 172.0 KB\n"
     ]
    }
   ],
   "source": [
    "pd.concat([X_train_undersample, y_train_undersample], axis=1).info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "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>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>V10</th>\n",
       "      <th>V11</th>\n",
       "      <th>V12</th>\n",
       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
       "      <th>V15</th>\n",
       "      <th>V16</th>\n",
       "      <th>V17</th>\n",
       "      <th>V18</th>\n",
       "      <th>V19</th>\n",
       "      <th>V20</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "      <td>688.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>88546.635174</td>\n",
       "      <td>-2.443642</td>\n",
       "      <td>1.748210</td>\n",
       "      <td>-3.490693</td>\n",
       "      <td>2.161294</td>\n",
       "      <td>-1.466909</td>\n",
       "      <td>-0.737723</td>\n",
       "      <td>-2.759190</td>\n",
       "      <td>0.361773</td>\n",
       "      <td>-1.222417</td>\n",
       "      <td>-2.808144</td>\n",
       "      <td>1.937783</td>\n",
       "      <td>-3.131850</td>\n",
       "      <td>-0.001132</td>\n",
       "      <td>-3.568854</td>\n",
       "      <td>-0.022936</td>\n",
       "      <td>-2.145811</td>\n",
       "      <td>-3.365430</td>\n",
       "      <td>-1.137238</td>\n",
       "      <td>0.377690</td>\n",
       "      <td>0.127157</td>\n",
       "      <td>0.446495</td>\n",
       "      <td>0.012945</td>\n",
       "      <td>-0.069031</td>\n",
       "      <td>-0.020203</td>\n",
       "      <td>0.031782</td>\n",
       "      <td>0.022154</td>\n",
       "      <td>0.114684</td>\n",
       "      <td>0.041557</td>\n",
       "      <td>0.036592</td>\n",
       "      <td>0.501453</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>48529.661753</td>\n",
       "      <td>5.382638</td>\n",
       "      <td>3.616426</td>\n",
       "      <td>6.020391</td>\n",
       "      <td>3.198221</td>\n",
       "      <td>4.227553</td>\n",
       "      <td>1.829535</td>\n",
       "      <td>5.498995</td>\n",
       "      <td>4.741154</td>\n",
       "      <td>2.336555</td>\n",
       "      <td>4.417548</td>\n",
       "      <td>2.771137</td>\n",
       "      <td>4.560753</td>\n",
       "      <td>1.081826</td>\n",
       "      <td>4.641960</td>\n",
       "      <td>0.981683</td>\n",
       "      <td>3.458663</td>\n",
       "      <td>6.062216</td>\n",
       "      <td>2.462689</td>\n",
       "      <td>1.287256</td>\n",
       "      <td>1.072960</td>\n",
       "      <td>2.749354</td>\n",
       "      <td>1.143940</td>\n",
       "      <td>1.283882</td>\n",
       "      <td>0.549485</td>\n",
       "      <td>0.689015</td>\n",
       "      <td>0.474411</td>\n",
       "      <td>0.923161</td>\n",
       "      <td>0.487077</td>\n",
       "      <td>0.834360</td>\n",
       "      <td>0.500362</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>117.000000</td>\n",
       "      <td>-30.552380</td>\n",
       "      <td>-15.799625</td>\n",
       "      <td>-31.103685</td>\n",
       "      <td>-3.863126</td>\n",
       "      <td>-22.105532</td>\n",
       "      <td>-10.261990</td>\n",
       "      <td>-37.060311</td>\n",
       "      <td>-37.353443</td>\n",
       "      <td>-11.126624</td>\n",
       "      <td>-23.228255</td>\n",
       "      <td>-2.613374</td>\n",
       "      <td>-18.431131</td>\n",
       "      <td>-3.223045</td>\n",
       "      <td>-19.214325</td>\n",
       "      <td>-4.498945</td>\n",
       "      <td>-13.563273</td>\n",
       "      <td>-25.162799</td>\n",
