CreditCardFrauds.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "CreditCardFrauds.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyP2r86krTDM6TGOJgmNM/MY",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/joaoaxerb/Data-Science/blob/master/CreditCardFrauds.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KmD56ByYpzJ_",
        "colab_type": "text"
      },
      "source": [
        "# **Fraud detection in online transactions**\n",
        "---\n",
        "As predicted,  since the *Coronavirus* outbreak, online sales has been growing at an astronomous rate worldwide. Global eCommerce sales rose 28 percent in June 2020 compared to June 2019, making it the largest year-over-year increase in sales since *COVID-19* restrictions were put in place in March, per [ACI Worldwide](https://www.businesswire.com/news/home/20200713005612/en/ACI-Worldwide-Research-Reveals-Increase-June-eCommerce?utm_source=Triggermail&utm_medium=email&utm_campaign=Post%20Blast%20bii-payments-and-commerce:%20June%20e-commerce%20growth%20was%20the%20highest%20of%20the%20pandemic%20so%20far%20%7C%20Alipay%20counts%201.3B%20users%20%7C%20Amex%20launches%20proprietary%20payables%20tool&utm_term=BII%20List%20PayCom%20ALL).\n",
        "\n",
        "With the high volume of transactions, comes a higher number of fraudulent transactions, and that's due to the fact that criminals also evolve, and use the same technological advancements as credit cards companies.\n",
        "\n",
        "Detecting fraudulent transactions with a high accuracy is a challenge companies will face for years to come as it gets more complex year after year."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SaPMNNczSxDf",
        "colab_type": "text"
      },
      "source": [
        "## **The Project** \n",
        "\n",
        "In this notebook I will develop a Machine Learning model to detect fraudulent transactions, and check the results in order to evaluate the model's performance. I will be using the `scikit-learn` library to construct a *Logistic Regression Model*.\n",
        "\n",
        "If you like to uderstand how  *Logist Regression* model work, I'll list below a great article on it: \n",
        "* [Introduction to Logistic Regression](https://towardsdatascience.com/introduction-to-logistic-regression-66248243c148)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sFKrc-w2V95e",
        "colab_type": "text"
      },
      "source": [
        "## **The Data**\n",
        "\n",
        "The data used in this analysis was provided by a few European credit card companies, and uploaded by [Kaggle]() and is available for anybody. \n",
        "\n",
        "The [*Dataset*]() represent online transactions that took place in a spam of two days, and contains about **290 thousand** transactions. Only **490** of them were classified as fraudulent, which represents **0.17%** of the *Dataset*.\n",
        "\n",
        "As we can see, the data is clearly unbalanced,  and thats is something that could affect the model, but dont't worry about it, there are techniques to solve that problem.\n",
        "\n",
        "It is also important to state that all of the *features* of this Dataset are numerical and have been uncharacterized, for privacy and security. That means the columns have been renamed and are represented by $[V1, V2, V3 \\dots, V28]$. \n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KR9SXeJefpa8",
        "colab_type": "text"
      },
      "source": [
        "### **Exploratory Data analysis**\n",
        "\n",
        "First of all, I'll import the *Dateset* and make an initial analysis in order to uderstand what I'm dealing with.\n",
        "\n",
        "\n",
        "\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Ye4geEZCpK7i",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 241
        },
        "outputId": "b96610b1-3432-44f7-c10d-feb7887af3e7"
      },
      "source": [
        "# Import necessary packages\n",
        "import pandas as pd\n",
        "import seaborn as sns \n",
        "import matplotlib.pyplot as plt\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "from sklearn.metrics import classification_report\n",
        "from sklearn.metrics import roc_auc_score, roc_curve, accuracy_score\n",
        "from imblearn.under_sampling import RandomUnderSampler\n",
        "\n",
        "# Import Dataset\n",
        "df = pd.read_csv(\"https://www.dropbox.com/s/b44o3t3ehmnx2b7/creditcard.csv?dl=1\")\n",
        "\n",
        "# Visualize daset shape and  first five lines \n",
        "print(\"Dimensions: {}\".format(df.shape))\n",
        "df.head()"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Dimensions: (284807, 31)\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>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>0</th>\n",
              "      <td>0.0</td>\n",
              "      <td>-1.359807</td>\n",
              "      <td>-0.072781</td>\n",
              "      <td>2.536347</td>\n",
              "      <td>1.378155</td>\n",
              "      <td>-0.338321</td>\n",
              "      <td>0.462388</td>\n",
              "      <td>0.239599</td>\n",
              "      <td>0.098698</td>\n",
              "      <td>0.363787</td>\n",
              "      <td>0.090794</td>\n",
              "      <td>-0.551600</td>\n",
              "      <td>-0.617801</td>\n",
              "      <td>-0.991390</td>\n",
              "      <td>-0.311169</td>\n",
              "      <td>1.468177</td>\n",
              "      <td>-0.470401</td>\n",
              "      <td>0.207971</td>\n",
              "      <td>0.025791</td>\n",
              "      <td>0.403993</td>\n",
              "      <td>0.251412</td>\n",
              "      <td>-0.018307</td>\n",
              "      <td>0.277838</td>\n",
              "      <td>-0.110474</td>\n",
              "      <td>0.066928</td>\n",
              "      <td>0.128539</td>\n",
              "      <td>-0.189115</td>\n",
              "      <td>0.133558</td>\n",
              "      <td>-0.021053</td>\n",
              "      <td>149.62</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0.0</td>\n",
              "      <td>1.191857</td>\n",
              "      <td>0.266151</td>\n",
              "      <td>0.166480</td>\n",
              "      <td>0.448154</td>\n",
              "      <td>0.060018</td>\n",
              "      <td>-0.082361</td>\n",
              "      <td>-0.078803</td>\n",
              "      <td>0.085102</td>\n",
              "      <td>-0.255425</td>\n",
              "      <td>-0.166974</td>\n",
              "      <td>1.612727</td>\n",
              "      <td>1.065235</td>\n",
              "      <td>0.489095</td>\n",
              "      <td>-0.143772</td>\n",
              "      <td>0.635558</td>\n",
              "      <td>0.463917</td>\n",
              "      <td>-0.114805</td>\n",
              "      <td>-0.183361</td>\n",
              "      <td>-0.145783</td>\n",
              "      <td>-0.069083</td>\n",
              "      <td>-0.225775</td>\n",
              "      <td>-0.638672</td>\n",
              "      <td>0.101288</td>\n",
              "      <td>-0.339846</td>\n",
              "      <td>0.167170</td>\n",
              "      <td>0.125895</td>\n",
              "      <td>-0.008983</td>\n",
              "      <td>0.014724</td>\n",
              "      <td>2.69</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>1.0</td>\n",
              "      <td>-1.358354</td>\n",
              "      <td>-1.340163</td>\n",
              "      <td>1.773209</td>\n",
              "      <td>0.379780</td>\n",
              "      <td>-0.503198</td>\n",
              "      <td>1.800499</td>\n",
              "      <td>0.791461</td>\n",
              "      <td>0.247676</td>\n",
              "      <td>-1.514654</td>\n",
              "      <td>0.207643</td>\n",
              "      <td>0.624501</td>\n",
              "      <td>0.066084</td>\n",
              "      <td>0.717293</td>\n",
              "      <td>-0.165946</td>\n",
              "      <td>2.345865</td>\n",
              "      <td>-2.890083</td>\n",
              "      <td>1.109969</td>\n",
              "      <td>-0.121359</td>\n",
              "      <td>-2.261857</td>\n",
              "      <td>0.524980</td>\n",
              "      <td>0.247998</td>\n",
              "      <td>0.771679</td>\n",
              "      <td>0.909412</td>\n",
              "      <td>-0.689281</td>\n",
              "      <td>-0.327642</td>\n",
              "      <td>-0.139097</td>\n",
              "      <td>-0.055353</td>\n",
              "      <td>-0.059752</td>\n",
              "      <td>378.66</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>1.0</td>\n",
              "      <td>-0.966272</td>\n",
