10.06-Scaling-to-unit-length.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 vector unit  length**.\n",
    "\n",
    "=================================================================\n",
    "\n",
    "## Scaling to vector unit  length / unit norm\n",
    "\n",
    "In this procedure we scale the components of a feature vector such that the complete vector has a length of 1 or, in other words a norm of 1. **Note** that this normalisation procedure normalises the **feature** vector, and not the **observation** vector. So we divide by the norm of the feature vector, observation per observation, across the different variables, and not by the norm of the **observation** vector, across observations for the same feature.\n",
    "\n",
    "First, let me give you the formulas, and then I illustrate with an example.\n",
    "\n",
    "### Scaling to unit norm, formulas\n",
    "\n",
    "Scaling to unit norm is achieved by dividing each feature vector by either the Manhattan distance (l1 norm) or the Euclidean distance of the vector (l2 norm):\n",
    "\n",
    "X_scaled_l1 = X / l1(X)\n",
    "\n",
    "X_scaled_l2 = X / l2(X)\n",
    "\n",
    "\n",
    "The **Manhattan distance** is given by the sum of the absolute components of the vector:\n",
    "\n",
    "l1(X) = |x1| + |x2| + ... + |xn|\n",
    "\n",
    "\n",
    "Whereas the **Euclidean distance** is given by the square root of the square sum of the component of the vector:\n",
    "\n",
    "l2(X) = sqr( x1^2 + x2^2 + ... + xn^2 )\n",
    "\n",
    "\n",
    "In the above example, x1 is variable 1, x2 variable 2, and xn variable n, and X is the data for 1 observation across variables (a row in other words).\n",
    "\n",
    "**Note** as well that as the euclidean distance squares the values of the feature vector components, outliers have a heavier weight. With outliers, we may prefer to use l1 normalisation.\n",
    "\n",
    "\n",
    "### Scaling to unit norm, examples\n",
    "\n",
    "For example, if our data has 1 observations (1 row) and 3 variables:\n",
    "\n",
    "- number of pets\n",
    "- number of children\n",
    "- age\n",
    "\n",
    "The values for each variable for that single observation are 10, 15 and 20. Our vector X = [10, 15, 20]. Then:\n",
    "\n",
    "l1(X) = 10 + 15 + 20 = 45\n",
    "\n",
    "l2(X) = sqr( 10^2 + 15^2 + 20^2) = sqr( 100 + 225 + 400) = **26.9**\n",
    "\n",
    "The euclidean distance is always smaller than the manhattan distance.\n",
    "\n",
    "\n",
    "The normalised vector values are therefore:\n",
    "\n",
    "X_scaled_l1 = [ 10/45, 15/45, 20/45 ]      =  [0.22, 0.33, 0.44]\n",
    "\n",
    "X_scaled_l2 = [10/26.9, 15/26.9, 20/26.9 ] =  [0.37, 0.55, 0.74]\n",
    "\n",
    "\n",
    "Scikit-learn recommends this scaling procedures for text classification or clustering. For example, they quote the dot product of two l2-normalized TF-IDF vectors is the cosine similarity of the vectors and is the base similarity metric for the Vector Space Model commonly used by the Information Retrieval community.\n",
    "\n",
    "\n",
    "## In this demo\n",
    "\n",
    "We will perform scaling to unit length using the Boston House Prices data set that comes with Scikit-learn"
   ]
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    "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 Normalizer"
   ]
  },
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   "cell_type": "code",
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       "  <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",
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       "      <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",
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       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</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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       "      <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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       "      <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",
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       "      <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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      ".. _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)"
   ]
  },
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   "source": [
    "When scaling to unit length, as we do it across the variables and observation per observation, the distance does vary for each observation. Therefore, we do not need to learn parameters and store them. The scaling occurs on an observation per observation level. Therefore, in essence, we do not need to divide into train and test.\n",
    "\n",
    "However, you probably did this to implement other feature engineering steps, so let's continue doing so here as well."