       "      <td>-9.498746</td>\n",
       "      <td>-3.602657</td>\n",
       "      <td>-7.242879</td>\n",
       "      <td>-16.922016</td>\n",
       "      <td>-8.887017</td>\n",
       "      <td>-19.254328</td>\n",
       "      <td>-2.028024</td>\n",
       "      <td>-4.781606</td>\n",
       "      <td>-1.214960</td>\n",
       "      <td>-7.263482</td>\n",
       "      <td>-2.735623</td>\n",
       "      <td>-0.353229</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>45531.000000</td>\n",
       "      <td>-2.867222</td>\n",
       "      <td>-0.164478</td>\n",
       "      <td>-5.049001</td>\n",
       "      <td>-0.212543</td>\n",
       "      <td>-1.703845</td>\n",
       "      <td>-1.691031</td>\n",
       "      <td>-3.105154</td>\n",
       "      <td>-0.220868</td>\n",
       "      <td>-2.205996</td>\n",
       "      <td>-4.731895</td>\n",
       "      <td>-0.194163</td>\n",
       "      <td>-5.643631</td>\n",
       "      <td>-0.767631</td>\n",
       "      <td>-6.767749</td>\n",
       "      <td>-0.562582</td>\n",
       "      <td>-3.612856</td>\n",
       "      <td>-5.277726</td>\n",
       "      <td>-1.816368</td>\n",
       "      <td>-0.373523</td>\n",
       "      <td>-0.197730</td>\n",
       "      <td>-0.142520</td>\n",
       "      <td>-0.510247</td>\n",
       "      <td>-0.246005</td>\n",
       "      <td>-0.373302</td>\n",
       "      <td>-0.320463</td>\n",
       "      <td>-0.281449</td>\n",
       "      <td>-0.061809</td>\n",
       "      <td>-0.050983</td>\n",
       "      <td>-0.346113</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>82526.500000</td>\n",
       "      <td>-0.874057</td>\n",
       "      <td>0.984845</td>\n",
       "      <td>-1.482880</td>\n",
       "      <td>1.285768</td>\n",
       "      <td>-0.400360</td>\n",
       "      <td>-0.741307</td>\n",
       "      <td>-0.740952</td>\n",
       "      <td>0.141389</td>\n",
       "      <td>-0.694910</td>\n",
       "      <td>-0.981569</td>\n",
       "      <td>1.154879</td>\n",
       "      <td>-0.845463</td>\n",
       "      <td>0.008049</td>\n",
       "      <td>-1.132761</td>\n",
       "      <td>0.001558</td>\n",
       "      <td>-0.750918</td>\n",
       "      <td>-0.495063</td>\n",
       "      <td>-0.392743</td>\n",
       "      <td>0.246478</td>\n",
       "      <td>0.030556</td>\n",
       "      <td>0.163323</td>\n",
       "      <td>0.076684</td>\n",
       "      <td>-0.027143</td>\n",
       "      <td>0.014360</td>\n",
       "      <td>0.046511</td>\n",
       "      <td>-0.026232</td>\n",
       "      <td>0.059798</td>\n",
       "      <td>0.036635</td>\n",
       "      <td>-0.273188</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>135096.750000</td>\n",
       "      <td>0.945582</td>\n",
       "      <td>2.850947</td>\n",
       "      <td>0.348579</td>\n",
       "      <td>4.166857</td>\n",
       "      <td>0.599892</td>\n",
       "      <td>0.033569</td>\n",
       "      <td>0.240843</td>\n",
       "      <td>0.919999</td>\n",
       "      <td>0.196633</td>\n",
       "      <td>-0.001047</td>\n",
       "      <td>3.625262</td>\n",
       "      <td>0.163104</td>\n",
       "      <td>0.744021</td>\n",
       "      <td>0.086669</td>\n",
       "      <td>0.665736</td>\n",
       "      <td>0.219809</td>\n",
       "      <td>0.314206</td>\n",
       "      <td>0.371481</td>\n",
       "      <td>0.978754</td>\n",
       "      <td>0.443495</td>\n",
       "      <td>0.680597</td>\n",
       "      <td>0.629109</td>\n",
       "      <td>0.174862</td>\n",
       "      <td>0.382076</td>\n",
       "      <td>0.406056</td>\n",
       "      <td>0.306403</td>\n",
