13.3_Scaling_to_median_and_quantiles.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "## Scaling to median and quantiles\n",
    "\n",
    "We saw in previous lectures that the magnitude of the variables affects different machine learning algorithms for different reasons. In this section, I will cover a few standard ways of squeezing the magnitude of the variables.\n",
    "\n",
    "\n",
    "Scaling using median and quantiles consists of substracting the median to all the observations, and then dividing by the interquantile difference. The interquantile difference is the difference between the 75th and 25th quantile:\n",
    "\n",
    "IQR = 75th quantile - 25th quantile\n",
    "\n",
    "X_scaled = (X - X.median) / IQR\n",
    "\n",
    "For an overview of the different scaling methods check:\n",
    "http://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#sphx-glr-auto-examples-preprocessing-plot-all-scaling-py\n",
    "\n",
    "\n",
    "Let's demonstrate the Median and Quantile scaling method using scikit-learn. The function of sklearn to perform this procedure is the RobustScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "# RobustScaler from sklearn performs the above described operation\n",
    "from sklearn.preprocessing import RobustScaler\n",
    "\n",
    "from sklearn.metrics import roc_auc_score\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "% matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>22.0</td>\n",
       "      <td>7.2500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
       "      <td>71.2833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>26.0</td>\n",
       "      <td>7.9250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>53.1000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>35.0</td>\n",
       "      <td>8.0500</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived  Pclass   Age     Fare\n",
       "0         0       3  22.0   7.2500\n",
       "1         1       1  38.0  71.2833\n",
       "2         1       3  26.0   7.9250\n",
       "3         1       1  35.0  53.1000\n",
       "4         0       3  35.0   8.0500"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the numerical variables of the Titanic Dataset\n",
    "data = pd.read_csv('titanic.csv', usecols = ['Pclass', 'Age', 'Fare', 'Survived'])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Age</th>\n",
       "      <th>Fare</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>891.000000</td>\n",
       "      <td>891.000000</td>\n",
       "      <td>714.000000</td>\n",
       "      <td>891.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.383838</td>\n",
       "      <td>2.308642</td>\n",
       "      <td>29.699118</td>\n",
