10.04-Maximum-Absolute-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 **Maximum Absolute Scaling**.\n",
    "\n",
    "=================================================================\n",
    "\n",
    "## Scaling to maximum value - MaxAbsScaling\n",
    "\n",
    "Maximum absolute scaling scales the data to its maximum value:\n",
    "\n",
    "X_scaled = X / X.max\n",
    "\n",
    "The result of the above transformation is a distribution which values vary within the range of -1 to 1. But the mean is not centered at zero and the standard deviation varies across variables.\n",
    "\n",
    "Scikit-learn suggests that this transformer is meant for data that is centered at zero, and for sparse data.\n",
    "\n",
    "\n",
    "In a nutshell, MaxAbsScaling:\n",
    "\n",
    "- does not center the mean at 0 (but it might be a good idea t center it with another method)\n",
    "- variance varies across variables\n",
    "- may not preserve the shape of the original distribution\n",
    "- sensitive outliers\n",
    "\n",
    "\n",
    "## In this demo\n",
    "\n",
    "We will perform scaling to the maximum value 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 MaxAbsScaling, with centering\n",
    "from sklearn.preprocessing import MaxAbsScaler, StandardScaler"
   ]
  },
  {
   "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",
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       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
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       "      <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()"
   ]
  },
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   "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>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",
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       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "      <th>MEDV</th>\n",
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       "      <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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       "             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 maximum values are are quite different in the different variables**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When performing maximum absolute scaling on the data set, we need to first identify the maximum values 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": [
    "### MaxAbsScaling\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 = MaxAbsScaler()\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([ 88.9762, 100.    ,  27.74  ,   1.    ,   0.871 ,   8.78  ,\n",
       "       100.    ,  12.1265,  24.    , 711.    ,  22.    , 396.9   ,\n",
       "        36.98  ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# the scaler stores the maximum values of the features as learned from train set\n",
    "scaler.max_abs_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.4</td>\n",
       "      <td>11.8</td>\n",
       "      <td>11.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.6</td>\n",
       "      <td>6.3</td>\n",
       "      <td>69.0</td>\n",
       "      <td>3.8</td>\n",
       "      <td>9.4</td>\n",
       "      <td>401.8</td>\n",
       "      <td>18.5</td>\n",
       "      <td>360.6</td>\n",
       "      <td>12.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.4</td>\n",
       "      <td>23.7</td>\n",
       "      <td>7.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.7</td>\n",
       "      <td>28.0</td>\n",
       "      <td>2.1</td>\n",
       "      <td>8.7</td>\n",
       "      <td>170.6</td>\n",
       "      <td>2.2</td>\n",
       "      <td>85.6</td>\n",
       "      <td>7.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>3.6</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.2</td>\n",
       "      <td>1.0</td>\n",
       "      <td>187.0</td>\n",
       "      <td>12.6</td>\n",
       "      <td>0.3</td>\n",
       "      <td>1.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
       "      <td>5.9</td>\n",
       "      <td>45.2</td>\n",
       "      <td>2.1</td>\n",
       "      <td>4.0</td>\n",
       "      <td>276.0</td>\n",
       "      <td>17.4</td>\n",
       "      <td>376.1</td>\n",
       "      <td>6.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>6.2</td>\n",
       "      <td>79.4</td>\n",
       "      <td>3.2</td>\n",
       "      <td>5.0</td>\n",
       "      <td>311.0</td>\n",
       "      <td>19.1</td>\n",
       "      <td>391.6</td>\n",
       "      <td>11.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.1</td>\n",
       "      <td>20.0</td>\n",
       "      <td>18.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>6.6</td>\n",
       "      <td>93.8</td>\n",
       "      <td>5.1</td>\n",
       "      <td>24.0</td>\n",
       "      <td>666.0</td>\n",
       "      <td>20.2</td>\n",
       "      <td>395.7</td>\n",
       "      <td>16.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>89.0</td>\n",
       "      <td>100.0</td>\n",
       "      <td>27.7</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>8.8</td>\n",
       "      <td>100.0</td>\n",
       "      <td>12.1</td>\n",
       "      <td>24.0</td>\n",
       "      <td>711.0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>396.9</td>\n",
       "      <td>37.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        CRIM     ZN  INDUS   CHAS    NOX     RM    AGE    DIS    RAD    TAX  \\\n",
       "count  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0   \n",
       "mean     3.4   11.8   11.1    0.1    0.6    6.3   69.0    3.8    9.4  401.8   \n",