              "      <td>-0.185226</td>\n",
              "      <td>1.792993</td>\n",
              "      <td>-0.863291</td>\n",
              "      <td>-0.010309</td>\n",
              "      <td>1.247203</td>\n",
              "      <td>0.237609</td>\n",
              "      <td>0.377436</td>\n",
              "      <td>-1.387024</td>\n",
              "      <td>-0.054952</td>\n",
              "      <td>-0.226487</td>\n",
              "      <td>0.178228</td>\n",
              "      <td>0.507757</td>\n",
              "      <td>-0.287924</td>\n",
              "      <td>-0.631418</td>\n",
              "      <td>-1.059647</td>\n",
              "      <td>-0.684093</td>\n",
              "      <td>1.965775</td>\n",
              "      <td>-1.232622</td>\n",
              "      <td>-0.208038</td>\n",
              "      <td>-0.108300</td>\n",
              "      <td>0.005274</td>\n",
              "      <td>-0.190321</td>\n",
              "      <td>-1.175575</td>\n",
              "      <td>0.647376</td>\n",
              "      <td>-0.221929</td>\n",
              "      <td>0.062723</td>\n",
              "      <td>0.061458</td>\n",
              "      <td>123.50</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2.0</td>\n",
              "      <td>-1.158233</td>\n",
              "      <td>0.877737</td>\n",
              "      <td>1.548718</td>\n",
              "      <td>0.403034</td>\n",
              "      <td>-0.407193</td>\n",
              "      <td>0.095921</td>\n",
              "      <td>0.592941</td>\n",
              "      <td>-0.270533</td>\n",
              "      <td>0.817739</td>\n",
              "      <td>0.753074</td>\n",
              "      <td>-0.822843</td>\n",
              "      <td>0.538196</td>\n",
              "      <td>1.345852</td>\n",
              "      <td>-1.119670</td>\n",
              "      <td>0.175121</td>\n",
              "      <td>-0.451449</td>\n",
              "      <td>-0.237033</td>\n",
              "      <td>-0.038195</td>\n",
              "      <td>0.803487</td>\n",
              "      <td>0.408542</td>\n",
              "      <td>-0.009431</td>\n",
              "      <td>0.798278</td>\n",
              "      <td>-0.137458</td>\n",
              "      <td>0.141267</td>\n",
              "      <td>-0.206010</td>\n",
              "      <td>0.502292</td>\n",
              "      <td>0.219422</td>\n",
              "      <td>0.215153</td>\n",
              "      <td>69.99</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   Time        V1        V2        V3  ...       V27       V28  Amount  Class\n",
              "0   0.0 -1.359807 -0.072781  2.536347  ...  0.133558 -0.021053  149.62      0\n",
              "1   0.0  1.191857  0.266151  0.166480  ... -0.008983  0.014724    2.69      0\n",
              "2   1.0 -1.358354 -1.340163  1.773209  ... -0.055353 -0.059752  378.66      0\n",
              "3   1.0 -0.966272 -0.185226  1.792993  ...  0.062723  0.061458  123.50      0\n",
              "4   2.0 -1.158233  0.877737  1.548718  ...  0.219422  0.215153   69.99      0\n",
              "\n",
              "[5 rows x 31 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xNjpFZbJKU0T",
        "colab_type": "text"
      },
      "source": [
        "This *Dataset* contains **284.807** lines and **31** columns."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "79yK66PEDTFs",
        "colab_type": "text"
      },
      "source": [
        "Now, I'm going to print out the statistical report for each of the columns in the *Datset*.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "R42wm704iUYp",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        },
        "outputId": "b23b532f-ac5c-4e11-c201-9a65b731ba49"
      },
      "source": [
        "# Print statistical report\n",
        "df.describe()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>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>284807.000000</td>\n",
              "      <td>284807.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>94813.859575</td>\n",
              "      <td>3.919560e-15</td>\n",
              "      <td>5.688174e-16</td>\n",
              "      <td>-8.769071e-15</td>\n",
              "      <td>2.782312e-15</td>\n",
              "      <td>-1.552563e-15</td>\n",
              "      <td>2.010663e-15</td>\n",
              "      <td>-1.694249e-15</td>\n",
              "      <td>-1.927028e-16</td>\n",
              "      <td>-3.137024e-15</td>\n",
              "      <td>1.768627e-15</td>\n",
              "      <td>9.170318e-16</td>\n",
              "      <td>-1.810658e-15</td>\n",
              "      <td>1.693438e-15</td>\n",
              "      <td>1.479045e-15</td>\n",
              "      <td>3.482336e-15</td>\n",
              "      <td>1.392007e-15</td>\n",
              "      <td>-7.528491e-16</td>\n",
              "      <td>4.328772e-16</td>\n",
              "      <td>9.049732e-16</td>\n",
              "      <td>5.085503e-16</td>\n",
              "      <td>1.537294e-16</td>\n",
              "      <td>7.959909e-16</td>\n",
              "      <td>5.367590e-16</td>\n",
              "      <td>4.458112e-15</td>\n",
              "      <td>1.453003e-15</td>\n",
              "      <td>1.699104e-15</td>\n",
              "      <td>-3.660161e-16</td>\n",
              "      <td>-1.206049e-16</td>\n",
              "      <td>88.349619</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>250.120109</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>0.000000</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>5.600000</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>22.000000</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>77.165000</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>25691.160000</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                Time            V1  ...         Amount          Class\n",
              "count  284807.000000  2.848070e+05  ...  284807.000000  284807.000000\n",
              "mean    94813.859575  3.919560e-15  ...      88.349619       0.001727\n",
              "std     47488.145955  1.958696e+00  ...     250.120109       0.041527\n",
              "min         0.000000 -5.640751e+01  ...       0.000000       0.000000\n",
              "25%     54201.500000 -9.203734e-01  ...       5.600000       0.000000\n",
              "50%     84692.000000  1.810880e-02  ...      22.000000       0.000000\n",
              "75%    139320.500000  1.315642e+00  ...      77.165000       0.000000\n",
              "max    172792.000000  2.454930e+00  ...   25691.160000       1.000000\n",
              "\n",
              "[8 rows x 31 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IqX6sdoXDwRr",
        "colab_type": "text"
      },
      "source": [
        "By printing out this report, I can understand which columns have a higher standart deviation, and it could help in identifying outliers in our data.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "6evomGzuHKL6",
        "colab_type": "text"
      },
      "source": [
        "its always good to have perfect data, but that's basically impossible, which is why we have to check our *Dataset* for missing values. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "54x-wMuLDQjQ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 561
        },
        "outputId": "b0d67acb-0f4c-4e43-b30d-8a2ff3e7da40"
      },
      "source": [
        "# Print missing values percentages\n",
        "df.isnull().sum() / df.shape[0]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Time      0.0\n",
              "V1        0.0\n",
              "V2        0.0\n",
              "V3        0.0\n",
              "V4        0.0\n",
              "V5        0.0\n",
              "V6        0.0\n",
              "V7        0.0\n",
              "V8        0.0\n",
              "V9        0.0\n",
              "V10       0.0\n",
              "V11       0.0\n",
              "V12       0.0\n",
              "V13       0.0\n",
              "V14       0.0\n",
              "V15       0.0\n",
              "V16       0.0\n",
              "V17       0.0\n",
              "V18       0.0\n",
              "V19       0.0\n",
              "V20       0.0\n",
              "V21       0.0\n",
              "V22       0.0\n",
              "V23       0.0\n",
              "V24       0.0\n",
              "V25       0.0\n",
              "V26       0.0\n",
              "V27       0.0\n",
              "V28       0.0\n",
              "Amount    0.0\n",
              "Class     0.0\n",
              "dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tg9iNH4mKsCk",
        "colab_type": "text"
      },
      "source": [