       "      <td>32.204208</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.486592</td>\n",
       "      <td>0.836071</td>\n",
       "      <td>14.526497</td>\n",
       "      <td>49.693429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.420000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>20.125000</td>\n",
       "      <td>7.910400</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>28.000000</td>\n",
       "      <td>14.454200</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>38.000000</td>\n",
       "      <td>31.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>80.000000</td>\n",
       "      <td>512.329200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Survived      Pclass         Age        Fare\n",
       "count  891.000000  891.000000  714.000000  891.000000\n",
       "mean     0.383838    2.308642   29.699118   32.204208\n",
       "std      0.486592    0.836071   14.526497   49.693429\n",
       "min      0.000000    1.000000    0.420000    0.000000\n",
       "25%      0.000000    2.000000   20.125000    7.910400\n",
       "50%      0.000000    3.000000   28.000000   14.454200\n",
       "75%      1.000000    3.000000   38.000000   31.000000\n",
       "max      1.000000    3.000000   80.000000  512.329200"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the values of those variables to get an idea of the magnitudes\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can see from the above statistics table that the magnitudes of the variables are different. The mean values and medians are different as well as the maximum values and the range over which the values are spread."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Survived      0\n",
       "Pclass        0\n",
       "Age         177\n",
       "Fare          0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's check at missing  data\n",
    "\n",
    "data.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Age contains missing information, so I will fill those observations with the median in the next cell."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((623, 3), (268, 3))"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's separate into training and testing set\n",
    "X_train, X_test, y_train, y_test = train_test_split(data[['Pclass', 'Age', 'Fare']],\n",
    "                                                    data.Survived, test_size=0.3,\n",
    "                                                    random_state=0)\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# let's fill the missing data\n",
    "\n",
    "X_train.Age.fillna(X_train.Age.median(), inplace=True)\n",