       "      <td>0.482488</td>\n",
       "      <td>0.235549</td>\n",
       "      <td>0.046539</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>172573.000000</td>\n",
       "      <td>2.335833</td>\n",
       "      <td>19.167239</td>\n",
       "      <td>3.228978</td>\n",
       "      <td>11.927512</td>\n",
       "      <td>14.103918</td>\n",
       "      <td>6.355986</td>\n",
       "      <td>5.802537</td>\n",
       "      <td>20.007208</td>\n",
       "      <td>6.816732</td>\n",
       "      <td>11.732926</td>\n",
       "      <td>12.018913</td>\n",
       "      <td>2.534876</td>\n",
       "      <td>3.091328</td>\n",
       "      <td>3.442422</td>\n",
       "      <td>2.364199</td>\n",
       "      <td>3.139656</td>\n",
       "      <td>6.739384</td>\n",
       "      <td>3.790316</td>\n",
       "      <td>5.228342</td>\n",
       "      <td>7.907378</td>\n",
       "      <td>27.202839</td>\n",
       "      <td>5.774087</td>\n",
       "      <td>5.303607</td>\n",
       "      <td>1.208141</td>\n",
       "      <td>2.208209</td>\n",
       "      <td>2.745261</td>\n",
       "      <td>3.052358</td>\n",
       "      <td>4.975792</td>\n",
       "      <td>8.146182</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time          V1          V2          V3          V4  \\\n",
       "count     688.000000  688.000000  688.000000  688.000000  688.000000   \n",
       "mean    88546.635174   -2.443642    1.748210   -3.490693    2.161294   \n",
       "std     48529.661753    5.382638    3.616426    6.020391    3.198221   \n",
       "min       117.000000  -30.552380  -15.799625  -31.103685   -3.863126   \n",
       "25%     45531.000000   -2.867222   -0.164478   -5.049001   -0.212543   \n",
       "50%     82526.500000   -0.874057    0.984845   -1.482880    1.285768   \n",
       "75%    135096.750000    0.945582    2.850947    0.348579    4.166857   \n",
       "max    172573.000000    2.335833   19.167239    3.228978   11.927512   \n",
       "\n",
       "               V5          V6          V7          V8          V9         V10  \\\n",
       "count  688.000000  688.000000  688.000000  688.000000  688.000000  688.000000   \n",
       "mean    -1.466909   -0.737723   -2.759190    0.361773   -1.222417   -2.808144   \n",
       "std      4.227553    1.829535    5.498995    4.741154    2.336555    4.417548   \n",
       "min    -22.105532  -10.261990  -37.060311  -37.353443  -11.126624  -23.228255   \n",
       "25%     -1.703845   -1.691031   -3.105154   -0.220868   -2.205996   -4.731895   \n",
       "50%     -0.400360   -0.741307   -0.740952    0.141389   -0.694910   -0.981569   \n",
       "75%      0.599892    0.033569    0.240843    0.919999    0.196633   -0.001047   \n",
       "max     14.103918    6.355986    5.802537   20.007208    6.816732   11.732926   \n",
       "\n",
       "              V11         V12         V13         V14         V15         V16  \\\n",
       "count  688.000000  688.000000  688.000000  688.000000  688.000000  688.000000   \n",
       "mean     1.937783   -3.131850   -0.001132   -3.568854   -0.022936   -2.145811   \n",
       "std      2.771137    4.560753    1.081826    4.641960    0.981683    3.458663   \n",
       "min     -2.613374  -18.431131   -3.223045  -19.214325   -4.498945  -13.563273   \n",
       "25%     -0.194163   -5.643631   -0.767631   -6.767749   -0.562582   -3.612856   \n",
       "50%      1.154879   -0.845463    0.008049   -1.132761    0.001558   -0.750918   \n",
       "75%      3.625262    0.163104    0.744021    0.086669    0.665736    0.219809   \n",
       "max     12.018913    2.534876    3.091328    3.442422    2.364199    3.139656   \n",
