10.05-Robust-Scaling.ipynb

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    "## Feature Scaling\n",
    "\n",
    "We discussed previously that the scale of the features is an important consideration when building machine learning models. Briefly:\n",
    "\n",
    "\n",
    "### Feature magnitude matters because:\n",
    "\n",
    "- The regression coefficients of linear models are directly influenced by the scale of the variable.\n",
    "- Variables with bigger magnitude / larger value range dominate over those with smaller magnitude / value range\n",
    "- Gradient descent converges faster when features are on similar scales\n",
    "- Feature scaling helps decrease the time to find support vectors for SVMs\n",
    "- Euclidean distances are sensitive to feature magnitude.\n",
    "- Some algorithms, like PCA require the features to be centered at 0.\n",
    "\n",
    "\n",
    "### The machine learning models affected by the feature scale are:\n",
    "\n",
    "- Linear and Logistic Regression\n",
    "- Neural Networks\n",
    "- Support Vector Machines\n",
    "- KNN\n",
    "- K-means clustering\n",
    "- Linear Discriminant Analysis (LDA)\n",
    "- Principal Component Analysis (PCA)\n",
    "\n",
    "\n",
    "### Feature Scaling\n",
    "\n",
    "**Feature scaling** refers to the methods or techniques used to normalize the range of independent variables in our data, or in other words, the methods to set the feature value range within a similar scale. Feature scaling is generally the last step in the data preprocessing pipeline, performed **just before training the machine learning algorithms**.\n",
    "\n",
    "There are several Feature Scaling techniques, which we will discuss throughout this section:\n",
    "\n",
    "- Standardisation\n",
    "- Mean normalisation\n",
    "- Scaling to minimum and maximum values - MinMaxScaling\n",
    "- Scaling to maximum value - MaxAbsScaling\n",
    "- Scaling to quantiles and median - RobustScaling\n",
    "- Normalization to vector unit length\n",
    "\n",
    "In this notebook, we will discuss **Scaling to quantiles and median**.\n",
    "\n",
    "=================================================================\n",
    "\n",
    "## Scaling to quantiles and median - RobustScaling\n",
    "\n",
    "In this procedure the median is removed from the observations and then they are scaled to the inter-quantile range (IQR). The IQR is the range between the 1st quartile (25th quantile) and the 3rd quartile (75th quantile).\n",
    "\n",
    "X_scaled = X - X_median / ( X.quantile(0.75) - X.quantile(0.25) )\n",
    "\n",
    "This robust scaling method produces more robust estimates for the center and range of the variable, and is recommended if the data shows outliers.\n",
    "\n",
    "In a nutshell, RobustScaling:\n",
    "\n",
    "- centers the median at 0\n",
    "- variance varies across variables\n",
    "- may not preserve the shape of the original distribution\n",
    "- the minimum and maximum values vary.\n",
    "- robust outliers\n",
    "\n",
    "\n",
    "## In this demo\n",
    "\n",
    "We will perform robust scaling using the Boston House Prices data set that comes with Scikit-learn"
   ]
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  {
   "cell_type": "code",
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   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "# dataset for the demo\n",
    "from sklearn.datasets import load_boston\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "# the scaler - for robust scaling\n",
    "from sklearn.preprocessing import RobustScaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
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       "      <td>24.0</td>\n",
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       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
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       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  MEDV  \n",
       "0     15.3  396.90   4.98  24.0  \n",
       "1     17.8  396.90   9.14  21.6  \n",
       "2     17.8  392.83   4.03  34.7  \n",
       "3     18.7  394.63   2.94  33.4  \n",
       "4     18.7  396.90   5.33  36.2  "
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   "source": [
    "# load the the Boston House price data\n",
    "\n",
    "# this is how we load the boston dataset from sklearn\n",
    "boston_dataset = load_boston()\n",
    "\n",
    "# create a dataframe with the independent variables\n",
    "data = pd.DataFrame(boston_dataset.data,\n",
    "                      columns=boston_dataset.feature_names)\n",
    "\n",
    "# add target\n",
    "data['MEDV'] = boston_dataset.target\n",