    "X_test.Age.fillna(X_train.Age.median(), inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Robust Scaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# robust scaler\n",
    "\n",
    "scaler = RobustScaler() # call the object\n",
    "X_train_scaled = scaler.fit_transform(X_train) # fit the scaler to the train set, and then scale it\n",
    "X_test_scaled = scaler.transform(X_test) # scale the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "means (Pclass, Age and Fare):  [-0.47512039  0.0567354   0.7440926 ]\n",
      "std (Pclass, Age and Fare):  [ 0.55998791  1.00109914  2.05514812]\n"
     ]
    }
   ],
   "source": [
    "#let's have a look at the scaled training dataset\n",
    "\n",
    "print('means (Pclass, Age and Fare): ', X_train_scaled.mean(axis=0))\n",
    "print('std (Pclass, Age and Fare): ', X_train_scaled.std(axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the distributions are not centered in zero and the standard deviation is not 1 as when normalising the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min values (Pclass, Age and Fare):  [-1.33333333 -2.17923077 -0.63931806]\n",
      "Max values (Pclass, Age and Fare):  [  0.           3.92307692  21.19676931]\n"
     ]
    }
   ],
   "source": [
    "# let's look at the new minimum and maximum values\n",
    "\n",
    "print('Min values (Pclass, Age and Fare): ', X_train_scaled.min(axis=0))\n",
    "print('Max values (Pclass, Age and Fare): ', X_train_scaled.max(axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neither are the minimum and maximum values set to a certain upper and lower boundaries like in the MinMaxScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  30.,   10.,   10.,   19.,   52.,   67.,   56.,  183.,   56.,\n",
       "          34.,   28.,   25.,   18.,   10.,   10.,    7.,    3.,    3.,\n",
       "           1.,    1.]),\n",
       " array([-2.17923077, -1.87411538, -1.569     , -1.26388462, -0.95876923,\n",
       "        -0.65365385, -0.34853846, -0.04342308,  0.26169231,  0.56680769,\n",
       "         0.87192308,  1.17703846,  1.48215385,  1.78726923,  2.09238462,\n",
       "         2.3975    ,  2.70261538,  3.00773077,  3.31284615,  3.61796154,\n",
       "         3.92307692]),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6lquqjgIbu/tutyd5dlWtqvsnSV4BHK6qXUkuGvX+mwr6qnrJyZYneQ3wCuDiWsHjShc7\nj1Vs0Vdj6NRK8jjmQ/7mqvrUpOvpo6r+I8mXmL9/sqqCHngBcGmS3wGeCDw1yd9U1R+MYudrpuum\n+yKUtwGXVtVPJl3PGuWrMVaQJAFuAO6pqvdNup5hJJk6NoIuyS8CLwXunWxVy1dV11TV2VU1zfzv\nxT+NKuRhDQU98EHgKcDOJLuTfGTSBQ0jyeVJ9gO/AXwmyecmXdNSdTfDj70a4x7g1tX4aowkO4Cv\nAM9Msj/JVZOuaUgvAF4NvLj7ndjdXVGuJmcCX0qyh/kLiZ1VNdKhiS3wyVhJatxauqKXpDXJoJek\nxhn0ktQ4g16SGmfQS1LjDHpJapxBL0mNM+glqXH/C/kX+IG+N9mhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf0b0f35da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's look at the distribution of Age transformed\n",