       "\n",
       "              V17         V18         V19         V20         V21         V22  \\\n",
       "count  688.000000  688.000000  688.000000  688.000000  688.000000  688.000000   \n",
       "mean    -3.365430   -1.137238    0.377690    0.127157    0.446495    0.012945   \n",
       "std      6.062216    2.462689    1.287256    1.072960    2.749354    1.143940   \n",
       "min    -25.162799   -9.498746   -3.602657   -7.242879  -16.922016   -8.887017   \n",
       "25%     -5.277726   -1.816368   -0.373523   -0.197730   -0.142520   -0.510247   \n",
       "50%     -0.495063   -0.392743    0.246478    0.030556    0.163323    0.076684   \n",
       "75%      0.314206    0.371481    0.978754    0.443495    0.680597    0.629109   \n",
       "max      6.739384    3.790316    5.228342    7.907378   27.202839    5.774087   \n",
       "\n",
       "              V23         V24         V25         V26         V27         V28  \\\n",
       "count  688.000000  688.000000  688.000000  688.000000  688.000000  688.000000   \n",
       "mean    -0.069031   -0.020203    0.031782    0.022154    0.114684    0.041557   \n",
       "std      1.283882    0.549485    0.689015    0.474411    0.923161    0.487077   \n",
       "min    -19.254328   -2.028024   -4.781606   -1.214960   -7.263482   -2.735623   \n",
       "25%     -0.246005   -0.373302   -0.320463   -0.281449   -0.061809   -0.050983   \n",
       "50%     -0.027143    0.014360    0.046511   -0.026232    0.059798    0.036635   \n",
       "75%      0.174862    0.382076    0.406056    0.306403    0.482488    0.235549   \n",
       "max      5.303607    1.208141    2.208209    2.745261    3.052358    4.975792   \n",
       "\n",
       "           Amount       Class  \n",
       "count  688.000000  688.000000  \n",
       "mean     0.036592    0.501453  \n",
       "std      0.834360    0.500362  \n",
       "min     -0.353229    0.000000  \n",
       "25%     -0.346113    0.000000  \n",
       "50%     -0.273188    1.000000  \n",
       "75%      0.046539    1.000000  \n",
       "max      8.146182    1.000000  "
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_train_undersample, y_train_undersample], axis=1).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Class\n",
       "1    345\n",
       "0    343\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_train_undersample, y_train_undersample], axis=1)['Class'].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Statistical measures of the test dataset of undersampled data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "Index: 296 entries, 102782 to 57921\n",
      "Data columns (total 31 columns):\n",
      " #   Column  Non-Null Count  Dtype  \n",
      "---  ------  --------------  -----  \n",
      " 0   Time    296 non-null    float64\n",
      " 1   V1      296 non-null    float64\n",
      " 2   V2      296 non-null    float64\n",
      " 3   V3      296 non-null    float64\n",
      " 4   V4      296 non-null    float64\n",
      " 5   V5      296 non-null    float64\n",
      " 6   V6      296 non-null    float64\n",
      " 7   V7      296 non-null    float64\n",
      " 8   V8      296 non-null    float64\n",
      " 9   V9      296 non-null    float64\n",
      " 10  V10     296 non-null    float64\n",
      " 11  V11     296 non-null    float64\n",
      " 12  V12     296 non-null    float64\n",
      " 13  V13     296 non-null    float64\n",
      " 14  V14     296 non-null    float64\n",
      " 15  V15     296 non-null    float64\n",
      " 16  V16     296 non-null    float64\n",
      " 17  V17     296 non-null    float64\n",
      " 18  V18     296 non-null    float64\n",