    "\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".. _boston_dataset:\n",
      "\n",
      "Boston house prices dataset\n",
      "---------------------------\n",
      "\n",
      "**Data Set Characteristics:**  \n",
      "\n",
      "    :Number of Instances: 506 \n",
      "\n",
      "    :Number of Attributes: 13 numeric/categorical predictive. Median Value (attribute 14) is usually the target.\n",
      "\n",
      "    :Attribute Information (in order):\n",
      "        - CRIM     per capita crime rate by town\n",
      "        - ZN       proportion of residential land zoned for lots over 25,000 sq.ft.\n",
      "        - INDUS    proportion of non-retail business acres per town\n",
      "        - CHAS     Charles River dummy variable (= 1 if tract bounds river; 0 otherwise)\n",
      "        - NOX      nitric oxides concentration (parts per 10 million)\n",
      "        - RM       average number of rooms per dwelling\n",
      "        - AGE      proportion of owner-occupied units built prior to 1940\n",
      "        - DIS      weighted distances to five Boston employment centres\n",
      "        - RAD      index of accessibility to radial highways\n",
      "        - TAX      full-value property-tax rate per $10,000\n",
      "        - PTRATIO  pupil-teacher ratio by town\n",
      "        - B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town\n",
      "        - LSTAT    % lower status of the population\n",
      "        - MEDV     Median value of owner-occupied homes in $1000's\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "\n",
      "    :Creator: Harrison, D. and Rubinfeld, D.L.\n",
      "\n",
      "This is a copy of UCI ML housing dataset.\n",
      "https://archive.ics.uci.edu/ml/machine-learning-databases/housing/\n",
      "\n",
      "\n",
      "This dataset was taken from the StatLib library which is maintained at Carnegie Mellon University.\n",
      "\n",
      "The Boston house-price data of Harrison, D. and Rubinfeld, D.L. 'Hedonic\n",
      "prices and the demand for clean air', J. Environ. Economics & Management,\n",
      "vol.5, 81-102, 1978.   Used in Belsley, Kuh & Welsch, 'Regression diagnostics\n",
      "...', Wiley, 1980.   N.B. Various transformations are used in the table on\n",
      "pages 244-261 of the latter.\n",
      "\n",
      "The Boston house-price data has been used in many machine learning papers that address regression\n",
      "problems.   \n",
      "     \n",
      ".. topic:: References\n",
      "\n",
      "   - Belsley, Kuh & Welsch, 'Regression diagnostics: Identifying Influential Data and Sources of Collinearity', Wiley, 1980. 244-261.\n",
      "   - Quinlan,R. (1993). Combining Instance-Based and Model-Based Learning. In Proceedings on the Tenth International Conference of Machine Learning, 236-243, University of Massachusetts, Amherst. Morgan Kaufmann.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Information about the boston house prince dataset\n",
    "# you will find details about the different variables\n",
    "\n",
    "# the aim is to predict the \"Median value of the houses\"\n",
    "# MEDV column in this dataset\n",
    "\n",
    "# and there are variables with characteristics about\n",
    "# the homes and the neighborhoods\n",
    "\n",
    "# print the dataset description\n",
    "print(boston_dataset.DESCR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
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       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
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       "  </thead>\n",
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       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.613524</td>\n",
       "      <td>11.363636</td>\n",
       "      <td>11.136779</td>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.554695</td>\n",
       "      <td>6.284634</td>\n",
       "      <td>68.574901</td>\n",
       "      <td>3.795043</td>\n",
       "      <td>9.549407</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>356.674032</td>\n",
       "      <td>12.653063</td>\n",
       "      <td>22.532806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.601545</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>91.294864</td>\n",
       "      <td>7.141062</td>\n",
       "      <td>9.197104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.006320</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.460000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.385000</td>\n",
       "      <td>3.561000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>1.129600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>1.730000</td>\n",