   ]
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   "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"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling to l1"
   ]
  },
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   "source": [
    "# set up the scaler\n",
    "scaler = Normalizer(norm='l1')\n",
    "\n",
    "# fit the scaler, this procedure does NOTHING\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)"
   ]
  },
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       "       1216.7,  807.1,  775.9,  707.8, 1260.5,  943.2,  706.4,  839.5,\n",
       "        759.2, 1221.5,  923.8, 1219.9,  780.6,  755.1,  701.2,  757.2,\n",
       "        797.2,  731.4, 1237.1,  802.4, 1265.4,  785.5,  766.3,  839.7,\n",
       "       1255.2,  792.9, 1224.5,  748.3,  743.8,  790.3,  808.3,  760.4,\n",
       "        828.9,  854.6, 1226.7,  797. ,  788. ,  807.4,  900.5,  962.7,\n",
       "        770.2,  830.6])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's calculate the norm for each observation (feature vector)\n",
    "# original data\n",
    "\n",
    "np.round( np.linalg.norm(X_train, ord=1, axis=1), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's calculate the norm for each observation (feature vector)\n",
    "# scaled data\n",
    "\n",
    "np.round( np.linalg.norm(X_train_scaled, ord=1, axis=1), 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, each feature vector has a l1 norm of 1."
   ]
  },
  {
   "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": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.358284</td>\n",
       "      <td>11.809322</td>\n",
       "      <td>11.078757</td>\n",
       "      <td>0.064972</td>\n",
       "      <td>0.556098</td>\n",
       "      <td>6.308427</td>\n",
       "      <td>68.994068</td>\n",
       "      <td>3.762459</td>\n",
       "      <td>9.353107</td>\n",
       "      <td>401.782486</td>\n",
       "      <td>18.473446</td>\n",
       "      <td>360.601186</td>\n",
       "      <td>12.440650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.353223</td>\n",
       "      <td>23.653056</td>\n",
       "      <td>6.993821</td>\n",
       "      <td>0.246825</td>\n",
       "      <td>0.115601</td>\n",
       "      <td>0.702009</td>\n",
       "      <td>28.038429</td>\n",
       "      <td>2.067661</td>\n",
       "      <td>8.671999</td>\n",
       "      <td>170.592404</td>\n",
       "      <td>2.224809</td>\n",
       "      <td>85.621945</td>\n",
       "      <td>7.078485</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>1.174200</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.073425</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.950000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.450000</td>\n",
       "      <td>5.895250</td>\n",
       "      <td>45.175000</td>\n",
       "      <td>2.107650</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>276.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>376.057500</td>\n",
       "      <td>6.735000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.262660</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.560000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.215500</td>\n",
       "      <td>79.450000</td>\n",
       "      <td>3.215700</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>311.000000</td>\n",
       "      <td>19.100000</td>\n",
       "      <td>391.605000</td>\n",
       "      <td>11.160000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.103700</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.629250</td>\n",
       "      <td>6.647250</td>\n",
       "      <td>93.750000</td>\n",
       "      <td>5.079300</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>395.690000</td>\n",
       "      <td>16.717500</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>36.980000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean     3.358284   11.809322   11.078757    0.064972    0.556098    6.308427   \n",
       "std      8.353223   23.653056    6.993821    0.246825    0.115601    0.702009   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.073425    0.000000    4.950000    0.000000    0.450000    5.895250   \n",
       "50%      0.262660    0.000000    8.560000    0.000000    0.538000    6.215500   \n",
       "75%      3.103700   20.000000   18.100000    0.000000    0.629250    6.647250   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean    68.994068    3.762459    9.353107  401.782486   18.473446  360.601186   \n",
       "std     28.038429    2.067661    8.671999  170.592404    2.224809   85.621945   \n",
       "min      2.900000    1.174200    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.175000    2.107650    4.000000  276.000000   17.400000  376.057500   \n",
       "50%     79.450000    3.215700    5.000000  311.000000   19.100000  391.605000   \n",
       "75%     93.750000    5.079300   24.000000  666.000000   20.200000  395.690000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT  \n",
       "count  354.000000  \n",
       "mean    12.440650  \n",
       "std      7.078485  \n",
       "min      1.730000  \n",
       "25%      6.735000  \n",
       "50%     11.160000  \n",
       "75%     16.717500  \n",
       "max     36.980000  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's look at the individual values of the variables in the original data\n",