      " 19  V19     296 non-null    float64\n",
      " 20  V20     296 non-null    float64\n",
      " 21  V21     296 non-null    float64\n",
      " 22  V22     296 non-null    float64\n",
      " 23  V23     296 non-null    float64\n",
      " 24  V24     296 non-null    float64\n",
      " 25  V25     296 non-null    float64\n",
      " 26  V26     296 non-null    float64\n",
      " 27  V27     296 non-null    float64\n",
      " 28  V28     296 non-null    float64\n",
      " 29  Amount  296 non-null    float64\n",
      " 30  Class   296 non-null    int64  \n",
      "dtypes: float64(30), int64(1)\n",
      "memory usage: 74.0 KB\n"
     ]
    }
   ],
   "source": [
    "pd.concat([X_test_undersample, y_test_undersample], axis=1).info()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "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>Time</th>\n",
       "      <th>V1</th>\n",
       "      <th>V2</th>\n",
       "      <th>V3</th>\n",
       "      <th>V4</th>\n",
       "      <th>V5</th>\n",
       "      <th>V6</th>\n",
       "      <th>V7</th>\n",
       "      <th>V8</th>\n",
       "      <th>V9</th>\n",
       "      <th>V10</th>\n",
       "      <th>V11</th>\n",
       "      <th>V12</th>\n",
       "      <th>V13</th>\n",
       "      <th>V14</th>\n",
       "      <th>V15</th>\n",
       "      <th>V16</th>\n",
       "      <th>V17</th>\n",
       "      <th>V18</th>\n",
       "      <th>V19</th>\n",
       "      <th>V20</th>\n",
       "      <th>V21</th>\n",
       "      <th>V22</th>\n",
       "      <th>V23</th>\n",
       "      <th>V24</th>\n",
       "      <th>V25</th>\n",
       "      <th>V26</th>\n",
       "      <th>V27</th>\n",
       "      <th>V28</th>\n",
       "      <th>Amount</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "      <td>296.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>88396.587838</td>\n",
       "      <td>-2.448419</td>\n",
       "      <td>1.857288</td>\n",
       "      <td>-3.552900</td>\n",
       "      <td>2.336519</td>\n",
       "      <td>-1.503755</td>\n",
       "      <td>-0.656035</td>\n",
       "      <td>-2.853058</td>\n",
       "      <td>0.086851</td>\n",
       "      <td>-1.324446</td>\n",
       "      <td>-2.919028</td>\n",
       "      <td>1.914227</td>\n",
       "      <td>-3.106154</td>\n",
       "      <td>-0.084562</td>\n",
       "      <td>-3.347887</td>\n",
       "      <td>-0.077981</td>\n",
       "      <td>-1.984526</td>\n",
       "      <td>-3.161909</td>\n",
       "      <td>-1.109686</td>\n",
       "      <td>0.264590</td>\n",
       "      <td>0.289212</td>\n",
       "      <td>0.065582</td>\n",
       "      <td>0.134902</td>\n",
       "      <td>0.056521</td>\n",
       "      <td>-0.077336</td>\n",
       "      <td>0.001963</td>\n",
       "      <td>0.040364</td>\n",
       "      <td>0.020281</td>\n",
       "      <td>0.058781</td>\n",
       "      <td>0.046845</td>\n",
       "      <td>0.496622</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>50147.105326</td>\n",
       "      <td>5.812072</td>\n",
       "      <td>3.934323</td>\n",
       "      <td>6.680660</td>\n",
       "      <td>3.308417</td>\n",
       "      <td>4.389263</td>\n",
       "      <td>1.693893</td>\n",
       "      <td>6.622008</td>\n",
       "      <td>5.121293</td>\n",
       "      <td>2.451914</td>\n",
       "      <td>4.891517</td>\n",
       "      <td>2.754439</td>\n",
       "      <td>4.681722</td>\n",
       "      <td>0.986937</td>\n",
       "      <td>4.683458</td>\n",
       "      <td>1.051296</td>\n",
       "      <td>3.484989</td>\n",
       "      <td>5.826410</td>\n",