    "\n",
    "plt.hist(X_train_scaled[:,1], bins=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 388.,  118.,   54.,   27.,   10.,   12.,    1.,    0.,    7.,\n",
       "           1.,    3.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,\n",
       "           0.,    2.]),\n",
       " array([ -0.63931806,   0.45248631,   1.54429068,   2.63609505,\n",
       "          3.72789941,   4.81970378,   5.91150815,   7.00331252,\n",
       "          8.09511689,   9.18692126,  10.27872563,  11.37052999,\n",
       "         12.46233436,  13.55413873,  14.6459431 ,  15.73774747,\n",
       "         16.82955184,  17.92135621,  19.01316058,  20.10496494,  21.19676931]),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0xf0b23dfbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's look at the distribution of Fare transformed\n",
    "\n",
    "plt.hist(X_train_scaled[:,2], bins=20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variable Age has a somewhat normal distribution after the transformation, reflecting the approximately Gaussian distribution that shows the original variable. Fare on the other had shows a skewed distribution, which is also evidenced after variable transformation in the previous plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0xf0b2735ba8>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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nD6FBIysnMISIBsAOiNSme7WE4/VuhSuJDYYQUT/iGUDsgihaOV0hVOViCBFp\nFjsgUqvsrhA60aCNbR0YQkSniXcAsQui4bCbDdDpBLhaeE6ISHPYAZHa6XQCMqxGuFq0sWoCQ4io\nSyICiF0QxYLDZoS7IwivL6h0KcPGECICA4iSi8MW3u7b1dKhcCXDx4tVKaVx+I2SUYbVCCAcQsX5\ndoWrGR52QpSyEhlA7IIoljK6OqHGtuSfnMAQopTEAKJk1t0JNWpg1QSGEKUcBhAlu+4Q0sLSPTwn\nRCkj0ed/GEAULyajCKNep4kQYidEKYEBRFoiCALSrUY0tnZAlmWlyxkWhhBpHgOItCjDakSHPwRv\nZ3JfK8ThONIsJaZfM4AoUbpnyNU3d2B0gUHhaqLHTog0iQFEWpedYQKQ/Fs6MIRIcxhAlApyNbKl\nA4fjSDOUWv2AAURKYCdEpCJcfodSjdEgwmlLQ1W9O6lnyDGEKOkpGUDsgkhJuU4zPL4gXEl8vdCw\nQmjPnj1YuXJlrGohGpLKmjYGEKW0kbk2AMBXR5sVriR6UYfQU089hfvuuw+dnZ2xrIcoIkoPvzGA\nSA2K88IraB9IxRAaNWoUfvOb38SyFqJBKd39AAwgUo/M9DRYTXocONqctOeFop4dt2zZMhw/fjyW\ntRANSOnwARhAFF9OpwV6vQh3QILRG4joOWNHOrDnUAN8EjAqCfcW4hRtSgrRBtCR6lOfV1oYfYgw\ngCjempu9AICmJk/EW3ePyLRgD4APPjuGS+YXx7G64cnJ6TsgOTuOVC2a4bcj1W09//V1H5GWjC3M\ngE4APv2qXulSosJOiFQrmvCJF3ZBpFbmND2K8+2oqGlHfbMXuU6L0iUNybA6oaKiIvz973+PVS1E\nPSINoIG6nlhhAJHaTRzlBAB8loTdEIfjSFWGMvyWiKE1BhAlg3FFGdDpBHx6gCFEFLWhdj/xxgCi\nZGEy6lFakI6qejeO1bUrXc6QMIRIFSIJoFiEz3BmxxGp2bQxWQCAD3afULiSoWEIkaIiGX5LVOfT\nG7sgSjalBemwWwz4ZF8tfP7k2W2VIUSKibT7STQGECUjnU7AtNIs+Pwh7Nhfp3Q5EWMIkSKU6H4i\nGYpjAFEymzYmC4IAfPDFiaRZxochRAkXSQApgQFEyc5uMWJsYQaO1rXj0PFWpcuJCEOIEkqpAOKE\nBEoVZ0/MBQC8/clRhSuJDFdMoIQZKICUXk6HXRBpRVGODYXZVuw53IhqlxuFOTalSxoQOyGKu8Fm\nwMU7gAa/YMOEAAAZNUlEQVTrghhApDVzJ4W7oX9+ekzhSgbHTojiKlbDb329TizCgwFEWjS2MAOZ\n6Wn4ZF8dvr2oFJnpJqVL6hc7IYqLSK//icXrDITngigVCYKAeZPyEJJkvPZRhdLlDIghRDEXi+nX\nidhBlV0QadmUkkxkZ5iw7csaVNW7lS6nXwwhiplYdD+xDJ+BuiAGEGmdTidgyYwRkAGs33QQkqTO\n64YYQjRssVp6J5adDwOICCgdkYEJoxz4uroV//qsSuly+sSJCRS1WC27E034MEiIInPhnJGoqndj\nw5bDmDDKgdEq+9lhJ0RDFsvOJx7nfdgFEZ1kSdPjknmjEJJkPP7yHtS3dChd0ikEOUELDLW6OxPx\nNhRHsZrtNlwDBQkDiNQmw5YW8WNdrvBeQMfq2uH1xXYl7C8OufDOzuPIc5px7/dmI91qjOnrDyYn\nx97n7RyOo0EN90LTeM9yiwQDiFLdzHE5aPMEsONAHdY9txO3LZ+Owmyr0mUxhGhg/QXIQOETz9CJ\ntgsiImDx9ALoRQHbymrx8HM78aNvTcXU0ixFa+JwHPVrKAGUiG6Hw3CUjNQyHNfb/somvL3jGGRZ\nxjcXlODyc0pg0Md3igCH42hI+gqVoYRPpKEUi4BgABENzeSSTGRYjXjj40q8+XElPi934QeXTlJk\n5hw7ITrD6QESSfgMtxMaLCz6u58BRGqnxk6oW2cghA93n8DurxsgCMCyuaNw2YJiWEyGmL9Xf50Q\nQ4hOMVgARRo+VTWNp3w9smDwcef+QoMBRMlMzSHU7WhtO/756TG0evywmPS4dH4xls4uQppBjNl7\nMIRoUEMJoNMfe3roDKavUIpVCDGASE2SIYQAIBCU8Hm5CzsO1MHnDyHDZsQV55Rg0fQR0IvDP1/E\nEKIBDRRA/YVPX8HTVH/8jNsyc4v6fM/Tg6iv8GAAUbJLlhDq5vMH8emBeuwqdyEQlJDjMOFbi0ox\nb3IedIIQ9esyhKhfww2gvoKnP6cH0mBB1FeocBiOkkmyhVA3d0cAn+yvw+6vGyBJMopyrPjO4jGY\nPjYLQhRhxNlx1KeBJhT0FUADhU+bq7LP10nPKTnlOf11RpFgABElhs1swAWzi3D2hBxsK6vFvsom\n/PqVvRhTmI5/WzwGE4udMXkfdkIpLpIu6PQA6h0+/QVPX3qHUe8g6t0N9Q6S00OFAUTJKFk7odM1\ntHbgo701OHS8FQAwZXQm/u28UpTkR/azx06IzhDLABoojLrDp81V2fP5cDui3hhARPGXnWHGtxeV\noqbRgy17arCvogn7Kpowe0IOvrO4FAVZ0S0BxBAiAEMLoEjDp/djendB0eBEBCJ1KMiy4uqlY3G0\nth1b9p7AroMu7D7UgMvOKcGlC4qHPJOOIZSiYrHMzqlhdOSM+9NzSk95bHpOScSBFEm4MICIlFOc\nb8f38sbj0PFWvPf5cby+tQK7DtbjhksnRTxEB3A/oZQ0nGG47uA5+fFInwE02H19Gcp0bAYQkfIE\nQcD4kQ7ccMkkTB+TheMuD9Y9uxNvf3I04tdgCNGgBgogIqI0o4hlc0fh6m+MhdVswMsfHMaHu6sj\nem5UISRJEh544AFcffXVWLlyJY4ejTz1SFnRdEG99XcOqM1V2fNffyKdSde7y2EXRJQ8ivPtuHrp\nWJjTRKzfdBB7vm4Y9DlRhdC7774Lv9+Pl156CatWrcIvfvGLaF6GkkBfkxHCXx/p9fnp9536NRGl\njky7Cf+2eAx0OgHPbTo46OOjCqFdu3Zh0aJFAIAZM2agrKwsmpehBBtuF9SXgTqjk5/HbtiOXRCR\n+o3ItmJElhXN7Z0IhqQBHxvV7Di32w2bzdbztSiKCAaD0Os52U6t4rXpXPeMt75uP/l56Rm3deu+\nULU7XAYaimMAkdY5nRbo9SLcAQlGb0DpcoYl3ZYG1LuhTzMix2nu93FRpYbNZoPH4+n5WpIkBlCS\n6W99uIEMtCzPUIfgYnWhKpGWNDd7AQBNTR7VrZgwFI1tPnx1tAk2sx6dHZ1wBYP9rpgQ1XDcrFmz\nsGXLFgDA7t27MX78+OirpbgbbhcUScCc2vn0/ry038cNhF0QUXIKhSS8tf0ogiEZ1y2bOOieRFG1\nLxdeeCG2bduGFStWQJZlPPLII1EVS/EX6TbdvR97+vmg3heZRrI8T6T3DTQUR0TJp83jx8ZtFaht\n8mLBlHzMmZg76HOiCiGdToef//zn0TyVEiiSDijaLik9p3TACQe9O6DuAOr+ONhQHLsgouRz5EQb\n3txeCZ8/hPlT8nDdxRMieh5P5GhUf+HSXxcUjdOD6PSht/BtJad87A4gdkFE2tDRGcTWL2vwxaEG\n6EUB1y2bgPNmjIh4zyGGkAZFGkADbdfdn9OH5PoKnu7Hnf55fwHUG7sgouQgSTL2HmnER3tPoKMz\nhLxMM354xZQhrRsHMIQ0J14dUO/w6R0wpwZSCU7XXwD1xqAhSi7VDR68u6sKdU0dSDOIWP6NMbhw\nzsghr6ANMIRSVqSdT2ZuUc+qCX1