    "X_train.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>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>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.003022</td>\n",
       "      <td>0.014491</td>\n",
       "      <td>0.011731</td>\n",
       "      <td>0.000073</td>\n",
       "      <td>0.000620</td>\n",
       "      <td>0.007221</td>\n",
       "      <td>0.075687</td>\n",
       "      <td>0.004479</td>\n",
       "      <td>0.009336</td>\n",
       "      <td>0.427642</td>\n",
       "      <td>0.020880</td>\n",
       "      <td>0.411273</td>\n",
       "      <td>0.013544</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.007018</td>\n",
       "      <td>0.028764</td>\n",
       "      <td>0.006854</td>\n",
       "      <td>0.000283</td>\n",
       "      <td>0.000115</td>\n",
       "      <td>0.001620</td>\n",
       "      <td>0.029466</td>\n",
       "      <td>0.002780</td>\n",
       "      <td>0.007262</td>\n",
       "      <td>0.114922</td>\n",
       "      <td>0.003751</td>\n",
       "      <td>0.124328</td>\n",
       "      <td>0.007204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000008</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000577</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000424</td>\n",
       "      <td>0.002996</td>\n",
       "      <td>0.004348</td>\n",
       "      <td>0.000919</td>\n",
       "      <td>0.001163</td>\n",
       "      <td>0.250885</td>\n",
       "      <td>0.014363</td>\n",
       "      <td>0.000374</td>\n",
       "      <td>0.001879</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000093</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.006243</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000545</td>\n",
       "      <td>0.006061</td>\n",
       "      <td>0.055411</td>\n",
       "      <td>0.002206</td>\n",
       "      <td>0.004740</td>\n",
       "      <td>0.346035</td>\n",
       "      <td>0.016876</td>\n",
       "      <td>0.318534</td>\n",
       "      <td>0.008473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000311</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.010421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000611</td>\n",
       "      <td>0.007376</td>\n",
       "      <td>0.078917</td>\n",
       "      <td>0.003923</td>\n",
       "      <td>0.006021</td>\n",
       "      <td>0.393483</td>\n",
       "      <td>0.021129</td>\n",
       "      <td>0.456271</td>\n",
       "      <td>0.012262</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.002983</td>\n",
       "      <td>0.024709</td>\n",
       "      <td>0.015120</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000657</td>\n",
       "      <td>0.008358</td>\n",
       "      <td>0.098186</td>\n",
       "      <td>0.006456</td>\n",
       "      <td>0.018223</td>\n",
       "      <td>0.526258</td>\n",
       "      <td>0.024014</td>\n",
       "      <td>0.498519</td>\n",
       "      <td>0.017204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.066782</td>\n",
       "      <td>0.121905</td>\n",
       "      <td>0.035787</td>\n",
       "      <td>0.001422</td>\n",
       "      <td>0.001337</td>\n",
       "      <td>0.011541</td>\n",
       "      <td>0.144310</td>\n",
       "      <td>0.016269</td>\n",
       "      <td>0.028684</td>\n",
       "      <td>0.795970</td>\n",
       "      <td>0.030523</td>\n",
       "      <td>0.578661</td>\n",
       "      <td>0.041723</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean     0.003022    0.014491    0.011731    0.000073    0.000620    0.007221   \n",
       "std      0.007018    0.028764    0.006854    0.000283    0.000115    0.001620   \n",
       "min      0.000008    0.000000    0.000577    0.000000    0.000424    0.002996   \n",
       "25%      0.000093    0.000000    0.006243    0.000000    0.000545    0.006061   \n",
       "50%      0.000311    0.000000    0.010421    0.000000    0.000611    0.007376   \n",
       "75%      0.002983    0.024709    0.015120    0.000000    0.000657    0.008358   \n",
       "max      0.066782    0.121905    0.035787    0.001422    0.001337    0.011541   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean     0.075687    0.004479    0.009336    0.427642    0.020880    0.411273   \n",
       "std      0.029466    0.002780    0.007262    0.114922    0.003751    0.124328   \n",
       "min      0.004348    0.000919    0.001163    0.250885    0.014363    0.000374   \n",
       "25%      0.055411    0.002206    0.004740    0.346035    0.016876    0.318534   \n",
       "50%      0.078917    0.003923    0.006021    0.393483    0.021129    0.456271   \n",
       "75%      0.098186    0.006456    0.018223    0.526258    0.024014    0.498519   \n",
       "max      0.144310    0.016269    0.028684    0.795970    0.030523    0.578661   \n",
       "\n",
       "            LSTAT  \n",
       "count  354.000000  \n",
       "mean     0.013544  \n",
       "std      0.007204  \n",
       "min      0.001879  \n",
       "25%      0.008473  \n",
       "50%      0.012262  \n",
       "75%      0.017204  \n",
       "max      0.041723  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's look at the individual values of the variables in the original data\n",
    "\n",
    "X_train_scaled.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values have been squeezed in a smaller value range."
