13.1_Normalisation-Standarisation.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalisation - Standarisation\n",
    "\n",
    "We saw in previous lectures in section 3 of this course, 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 setting the magnitude of the variables to the same range of values.\n",
    "\n",
    "\n",
    "#### Normalisation\n",
    "\n",
    "One method utilised to bring all the variables to a more homogeneous scale is normalisation. Normalisation is synonym of centering the distribution. This means subtracting the mean of the variable to each observation. This procedure will \"center\" the new distribution at zero (the new mean of the variable will now be zero).\n",
    "\n",
    "#### Standarisation\n",
    "\n",
    "Standarisation is also used to bring all the variables to a similar scale. Standarisation means centering the variable at zero, and standarising the variance at 1. The procedure involves subtracting the mean of each observation and then dividing by the standard deviation:\n",
    "\n",
    "z = (x - x_mean) /  std\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",
    "Let's demonstrate the procedure of standarisation on the titanic dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\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": {
      "text/html": [
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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",
    "\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": [
    "The different variables present different value ranges, therefore different magnitudes. Not only the minimum and maximum values are different, but they also spread over ranges of different widths."
   ]
  },
  {
   "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 look 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 first 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": [
    "### Standarisation\n",
    "\n",
    "StandardScaler from scikit-learn removes the mean and scales the data to unit variance. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# standarisation: we use the StandardScaler from sklearn\n",
    "\n",
    "scaler = StandardScaler() # create an object\n",
    "X_train_scaled = scaler.fit_transform(X_train) # fit the scaler to the train set, and then transform it\n",
    "X_test_scaled = scaler.transform(X_test) # transform the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "means (Pclass, Age and Fare):  [  4.98976640e-17   1.16903099e-16   5.41746067e-17]\n",
      "std (Pclass, Age and Fare):  [ 1.  1.  1.]\n"
     ]
    }
   ],
   "source": [
    "#let's have a look at the scaled training dataset: mean and standard deviation\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 expected, the mean of each variable is now around zero and the standard deviation is set to 1. Thus, all the variable  values lie within the same range."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Min values (Pclass, Age and Fare):  [-1.5325562  -2.23351124 -0.67314402]\n",
      "Max values (Pclass, Age and Fare):  [ 0.84844757  3.86209655  9.95192344]\n"
     ]
    }
   ],
   "source": [
    "# let's look at the transformed min and max 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": [
    "However, the minimum and maximum values vary according to how spread the variable was to begin with and is highly influenced by the presence of outliers. We observed in previous lectures that the variable Fare has a few extreme outliers, that is, people that paid extraordinarily high Fares. Those observations would drive the value of the maximum value far away from the unit variance (a value of 9.9 in this case)."
   ]
  },
  {
   "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([-2.23351124, -1.92873085, -1.62395046, -1.31917007, -1.01438968,\n",
       "        -0.70960929, -0.4048289 , -0.10004851,  0.20473188,  0.50951227,\n",
       "         0.81429266,  1.11907305,  1.42385344,  1.72863383,  2.03341422,\n",
       "         2.33819461,  2.642975  ,  2.94775539,  3.25253577,  3.55731616,\n",
       "         3.86209655]),\n",
       " <a list of 20 Patch objects>)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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GUVWHgfXdfbfbkjy/qlbU/ZMkrwUOVtWOJBeMYp/NBn1VveJ4y5O8EXgtcGEt4zGmi53H\nCrboazJ08iR5EvMhf1NVfW7S9fRVVf+e5GvM3z9ZUUEPvAS4OMlrgKcCz0zy11X1+8PucFV23XRf\nivIu4OKq+umk61mlfE3GMpEkwPXAfVX1oUnXM6wkU0dG0CX5ReCVwP2TrerEVdXVVXVmVU0z/3vx\nj31CHlZp0AMfBZ4BbE+yM8knJl3QMJJcmmQv8BvAF5J8adI1LVV3M/zIazLuA25Zia/JSLIN+Abw\n3CR7k1wx6ZqG8BLgDcDLu9+Hnd3V5EpzOvC1JLuYv5DYXlW9hya2wCdjJalxq/WKXpJWDYNekhpn\n0EtS4wx6SWqcQS9JjTPoJalxBr0kNc6gl6TG/Q9XhviBZx6RkwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb47c31a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's look at the distribution of the transformed variable Age\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([-0.67314402, -0.14189064,  0.38936273,  0.9206161 ,  1.45186948,\n",
       "         1.98312285,  2.51437622,  3.04562959,  3.57688297,  4.10813634,\n",
       "         4.63938971,  5.17064309,  5.70189646,  6.23314983,  6.76440321,\n",
       "         7.29565658,  7.82690995,  8.35816333,  8.8894167 ,  9.42067007,\n",
       "         9.95192344]),\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 0xb47d79bbe0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's look at the distribution of the transformed variable Fare\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. In fact, we can see that the standarisation of Fare, shrinks the majority of the observations towards the lowest values."
   ]
  },
  {
   "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 0xb47db0f748>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KIA7FUTSyHUb4/CE0qmTlBIYQ0RDYAZHS9KyWcLzBLXMlscEQIhpEPAOIXRBF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\nNv8f3tvjH3hEHB8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb47db0f710>"
      ]
     },
     "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": "markdown",
   "metadata": {},
   "source": [
    "The transformed variable has a good correlation with the original one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<seaborn.axisgrid.JointGrid at 0xb47dd46278>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IFMy7Umy9jS0kIiKSka+FxEAiIiI5eVeKNVsZSEREJKMEQxQAoKLWKnMlwcdA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\nDCQiIlIEBhIRESkCA4mIiBTh/wM8mHiybPqttwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb47dd461d0>"
      ]
     },
     "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": [
    "The values are concentrated on the lower left side of the plot, because Fare is highly skewed: the outliers have an influence when computing the empirical mean and standard deviation which shrink the range of the feature values as shown in the left figure above.\n",
    "\n",
    "Other scaling methods account for the presence of outliers. I will discuss those in the next lectures."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
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