        "This *Dataset* contains no missing values! But don't get used to it, the only reason why the data is so clean is because it has been pre-processed beforehand."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pisSFgEXLGVc",
        "colab_type": "text"
      },
      "source": [
        "Right now, I'm going to plot a bar chart in order to visualize how unbalanced the data is."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7yy0tZcZI3Ka",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "outputId": "3d65d3bd-5fba-4d44-eef0-b84f7c416380"
      },
      "source": [
        "# Plotting bar chart\n",
        "fig, ax = plt.subplots(figsize=(8,5))\n",
        "sns.set_style('dark')\n",
        "\n",
        "df.Class.value_counts().plot(kind='bar',ax=ax )\n",
        "plt.xticks(rotation='horizontal')\n",
        "plt.title(\"Class Distribuition\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x360 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0y3UGfO4eH9i",
        "colab_type": "text"
      },
      "source": [
        "As we can see on the bar chart above, the data is clearly unbalanced as I previously stated. I will print below the exact number of each class so we can have a better idea of it. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Pt6I6OyJMEgR",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 68
        },
        "outputId": "2fe9445f-2368-47b7-97b4-08f086478a54"
      },
      "source": [
        "# Print Class values \n",
        "df.Class.value_counts()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    284315\n",
              "1       492\n",
              "Name: Class, dtype: int64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PpyCTWjRenr1",
        "colab_type": "text"
      },
      "source": [
        "We've got **284.315** samples classified as 0, which means legal transactions, and **492** classified as 1, which means fraudulent transactions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "I7k8EpfkpFph",
        "colab_type": "text"
      },
      "source": [
        "Right now, I'm going to plot two histograms for the variable `time`, one of them for *legal* transactions and the other one for *fraudulent* trasactions so we can compare the frequencies and try to extract some information from it that could help our model classify these samples.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xNnOtN0Tdzmh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "outputId": "e2e3b759-daba-452f-d487-616dbde8b7fa"
      },
      "source": [
        "# plot hsitogram \n",
        "fig,ax = plt.subplots(2,1, figsize=(12,6))\n",
        "num_bins=40\n",
        "\n",
        "ax[0].hist(df.Time[df.Class == 0], bins=num_bins)\n",
        "ax[0].set_title(\"Legal transactions\")\n",
        "\n",
        "ax[1].hist(df.Time[df.Class == 1], bins=num_bins)\n",
        "ax[1].set_title(\"Fraudulent transactions\")\n",
        "ax[1].set_xlabel(\"Time(seconds)\")\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 864x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XQ2Sh4GZrmuE",
        "colab_type": "text"
      },
      "source": [
        "We can't really tell anything from looking at this histograms other that fraudulent transactions represent a small fraction of the *Dataset*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UJ7xnoZ5sYw2",
        "colab_type": "text"
      },
      "source": [
        "Now I'm going to plot the histograms for the variable `amount`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T5JsNpImqEIh",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 441
        },
        "outputId": "760f6ada-0bb2-4557-c64b-ce02c7fd2dbe"
      },
      "source": [
        "# Plot histograms\n",
        "fig, ax = plt.subplots(2,1, figsize=(12,6))\n",
        "\n",
        "ax[0].hist(df.Amount[df.Class == 0], bins=15)\n",
        "ax[0].set_title(\"Legal Transactions\")\n",
        "\n",
        "ax[1].hist(df.Amount[df.Class == 1], bins=15)\n",
        "ax[1].set_title(\"Fraudulent Transactions\")\n",
        "ax[1].set_xlabel(\"Amount\")\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAGoCAYAAABbkkSYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nOzde3RV9Zn/8fchIUpNIIDJiSjFoYOXoShYLEZuNZhECZFwG+ty7JBqnY5UCnRoQUdLAzK0Qwur6FgoTofOeCuMCZYw5RIqgSmKqBh1dEbapgVLTmhMwk3Ixf37w+X5lQpy2+QEfL/WYq2cZ9+evdlrhw/7u/eJBEEQIEmSJEk6bR0S3YAkSZIknSsMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliSp3br88sv53e9+l+g2zriCggJeeOGFRLchSQpBcqIbkCSdHXJycpgzZw7XX399oluhoKCAP/zhDwAcOnSI5ORkkpM/+JX2d3/3d3z1q19NZHsfa8aMGUSjUaZOnRqvlZeXJ7AjSVKYDFiSpLPOnwaSO+64g1tuuYUJEyZ8ZL6WlpZ48JIkqS04RFCSdFref/99lixZwo033sigQYP4+te/TkNDQ3x6WVkZN9xwA4MGDeKRRx4hJyeHX/3qVwBUVVVx6623MnDgQIYMGUJJSQlNTU2n3MuuXbu4/PLLWb58OV/4whf427/9WwAmT57M4MGD+dznPsftt9/O22+/HV9mxowZfOc73+Huu+9mwIABTJgwgd///vcABEHA3Llzyc7O5pprrqGwsJD/+7//A+C5556jqKiIa665huHDh7No0aIjetm2bRtf/OIXGThwIMOHD+eZZ57h6aef5uc//zmPPfYYAwYMiN9p+9Nj0tTUxEMPPcSQIUMYMmQIDz30UPyYvPDCCwwbNox//dd/JTs7myFDhvCf//mf8W1u3LiRkSNHMmDAAIYOHcpjjz12ysdSknRqDFiSpNPy7//+76xfv57/+I//YNOmTXTp0oWSkhIAduzYwXe+8x3++Z//mU2bNrF//35isVh82Q4dOjBz5kyef/55nnrqKbZs2cITTzxx2j29+OKLrF69Oh4whg0bxpo1a9iyZQt/9Vd/xT/8wz8cMf/q1av52te+xosvvsinP/1pFixYAMDmzZvZtm0ba9as4aWXXmLhwoWkp6cD0KlTJ7773e+ybds2Fi9ezJNPPsn69esBeOedd/jKV77C3/zN37BlyxbKysq48sorufXWWyksLOTOO+/klVde4Uc/+tFHen/00Ud59dVXWblyJc8++yyvvfYa//Iv/xKf/sc//pF9+/ZRWVnJQw89RElJCY2NjQDcf//9lJSU8Morr7Bq1Squu+660z6WkqSTY8CSJJ2Wp556iqlTp5KVlUVKSgpf+9rXWLNmDS0tLfziF7/ghhtuYODAgaSkpDB58mQikUh82c9+9rP079+f5ORkLrnkEm699VZefPHF0+7p3nvv5VOf+hTnn38+AOPHjyc1NZWUlBTuvfde3nrrLfbt2xef/8Ybb+Sqq64iOTmZW265hTfffBOA5ORkDhw4wG9+8xuCIOAzn/kMmZmZAAwaNIjLL7+cDh06cMUVV1BQUMDWrVsBWLVqFddffz2jRo2iY8eOdO3alSuvvPKEev/5z3/OpEmT6N69O926dWPSpEk8++yz8enJyclMmjSJjh07Mnz4cD71qU/x29/+Nj5tx44d7N+/ny5dutC3b9/TPpaSpJPjwHRJ0mn5wx/+wKRJk+jQ4f//n12HDh2oq6ujtraWrKyseL1Tp07xO0AAv/3tb5k3bx6vv/467733Hq2traGEgj/dZmtrKwsWLOAXv/gF7777brzP+vp60tLSALjwwgvj859//vkcPHgQgOzsbG6//XZKSkp45513yMvL41vf+hapqam8+uqrzJ8/n7fffpvm5maampq46aabANi9ezef/vSnT6n32tpaevToEf/co0cPamtr45/T09OPeK6sU6dO8X5/+MMf8uijj/L973+fyy+/nG984xsMGDDglPqQJJ0a72BJkk5LVlYWP/7xj9m2bVv8z2uvvUY0GiUzM/OIIYGHDh064vmsWbNm0bt3b9asWcPLL7/M1KlTCYLgtHv607tkP//5z6moqOAnP/kJL730Ehs2bAA44e186Utf4plnnmH16tVUV1ezdOlSAL7xjW8wYsQINm7cyEsvvcQXv/jF+Dovuuii+HNcH9fb0WRmZsbfkAgfhLUP75odz1VXXcWjjz7Kr371K2688UamTJlyQstJksJjwJIknbDm5mYOHz4c/9PS0sJtt93GwoULeeeddwB49913488i5efns2HDBl5++WWamppYtGjREcHmwIEDXHDBBVxwwQX8+te/5sknnwy95wMHDpCSkkLXrl157733+MEPfnDCy1ZVVfHqq6/S3NxMp06dSElJid8BO3DgAF26dOG8886jqqqKVatWxZcrLCzkV7/6FatXr6alpYX6+vr4sMPu3buza9euY26zoKCARx99lHfffZd3332XRx55hMLCwuP22tTUxLPPPsu+ffvo2LEjF1xwwRF3FSVJbcMrryTphN19991cddVV8T+LFi3iS1/6Ejk5OXz5y19mwIAB/PVf/zVVVVUA9OnThwceeIBp06YxdOhQPvWpT9GtWzdSUlIA+Na3vsWqVau45ppreOCBBxg5cmToPRcVFdGjRw+GDh1KQUEB/fv3P+FlDxw4wD/+4z/y+c9/nhtuuIH09HTuvPNOAL797W/zwx/+kAEDBvDII49w8803x5fr0aMHP/7xj/nJT37C5z//eYqKinjrrbeAD54H27FjBwMHDuSee+75yDbvuecePvvZz3LLLbdwyy230Ldv36POdzQrV64kJyeHa665hqeeeop//ud/PuF9lSSFIxKEMRZDkqQTcODAAa699lrWrFlDz549E92OJEmh8w6WJOmM2rBhA++99x4HDx7ku9/9LpdddhmXXHJJotuSJOmMMGBJks6oiooKhg4dytChQ/nd737HD37wg+O+6EGSpLOVQwQlSZIkKSTewZIkSZKkkJxzXzT8/vvv09rqTTlJkiRJZ07HjklHrZ9zAau1NaCh4WCi25AkSZJ0DsvISDtq3SGCkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXknHtNe3uT2rkTnc47uw/ze4db2L/3vUS3IUmSJLV7Z/e//M8Cnc5L5tIZ5Ylu47RUzytgf6KbkCRJks4CDhGUJEmSpJAYsCRJkiQpJAYsSZIkSQqJAUuSJEmSQmLAkiRJkqSQGLAkSZIkKSQGLEmSJEkKiQFLkiRJkkJiwJIkSZKkkBiwJEmSJCkkBixJkiRJCokBS5IkSZJCYsCSJEmSpJAcN2Dt3r2bO+64g5EjR1JQUMCyZcsAWLRoEUOHDmX06NGMHj2ajRs3xpdZvHgxubm55Ofns2nTpni9srKS/Px8cnNzWbJkSby+c+dOJkyYQG5uLlOmTKGpqQmApqYmpkyZQm5uLhMmTGDXrl2h7bgkSZIkhe24ASspKYkZM2awevVqnn76aZ544gl27NgBwMSJE1m5ciUrV65k+PDhAOzYsYPy8nLKy8tZunQp3/nOd2htbaW1tZWSkhKWLl1KeXk5q1atiq9n/vz5TJw4kXXr1tG5c2dWrFgBwPLly+ncuTPr1q1j4sSJzJ8//0wdB0mSJEk6bccNWJmZmfTt2xeA1NRUevfuTSwWO+b8FRUVFBQUkJKSQs+ePenVqxdVVVVUVVXRq1cvevbsSUpKCgUFBVRUVBAEAc8//zz5+fkAjBkzhoqKCgA2bNjAmDFjAMjPz2fLli0EQXDaOy1JkiRJZ8JJPYO1a9cu3nzzTa6++moAHn/8cQoLC5k5cyaNjY0AxGIxsrKy4stEo1Fisdgx6/X19XTu3Jnk5GQAsrKy4gEuFotx0UUXAZCcnExaWhr19fWnsbuSJEmSdOaccMA6cOAAkydP5r777iM1NZXbbruNdevWsXLlSjIzM5k3b96Z7FOSJEmS2r0TCljNzc1MnjyZwsJC8vLyALjwwgtJSkqiQ4cOTJgwgddeew344M5UTU1NfNlYLEY0Gj1mvWvXruzdu5eWlhYAampqiEaj8XXt3r0bgJaWFvbt20fXrl1D2G1JkiRJCt9xA1YQBNx///307t2b4uLieL22tjb+8/r16+nTpw8AOTk5lJeX09TUxM6dO6muruaqq66iX79+VFdXs3PnTpqamigvLycnJ4dIJMKgQYNYs2YNAKWlpeTk5MTXVVpaCsCaNWu47rrriEQi4e29JEmSJIUo+XgzvPTSS6xcuZLLLruM0aNHAzBt2jRWrVrFW2+9BcDFF19MSUkJAH369OHmm29m5MiRJCUl8eCDD5KUlATAgw8+yF133UVrayvjxo2Lh7Lp06czdepUFi5cyJVXXsmECRMAGD9+PNOnTyc3N5cuXbqwYMGC8I+AJEmSJIUkEpxjr+Vrbm6loeFgotuIy8hI49IZ5Ylu47RUzytgz559iW5DkiRJajcyMtKOWj+ptwhKkiRJko7NgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSE5bsDavXs3d9xxByNHjqSgoIBly5YB0NDQQHFxMXl5eRQXF9PY2AhAEATMmTOH3NxcCgsLeeONN+LrKi0tJS8vj7y8PEpLS+P1119/ncLCQnJzc5kzZw5BEHzsNiRJkiSpPTpuwEpKSmLGjBmsXr2ap59+mieeeIIdO3awZMkSsrOzWbt2LdnZ2SxZsgSAyspKqqurWbt2LbNnz2bWrFnAB2Hp4Ycf5mc/+xnLly/n4YcfjgemWbNmMXv2bNauXUt1dTWVlZUAx9yGJEmSJLVHxw1YmZmZ9O3bF4DU1FR69+5NLBajoqKCoqIiAIqKili/fj1AvB6JROjfvz979+6ltraWzZs3M3jwYNLT0+nSpQuDBw9m06ZN1NbWsn//fvr3708kEqGoqIiKiooj1vXn25AkSZKk9uiknsHatWsXb775JldffTV1dXVkZmYCkJGRQV1dHQCxWIysrKz4MllZWcRisY/Uo9HoUesfzg8ccxuSJEmS1B6dcMA6cOAAkydP5r777iM1NfWIaZFIhEgkEnpzbb0NSZIkSTodJxSwmpubmTx5MoWFheTl5QHQvXt3amtrAaitraVbt27AB3emampq4svW1NQQjUY/Uo/FYketfzj/x21DkiRJktqj4wasIAi4//776d27N8XFxfF6Tk4OZWVlAJSVlTFixIgj6kEQsH37dtLS0sjMzGTIkCFs3ryZxsZGGhsb2bx5M0OGDCEzM5PU1FS2b99OEARHXdefb0OSJEmS2qNI8OE70Y9h27Zt3H777Vx22WV06PBBHps2bRpXXXUVU6ZMYffu3fTo0YOFCxeSnp5OEASUlJSwadMmOnXqxNy5c+nXrx8AK1asYPHixQB89atfZdy4cQC89tprzJw5k0OHDjFs2DAeeOABIpEI9fX1R93Gx2lubqWh4eBpH5iwZGSkcemM8kS3cVqq5xWwZ8++RLchSZIktRsZGWlHrR83YJ1tDFjhM2BJkiRJRzpWwDqptwhKkiRJko7NgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSF5LgBa+bMmWRnZzNq1Kh4bdGiRQwdOpTRo0czevRoNm7cGJ+2ePFicnNzyc/PZ9OmTfF6ZWUl+fn55ObmsmTJknh9586dTJgwgdzcXKZMmUJTUxMATU1NTJkyhdzcXCZMmMCuXbtC2WFJkiRJOlOOG7DGjh3L0qVLP1KfOHEiK1euZOXKlQwfPhyAHTt2UF5eTnl5OUuXLuU73/kOra2ttLa2UlJSwtKlSykvL2fVqlXs2LEDgPnz5zNx4kTWrVtH586dWbFiBQDLly+nc+fOrFu3jokTJzJ//vww91uSJEmSQnfcgHXttdfSpUuXE1pZRUUFBQUFpKSk0LNnT3r16kVVVRVVVVX06tWLnj17kpKSQkFBARUVFQRBwPPPP09+fj4AY8aMoaKiAoANGzYwZswYAPLz89myZQtBEJzqfkqSJEnSGXfKz2A9/vjjFBYWMnPmTBobGwGIxWJkZWXF54lGo8RisWPW6+vr6dy5M8nJyQBkZWURi8Xi67rooosASE5OJi0tjfr6+lNtV5IkSZLOuFMKWLfddhvr1q1j5cqVZGZmMm/evLD7kiRJkqSzzikFrAsvvJCkpCQ6dOjAhAkTeO2114AP7kzV1NTE54vFYkSj0WPWu3btyt69e2lpaQGgpqaGaDQaX9fu3bsBaGlpYd++fXTt2vXU9lKSJEmS2sApBaza2tr4z+vXr6dPnz4A5OTkUF5eTlNTEzt37qS6upqrrrqKfv36UV1dzc6dO2lqaqK8vJycnBwikQiDBg1izZo1AJSWlpKTkxNfV2lpKQBr1qzhuuuuIxKJnNbOSpIkSdKZlHy8GaZNm8bWrVupr69n2LBh3HvvvWzdupW33noLgIsvvpiSkhIA+vTpw80338zIkSNJSkriwQcfJCkpCYAHH3yQu+66i9bWVsaNGxcPZdOnT2fq1KksXLiQK6+8kgkTJgAwfvx4pk+fTm5uLl26dGHBggVn5ABIkiRJUlgiwTn2ar7m5lYaGg4muo24jIw0Lp1Rnug2Tkv1vAL27NmX6DYkSZKkdiMjI+2o9VN+i6AkSZIk6UgGLEmSJEkKiQFLkiRJkkJiwJIkSZKkkBiwJEmSJCkkBixJkiRJCokBS5IkSZJCYsCSJEmSpJAYsCRJkiQpJAYsSZIkSQqJAUuSJEmSQmLAkiRJkqSQGLAkSZIkKSQGLEmSJEkKiQFLkiRJkkJiwJIkSZKkkBiwJEmSJCkkBixJkiRJCslxA9bMmTPJzs5m1KhR8VpDQwPFxcXk5eVRXFxMY2MjAEEQMGfOHHJzcyksLOSNN96IL1NaWkpeXh55eXmUlpbG66+//jqFhYXk5uYyZ84cgiD42G1IkiRJUnt13IA1duxYli5dekRtyZIlZGdns3btWrKzs1myZAkAlZWVVFdXs3btWmbPns2sWbOAD8LSww8/zM9+9jOWL1/Oww8/HA9Ms2bNYvbs2axdu5bq6moqKys/dhuSJEmS1F4dN2Bde+21dOnS5YhaRUUFRUVFABQVFbF+/foj6pFIhP79+7N3715qa2vZvHkzgwcPJj09nS5dujB48GA2bdpEbW0t+/fvp3///kQiEYqKiqioqPjYbUiSJElSe3VKz2DV1dWRmZkJQEZGBnV1dQDEYjGysrLi82VlZRGLxT5Sj0ajR61/OP/HbUOSJEmS2qvTfslFJBIhEomE0UtCtyFJkiRJp+uUAlb37t2pra0FoLa2lm7dugEf3JmqqamJz1dTU0M0Gv1IPRaLHbX+4fwftw1JkiRJaq9OKWDl5ORQVlYGQFlZGSNGjDiiHgQB27dvJy0tjczMTIYMGcLmzZtpbGyksbGRzZs3M2TIEDIzM0lNTWX79u0EQXDUdf35NiRJkiSpvUo+3gzTpk1j69at1NfXM2zYMO69917uvvtupkyZwooVK+jRowcLFy4EYPjw4WzcuJHc3Fw6derE3LlzAUhPT+eee+5h/PjxAEyaNIn09HQAvv3tbzNz5kwOHTrEsGHDGDZsGMAxtyFJkiRJ7VUk+PCLp84Rzc2tNDQcTHQbcRkZaVw6ozzRbZyW6nkF7NmzL9FtSJIkSe1GRkbaUeun/ZILSZIkSdIHDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhSS0wpYOTk5FBYWMnr0aMaOHQtAQ0MDxcXF5OXlUVxcTGNjIwBBEDBnzhxyc3MpLCzkjTfeiK+ntLSUvLw88vLyKC0tjddff/11CgsLyc3NZc6cOQRBcDrtSpIkSdIZddp3sJYtW8bKlSt55plnAFiyZAnZ2dmsXbuW7OxslixZAkBlZSXV1dWsXbuW2bNnM2vWLOCDQPbwww/zs5/9jOXLl/Pwww/HQ9msWbOYPXs2a9eupbq6msrKytNtV5IkSZLOmNCHCFZUVFBUVARAUVER69evP6IeiUTo378/e/fupba2ls2bNzN48GDS09Pp0qULgwcPZtOmTdTW1rJ//3769+9PJBKhqKiIioqKsNuVJEmSpNCcdsC68847GTt2LE8//TQAdXV1ZGZmApCRkUFdXR0AsViMrKys+HJZWVnEYrGP1KPR6FHrH84vSZIkSe1V8uks/OSTTxKNRqmrq6O4uJjevXsfMT0SiRCJRE6rQUmSJEk6W5zWHaxoNApA9+7dyc3Npaqqiu7du1NbWwtAbW0t3bp1i89bU1MTX7ampoZoNPqReiwWO2r9w/klSZIkqb065YB18OBB9u/fH//5v//7v+nTpw85OTmUlZUBUFZWxogRIwDi9SAI2L59O2lpaWRmZjJkyBA2b95MY2MjjY2NbN68mSFDhpCZmUlqairbt28nCIIj1iVJkiRJ7dEpDxGsq6tj0qRJALS2tjJq1CiGDRtGv379mDJlCitWrKBHjx4sXLgQgOHDh7Nx40Zyc3Pp1KkTc+fOBSA9PZ177rmH8ePHAzBp0iTS09MB+Pa3v83MmTM5dOgQw4YNY9iwYae1s5IkSZJ0JkWCc+zLpZqbW2loOJjoNuIyMtK4dEZ5ots4LdXzCtizZ1+i25AkSZLajYyMtKPWQ39NuyRJkiR9UhmwJEmSJCkkBixJkiRJCokBS5IkSZJCYsCSJEmSpJAYsCRJkiQpJAYsSZIkSQqJAUuSJEmSQmLAkiRJkqSQGLAkSZIkKSQGLEmSJEkKiQFLkiRJkkJiwJIkSZKkkBiwJEmSJCkkBixJkiRJCokBS5IkSZJCYsCSJEmSpJAYsCRJkiQpJO0+YFVWVpKfn09ubi5LlixJdDuSJEmSdEztOmC1trZSUlLC0qVLKS8vZ9WqVezYsSPRbUmSJEnSUbXrgFVVVUWvXr3o2bMnKSkpFBQUUFFRkei2JEmSJOmokhPdwMeJxWJkZWXFP0ejUaqqqj52mY4dk8jISDvTrZ2U6nkFiW7htLW3YypJkiS1R+36DpYkSZIknU3adcCKRqPU1NTEP8diMaLRaAI7kiRJkqRja9cBq1+/flRXV7Nz506ampooLy8nJycn0W1JkiRJ0lG162ewkpOTefDBB7nrrrtobW1l3Lhx9OnTJ9FtSZIkSdJRRYIgCBLdhCRJkiSdC9r1EEFJkiRJOpsYsCRJkiQpJAasM6iyspL8/Hxyc3NZsmRJottRguXk5FBYWMjo0aMZO3YsAA0NDRQXF5OXl0dxcTGNjY0ABEHAnDlzyM3NpbCwkDfeeCO+ntLSUvLy8sjLy6O0tDQh+6IzY+bMmWRnZzNq1Kh4Lcxz5PXXX6ewsJDc3FzmzJmDI8TPfkc7ZxYtWsTQoUMZPXo0o0ePZuPGjfFpixcvJjc3l/z8fDZt2hSvH+v31c6dO5kwYQK5ublMmTKFpqamttkxnTG7d+/mjjvuYOTIkRQUFLBs2TLAa42O7VjnjNeajxHojGhpaQlGjBgR/P73vw8OHz4cFBYWBm+//Xai21IC3XDDDUFdXd0Rte9+97vB4sWLgyAIgsWLFwff+973giAIgueeey648847g/fffz945ZVXgvHjxwdBEAT19fVBTk5OUF9fHzQ0NAQ5OTlBQ0ND2+6IzpitW7cGr7/+elBQUBCvhXmOjBs3LnjllVeC999/P7jzzjuD5557ro33UGE72jnzwx/+MFi6dOlH5n377beDwsLC4PDhw8Hvf//7YMSIEUFLS8vH/r6aPHlysGrVqiAIguCBBx4IHn/88bbZMZ0xsVgseP3114MgCIJ9+/YFeXl5wdtvv+21Rsd0rHPGa82xeQfrDKmqqqJXr1707NmTlJQUCgoKqKioSHRbamcqKiooKioCoKioiPXr1x9Rj0Qi9O/fn71791JbW8vmzZsZPHgw6enpdOnShcGDBx/xP0M6u1177bV06dLliFpY50htbS379++nf//+RCIRioqKvCadA452zhxLRUUFBQUFpKSk0LNnT3r16kVVVdUxf18FQcDzzz9Pfn4+AGPGjPGcOQdkZmbSt29fAFJTU+nduzexWMxrjY7pWOfMsXitcYjgGROLxcjKyop/jkajH3sy6pPhzjvvZOzYsTz99NMA1NXVkZmZCUBGRgZ1dXXAR8+frKwsYrGY59UnUFjnyLHm17np8ccfp7CwkJkzZ8aHep3oufFhvb6+ns6dO5Oc/ME3unjOnHt27drFm2++ydVXX+21RifkT88Z8FpzLAYsqY08+eSTlJaW8uMf/5jHH3+cF1988YjpkUiESCSSoO50NvAc0Ym47bbbWLduHStXriQzM5N58+YluiW1QwcOHGDy5Mncd999pKamHjHNa42O5s/PGa81x2bAOkOi0Sg1NTXxz7FYjGg0msCOlGgf/v13796d3Nxcqqqq6N69O7W1tQDU1tbSrVu3+Lx/ev7U1NQQjUY9rz6BwjpHjjW/zj0XXnghSUlJdOjQgQkTJvDaa68Bx/69dKx6165d2bt3Ly0tLYDnzLmkubmZyZMnU1hYSF5eHuC1Rh/vaOeM15pjM2CdIf369aO6upqdO3fS1NREeXk5OTk5iW5LCXLw4PuOBe0AAB+FSURBVEH2798f//m///u/6dOnDzk5OZSVlQFQVlbGiBEjAOL1IAjYvn07aWlpZGZmMmTIEDZv3kxjYyONjY1s3ryZIUOGJGy/dOaFdY5kZmaSmprK9u3bCYLgiHXp3PLhP5IB1q9fT58+fYAPzpny8nKamprYuXMn1dXVXHXVVcf8fRWJRBg0aBBr1qwBPnhjnL/Hzn5BEHD//ffTu3dviouL43WvNTqWY50zXmuOLRIEvjvzTNm4cSNz586ltbWVcePG8fd///eJbkkJsnPnTiZNmgRAa2sro0aN4u///u+pr69nypQp7N69mx49erBw4ULS09MJgoCSkhI2bdpEp06dmDt3Lv369QNgxYoVLF68GICvfvWrjBs3LmH7pXBNmzaNrVu3Ul9fT/fu3bn33nu58cYbQztHXnvtNWbOnMmhQ4cYNmwYDzzwgMOAznJHO2e2bt3KW2+9BcDFF19MSUlJ/NmaRx99lP/8z/8kKSmJ++67j+HDhwPH/n21c+dOpk6dSmNjI1deeSXz588nJSUlMTurUGzbto3bb7+dyy67jA4dPvh/9mnTpnHVVVd5rdFRHeucWbVqldeaYzBgSZIkSVJIHCIoSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSTqjZsyYwYIFC0KfV//fXXfdRWlpaaLbkCQByYluQJLUNnJycvjjH/9IUlJSvPaLX/yCaDSawK7OjBdeeIHp06dTWVl51Ol33XUXL730EgBNTU1EIhE6duwIQGFhISUlJW3W68latGgRv/vd75g/f368tnTp0gR2JEn6UwYsSfoE+dGPfsT1119/zOktLS0kJ5/7vxr+NJDMmDGDaDTK1KlTPzLfJ+V4SJLC4xBBSfqEu/zyy3n88cfJy8sjLy8PgDlz5jB8+HCuueYaxo4dy7Zt2+Lz//kwvhdeeIFhw4bFP//P//wPY8aMYcCAAUyZMoXDhw/Hpz3zzDPcdtttH9n+7373u6P29stf/pLRo0czcOBAvvjFL/LWW2/Fp+Xk5PDYY49RWFjI5z73ufi2Dh48yFe+8hVqa2sZMGAAAwYMIBaLnbHjsWjRIr7+9a/zzW9+kwEDBlBQUMBrr70Wn75kyRKGDh3KgAEDyM/PZ8uWLQBUVVVx6623MnDgQIYMGUJJSQlNTU3x5d5++22Ki4v5/Oc/z/XXX8+PfvQjKisrWbx4Mf/1X//FgAEDuOWWWwC44447WL58OQDvv/8+//Iv/8INN9xAdnY23/zmN9m3bx8Au3bt4vLLL6e0tJQvfOELDBo0iEcffTS+zaqqKsaOHcs111zD9ddfzz/90z+d8HGTJH3AgCVJYv369fzsZz9j9erVAPTr14+ysjK2bt3KqFGj+PrXv35EUDqWpqYmJk2axOjRo9m6dSs33XQTa9euPaWe/ud//of77ruPkpISXnjhBW699VbuueeeI0LIf/3Xf7F06VIqKir43//9X5555hk+9alP8eMf/5jMzExeeeUVXnnllZMeBnmyx2PDhg0UFBSwbds2cnJymD17NgC/+c1vePzxx1mxYgWvvPIKjz32GBdffDEAHTp0YObMmTz//PM89dRTbNmyhSeeeAKA/fv3U1xczNChQ9m0aRNr164lOzubYcOG8Xd/93fcfPPNvPLKKzz77LMf6f2ZZ56htLSUn/70p6xfv56DBw9+ZMjjSy+9xC9+8QuWLVvGI488wq9//WsAHnroIb70pS/x8ssvs27dOm6++eaTOm6SJAOWJH2iTJo0iYEDBzJw4EDuueeeeP3uu+8mPT2d888/H4DRo0fTtWtXkpOT+fKXv0xTUxO//e1vj7v+V199lebmZv72b/+Wjh07ctNNN9GvX79T6vXpp5/m1ltv5eqrryYpKYkxY8bQsWNHtm/fHp/njjvuIBqNkp6ezg033MCbb755Stv6cyd7PD73uc8xfPhwkpKSGD16dPxOW1JSEk1NTfz617+mubmZSy65hE9/+tMAfPazn6V///4kJydzySWXcOutt/Liiy8C8Nxzz3HhhRfy5S9/mfPOO4/U1FSuvvrqE+r95z//ORMnTqRnz55ccMEFTJs2jdWrV9PS0hKf52tf+xrnn38+V1xxBVdccUW83+TkZH7/+9/z7rvvcsEFF9C/f//TP5iS9AnjwHJJ+gR55JFHjvoM1kUXXXTE58cee4wVK1ZQW1tLJBJh//791NfXH3f9tbW1RKNRIpFIvNajR49T6vUPf/gDZWVl/Md//Ee81tzcTG1tbfxzRkZG/OdOnTodMe10nOzxuPDCC+M/n3/++Rw+fJiWlhZ69erFfffdx6JFi9ixYwdDhgyJP/P129/+lnnz5vH666/z3nvv0draSt++fQHYvXt3PIidrNra2vhdMoCLL76YlpYW6urqjtpvp06dOHjwIPDBHawf/vCH3HzzzVxyySV87Wtf44YbbjilPiTpk8o7WJKkIwLRtm3bWLp0KQsXLuTFF19k27ZtpKWlEQQB8ME/yA8dOhSf/49//GP854yMDGKxWHxe+CAofejPl92zZ88xe7rooov46le/yrZt2+J/Xn31VUaNGnVS+3MqTuZ4HE9hYSFPPvkkv/zlL4lEIvG3/82aNYvevXuzZs0aXn75ZaZOnRpf50UXXcTOnTtPad8yMzN555134p//8Ic/kJycTPfu3Y/b66WXXsoPfvADtmzZwle+8hUmT54cD1+SpBNjwJIkHeHAgQMkJSXRrVs3WlpaePjhh9m/f398+pVXXsnGjRtpaGhgz549LFu2LD7twyFvP/3pT2lubmbt2rVHvPDhiiuu4O233+bNN9/k8OHDLFq06Jh9TJgwgaeeeopXX32VIAg4ePAgzz333BG9HEv37t1paGiIv9zhdBzveHyc3/zmN2zZsoWmpiZSUlI477zz6NChQ3y9F1xwARdccAG//vWvefLJJ+PLfeELX2DPnj3