       "std      8.4   23.7    7.0    0.2    0.1    0.7   28.0    2.1    8.7  170.6   \n",
       "min      0.0    0.0    0.5    0.0    0.4    3.6    2.9    1.2    1.0  187.0   \n",
       "25%      0.1    0.0    5.0    0.0    0.4    5.9   45.2    2.1    4.0  276.0   \n",
       "50%      0.3    0.0    8.6    0.0    0.5    6.2   79.4    3.2    5.0  311.0   \n",
       "75%      3.1   20.0   18.1    0.0    0.6    6.6   93.8    5.1   24.0  666.0   \n",
       "max     89.0  100.0   27.7    1.0    0.9    8.8  100.0   12.1   24.0  711.0   \n",
       "\n",
       "       PTRATIO      B  LSTAT  \n",
       "count    354.0  354.0  354.0  \n",
       "mean      18.5  360.6   12.4  \n",
       "std        2.2   85.6    7.1  \n",
       "min       12.6    0.3    1.7  \n",
       "25%       17.4  376.1    6.7  \n",
       "50%       19.1  391.6   11.2  \n",
       "75%       20.2  395.7   16.7  \n",
       "max       22.0  396.9   37.0  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the original training dataset: maximum values\n",
    "# I use np.round to reduce the number of decimals to 1.\n",
    "\n",
    "np.round(X_train.describe(), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
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       "      <td>354.0</td>\n",
       "      <td>354.0</td>\n",
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       "      <th>mean</th>\n",
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       "      <td>0.7</td>\n",
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       "      <td>0.9</td>\n",
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       "    <tr>\n",
       "      <th>std</th>\n",
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       "      <td>0.2</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.4</td>\n",
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       "      <td>0.1</td>\n",
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       "      <td>0.6</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.6</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.4</td>\n",
       "      <td>0.9</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0.8</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.9</td>\n",
       "      <td>0.9</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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      "text/plain": [
       "        CRIM     ZN  INDUS   CHAS    NOX     RM    AGE    DIS    RAD    TAX  \\\n",
       "count  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0  354.0   \n",
       "mean     0.0    0.1    0.4    0.1    0.6    0.7    0.7    0.3    0.4    0.6   \n",
       "std      0.1    0.2    0.3    0.2    0.1    0.1    0.3    0.2    0.4    0.2   \n",
       "min      0.0    0.0    0.0    0.0    0.4    0.4    0.0    0.1    0.0    0.3   \n",
       "25%      0.0    0.0    0.2    0.0    0.5    0.7    0.5    0.2    0.2    0.4   \n",
       "50%      0.0    0.0    0.3    0.0    0.6    0.7    0.8    0.3    0.2    0.4   \n",
       "75%      0.0    0.2    0.7    0.0    0.7    0.8    0.9    0.4    1.0    0.9   \n",
       "max      1.0    1.0    1.0    1.0    1.0    1.0    1.0    1.0    1.0    1.0   \n",
       "\n",
       "       PTRATIO      B  LSTAT  \n",
       "count    354.0  354.0  354.0  \n",
       "mean       0.8    0.9    0.3  \n",
       "std        0.1    0.2    0.2  \n",
       "min        0.6    0.0    0.0  \n",
       "25%        0.8    0.9    0.2  \n",
       "50%        0.9    1.0    0.3  \n",
       "75%        0.9    1.0    0.5  \n",
       "max        1.0    1.0    1.0  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's have a look at the scaled training dataset: maximum values\n",
    "# I use np.round to reduce the number of decimals to 1.\n",
    "\n",
    "np.round(X_train_scaled.describe(), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum values are re-scaled to 1. Every other parameter, changes across variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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 Max Abs 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": "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['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 Max Abs 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": {
    "collapsed": true
   },
   "source": [
    "## Centering + MaxAbsScaling\n",
    "\n",
    "We can center the distributions at zero and then scale to its absolute maximum, as recommended by Scikit-learn by combining the use of 2 transformers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the StandardScaler so that it removes the mean\n",
    "# but does not divide by the standard deviation\n",
    "scaler_mean = StandardScaler(with_mean=True, with_std=False)\n",
    "\n",
    "# set up the MaxAbsScaler normally\n",
    "scaler_maxabs = MaxAbsScaler()\n",
    "\n",
    "# fit the scalers to the train set, it will learn the parameters\n",
    "scaler_mean.fit(X_train)\n",
    "scaler_maxabs.fit(X_train)\n",
    "\n",
    "# transform train and test sets\n",
    "X_train_scaled = scaler_maxabs.transform(scaler_mean.transform(X_train))\n",
    "X_test_scaled = scaler_maxabs.transform(scaler_mean.transform(X_test))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": 15,
   "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 Max Abs 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": [
    "Similar effect to mean normalisation, but in this case, the values vary across a narrower range. "
   ]
  },
  {
   "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
}