       "      <td>2.293910</td>\n",
       "      <td>1.298310</td>\n",
       "      <td>1.235841</td>\n",
       "      <td>2.862463</td>\n",
       "      <td>1.216935</td>\n",
       "      <td>0.877975</td>\n",
       "      <td>0.555090</td>\n",
       "      <td>0.650752</td>\n",
       "      <td>0.481822</td>\n",
       "      <td>1.224166</td>\n",
       "      <td>0.460841</td>\n",
       "      <td>0.892432</td>\n",
       "      <td>0.500835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>60.000000</td>\n",
       "      <td>-29.876366</td>\n",
       "      <td>-8.402154</td>\n",
       "      <td>-30.558697</td>\n",
       "      <td>-2.956827</td>\n",
       "      <td>-21.665654</td>\n",
       "      <td>-5.773192</td>\n",
       "      <td>-43.557242</td>\n",
       "      <td>-41.044261</td>\n",
       "      <td>-13.434066</td>\n",
       "      <td>-24.588262</td>\n",
       "      <td>-2.383066</td>\n",
       "      <td>-18.683715</td>\n",
       "      <td>-3.076318</td>\n",
       "      <td>-17.620634</td>\n",
       "      <td>-3.092108</td>\n",
       "      <td>-14.129855</td>\n",
       "      <td>-22.541652</td>\n",
       "      <td>-9.090892</td>\n",
       "      <td>-3.681904</td>\n",
       "      <td>-5.225849</td>\n",
       "      <td>-22.797604</td>\n",
       "      <td>-8.887017</td>\n",
       "      <td>-5.988806</td>\n",
       "      <td>-1.742803</td>\n",
       "      <td>-2.079928</td>\n",
       "      <td>-1.170476</td>\n",
       "      <td>-7.263482</td>\n",
       "      <td>-1.931920</td>\n",
       "      <td>-0.353229</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>45977.500000</td>\n",
       "      <td>-2.867766</td>\n",
       "      <td>-0.130600</td>\n",
       "      <td>-5.417818</td>\n",
       "      <td>-0.118496</td>\n",
       "      <td>-1.667035</td>\n",
       "      <td>-1.477544</td>\n",
       "      <td>-2.835885</td>\n",
       "      <td>-0.168935</td>\n",
       "      <td>-2.345829</td>\n",
       "      <td>-4.445615</td>\n",
       "      <td>-0.144802</td>\n",
       "      <td>-5.340188</td>\n",
       "      <td>-0.815218</td>\n",
       "      <td>-6.363108</td>\n",
       "      <td>-0.729637</td>\n",
       "      <td>-3.303237</td>\n",
       "      <td>-5.358990</td>\n",
       "      <td>-1.747789</td>\n",
       "      <td>-0.563676</td>\n",
       "      <td>-0.165023</td>\n",
       "      <td>-0.178103</td>\n",
       "      <td>-0.483530</td>\n",
       "      <td>-0.212828</td>\n",
       "      <td>-0.405811</td>\n",
       "      <td>-0.324214</td>\n",
       "      <td>-0.270853</td>\n",
       "      <td>-0.056831</td>\n",
       "      <td>-0.042639</td>\n",
       "      <td>-0.349231</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>84069.000000</td>\n",
       "      <td>-0.740915</td>\n",
       "      <td>0.941852</td>\n",
       "      <td>-1.139964</td>\n",
       "      <td>1.340723</td>\n",
       "      <td>-0.369227</td>\n",
       "      <td>-0.596589</td>\n",
       "      <td>-0.501864</td>\n",
       "      <td>0.169642</td>\n",
       "      <td>-0.696902</td>\n",
       "      <td>-0.875521</td>\n",
       "      <td>1.267304</td>\n",
       "      <td>-0.938658</td>\n",
       "      <td>-0.060414</td>\n",
       "      <td>-1.059352</td>\n",
       "      <td>-0.012904</td>\n",
       "      <td>-0.547678</td>\n",
       "      <td>-0.527389</td>\n",
       "      <td>-0.318904</td>\n",
       "      <td>0.169827</td>\n",
       "      <td>0.056998</td>\n",
       "      <td>0.130060</td>\n",
       "      <td>0.081904</td>\n",
       "      <td>-0.035614</td>\n",
       "      <td>-0.010232</td>\n",