827/9G01NTezfv59XX301vm/vvPMO77///lG3OWrUKJYtW8bOnTs5cOAACxYs4Oabbz6htyGuXLmSd999lw4dOtC5c2eAeL+SpBPjVVOSdIQhQ4YwdOhQ8vPzycnJ4bzzzjtiyNzo0aO54ooryMnJ4ctf/jIjR46MT0tJSWHRokWUlpby+c9/ntWrV5Obmxuf/hd/8RdMmjSJiRMnkpeXx+c+97lj9tGvXz9mz55NSUkJ1157LXl5eTzzzDMntA+f+cxnKCgo4MYbb2TgwIEn9RbBP3e84/Fxmpqa+P73v8+gQYMYMmQI7777LtOmTQPgW9/6FqtWreKaa67hgQceOOI4pqam8q//+q/88pe/ZPDgweTn5/PCCy8AcNNNNwEwaNAgxowZ85Ftjhs3jltuuYW/+Zu/YcSIEaSkpPDAAw+cUL+bNm2ioKCAAQMG8NBDD7FgwYL4c2iSpBMTCU50jIMkSZIk6WN5B0uSJEmSQmLAkiRJkqSQGLAkSZIkKSQGLEmSJEkKyTn3RcPvv/8+ra2+t0OSJEnSmdOxY9JR6wkJWK2trYwbN45oNMrixYvZuXMn06ZNo6Ghgb59+/K9732PlJQUmpqa+OY3v8kbb7xBeno6CxYs4JJLLjnOugMaGvxSREmSJElnTkZG2lHrCRki+NOf/pTPfOYz8c/z589n4sSJrFu3js6dO7NixQoAli9fTufOnVm3bh0TJ05k/vz5iWhXkiRJkk5ImwesmpoannvuOcaPHw9AEAQ8//zz5OfnAzBmzBgqKioA2LBhQ/xLFPPz89myZQt+bZckSZKk9qrNA9bcuXOZPn06HTp8sOn6+no6d+5McvIHoxWzsrKIxWIAxGIxLrroIgCSk5NJS0ujvr6+rVuWJEmSpBPSpgHrl7/8Jd26deOzn/1sW25WkiRJktpEm77k4uWXX2bDhg1UVlZy+PBh9u/fz0MPPcTevXtpaWkhOTmZmpoaotEoANFolN27d5OVlUVLSwv79u2ja9eubdmyJEmSJJ2wNr2D9Y1vfIPKyko2bNjAD37wA6677jq+//3vM2jQINasWQNAaWkpOTk5AOTk5FBaWgrAmjVruO6664hEIm3ZsiRJkiSdsHbxPVjTp09n6tSpLFy4kCuvvJIJEyYAMH78eKZPn05ubi5dunRhwYIFCe705KV27kSn89rFYT5l7x1uYf/e9xLdhiRJktTuRYJz7LV8zc2t7ep7sDIy0rh0Rnmi2zgt1fMK2LNnX6LbkCRJktqNdvU9WJIkSZJ0LjJgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSJLbcmOHDx/m9ttvp6mpidbWVvLz85k8eTI7d+5k2rRpNDQ00LdvX773ve+RkpJCU1MT3/zmN3njjTdIT09nwYIFXHLJJW3ZsiRJkiSdsDa9g5WSksKyZct49tlnKSsrY9OmTWzfvp358+czceJE1q1bR+fOnVmxYgUAy5cvp3Pnzqxbt46JEycyf/78tmxXkiRJkk5KmwasSCTCBRdcAEBLSwstLS1EIhGef/558vPzARgzZgwVFRUAbNiwgTFjxgCQn5/Pli1bCIKgLVuWJEmSpBPW5s9gtba2Mnr0aK6//nquv/56evbsSefOnUlO/mC0YlZWFrFYDIBYLMZFF10EQHJyMmlpadTX17d1y5IkSZJ0Qto8YCUlJbFy5Uo2btxIVVUVv/nNb9q6BUmSJEk6IxL2FsHOnTszaNAgtm/fzt69e2lpaQGgpqaGaDQKQDQaZffu3cAHQwr37dtH165dE9WyJEmSJH2sNg1Y7777Lnv37gXg0KFD/OpXv+Izn/kMgwYNYs2aNQCUlpaSk5MDQE5ODqWlpQCsWbOG6667jkgk0pYtS5IkSdIJa9PXtNfW1jJjxgxaW1sJgoCbbrqJG264gb/8y79k6tSpLFy4kCuvvJIJEyYAMH78eKZPn05ubi5dunRhwYIFbdmuJEmSJJ2USHCOvZavubmVhoaDiW4jLiMjjUtnlCe6jdNSPa+APXv2JboNSZIkqd3IyEg7aj1hz2BJkiRJ0rnGgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSFp04C1e/du7rjjDkaOHElBQQHLli0DoKGhgeLiYvLy8iguLqaxsRGAIAiYM2cOubm5FBYW8sYbb7Rlu5IkSZJ0Uto0YCUlJTFjxgxWr17N008/zRNPPMGOHTtYsmQJ2dnZrF27luzsbJYsWQJAZWUl1dXVrF27ltmzZzNr1qy2bFeSJEmSTkqbBqzMzEz69u0LQGpqKr179yYWi1FRUUFRUREARUVFrF+/HiBej0Qi9O/fn71791JbW9uWLUuSJEnSCUvYM1i7du3izTff5Oqrr6auro7MzEwAMjIyqKurAyAWi5GVlRVfJisri1gslpB+JUmSJOl4EhKwDhw4wOTJk7nvvvtITU09YlokEiESiSSiLUmSJEk6LW0esJqbm5k8eTKFhYXk5eUB0L179/jQv9raWrp16wZANBqlpqYmvmxNTQ3RaLStW5YkSZKkE9KmASsIAu6//3569+5NcXFxvJ6Tk0NZWRkAZWVljBgx4oh6EARs376dtLS0+FBCSZIkSWpvkttyYy+99BIrV67ksssuY/To0QBMmzaNu+++mylTprBixQp69OjBwoULARg+fDgbN24kNzeXTp06MXfu3LZsV5IkSZJOSiQIgiDRTYSpubmVhoaDiW4jLiMjjUtnlCe6jdNSPa+APXv2JboNSZIkqd3IyEg7aj1hbxGUJEmSpHONAUuSJEmSQmLAkiRJkqSQGLAkSZIkKSQGLEmSJEkKiQFLkiRJkkJiwJIkSZKkkBiwJEmSJCkkBixJkiRJCokBS5IkSZJCYsCSJEmSpJAYsCRJkiQpJAYsSZIkSQqJAUuSJEmSQmLAkiRJkqSQGLAkSZIkKSQGLEmSJEkKiQFLkiRJkkJiwJIkSZKkkBiwJEmSJCkkBixJkiRJCokBS5IkSZJCYsCSJEmSpJAYsCRJkiQpJAYsSZIkSQqJAUuSJEmSQmLAkiRJkqSQGLAkSZIkKSQGLEmSJEkKiQFLkiRJkkLSpgFr5syZZGdnM2rUqHitoaGB4uJi8vLyKC4uprGxEYAgCJgzZw65ubkUFhbyxhtvtGWrkiRJknTS2jRgjR07lqVLlx5RW7JkCdnZ2axdu5bs7GyWLFkCQGVlJdXV1axdu5bZs2cza9astmxVkiRJkk5amwasa6+9li5duhxRq6iooKioCICioiLWr19/RD0SidC/f3/27t1LbW1tW7YrSZIkSScl4c9g1dXVkZmZCUBGRgZ1dXUAxGIxsrKy4vNlZWURi8US0qMkSZIknYiEB6w/FYlEiEQiiW5DkiRJkk5JwgNW9+7d40P/amtr6datGwDRaJSampr4fDU1NUSj0YT0KEmSJEknIuEBKycnh7KyMgDKysoYMWLEEfUgCNi+fTtpaWnxoYSSJEmS1B4lt+XGpk2bxtatW6mvr2fYsGHce++93H333UyZMoUVK1bQo0cPFi5cCMDw4cPZuHEjubm5dOrUiblz57Zlq5IkSZJ00iJBEASJbiJMzc2tNDQcTHQbcRkZaVw6ozzRbZyW6nkF7NmzL9FtSJIkSe1GRkbaUesJHyIoSZIkSecKA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJITFgSZIkSVJIDFiSJEmSFBIDliRJkiSFxIAlSZIkSSExYEmSJElSSAxYkiRJkhQSA5YkSZIkhcSAJUmSJEkhMWBJkiRJUkgMWJIkSZIUEgOWJEmSJIXEgCVJkiRJIUlOdANq/w41t5KRkZboNk7Ze4db2L/3vUS3IUmSpE8AA5aO6/yOSVw6ozzRbZyy6nkF7E90E5IkSfpEcIigJEmSJIXEgCVJkiRJIXGIoM55PkMmSZKktmLA0jnPZ8gkSZLUVhwiKEmSJEkhMWBJkiRJUkgMWJIkSZIUEp/Bktq5s/0lHXD2v6gjtXMnOp139l4uz/bjL0nS2eTs/ReD9Alxtr+kA87+F3V0Oi/5rP47ONuPvyRJZ5N2H7AqKyt56KGHeP/995kwYQJ33313oluSdJLOhbtwkiRJJ6JdB6zW1lZKSkr4yU9+QjQaZfz48eTk5PCXf/mXiW5N0kk42+/CVc8rSHQLUkKd7cNkwaGyktpOu75aVlVV0atXL3r27AlAQUEBFRUVBixJOgnnwh3EQ82t/6+dO4qJ4lzDOP7srofU1kYrdpfUWlMT1MSAkrYXDRrTRVbjMl0r1MQoEqIXElPS2BvFaKIHTdv0oqkXhrYX1cY0TWyB6lqNYItgoijBICiRmBDAypIQoJU2gst3LpozkVSOpWfZYeH/u2K+WWbeWV6+zLMzO3rmXx6ny/jHEr1+SQn9IYkktf57XUL/HyR6QCSkOy/R/waJ9P67jDHG6SLGcu7cOdXW1urw4cOSpIqKCjU1NenAgQMOVwYAAAAAf8Vj2gEAAAAgRiZ1wPL5fOru7raXI5GIfD6fgxUBAAAAwNgmdcBKS0tTe3u7Ojs7NTQ0pHA4LL/f73RZAAAAAPBEk/qbbjNmzNCBAwe0Y8cORaNR5ebmKjU11emyAAAAAOCJJvVDLgAAAAAgkUzqWwQBAAAAIJEQsAAAAAAgRghYE+jSpUtau3atsrOz9fnnnztdDqY5v98vy7IUCoW0ceNGSVJ/f78KCwsVCARUWFiogYEBSZIxRqWlpcrOzpZlWWppaXGydExxe/fu1ZtvvqmcnBx77J/0Znl5uQKBgAKBgMrLy+N+HJjantSnR48e1apVqxQKhRQKhVRTU2OvKysrU3Z2ttauXava2lp7nHMDTLT79+8rPz9f69evVzAY1PHjxyUxr8aVwYR49OiRycrKMh0dHebhw4fGsizT1tbmdFmYxt566y3T29s7auyjjz4yZWVlxhhjysrKzMcff2yMMebnn38227dvNyMjI6axsdHk5eXFvV5MH/X19aa5udkEg0F7bLy92dfXZ/x+v+nr6zP9/f3G7/eb/v7++B8Mpqwn9elnn31mvvzyy7+8tq2tzViWZR4+fGg6OjpMVlaWefToEecGiItIJGKam5uNMcb89ttvJhAImLa2NubVOOIK1gRpamrSwoULtWDBAiUlJSkYDKq6utrpsoBRqqurtWHDBknShg0bVFVVNWrc5XJpxYoV+vXXX9XT0+NkqZjC3njjDc2ePXvU2Hh7s66uTpmZmZozZ45mz56tzMzMUVcNgP/Xk/p0LNXV1QoGg0pKStKCBQu0cOFCNTU1cW6AuPB6vVq2bJkkadasWVq0aJEikQjzahwRsCZIJBJRSkqKvezz+RSJRBysCJC2b9+ujRs36ttvv5Uk9fb2yuv1SpJefPFF9fb2Svpr/6akpNC/iKvx9iZzLpxy8uRJWZalvXv32rdcjdWP9CniraurS7dv39by5cuZV+OIgAVME998843Ky8v1xRdf6OTJk7p27dqo9S6XSy6Xy6HqgLHRm5isNm/erAsXLqiyslJer1cffvih0yUBtsHBQRUXF6ukpESzZs0atY55dWIRsCaIz+dTd3e3vRyJROTz+RysCNPdf/svOTlZ2dnZampqUnJysn3rX09Pj+bOnWu/9vH+7e7upn8RV+PtTeZcOGHevHnyeDxyu9169913dfPmTUljnwPQp4iX4eFhFRcXy7IsBQIBScyr8UTAmiBpaWlqb29XZ2enhoaGFA6H5ff7nS4L09Tvv/+uBw8e2D9fvnxZqamp8vv9qqiokCRVVFQoKytLkuxxY4xu3Lih559/3r6tAIiH8fbmypUrVVdXp4GBAQ0MDKiurk4rV6508hAwDTz+3dSqqiqlpqZK+rNPw+GwhoaG1NnZqfb2dqWnp3NugLgwxmjfvn1atGiRCgsL7XHm1fhxGWOM00VMVTU1NTpy5Iii0ahyc3NVVFTkdEmYpjo7O7Vr1y5JUjQaVU5OjoqKitTX16f3339f9+/f10svvaRPP/1Uc+bMkTFGhw4dUm1trWbOnKkjR44oLS3N4aPAVLV7927V19err69PycnJeu+997RmzZpx9+apU6dUVlYmSdq5c6dyc3OdPCxMMU/q0/r6erW2tkqS5s+fr0OHDtkfRh07dkzfffedPB6PSkpKtHr1akmcG2DiXb9+XVu2bNHixYvldv95LWX37t1KT09nXo0TAhYAAAAAxAi3CAIAAABAjBCwAAAAACBGCFgAAAAAECMELAAAAACIEQIWAAAAAMQIAQsAkLCqqqq0ZMkS3b1717EavvrqK/3xxx+O7R8AMLkQsAAACevMmTN67bXXFA6HHavhxIkTBCwAgI2ABQBISIODg2poaNDhw4ftgHX16lVt3bpVRUVFysrK0ieffKIffvhBeXl5sixLHR0dkqSuri5t27ZNlmWpoKBAv/zyiyRpz549OnfunL2PjIwMe7v5+fkqLi7WunXr9MEHH8gYoxMnTqinp0cFBQXKz8+P8zsAAJiMCFgAgIRUXV2tVatW6dVXX9ULL7yg5uZmSVJra6sOHjyoH3/8UZWVlWpvb9epU6eUl5enr7/+WpJUWlqqd955R6dPn5ZlWSotLX3q/m7duqWSkhKdPXtWXV1damho0LZt2+T1enX8+HF72wCA6Y2ABQBISOFwWMFgUJK0fv16+ypWWlqavF6vkpKS9MorrygzM1OStHjxYt27d0+S1NjYqJycHElSKBRSQ0PDU/eXnp6ulJQUud1uLV261N4WAACPm+F0AQAAjFd/f7+uXLmiO3fuyOVyKRqNyuVyafXq1UpKSrJf53a77WW3261oNPo/t+vxeDQyMiJJGhkZ0fDwsL3u8e16PJ6nbgsAMD1xBQsAkHDOnz+vUCikn376SRcvXlRNTY1efvllXb9+/W/9fkZGhn3F6/Tp03r99dclSfPnz1dLS4sk6eLFi6MC1liee+45DQ4O/sMjAQBMNQQsAEDCOXPmjNasWTNqLBAI/O2nCe7fv1/ff/+9LMtSZWWl9u3bJ0natGmTrl27prfffluNjY169tlnn7qtTZs2aceOHTzkAgAgSXIZY4zTRQAAAADAVMAVLAAAAACIEQIWAAAAAMQIAQsAAAAAYoSABQAAAAAxQsACAAAAgBghYAEAAABAjBCwAAAAACBG/gNUb616sZlclwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 864x432 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JJ4kdsS3t3xF",
        "colab_type": "text"
      },
      "source": [
        "We can tell that legal transactions tend to have **lower** amounts, while **high** amounts are more frequent among fraudulent transactions."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oqNTwt-sxiJm",
        "colab_type": "text"
      },
      "source": [
        "Right now I'm going to plot boxplots for the variable `Amount`, for both **legal** and **fraudulent** transactions so that we can visualize the descrepancies between the categories."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DghdKgZltYBB",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 585
        },
        "outputId": "0f64c62d-84b4-437d-bd7c-0c5be0198694"
      },
      "source": [
        "# Plot boxplots\n",
        "fig, ax = plt.subplots(figsize=(8,8))\n",
        "\n",
        "sns.boxplot(df.Class, df.Amount,showmeans=True,  ax=ax)\n",
        "plt.ylim((-20, 400))\n",
        "plt.xticks([0, 1], ['Legal', 'Fraudulent'])\n",
        "\n",
        "plt.tight_layout()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4RufMKm-zLid",
        "colab_type": "text"
      },
      "source": [
        "Let's see what the boxplots are telling us. We can tell there are diferences by looking at it. I'll print below, stats on the Amount for both categories so we can compare."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OoBdWe3XySKG",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 390
        },
        "outputId": "8c96a90a-0500-409b-95d0-c46e5163dbb1"