       "      <td>5.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.082045</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.190000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.449000</td>\n",
       "      <td>5.885500</td>\n",
       "      <td>45.025000</td>\n",
       "      <td>2.100175</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>375.377500</td>\n",
       "      <td>6.950000</td>\n",
       "      <td>17.025000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.256510</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.690000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.208500</td>\n",
       "      <td>77.500000</td>\n",
       "      <td>3.207450</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>330.000000</td>\n",
       "      <td>19.050000</td>\n",
       "      <td>391.440000</td>\n",
       "      <td>11.360000</td>\n",
       "      <td>21.200000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.677083</td>\n",
       "      <td>12.500000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.624000</td>\n",
       "      <td>6.623500</td>\n",
       "      <td>94.075000</td>\n",
       "      <td>5.188425</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>396.225000</td>\n",
       "      <td>16.955000</td>\n",
       "      <td>25.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>88.976200</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>27.740000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.871000</td>\n",
       "      <td>8.780000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>12.126500</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>396.900000</td>\n",
       "      <td>37.970000</td>\n",
       "      <td>50.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     3.613524   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.601545   23.322453    6.860353    0.253994    0.115878    0.702617   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.082045    0.000000    5.190000    0.000000    0.449000    5.885500   \n",
       "50%      0.256510    0.000000    9.690000    0.000000    0.538000    6.208500   \n",
       "75%      3.677083   12.500000   18.100000    0.000000    0.624000    6.623500   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean    68.574901    3.795043    9.549407  408.237154   18.455534  356.674032   \n",
       "std     28.148861    2.105710    8.707259  168.537116    2.164946   91.294864   \n",
       "min      2.900000    1.129600    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.025000    2.100175    4.000000  279.000000   17.400000  375.377500   \n",
       "50%     77.500000    3.207450    5.000000  330.000000   19.050000  391.440000   \n",
       "75%     94.075000    5.188425   24.000000  666.000000   20.200000  396.225000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT        MEDV  \n",
       "count  506.000000  506.000000  \n",
       "mean    12.653063   22.532806  \n",
       "std      7.141062    9.197104  \n",
       "min      1.730000    5.000000  \n",
       "25%      6.950000   17.025000  \n",
       "50%     11.360000   21.200000  \n",
       "75%     16.955000   25.000000  \n",
       "max     37.970000   50.000000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the main statistical parameters of the variables\n",
    "# to get an idea of the feature magnitudes\n",
    "\n",
    "data.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The different variables present different value ranges, mean, max, min, standard deviations, etc. In other words, they show different magnitudes or scales. Note for this demo, how **the 75th and 25th quantiles are quite different in the different variables**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When performing robust  absolute scaling of the data set, we need to first identify the median and quantiles of the variables. These parameters need to be learned from the train set, stored, and then used to scale test and future data. Thus, we will first divide the data set into train and test, as we have done throughout the course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((354, 13), (152, 13))"
      ]
     },
     "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.drop('MEDV', axis=1),\n",
    "                                                    data['MEDV'],\n",
    "                                                    test_size=0.3,\n",
    "                                                    random_state=0)\n",
    "\n",
    "X_train.shape, X_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RobustScaling\n",
    "\n",
    "The MaxAbsScaler from scikit-learn re-scales features to their maximum value, so that the new maximum value is 1. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the scaler\n",