       "      <td>0.068890</td>\n",
       "      <td>0.031911</td>\n",
       "      <td>0.073702</td>\n",
       "      <td>0.046030</td>\n",
       "      <td>-0.300834</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>135023.500000</td>\n",
       "      <td>0.879511</td>\n",
       "      <td>2.700371</td>\n",
       "      <td>0.394765</td>\n",
       "      <td>4.305361</td>\n",
       "      <td>0.624459</td>\n",
       "      <td>0.139244</td>\n",
       "      <td>0.306788</td>\n",
       "      <td>0.833392</td>\n",
       "      <td>0.011527</td>\n",
       "      <td>-0.051012</td>\n",
       "      <td>3.542336</td>\n",
       "      <td>0.234752</td>\n",
       "      <td>0.609629</td>\n",
       "      <td>0.173916</td>\n",
       "      <td>0.685300</td>\n",
       "      <td>0.351119</td>\n",
       "      <td>0.309636</td>\n",
       "      <td>0.237358</td>\n",
       "      <td>0.948371</td>\n",
       "      <td>0.461180</td>\n",
       "      <td>0.568611</td>\n",
       "      <td>0.617588</td>\n",
       "      <td>0.200328</td>\n",
       "      <td>0.317653</td>\n",
       "      <td>0.386804</td>\n",
       "      <td>0.355382</td>\n",
       "      <td>0.395412</td>\n",
       "      <td>0.192766</td>\n",
       "      <td>0.028048</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>172733.000000</td>\n",
       "      <td>2.306769</td>\n",
       "      <td>22.057729</td>\n",
       "      <td>3.476268</td>\n",
       "      <td>12.114672</td>\n",
       "      <td>9.880564</td>\n",
       "      <td>6.474115</td>\n",
       "      <td>3.791907</td>\n",
       "      <td>19.587773</td>\n",
       "      <td>4.866316</td>\n",
       "      <td>6.367661</td>\n",
       "      <td>11.152491</td>\n",
       "      <td>1.725185</td>\n",
       "      <td>2.897044</td>\n",
       "      <td>2.654275</td>\n",
       "      <td>2.471358</td>\n",
       "      <td>2.696475</td>\n",
       "      <td>6.443649</td>\n",
       "      <td>2.591846</td>\n",
       "      <td>4.851255</td>\n",
       "      <td>11.059004</td>\n",
       "      <td>27.202839</td>\n",
       "      <td>8.361985</td>\n",
       "      <td>5.466230</td>\n",
       "      <td>1.077407</td>\n",
       "      <td>2.156042</td>\n",
       "      <td>1.458828</td>\n",
       "      <td>2.706566</td>\n",
       "      <td>3.042406</td>\n",
       "      <td>5.663610</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Time          V1          V2          V3          V4  \\\n",
       "count     296.000000  296.000000  296.000000  296.000000  296.000000   \n",
       "mean    88396.587838   -2.448419    1.857288   -3.552900    2.336519   \n",
       "std     50147.105326    5.812072    3.934323    6.680660    3.308417   \n",
       "min        60.000000  -29.876366   -8.402154  -30.558697   -2.956827   \n",
       "25%     45977.500000   -2.867766   -0.130600   -5.417818   -0.118496   \n",
       "50%     84069.000000   -0.740915    0.941852   -1.139964    1.340723   \n",
       "75%    135023.500000    0.879511    2.700371    0.394765    4.305361   \n",
       "max    172733.000000    2.306769   22.057729    3.476268   12.114672   \n",
       "\n",
       "               V5          V6          V7          V8          V9         V10  \\\n",
       "count  296.000000  296.000000  296.000000  296.000000  296.000000  296.000000   \n",
       "mean    -1.503755   -0.656035   -2.853058    0.086851   -1.324446   -2.919028   \n",
       "std      4.389263    1.693893    6.622008    5.121293    2.451914    4.891517   \n",
       "min    -21.665654   -5.773192  -43.557242  -41.044261  -13.434066  -24.588262   \n",