NTOhvMkJfG9j1tXkdrwsiSh7ujgA+3H0C+yqbAAALpuThqiVj\n4bRHvnHf6RhCGhLNMNxAz+vLULoggAFEpAWhkIRd5S58vK8W/oCEUXk2XHvheIwrcgz7tRlCGhHL\nYbiRBVmnTNPu3Q31Nljw9H69bpEEEBGpx3GXG5s+q0Jjqw9Wkx4rlo7D4ukjoNNFNvFgMAwhDRhK\nAEU7Jbt3sPQOpIGmW/cVPqd/3hd2QUTK6/SH8OGeE9j9dQMEAEtmFuI7i0thMxti+j4MoSQ33ADq\n7/mnd0O9DXadz+mTDwYKIA7DEanP4ROt2PRpFdwdAYzIsuD6SyZhbFFGXN6LIZTE4t0BdYfJQCtq\n9zXbrdvpgcJ9gojUTZJkbCurwfZ9ddCLAr61cDQumV8Mgz5++58yhJJULAIo0mAaKGhO11eQDNb9\n9Pc8Ikocb2cQb35cicradmRnmHDLt89CcX7fi47GEkMoCSXiHNBQ9BcgkVyMOtDziSgx2r1+/O29\nQ2hx+zFtTBZuvHwyrKbYnvvpD0MoycQqgIYTTtFMLOhvBhwDiEhZ7o4AXnr/a7S4/bhk/ij823lj\noItwyZ1YYAglESU7oGhntA00/ZoBRKQsnz+IlzZ/jab2TlwyfxSuOm9MxGu+xQpDKEnE8jqgSAIq\nkoAY6DEMHyJ1k2UZmz4NX/9zwZwiRQIIYAglhaEGUDyH2gZ7DMOHKDmUVTThYFULxhVlYMXScYoE\nEMAQUr1YB9BA9w/nItLBVj1gABGph6cjgPd2HYfJKOLGyyfHbPWDaDCEVGyoHU20HdBwuh+GD1Hy\n2b6/Dv6ghGsvHI/sDLOitTCEktBwJiKUFKT3PJbhQ5R6Wt2d2P11A3IcJpw3Y4TS5TCE1CqeM+Ei\nDQgGEJH27DzogiTJuHLh6Kj2/4k1hpAKJWJr7sFwyjWR9vj8QXx5pBFOWxrmTspTuhwADCHVSeRM\nuP4M5WLT/h5PROqz53Aj/EEJl88uVEUXBDCEklqiLkhlABElv5Ak4/NyF9IMOiyZWah0OT3UEYUE\nQNlhOAYQkbZ9dawZ7d4AFk4bkbB14SLBEFIJJYfhGEBE2ibLMj77qh6CAFx49kilyzkFh+OSkJIB\nxPAhSj7H6t2ob+7AnAk5yHUoe13Q6dgJqYBSw3AMICLtk2UZ28tqAQDL5o5SuJozsRNKQdEsv8MA\nIkpOR2racKzejWljsjCmMD5bdA8HQ0hhiT4XxPM/RKkjJMn4cPcJCAJw1ZIxSpfTJw7HpRAGEFFq\n+fRAHRpafVg8fQSKcmxKl9MndkIKSsTW2wC3XiBKRU1tPnxcVosMqxHLVdoFAeyEVGmgCQlDDQYG\nEFHqCQQlbNxWiZAk49oLx8OiouuCTsdOSKMGCxEGEJE2ybKMd3ZWob6lA4unj8CciblKlzQghpBC\n4jUUN5zwieT5RKRuew43oqyiCSX5dlx74TilyxkUQygJRRsUDCAibatp9OC9XcdhNenxo29PhUEv\nKl3SoIZ1Tuidd97BqlWrYlULxdFgw28MIKLk5vUF8NrWCkiSjB9eOUXxHVMjFXUntG7dOmzduhWT\nJk2KZT0UY+x+iLRPkmS88XEl2r0BfHtxKaaOzlK6pIhF3QnNmjULa9eujWEp1G2w4IjV6zCAiLRh\n65c1OFrnxoyx2bh0QbHS5QzJoJ3Qyy+/jGefffaU2x555BF885vfxI4dO+JWGEUvkhBjABGpj9Np\ngV4vwh2QYPQGInrO/opGfLK/DvlZFqy+fi5sZvVOx+7LoCG0fPlyLF++PBG1UC+lhelDXsA00g6K\nAUSkTs3NXgBAU5MHXl9w0Mc3tfvw8nvlMOh1uPnKqehw+9Dh9sW7zKjk5Nj7vJ2z41SsO1QGCyOG\nD1HqCQQlvPZRBToDEm68bDJG5qpzWZ7BMISSQCzOETGAiLTl/c+Po6HVh2/MKsSCqflKlxO1YYXQ\nvHnzMG/evFjVQnHA8CHSnvKqFuw53IiRuTasWDpW6XKGhWvHKSQR4cAAItIery+Af356DAa9Dj+8\nYkpSXJA6EA7HaRDDh0i7Pth9Aj5/CCvOH4cR2Valyxk2dkIKinVYcOUDIm077nKjrKIJI3NtOH92\nodLlxARDSGGxCA2GD1Fq2Lq3BgCwctkEiDpt/PrmcJwKdAfIUFbWZugQpZbqBg+O1bsxZXQmxhZm\nKF1OzDCEVITBQkT92XmwHgBwWZItyzMYbfRzREQa5g+EcLi6FXmZZowf6VC6nJhiCBERqdzhE20I\nhmScPTEPgiAoXU5MMYSIiFSuqt4NAJgxNlvhSmKPIUREpHI1TR7oRQGj8pJzfbiBMISIiFRMlmW4\nWnwozLFBL2rvV7b2viMiIg3x+oKQJBnZGSalS4kLhhARkYq5feHN7RzWNIUriQ+GEBGRigWCEgDA\nbNLmZZ0MISIiFQtJMgBA1GlranY3hhARkZrJShcQXwwhIiIVM+jDv6b9gZDClcQHQ4iISMW6Q8jn\nZwgREVGCWbsmJLR6/ApXEh8MISIiFTOn6aEXBTS2+ZQuJS4YQkREKiYIAuwWI5oYQkREpIR0iwHt\n3oAmJycwhIiIVC7dYgQATQ7JMYSIiFQuMz28bly1y6NwJbHHECIiUrlcpxnAyX2FtIQhRESkcrkO\nhhARESnEajbAatJrMoS0uSxrhCpr2s64raQgXYFKiIgGluMwo7K2HV5fABaTQelyYiblOqHKmrae\n//q7n4hIbbQ6JJcyITRQ8PT1WCIiNcnR6OQEzYfQUMLn9OcREakFO6EkxCAhIq3ITDdB1AkMoWTB\nACIiLRF1ArLSTahu8ECWtbPTnSZDiAFERFqUbjUiEJTg8QWVLiVmopqi3d7ejrvuugtutxuBQAD3\n3HMPZs6cGevaosIAIiKtslvCU7Ob2zthM2tjmnZUIfTMM89g/vz5uP7663HkyBGsWrUKr776aqxr\nIyKiXtIMIgCgozPFO6Hrr78eRmN4VddQKIS0tLSYFhUtdkFEpGWCIACAps4JDRpCL7/8Mp599tlT\nbnvkkUcwbdo0uFwu3HXXXVizZk3cCiQiShVOpwV6vQh3QILRGzjj/rS08K/sDIcFOTn2RJcXF4OG\n0PLly7F8+fIzbj948CB+8pOf4O6778bcuXPjUpySuHwPESVac7MXANDU5IG3j8kHTa0dAAA5EITL\n1Z7Q2oarv9CMajju66+/xm233YbHH38cEydOHFZhREQUGXdXd+SwqeMUSCxEFUL//d//Db/fj4cf\nfhgAYLPZ8OSTT8a0sKGK5fkgdkFEpDayLKOu2QuHzQhzmnbWno7qO1E6cPpSUpAekyBiABGRGrV7\nA/D4gpg9PkfpUmJKkxerRosBRERqdaTrj+yxRRkKVxJbDCEioiSwr6IJAoCzJ+YqXUpMaSqEhtPJ\nsAsiIrVqbu9EdYMHE4udyEw3KV1OTGkqhIChh0lJQToDiIhUbV9lEwDg3LPyFa4k9jQXQkBkQcTw\nIaJkIMsy9lU0Ic2gwyyNTUoAopwdlwx6B0z3rDmGDhElm+MuD1o9fpw7NR8mo/Z+ZWvvO+oDw4eI\nklVZRXgo7pyp2huKAzQ6HEdEpAWBoISDx5qRaU/DhGKn0uXEBUOIiEilDh1vgT8oYcHUfOi6VtDW\nGoYQEZFKdc+K0+pQHMAQIiJSJW9nEJW17RhdYEdBllXpcuKGIUREpEKHjrdAloGzJ+YpXUpcMYSI\niFTo0PFWAMCcCdq7Nqg3hhARkcoEQxKq6twoyLIg22FWupy4YggREalMtcuDQEjC5OJMpUuJO4YQ\nEZHKHHe5AQDjRzkUriT+GEJERCpT0+gFABTn2xWuJP4YQkREKlPb5IXZKCInQ1vbNvSFIUREpCKS\nLKPF3YncTAsEja6S0BtDiIhIRVrdfgRDMnI0PiuuG0OIiEhF2jx+AIDDZlS4ksRgCBERqYjHFwAA\nWE0GhStJDIYQEZGKeH1BAIDFlBLbvTGEiIjU5GQnxBAiIqIEO9kJcTiOiIgSzB+UAABp+tT49Zwa\n3yURUZIISeEQEsXU+PWcGt8lEVGSCIVkAICo0/6FqgBDiIhIVUJSVwiJDCEiIkowqSuE9CkyHCfI\nsiwrXQQREaWm1IhaIiJSJYYQEREphiFERESKYQgREZFiGEJERKQYhhARESlGE8u0SpKEtWvX4uDB\ngzAajVi3bh2Ki4uVLishAoEA1qxZg+rqavj9ftx8880YO3Ys7rnnHgiCgHHjxuFnP/sZdLrU+Xuj\nsbER3/nOd/D0009Dr9en5LH4wx/+gPfffx+BQADf/e53MXfu3JQ7DoFAAPfccw+qq6uh0+nw0EMP\npey/BzXTxNF/99134ff78dJLL2HVqlX4xS9+oXRJCbNx40Y4HA688MIL+NOf/oSHHnoI//mf/4nb\nb78dL7zwAmRZxnvvvad0mQkTCATwwAMPwGQyAUBKHosdO3bgiy++wN/+9jesX78etbW1KXkcPvzw\nQwSDQbz44ou45ZZb8Pjjj6fkcVA7TYTQrl27sGjRIgDAjBkzUFZWpnBFiXPxxRfjtttuAwDIsgxR\nFLFv3z7MnTsXALB48WJ8/PHHSpaYUI8++ihWrFiB3NxcAEjJY7F161aMHz8et9xyC2666SYsWbIk\nJY/D6NGjEQqFIEkS3G439Hp9Sh4HtdNECLndbthstp6vRVFEMBhUsKLEsVqtsNlscLvduPXWW3H7\n7bdDlmUIgtBzf3t7u8JVJsaGDRuQmZnZ8wcJgJQ8Fs3NzSgrK8MTTzyBBx98EHfeeWdKHgeLxYLq\n6mpccskluP/++7Fy5cqUPA5qp4lzQjabDR6Pp+drSZKg12viW4tITU0NbrnlFlxzzTW4/PLL8dhj\nj/Xc5/F4kJ6ermB1ifPKK69AEARs374dBw4cwOrVq9HU1NRzf6ocC4fDgdLSUhiNRpSWliItLQ21\ntbU996fKcfjLX/6ChQsXYtWqVaipqcH3v/99BAKBnvtT5TionSY6oVmzZmHLli0AgN27d2P8+PEK\nV5Q4DQ0NuOGGG3DXXXfhqquuAgBMnjwZO3bsAABs2bIFc+bMUbLEhHn++efx17/+FevXr8ekSZPw\n6KOPYvHixSl3LGbPno2PPvoIsiyjrq4OHR0dWLBgQcodh/T0dNjtdgBARkYGgsFgyv5sqJkmFjDt\nnh1XXl4OWZbxyCOPYMyYMUqXlRDr1q3D22+/jdLS0p7bfvrTn2LdunUIBAIoLS3FunXrIIqiglUm\n3sqVK7F27VrodDrcf//9KXcs/uu//gs7duyALMu44447UFRUlHLHwePxYM2aNXC5XAgEArjuuusw\nderUlDsOaqeJECIiouSkieE