   ]
  },
  {
   "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 Unit Norm 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": []
  },
  {
   "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",
    "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 Unit Norm 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": [
    "See how this normalisation changes the distribution of the original variable quite dramatically. Go ahead and comment in an out the different variables to have a better look."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Scaling to l2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# set up the scaler\n",
    "scaler = Normalizer(norm='l2')\n",
    "\n",
    "# fit the scaler, this procedure does NOTHING\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": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([600.5, 458.4, 598. , 519.1, 434. , 511. , 527.9, 496.7, 675.2,\n",
       "       496.5, 450.2, 492.1, 453.5, 492.4, 492.9, 491.5, 770.1, 782.2,\n",
       "       465.2, 759.8, 778.6, 535.3, 764.4, 781.5, 561.9, 562.8, 768.1,\n",
       "       468.2, 725.5, 673.1, 458.8, 572.5, 559.8, 488. , 490.2, 488.9,\n",
       "       441.3, 680.4, 675.6, 483.9, 483.9, 506.2, 474.8, 481.9, 517.8,\n",
       "       747.8, 503.3, 438.2, 483. , 424. , 478.8, 519.9, 451.4, 546.2,\n",
       "       558.3, 516.9, 773.8, 470.4, 467.5, 501.6, 674.5, 528.1, 508.2,\n",
       "       677.1, 593.2, 556.5, 781.9, 465.9, 707.6, 509.6, 501.3, 449.4,\n",
       "       512.5, 778.8, 483.6, 587.7, 485.4, 558.1, 673.1, 504.6, 494.9,\n",
       "       509. , 589.2, 510.6, 777. , 439.2, 478.8, 593.3, 760. , 534.5,\n",
       "       779.9, 586.6, 551.3, 558.4, 446.2, 418.8, 496. , 407.8, 676.2,\n",
       "       782.8, 671. , 499. , 593.6, 482.6, 779.2, 456.1, 483.4, 573.4,\n",
       "       456.5, 477.3, 493.3, 485.7, 490.5, 716.1, 497.2, 760.6, 524.9,\n",
       "       672.1, 488.2, 443.7, 751. , 492.5, 424.3, 458.7, 783. , 596.4,\n",
       "       482.9, 557.2, 515.4, 523.3, 510.3, 483.8, 782.2, 565.5, 447.2,\n",
       "       461.6, 478.5, 483.8, 526.5, 509.4, 484.1, 508.7, 599. , 591.9,\n",
       "       555.7, 733.4, 752.5, 475.7, 474.5, 759.2, 563.3, 502.8, 503.7,\n",
       "       506.2, 497.6, 682.7, 563.5, 487.4, 558.2, 484.7, 490.9, 774.6,\n",
       "       553.2, 544.4, 537.4, 495.4, 548.7, 556.5, 770. , 599.5, 502. ,\n",
       "       481.1, 774.1, 505.8, 483.4, 779.9, 502.8, 475.3, 781.2, 502.6,\n",
       "       576.5, 491. , 455.7, 502.3, 681.5, 455.6, 439. , 439. , 449. ,\n",
       "       427.5, 557.6, 445.8, 786.8, 775.3, 475.3, 493.4, 782.2, 448.9,\n",
       "       772.3, 488.6, 461.9, 476.8, 511.7, 782.7, 469.5, 474.6, 474.1,\n",
       "       778.3, 485.2, 450.9, 451.2, 467.6, 495.3, 772.6, 783. , 746.1,\n",
       "       428.5, 503.2, 494. , 782.9, 598.3, 563.6, 510.8, 458.7, 778.2,\n",
       "       500. , 533.7, 772. , 678.4, 482.5, 517.3, 455.6, 560.4, 496.7,\n",
       "       771.5, 467.4, 487.8, 780.8, 456.2, 765.8, 530.3, 527.6, 457.2,\n",
       "       471.5, 490.4, 783.4, 780.8, 484.3, 453.8, 489.5, 547.8, 575.6,\n",
       "       451.5, 448.5, 773. , 599.3, 674. , 487.8, 478. , 492. , 463.6,\n",
       "       470.5, 431.7, 819.6, 779.5, 673. , 720. , 732.3, 483.4, 488.5,\n",
       "       472. , 587.2, 780. , 474.6, 481.6, 674.5, 493.4, 479.4, 765.6,\n",
       "       775.9, 449.2, 559.4, 771.4, 780.9, 453.9, 673.7, 483.9, 782.8,\n",
       "       466.9, 746.2, 777.8, 599.6, 474.6, 504.4, 452. , 779.9, 568.2,\n",
       "       538.5, 504.7, 533.7, 496.9, 395.5, 596. , 438.6, 781.7, 740. ,\n",
       "       498.7, 672.9, 784.1, 780.8, 571.4, 500.2, 786.5, 499.9, 487.9,\n",
       "       457.3, 782.7, 678.9, 457.7, 491.8, 481.5, 779.1, 560.5, 750.5,\n",
       "       477.9, 496.5, 451.7, 441. , 479.1, 458.5, 797.1, 497.4, 819.4,\n",
       "       476. , 478.6, 507.2, 782.3, 488.2, 778.1, 490.8, 470. , 474.3,\n",
       "       482.9, 471.3, 491.8, 504.5, 777.4, 477.7, 502.2, 491.5, 560.3,\n",
       "       591.3, 465.4, 503.5])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's calculate the norm for each observation (feature vector)\n",
    "# original data\n",
    "\n",
    "np.round( np.linalg.norm(X_train, ord=2, axis=1), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.,\n",
       "       1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1., 1.])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# let's calculate the norm for each observation (feature vector)\n",
    "# scaledl data\n",
    "\n",