    "scaler = RobustScaler()\n",
    "\n",
    "# fit the scaler to the train set, it will learn the parameters\n",
    "scaler.fit(X_train)\n",
    "\n",
    "# transform train and test sets\n",
    "X_train_scaled = scaler.transform(X_train)\n",
    "X_test_scaled = scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.62660e-01, 0.00000e+00, 8.56000e+00, 0.00000e+00, 5.38000e-01,\n",
       "       6.21550e+00, 7.94500e+01, 3.21570e+00, 5.00000e+00, 3.11000e+02,\n",
       "       1.91000e+01, 3.91605e+02, 1.11600e+01])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the scaler stores the median values of the features as learned from train set\n",
    "scaler.center_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.030275e+00, 2.000000e+01, 1.315000e+01, 1.000000e+00,\n",
       "       1.792500e-01, 7.520000e-01, 4.857500e+01, 2.971650e+00,\n",
       "       2.000000e+01, 3.900000e+02, 2.800000e+00, 1.963250e+01,\n",
       "       9.982500e+00])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the scaler stores the IQR values of the features as learned from train set\n",
    "\n",
    "scaler.scale_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# let's transform the returned NumPy arrays to dataframes for the rest of\n",
    "# the demo\n",
    "\n",
    "X_train_scaled = pd.DataFrame(X_train_scaled, columns=X_train.columns)\n",
    "X_test_scaled = pd.DataFrame(X_test_scaled, columns=X_test.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CRIM         0.3\n",
       "ZN           0.0\n",
       "INDUS        8.6\n",
       "CHAS         0.0\n",
       "NOX          0.5\n",
       "RM           6.2\n",
       "AGE         79.4\n",
       "DIS          3.2\n",
       "RAD          5.0\n",
       "TAX        311.0\n",
       "PTRATIO     19.1\n",
       "B          391.6\n",
       "LSTAT       11.2\n",
       "dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the original training dataset: median values\n",
    "# I use np.round to reduce the number of decimals to 1.\n",
    "\n",
    "np.round(X_train.median(), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "CRIM      -0.0\n",
       "ZN         0.0\n",
       "INDUS      0.0\n",
       "CHAS       0.0\n",
       "NOX        0.0\n",
       "RM        -0.0\n",
       "AGE        0.0\n",
       "DIS        0.0\n",
       "RAD        0.0\n",
       "TAX        0.0\n",
       "PTRATIO    0.0\n",
       "B         -0.0\n",
       "LSTAT      0.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the scaled training dataset: median values\n",
    "# I use np.round to reduce the number of decimals to 1.\n",
    "\n",
    "np.round(X_train_scaled.median(), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The variables were centered to the median values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's compare the variable distributions before and after scaling\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(12, 5))\n",
    "\n",
    "# before scaling\n",
    "ax1.set_title('Before Scaling')\n",
    "sns.kdeplot(X_train['RM'], ax=ax1)\n",
    "sns.kdeplot(X_train['LSTAT'], ax=ax1)\n",
    "sns.kdeplot(X_train['CRIM'], ax=ax1)\n",
    "\n",
    "# after scaling\n",
    "ax2.set_title('After Robust Scaling')\n",
    "sns.kdeplot(X_train_scaled['RM'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['LSTAT'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['CRIM'], ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The median of the distributions are centered at zero, but every other parameter may vary in the different variables. It does, though, squeeze the value range in the original variables, particularly for those highly skewed, like CRIM."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# let's compare the variable distributions before and after scaling\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(12, 5))\n",
    "\n",
    "# before scaling\n",
    "ax1.set_title('Before Scaling')\n",
    "sns.kdeplot(X_train['AGE'], ax=ax1)\n",
    "sns.kdeplot(X_train['DIS'], ax=ax1)\n",
    "sns.kdeplot(X_train['NOX'], ax=ax1)\n",
    "\n",
    "# after scaling\n",
    "ax2.set_title('After Robust Scaling')\n",
    "sns.kdeplot(X_train_scaled['AGE'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['DIS'], ax=ax2)\n",
    "sns.kdeplot(X_train_scaled['NOX'], ax=ax2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare this scaling with mean normalisation, to see how this procedure affects the distribution shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "feml",
   "language": "python",
   "name": "feml"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": "block",
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}