4IiJKTgwhIiJSDEOIiIgUwxAiIiLFMISIiEgxDCHShPLyckyYMAGb\nNm1SuhQiGgKGEGnChg0bsGzZMrz44otKl0JEQ5A6a9uQZgWDQWzcuBHPP/88VqxYgWPHjmHUqFHY\nsWNHz8WIM2bMwOHDh7F+/XocPXoUa9euRUtLC0wmE+6//35MnjxZ6W+DKCWxE6Kk98EHH2DEiBEY\nPXo0LrjgArz44osIBAK4++678dhjj+G11147ZS3B1atX46677sKrr76Khx56CHfccYeC1ROlNoYQ\nJb0NGzbgsssuAwB885vfxKuvvooDBw4gKysLEydOBICedfU8Hg/Kyspw77334sorr8SqVavg9XrR\n3NysWP1EqYzDcZTUGhsbsWXLFpSVleG5556DLMtoa2vDli1bIEnSGY+XJAlGoxGvv/56z221tbVw\nOByJLJuIurAToqS2ceNGzJ8/H1u2bMH777+PzZs346abbsLWrVvR1taGgwcPAgDeeOMNAIDdbkdJ\nSUlPCG3btg3XXnutYvUTpTouYEpJ7fLLL8cdd9yBpUuX9tzW2NiIpUuX4s9//jPWrVsHnU6H0aNH\no62tDU899RQOHz7cMzHBYDBg7dq1mDZtmoLfBVHqYgiRJkmShF/+8pf48Y9/DIvFgmeeeQZ1dXW4\n5557lC6NiHrhOSHSJJ1OB4fDgauuugoGgwGFhYV4+OGHlS6LiE7DToiIiBTDiQlERKQYhhARESmG\nIURERIphCBERkWIYQkREpBiGEBERKeb/AUZk7/J5Tht2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf0b2735b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's look at how transformed age looks like compared to the original variable\n",
    "\n",
    "sns.jointplot(X_train.Age, X_train_scaled[:,1], kind='kde')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0xf0b285f2b0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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24dS5Bjz9VjGKphdi8XUjYlildHq80uKGDRvws5/9DLfccgvefvttJCUlwWg0wmazBR9j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\nWRBZqkpgzshHbWUZ0jJzu9w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      "text/plain": [
       "<matplotlib.figure.Figure at 0xf0b285f518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's look at how transformed Fare looks like compared to the original variable\n",
    "\n",
    "sns.jointplot(X_train.Fare, X_train_scaled[:,2], kind='kde', xlim=(0,200), ylim=(-1,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "As we can see, The robust scaler does a better job at preserving the spread of the variable after transformation for skewed variables like Fare (compare with the standard scaler or the MinMaxScaler)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### Conclusions\n",
    "\n",
    "Typically, at the time of setting the features within a similar scale for Machine Learning, standarisation is the normalisation method of choice. And this is done without taking into account the distribution of the variable.\n",
    "\n",
    "However, we have seen in the past 3 lectures that the different normalisation methods have different advantages and disadvantages, and when the distribution of the variable is skewed, perhaps it is better to scale using the mean and quantiles method, which is more robust to the presence of outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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