       "25%     -1.667035   -1.477544   -2.835885   -0.168935   -2.345829   -4.445615   \n",
       "50%     -0.369227   -0.596589   -0.501864    0.169642   -0.696902   -0.875521   \n",
       "75%      0.624459    0.139244    0.306788    0.833392    0.011527   -0.051012   \n",
       "max      9.880564    6.474115    3.791907   19.587773    4.866316    6.367661   \n",
       "\n",
       "              V11         V12         V13         V14         V15         V16  \\\n",
       "count  296.000000  296.000000  296.000000  296.000000  296.000000  296.000000   \n",
       "mean     1.914227   -3.106154   -0.084562   -3.347887   -0.077981   -1.984526   \n",
       "std      2.754439    4.681722    0.986937    4.683458    1.051296    3.484989   \n",
       "min     -2.383066  -18.683715   -3.076318  -17.620634   -3.092108  -14.129855   \n",
       "25%     -0.144802   -5.340188   -0.815218   -6.363108   -0.729637   -3.303237   \n",
       "50%      1.267304   -0.938658   -0.060414   -1.059352   -0.012904   -0.547678   \n",
       "75%      3.542336    0.234752    0.609629    0.173916    0.685300    0.351119   \n",
       "max     11.152491    1.725185    2.897044    2.654275    2.471358    2.696475   \n",
       "\n",
       "              V17         V18         V19         V20         V21         V22  \\\n",
       "count  296.000000  296.000000  296.000000  296.000000  296.000000  296.000000   \n",
       "mean    -3.161909   -1.109686    0.264590    0.289212    0.065582    0.134902   \n",
       "std      5.826410    2.293910    1.298310    1.235841    2.862463    1.216935   \n",
       "min    -22.541652   -9.090892   -3.681904   -5.225849  -22.797604   -8.887017   \n",
       "25%     -5.358990   -1.747789   -0.563676   -0.165023   -0.178103   -0.483530   \n",
       "50%     -0.527389   -0.318904    0.169827    0.056998    0.130060    0.081904   \n",
       "75%      0.309636    0.237358    0.948371    0.461180    0.568611    0.617588   \n",
       "max      6.443649    2.591846    4.851255   11.059004   27.202839    8.361985   \n",
       "\n",
       "              V23         V24         V25         V26         V27         V28  \\\n",
       "count  296.000000  296.000000  296.000000  296.000000  296.000000  296.000000   \n",
       "mean     0.056521   -0.077336    0.001963    0.040364    0.020281    0.058781   \n",
       "std      0.877975    0.555090    0.650752    0.481822    1.224166    0.460841   \n",
       "min     -5.988806   -1.742803   -2.079928   -1.170476   -7.263482   -1.931920   \n",
       "25%     -0.212828   -0.405811   -0.324214   -0.270853   -0.056831   -0.042639   \n",
       "50%     -0.035614   -0.010232    0.068890    0.031911    0.073702    0.046030   \n",
       "75%      0.200328    0.317653    0.386804    0.355382    0.395412    0.192766   \n",
       "max      5.466230    1.077407    2.156042    1.458828    2.706566    3.042406   \n",
       "\n",
       "           Amount       Class  \n",
       "count  296.000000  296.000000  \n",
       "mean     0.046845    0.496622  \n",
       "std      0.892432    0.500835  \n",
       "min     -0.353229    0.000000  \n",
       "25%     -0.349231    0.000000  \n",
       "50%     -0.300834    0.000000  \n",
       "75%      0.028048    1.000000  \n",
       "max      5.663610    1.000000  "
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_test_undersample, y_test_undersample], axis=1).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Class\n",
       "0    149\n",
       "1    147\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.concat([X_test_undersample, y_test_undersample], axis=1)['Class'].value_counts()"
   ]
  }
 ],
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