      },
      "source": [
        "# print Stats for Amount for Legal Transactions\n",
        "print(\"Legal Transactions: \\n \", df.Amount[df.Class == 0].describe(), \"\\n \\nFraudulent Transactions: \\n\",df.Amount[df.Class == 1].describe() )"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Legal Transactions: \n",
            "  count    284315.000000\n",
            "mean         88.291022\n",
            "std         250.105092\n",
            "min           0.000000\n",
            "25%           5.650000\n",
            "50%          22.000000\n",
            "75%          77.050000\n",
            "max       25691.160000\n",
            "Name: Amount, dtype: float64 \n",
            " \n",
            "Fraudulent Transactions: \n",
            " count     492.000000\n",
            "mean      122.211321\n",
            "std       256.683288\n",
            "min         0.000000\n",
            "25%         1.000000\n",
            "50%         9.250000\n",
            "75%       105.890000\n",
            "max      2125.870000\n",
            "Name: Amount, dtype: float64\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dXschEeB1eBK",
        "colab_type": "text"
      },
      "source": [
        "From comparing both statistical reports for the column `Amount`, we can tell that fraudulent transactions shows a higher average 'Amount' value with a mean of **122.21**, while legal transactions shows a average of **88.29**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wIdGDhWdnvAi",
        "colab_type": "text"
      },
      "source": [
        "### **Preparing the Data**\n",
        "\n",
        "Now I a going to prepare the data in order to build the *Machine Learning* model. \n",
        "\n",
        "For the *Logistic Regression* model, it is required that every single variable of the *Dataset* is standardized. As we can see, the variables `Time` and `Amount` have not been standardized, so I'm going to do that now."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VZAuP-4c3hvy",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 217
        },
        "outputId": "278d27c1-9b10-499b-8f31-f7521bb3dd70"
      },
      "source": [
        "# standardize columns Time and Amount\n",
        "df_clean = df.copy()\n",
        "\n",
        "scaler = StandardScaler()\n",
        "df_clean['std_Time'] = scaler.fit_transform(df_clean.Time.values.reshape(-1,1))\n",
        "df_clean['std_Amount'] = scaler.fit_transform(df_clean.Amount.values.reshape(-1,1))\n",
        "\n",
        "df_clean.drop(['Time', 'Amount'], axis=1, inplace=True)\n",
        "\n",
        "df_clean.head()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>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>Class</th>\n",
              "      <th>std_Time</th>\n",
              "      <th>std_Amount</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>-1.359807</td>\n",
              "      <td>-0.072781</td>\n",
              "      <td>2.536347</td>\n",
              "      <td>1.378155</td>\n",
              "      <td>-0.338321</td>\n",
              "      <td>0.462388</td>\n",
              "      <td>0.239599</td>\n",
              "      <td>0.098698</td>\n",
              "      <td>0.363787</td>\n",
              "      <td>0.090794</td>\n",
              "      <td>-0.551600</td>\n",
              "      <td>-0.617801</td>\n",
              "      <td>-0.991390</td>\n",
              "      <td>-0.311169</td>\n",
              "      <td>1.468177</td>\n",
              "      <td>-0.470401</td>\n",
              "      <td>0.207971</td>\n",
              "      <td>0.025791</td>\n",
              "      <td>0.403993</td>\n",
              "      <td>0.251412</td>\n",
              "      <td>-0.018307</td>\n",
              "      <td>0.277838</td>\n",
              "      <td>-0.110474</td>\n",
              "      <td>0.066928</td>\n",
              "      <td>0.128539</td>\n",
              "      <td>-0.189115</td>\n",
              "      <td>0.133558</td>\n",
              "      <td>-0.021053</td>\n",
              "      <td>0</td>\n",
              "      <td>-1.996583</td>\n",
              "      <td>0.244964</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1.191857</td>\n",
              "      <td>0.266151</td>\n",
              "      <td>0.166480</td>\n",
              "      <td>0.448154</td>\n",
              "      <td>0.060018</td>\n",
              "      <td>-0.082361</td>\n",
              "      <td>-0.078803</td>\n",
              "      <td>0.085102</td>\n",
              "      <td>-0.255425</td>\n",
              "      <td>-0.166974</td>\n",
              "      <td>1.612727</td>\n",
              "      <td>1.065235</td>\n",
              "      <td>0.489095</td>\n",
              "      <td>-0.143772</td>\n",
              "      <td>0.635558</td>\n",
              "      <td>0.463917</td>\n",
              "      <td>-0.114805</td>\n",
              "      <td>-0.183361</td>\n",
              "      <td>-0.145783</td>\n",
              "      <td>-0.069083</td>\n",
              "      <td>-0.225775</td>\n",
              "      <td>-0.638672</td>\n",
              "      <td>0.101288</td>\n",
              "      <td>-0.339846</td>\n",
              "      <td>0.167170</td>\n",
              "      <td>0.125895</td>\n",
              "      <td>-0.008983</td>\n",
              "      <td>0.014724</td>\n",
              "      <td>0</td>\n",
              "      <td>-1.996583</td>\n",
              "      <td>-0.342475</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.358354</td>\n",
              "      <td>-1.340163</td>\n",
              "      <td>1.773209</td>\n",
              "      <td>0.379780</td>\n",
              "      <td>-0.503198</td>\n",
              "      <td>1.800499</td>\n",
              "      <td>0.791461</td>\n",
              "      <td>0.247676</td>\n",
              "      <td>-1.514654</td>\n",
              "      <td>0.207643</td>\n",
              "      <td>0.624501</td>\n",
              "      <td>0.066084</td>\n",
              "      <td>0.717293</td>\n",
              "      <td>-0.165946</td>\n",
              "      <td>2.345865</td>\n",
              "      <td>-2.890083</td>\n",
              "      <td>1.109969</td>\n",
              "      <td>-0.121359</td>\n",
              "      <td>-2.261857</td>\n",
              "      <td>0.524980</td>\n",
              "      <td>0.247998</td>\n",
              "      <td>0.771679</td>\n",
              "      <td>0.909412</td>\n",
              "      <td>-0.689281</td>\n",
              "      <td>-0.327642</td>\n",
              "      <td>-0.139097</td>\n",
              "      <td>-0.055353</td>\n",
              "      <td>-0.059752</td>\n",
              "      <td>0</td>\n",
              "      <td>-1.996562</td>\n",
              "      <td>1.160686</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-0.966272</td>\n",
              "      <td>-0.185226</td>\n",
              "      <td>1.792993</td>\n",
              "      <td>-0.863291</td>\n",
              "      <td>-0.010309</td>\n",
              "      <td>1.247203</td>\n",
              "      <td>0.237609</td>\n",
              "      <td>0.377436</td>\n",
              "      <td>-1.387024</td>\n",
              "      <td>-0.054952</td>\n",
              "      <td>-0.226487</td>\n",
              "      <td>0.178228</td>\n",
              "      <td>0.507757</td>\n",
              "      <td>-0.287924</td>\n",
              "      <td>-0.631418</td>\n",
              "      <td>-1.059647</td>\n",
              "      <td>-0.684093</td>\n",
              "      <td>1.965775</td>\n",
              "      <td>-1.232622</td>\n",
              "      <td>-0.208038</td>\n",
              "      <td>-0.108300</td>\n",
              "      <td>0.005274</td>\n",
              "      <td>-0.190321</td>\n",
              "      <td>-1.175575</td>\n",
              "      <td>0.647376</td>\n",
              "      <td>-0.221929</td>\n",
              "      <td>0.062723</td>\n",
              "      <td>0.061458</td>\n",
              "      <td>0</td>\n",
              "      <td>-1.996562</td>\n",
              "      <td>0.140534</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.158233</td>\n",
              "      <td>0.877737</td>\n",
              "      <td>1.548718</td>\n",
              "      <td>0.403034</td>\n",
              "      <td>-0.407193</td>\n",
              "      <td>0.095921</td>\n",
              "      <td>0.592941</td>\n",
              "      <td>-0.270533</td>\n",
              "      <td>0.817739</td>\n",
              "      <td>0.753074</td>\n",
              "      <td>-0.822843</td>\n",
              "      <td>0.538196</td>\n",
              "      <td>1.345852</td>\n",
              "      <td>-1.119670</td>\n",
              "      <td>0.175121</td>\n",
              "      <td>-0.451449</td>\n",
              "      <td>-0.237033</td>\n",
              "      <td>-0.038195</td>\n",
              "      <td>0.803487</td>\n",
              "      <td>0.408542</td>\n",
              "      <td>-0.009431</td>\n",
              "      <td>0.798278</td>\n",
              "      <td>-0.137458</td>\n",
              "      <td>0.141267</td>\n",
              "      <td>-0.206010</td>\n",
              "      <td>0.502292</td>\n",
              "      <td>0.219422</td>\n",
              "      <td>0.215153</td>\n",
              "      <td>0</td>\n",
              "      <td>-1.996541</td>\n",
              "      <td>-0.073403</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         V1        V2        V3  ...  Class  std_Time  std_Amount\n",
              "0 -1.359807 -0.072781  2.536347  ...      0 -1.996583    0.244964\n",
              "1  1.191857  0.266151  0.166480  ...      0 -1.996583   -0.342475\n",
              "2 -1.358354 -1.340163  1.773209  ...      0 -1.996562    1.160686\n",
              "3 -0.966272 -0.185226  1.792993  ...      0 -1.996562    0.140534\n",
              "4 -1.158233  0.877737  1.548718  ...      0 -1.996541   -0.073403\n",
              "\n",
              "[5 rows x 31 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JDU6Em2kutKv",
        "colab_type": "text"
      },
      "source": [
        "Now that every single column of the *Dataset* is standardized, I'll divide the data for **train** and **test** samples.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NXxxN5JGswU8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Dividing in feature matrix and target vector\n",
        "x = df_clean.drop('Class', axis=1)\n",
        "y = df.Class\n",
        "\n",
        "# Spliting into train and test samples\n",
        "x_train, x_test, y_train, y_test = train_test_split(x,y, stratify=y, shuffle=True)"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z5GHM8wVAoW6",
        "colab_type": "text"
      },
      "source": [
        "As I stated in the begining of this project, the data is exremely unbalanced, that means that most of the  *Dataset* consists of legal transactions samples.\n",
        "\n",
        "That could be a problem for the model, because if we use unbalanced data to train our *Machine Learning* project, the model will tend to classify many samples wrongfully.\n",
        "\n",
        "In order to fix that, I'm going to use the libary `imblearn` to balance our data correctly.\n",
        "\n",
        "In this case, I'm going to use the *under-sampling* technique, that means I'm going to randomly delete samples from the majoritary Class, which is the **Legal Transactions**. By doing that I'm able to maximize the model's performance for the minority Class, which is **Fraudulent Transactions**."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SS8XKDQRv9f4",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 336
        },
        "outputId": "67e667ba-c5b3-4d04-fa0e-121e48a23d92"
      },
      "source": [
        "# uder-sampling the dataset\n",
        "rus = RandomUnderSampler()\n",
        "x_rus, y_rus = rus.fit_sample(x_train, y_train)\n",
        "\n",
        "# Plot Class distribution\n",
        "sns.set_style('dark')\n",
        "sns.countplot(y_rus)\n",
        "plt.title(\"Class Distribution\")\n",
        "plt.show();"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/sklearn/utils/deprecation.py:87: FutureWarning: Function safe_indexing is deprecated; safe_indexing is deprecated in version 0.22 and will be removed in version 0.24.\n",
            "  warnings.warn(msg, category=FutureWarning)\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYUAAAEICAYAAACwDehOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAaU0lEQVR4nO3df1BVdf7H8df1AkqIgCiXdPk6uZE0bJYbZvhzvIqYyEKo25iaoq0rmaRMFuSMKSVrP6ZY3dVibB1q27bRDDQqEWqQ1spZU7HG2pzSr6XcW/zyRylwvd8//O5nYhW7bh4uyfPx1+Xcc859wxjPzo97sXm9Xq8AAJDUzd8DAAA6D6IAADCIAgDAIAoAAIMoAAAMogAAMIgCfhbWrl2rBx980N9jtHHvvffq9ddfvyL7+uc//6nk5GTztdPp1K5du67IviUpJSVFH3744RXbH65eAf4eAPi3bdu2aePGjfryyy8VEhKiuLg4LViwQAkJCR0+y6BBgxQcHCybzaagoCDFxcXprrvu0qRJk8w6GzZs8Hlf5eXlGjBgQLvrJCQkaPv27T95bknKzc2Vw+HQkiVLzLKysrIrsm9c/YgCOoWNGzeqqKhIK1eu1MiRIxUYGKjq6mpVVlb6JQqSVFpaqgEDBqi+vl47d+5Ufn6+vvjiC91///1X9HVaW1sVEMB/iugcOH0Evzt58qTWrFmj5cuXa8KECbrmmmsUGBgop9Ophx9++KLbZGdna8SIEbr11ls1Y8YMff755+a5qqoqTZo0SUOGDNGoUaP0wgsvSJLq6+v1+9//XgkJCbrtttt0991369y5cz86X+/evZWenq4VK1bo+eefV0NDgyRp1qxZ2rRpkyTpyJEjmjlzpm699VYNGzZMixcvliTNmDFDkpSWlqYhQ4bozTff1IcffqjRo0erqKhII0aMUF5enln2QwcOHNCkSZM0dOhQ5eXl6ezZs5KkLVu2aPr06W3WHTRokI4cOaJXX31V27Zt0wsvvKAhQ4ZowYIFktqejmpubtaqVas0cuRIjRw5UqtWrVJzc7MkmTn+8pe/KDExUSNHjtRrr732oz8jXD343xP43d69e3X27FklJSX5vM3o0aNVUFCgoKAgPfXUU3rwwQdVWloqSVq2bJkKCwuVkJCgpqYmffXVV5LOH404HA69//77kqT9+/fLZrP5/Jrjxo2Tx+NRTU2NxowZ0+a5P/7xjxoxYoRefPFFtbS06MCBA5Kkl19+WYMGDTJHHdL5X7zffvutmpqa9O677+rcuXPav3//Ba/371/uwcHBWrBggdatW9fmlNDF3HXXXdq7d+8Fp49+aP369dq/f79KS0tls9l03333ad26dSZk3377rU6ePKmdO3dq165dys7O1vjx4xUWFubzzwo/XxwpwO8aGxsVERFxWadQpk6dqp49eyooKEiLFi3Sp59+qpMnT0qSAgICdOjQIZ06dUphYWGKj483y7/55hsdO3ZMgYGBSkhIuKwoBAYGKiIiQk1NTRc8FxAQoGPHjsntdqt79+4/esqrW7duys7OVlBQkHr06HHRdWbMmKFrr71W4eHhysrKumLXBbZt26aFCxcqMjJSvXv31sKFC7V169Y238vChQsVGBioMWPG6JprrtGXX355RV4bnR9RgN+Fh4eroaFBra2tPq3v8Xj09NNPa/z48fr1r38tp9MpSea0zpo1a1RVVaWxY8dq5syZ2rt3ryRp3rx5GjBggObOnatx48apqKjosuZsaWlRfX39Rf+PeenSpfJ6vZo6dapSUlK0efPmS+4rIiJC3bt3v+Q61157rXncr18/ud3uy5q3PW63W/369Wt33+Hh4W0CHRwcrO++++6KvDY6P6IAvxsyZIiCgoJUUVHh0/rbtm1TZWWlNm7cqD179uidd96RJP37A38HDx6s9evXa9euXRo/frw5LdKzZ0/l5uaqsrJS69ev18aNG82pJF9UVlbKbrdr8ODBFzzXt29fPf7443rvvfe0cuVKrVy5UkeOHGl3X74coRw/ftw8PnbsmKKioiSd/yV95swZ89w333xzWfuOiorSsWPH2rzOv/cNEAX4XWhoqLKzs5Wfn6+Kigp9//33amlpUVVVlZ588skL1j99+rSCgoIUERGh77//Xs8884x5rrm5WVu3btXJkycVGBiokJAQdet2/p/5u+++qyNHjsjr9So0NFR2u92nX86NjY3aunWr8vPz9bvf/U4REREXrPPWW2+ptrZWkhQWFiabzWZet0+fPjp69Ohl/1z+9re/qba2Vo2NjXruuefM7bBxcXH6/PPPdfDgQZ09e1Zr165ts11kZKS5jnIxKSkpWr9+verr61VfX68///nPSk1Nvez5cHXiQjM6hblz56pPnz5at26dHnzwQYWEhCg+Pt7cPfND6enpeu+99zRq1CiFh4frgQce0CuvvGKeLy0t1WOPPSaPx6PrrrtOTz31lKTzdwg99thjqq+vV69evTR9+nTdfvvt7c6UlpYmm82mwMBADRo0SHl5ee3+8jxw4IAKCgp06tQpRUZGatmyZYqJiZEk3X///crNzdWZM2eUn5+vyMhIn34mkydP1ty5c+V2uzVu3DhlZWVJkq677jotXLhQc+bMUY8ePZSTk6NXX33VbDd16lQ98MAD5i6rdevWtdnvfffdp9OnT+s3v/mNJGnixIm67777fJoJVz8bf2QHAPBvnD4CABhEAQBgEAUAgEEUAADGz/ruo3Pnzsnj4To5AFyOwEB7u8/9rKPg8XjV2Mg7LQHgcvTtG9ruc5w+AgAYRAEAYBAFAIBBFAAABlEAABhEAQBgEAUAgEEUAAAGUQAAGD/rdzRfCT179VBw90B/j4FO5vuzLTp14syPr2ih3mGBsgf18OsM6Hw8zWdU39Ri2f67fBSCuwfq1qUv+nsMdDJ7nrpHp+TfKNiDeuh/82/y6wzofP5n+QFJ1kWB00cAAIMoAAAMogAAMIgCAMAgCgAAw7K7j86ePasZM2aoublZHo9HycnJys7OVm5urnbv3q3Q0PN/5GH16tW68cYb5fV6tWrVKlVVValHjx5avXq14uPjrRoPAHARlkUhKChIxcXFCgkJUUtLi+6++26NHj1akvTQQw9p4sSJbdbfuXOnDh8+rPLycu3fv18rVqzQpk2brBoPAHARlp0+stlsCgkJkSS1traqtbVVNput3fUrKyuVnp4um82mW265RSdOnJDb7bZqPADARVh6TcHj8SgtLU3Dhw/X8OHDdfPNN0uSnn32WaWmpqqgoEDNzc2SJJfLpejoaLNtdHS0XC6XleMBAP6DpVGw2+0qLS1VVVWVampq9K9//Us5OTl6++239dprr6mpqUlFRUVWjgAAuAwdcvdRr169NGzYMFVXVysqKko2m01BQUHKyMjQgQMHJEkOh0O1tbVmm9raWjkcjo4YDwDw/yyLQn19vU6cOCFJOnPmjHbt2qWBAwea6wRer1cVFRWKjY2VJDmdTpWUlMjr9Wrfvn0KDQ1VVFSUVeMBAC7CsruP3G63cnNz5fF45PV6NXHiRI0dO1b33HOPGhoa5PV6FRcXp5UrV0qSxowZo6qqKiUlJSk4OFgFBQVWjQYAaIdlUYiLi1NJSckFy1988eKfSGqz2fToo49aNQ4AwAe8oxkAYBAFAIBBFAAABlEAABhEAQBgEAUAgEEUAAAGUQAAGEQBAGAQBQCAQRQAAAZRAAAYRAEAYBAFAIBBFAAABlEAABhEAQBgEAUAgEEUAACGZX+j+ezZs5oxY4aam5vl8XiUnJys7OxsHT16VDk5OWpsbFR8fLyefPJJBQUFqbm5WQ899JA++eQThYeH69lnn9UvfvELq8YDAFyEZUcKQUFBKi4u1tatW1VSUqLq6mrt27dPTz/9tObMmaMdO3aoV69e2rx5syRp06ZN6tWrl3bs2KE5c+bo6aeftmo0AEA7LIuCzWZTSEiIJKm1tVWtra2y2Wz64IMPlJycLEm68847VVlZKUl65513dOedd0qSkpOT9f7778vr9Vo1HgDgIiy9puDxeJSWlqbhw4dr+PDhiomJUa9evRQQcP6sVXR0tFwulyTJ5XLp2muvlSQFBAQoNDRUDQ0NVo4HAPgPlkbBbrertLRUVVVVqqmp0RdffGHlywEAfqIOufuoV69eGjZsmPbt26cTJ06otbVVklRbWyuHwyFJcjgcOn78uKTzp5tOnjypiIiIjhgPAPD/LItCfX29Tpw4IUk6c+aMdu3apV/+8pcaNmyYtm/fLkl6/fXX5XQ6JUlOp1Ovv/66JGn79u26/fbbZbPZrBoPAHARlt2S6na7lZubK4/HI6/Xq4kTJ2rs2LG6/vrrtWTJEhUWFurGG2/UtGnTJElTp07V0qVLlZSUpLCwMD377LNWjQYAaIdlUYiLi1NJSckFy2NiYsxtqD/UvXt3rVmzxqpxAAA+4B3NAACDKAAADKIAADCIAgDAIAoAAIMoAAAMogAAMIgCAMAgCgAAgygAAAyiAAAwiAIAwCAKAACDKAAADKIAADCIAgDAIAoAAIMoAAAMogAAMCyLwvHjxzVr1ixNmjRJKSkpKi4uliStXbtWo0aNUlpamtLS0lRVVWW2ef7555WUlKTk5GRVV1dbNRoAoB0BVu3YbrcrNzdX8fHxOnXqlKZMmaIRI0ZIkubMmaN58+a1Wf/QoUMqKytTWVmZXC6XMjMztX37dtntdqtGBAD8B8uOFKKiohQfHy9J6tmzpwYOHCiXy9Xu+pWVlUpJSVFQUJBiYmI0YMAA1dTUWDUeAOAiOuSawldffaWDBw/q5ptvliS9/PLLSk1NVV5enpqamiRJLpdL0dHRZhuHw3HJiAAArjzLo3D69GllZ2frkUceUc+ePTV9+nTt2LFDpaWlioqK0urVq60eAQDgI0uj0NLSouzsbKWmpmrChAmSpD59+shut6tbt26aNm2aDhw4IOn8kUFtba3Z1uVyyeFwWDkeAOA/WBYFr9erZcuWaeDAgcrMzDTL3W63eVxRUaHY2FhJktPpVFlZmZqbm3X06FEdPnxYgwcPtmo8AMBFWHb30Z49e1RaWqobbrhBaWlpkqScnBy98cYb+vTTTyVJ/fv3V35+viQpNjZWd9xxhyZNmiS73a7ly5dz5xEAdDDLopCQkKDPPvvsguVjxoxpd5usrCxlZWVZNRIA4EfwjmYAgEEUAAAGUQAAGEQBAGAQBQCAQRQAAAZRAAAYRAEAYBAFAIBBFAAABlEAABhEAQBgEAUAgEEUAAAGUQAAGD5FYfbs2T4tAwD8vF3yj+ycPXtW33//vRoaGtTU1CSv1ytJOnXqlFwuV4cMCADoOJeMwt///ncVFxfL7XYrIyPDRKFnz56aOXNmhwwIAOg4l4zC7NmzNXv2bL300kuaNWtWR80EAPATn/5G86xZs/TRRx/p66+/lsfjMcvT09Pb3eb48eN66KGHVFdXJ5vNpt/+9reaPXu2GhsbtWTJEn399dfq37+/CgsLFRYWJq/Xq1WrVqmqqko9evTQ6tWrFR8f/9O/QwCAz3yKwtKlS3X06FHFxcXJbrdLkmw22yWjYLfblZubq/j4eJ06dUpTpkzRiBEjtGXLFiUmJmr+/PkqKipSUVGRli5dqp07d+rw4cMqLy/X/v37tWLFCm3atOnKfJcAAJ/4FIWPP/5Yb775pmw2m887joqKUlRUlKTz1yAGDhwol8ulyspKvfTSS5LOH2nMmjVLS5cuVWVlpdLT02Wz2XTLLbfoxIkTcrvdZh8AAOv5dEtqbGysvvnmm//6Rb766isdPHhQN998s+rq6swv+r59+6qurk6S5HK5FB0dbbaJjo7mDicA6GA+HSk0NDQoJSVFgwcPVmBgoFn+3HPP/ei2p0+fVnZ2th555BH17NmzzXM2m+2yjj4AANbyKQqLFi36r3be0tKi7OxspaamasKECZKkyMhIc1rI7Xard+/ekiSHw6Ha2lqzbW1trRwOx3/1ugCA/45PUbjtttsue8der1fLli3TwIEDlZmZaZY7nU6VlJRo/vz5Kikp0bhx48zyv/71r0pJSdH+/fsVGhrK9QQA6GA+RWHIkCHmNE9LS4taW1sVHBysjz76qN1t9uzZo9LSUt1www1KS0uTJOXk5Gj+/PlavHixNm/erH79+qmwsFCSNGbMGFVVVSkpKUnBwcEqKCj4qd8bAOAy+RSFvXv3msder1eVlZXat2/fJbdJSEjQZ599dtHniouLL1hms9n06KOP+jIOAMAil/0pqTabTePHj9d7771nxTwAAD/y6UihvLzcPD537pw+/vhjde/e3bKhAAD+4VMU3n33XfPYbrerf//+WrdunWVDAQD8w6co/OEPf7B6DgBAJ+DTNYXa2lotXLhQiYmJSkxM1KJFi9q8pwAAcHXwKQp5eXlyOp2qrq5WdXW1xo4dq7y8PKtnAwB0MJ+iUF9frylTpiggIEABAQHKyMhQfX291bMBADqYT1EIDw9XaWmpPB6PPB6PSktLFR4ebvVsAIAO5lMUCgoK9NZbb2nEiBEaOXKktm/frtWrV1s9GwCgg/l099GaNWv0xBNPKCwsTJLU2NioJ554gruSAOAq49ORwmeffWaCIJ0/nXTw4EHLhgIA+IdPUTh37pyamprM142NjW3+VjMA4Org0+mjuXPn6q677tLEiRMlSW+//bYWLFhg6WAAgI7nUxTS09P1q1/9Sh988IEk6U9/+pOuv/56SwcDAHQ8n6IgSddffz0hAICr3GV/dDYA4OpFFAAABlEAABhEAQBgWBaFvLw8JSYmavLkyWbZ2rVrNWrUKKWlpSktLU1VVVXmueeff15JSUlKTk5WdXW1VWMBAC7B57uPLldGRoZmzpyphx9+uM3yOXPmaN68eW2WHTp0SGVlZSorK5PL5VJmZqa2b98uu91u1XgAgIuw7Ehh6NChbT4a41IqKyuVkpKioKAgxcTEaMCAAaqpqbFqNABAOzr8msLLL7+s1NRU5eXlmY/OcLlcio6ONus4HA65XK6OHg0AurwOjcL06dO1Y8cOlZaWKioqio/fBoBOpkOj0KdPH9ntdnXr1k3Tpk3TgQMHJJ0/Mvjh33x2uVxyOBwdORoAQB0cBbfbbR5XVFQoNjZWkuR0OlVWVqbm5mYdPXpUhw8f1uDBgztyNACALLz7KCcnR7t371ZDQ4NGjx6tRYsWaffu3fr0008lSf3791d+fr4kKTY2VnfccYcmTZoku92u5cuXc+cRAPiBZVF45plnLlg2bdq0dtfPyspSVlaWVeMAAHzAO5oBAAZRAAAYRAEAYBAFAIBBFAAABlEAABhEAQBgEAUAgEEUAAAGUQAAGEQBAGAQBQCAQRQAAAZRAAAYRAEAYBAFAIBBFAAABlEAABhEAQBgEAUAgGFZFPLy8pSYmKjJkyebZY2NjcrMzNSECROUmZmppqYmSZLX69Xjjz+upKQkpaam6pNPPrFqLADAJVgWhYyMDG3YsKHNsqKiIiUmJqq8vFyJiYkqKiqSJO3cuVOHDx9WeXm5HnvsMa1YscKqsQAAl2BZFIYOHaqwsLA2yyorK5Weni5JSk9PV0VFRZvlNptNt9xyi06cOCG3223VaACAdnToNYW6ujpFRUVJkvr27au6ujpJksvlUnR0tFkvOjpaLperI0cDAMiPF5ptNptsNpu/Xh4AcBEdGoXIyEhzWsjtdqt3796SJIfDodraWrNebW2tHA5HR44GAFAHR8HpdKqkpESSVFJSonHjxrVZ7vV6tW/fPoWGhprTTACAjhNg1Y5zcnK0e/duNTQ0aPTo0Vq0aJHmz5+vxYsXa/PmzerXr58KCwslSWPGjFFVVZWSkpIUHBysgoICq8YCAFyCZVF45plnLrq8uLj4gmU2m02PPvqoVaMAAHzEO5oBAAZRAAAYRAEAYBAFAIBBFAAABlEAABhEAQBgEAUAgEEUAAAGUQAAGEQBAGAQBQCAQRQAAAZRAAAYRAEAYBAFAIBBFAAABlEAABhEAQBgWPY3mi/F6XQqJCRE3bp1k91u15YtW9TY2KglS5bo66+/Vv/+/VVYWKiwsDB/jAcAXZbfjhSKi4tVWlqqLVu2SJKKioqUmJio8vJyJSYmqqioyF+jAUCX1WlOH1VWVio9PV2SlJ6eroqKCj9PBABdj9+iMG/ePGVkZOjVV1+VJNXV1SkqKkqS1LdvX9XV1flrNADosvxyTeGVV16Rw+FQXV2dMjMzNXDgwDbP22w22Ww2f4wGAF2aX44UHA6HJCkyMlJJSUmqqalRZGSk3G63JMntdqt3797+GA0AurQOj8J3332nU6dOmcf/+Mc/FBsbK6fTqZKSEklSSUmJxo0b19GjAUCX1+Gnj+rq6rRw4UJJksfj0eTJkzV69GjddNNNWrx4sTZv3qx+/fqpsLCwo0cDgC6vw6MQExOjrVu3XrA8IiJCxcXFHT0OAOAHOs0tqQAA/yMKAACDKAAADKIAADCIAgDAIAoAAIMoAAAMogAAMIgCAMAgCgAAgygAAAyiAAAwiAIAwCAKAACDKAAADKIAADCIAgDAIAoAAIMoAACMTheFnTt3Kjk5WUlJSSoqKvL3OADQpXSqKHg8HuXn52vDhg0qKyvTG2+8oUOHDvl7LADoMjpVFGpqajRgwADFxMQoKChIKSkpqqys9PdYANBlBPh7gB9yuVyKjo42XzscDtXU1LS7fmCgXX37hv7k193z1D0/eR+4+lyJf1s/1f8sP+DvEdAJWflvs1MdKQAA/KtTRcHhcKi2ttZ87XK55HA4/DgRAHQtnSoKN910kw4fPqyjR4+qublZZWVlcjqd/h4LALqMTnVNISAgQMuXL9e9994rj8ejKVOmKDY21t9jAUCXYfN6vV5/DwEA6Bw61ekjAIB/EQUAgEEUwEeLoNPKy8tTYmKiJk+e7O9Rugyi0MXx0SLozDIyMrRhwwZ/j9GlEIUujo8WQWc2dOhQhYWF+XuMLoUodHEX+2gRl8vlx4kA+BNRAAAYRKGL46NFAPwQUeji+GgRAD/EO5qhqqoqFRQUmI8WycrK8vdIgCQpJydHu3fvVkNDgyIjI7Vo0SJNmzbN32Nd1YgCAMDg9BEAwCAKAACDKAAADKIAADCIAgDAIAoAAIMoAACM/wNEZ7iIgjSqpgAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KbnWH58VFKMq",
        "colab_type": "text"
      },
      "source": [
        "As we can see in the bar chart above, the classes are now equally ditributed,and the data is now balanced."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z6hnjq92N-IU",
        "colab_type": "text"
      },
      "source": [
        "### **The Machine Learning Model**\n",
        "\n",
        "With the data properly structured, I'm going to build a classification model, using *Logistic Regression*, intended to classify the samples above as **Legal** or **Fraudulent Transactions**, using the train and test data specified above. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pN64phx2EfKI",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Choose and import a model\n",
        "from sklearn.linear_model import LogisticRegression\n",
        "\n",
        "# Create an instace for the model\n",
        "logisticModel = LogisticRegression()\n",
        "\n",
        "# Train the model\n",
        "logisticModel.fit(x_rus, y_rus)\n",
        "\n",
        "# Make predictions on test data\n",
        "y_pred = logisticModel.predict(x_test)\n",
        "y_prob = logisticModel.predict_proba(x_test)"
      ],
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "734rsQvr3HYy",
        "colab_type": "text"
      },
      "source": [
        "Now that I have built the *Logistic Regression* model, trained it, and predicted the test data, it's time to evaluate it's preformance.\n",
        "\n",
        "I'll plot below a confusion matrix, and print out the classification report in order to understand how well the model performed."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qVBq_u93QrR9",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "outputId": "686737c1-344d-404c-a454-883ad9debbfd"
      },
      "source": [
        "# Import Consusion Matrix metric\n",
        "from sklearn.metrics import confusion_matrix\n",
        "\n",
        "# Plot confusion matrix\n",
        "fig, ax = plt.subplots()\n",
        "sns.heatmap(confusion_matrix(y_test, y_pred, normalize=\"true\"), ax=ax, annot=True)\n",
        "\n",
        "plt.title(\"Confusion Matrix\")\n",
        "plt.xlabel(\"Predicted\")\n",
        "plt.ylabel(\"Real\")\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eK2bibIy_iEM",
        "colab_type": "text"
      },
      "source": [
        "From looking at the Confusion Matrix above, we can see some pretty good results. The model classified **94%** of **Fraudulent** transacitons correctly, and **97%** of **Legal** transactions correctly. \n",
        "\n",
        "I'm going print below the classification report and check **accuracy**, **precision**,  and **recall** numbers."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "plLXeCgW50ox",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 194
        },
        "outputId": "83d84457-f981-4363-b1dd-2b807d098d77"
      },
      "source": [
        "# Print classification report\n",
        "print(\"Classification Report: \\n\",classification_report(y_test, y_pred, digits=4))"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Classification Report: \n",
            "               precision    recall  f1-score   support\n",
            "\n",
            "           0     0.9999    0.9701    0.9848     71079\n",
            "           1     0.0517    0.9431    0.0980       123\n",
            "\n",
            "    accuracy                         0.9700     71202\n",
            "   macro avg     0.5258    0.9566    0.5414     71202\n",
            "weighted avg     0.9983    0.9700    0.9832     71202\n",
            "\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QiL6eFIkajm0",
        "colab_type": "text"
      },
      "source": [
        "For unbalanced Datasets, accuracy isn't a great way to evaluate the model's performance, due to the fact that the model could be extremely accurate and still only detect 60 or less percent of Fraudulent transactions. The ideal here is to look at the recall, or just focus on the confusion matrix."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bCE2AhmEcnhE",
        "colab_type": "text"
      },
      "source": [
        "### **Conclusion**\n",
        "The model performed better than I expected, but I'm no Machine Learnig expert(yet). I didnt't have to do much work pre-processing the data because it was as clean as it gets, and even though we may believe that  there aren't many diferences between Legal and fraudulent transactions, this Machine Learning model showed us that there are, and that we can classify and prevent them. \n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gA0rPoROBjva",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}