    "np.round( np.linalg.norm(X_train_scaled, ord=2, axis=1), 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.358284</td>\n",
       "      <td>11.809322</td>\n",
       "      <td>11.078757</td>\n",
       "      <td>0.064972</td>\n",
       "      <td>0.556098</td>\n",
       "      <td>6.308427</td>\n",
       "      <td>68.994068</td>\n",
       "      <td>3.762459</td>\n",
       "      <td>9.353107</td>\n",
       "      <td>401.782486</td>\n",
       "      <td>18.473446</td>\n",
       "      <td>360.601186</td>\n",
       "      <td>12.440650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.353223</td>\n",
       "      <td>23.653056</td>\n",
       "      <td>6.993821</td>\n",
       "      <td>0.246825</td>\n",
       "      <td>0.115601</td>\n",
       "      <td>0.702009</td>\n",
       "      <td>28.038429</td>\n",
       "      <td>2.067661</td>\n",
       "      <td>8.671999</td>\n",
       "      <td>170.592404</td>\n",
       "      <td>2.224809</td>\n",
       "      <td>85.621945</td>\n",
       "      <td>7.078485</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>1.174200</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.073425</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.950000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.450000</td>\n",
       "      <td>5.895250</td>\n",
       "      <td>45.175000</td>\n",
       "      <td>2.107650</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>276.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>376.057500</td>\n",
       "      <td>6.735000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.262660</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8.560000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.215500</td>\n",
       "      <td>79.450000</td>\n",
       "      <td>3.215700</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>311.000000</td>\n",
       "      <td>19.100000</td>\n",
       "      <td>391.605000</td>\n",
       "      <td>11.160000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.103700</td>\n",
       "      <td>20.000000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.629250</td>\n",
       "      <td>6.647250</td>\n",
       "      <td>93.750000</td>\n",
       "      <td>5.079300</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>395.690000</td>\n",
       "      <td>16.717500</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>36.980000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean     3.358284   11.809322   11.078757    0.064972    0.556098    6.308427   \n",
       "std      8.353223   23.653056    6.993821    0.246825    0.115601    0.702009   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.073425    0.000000    4.950000    0.000000    0.450000    5.895250   \n",
       "50%      0.262660    0.000000    8.560000    0.000000    0.538000    6.215500   \n",
       "75%      3.103700   20.000000   18.100000    0.000000    0.629250    6.647250   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean    68.994068    3.762459    9.353107  401.782486   18.473446  360.601186   \n",
       "std     28.038429    2.067661    8.671999  170.592404    2.224809   85.621945   \n",
       "min      2.900000    1.174200    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.175000    2.107650    4.000000  276.000000   17.400000  376.057500   \n",
       "50%     79.450000    3.215700    5.000000  311.000000   19.100000  391.605000   \n",
       "75%     93.750000    5.079300   24.000000  666.000000   20.200000  395.690000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT  \n",
       "count  354.000000  \n",
       "mean    12.440650  \n",
       "std      7.078485  \n",
       "min      1.730000  \n",
       "25%      6.735000  \n",
       "50%     11.160000  \n",
       "75%     16.717500  \n",
       "max     36.980000  "
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <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>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "      <td>354.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.004688</td>\n",
       "      <td>0.024027</td>\n",
       "      <td>0.018758</td>\n",
       "      <td>0.000120</td>\n",
       "      <td>0.000997</td>\n",
       "      <td>0.011640</td>\n",
       "      <td>0.122166</td>\n",
       "      <td>0.007251</td>\n",
       "      <td>0.014647</td>\n",
       "      <td>0.682156</td>\n",
       "      <td>0.033589</td>\n",
       "      <td>0.668592</td>\n",
       "      <td>0.021765</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.011049</td>\n",
       "      <td>0.048105</td>\n",
       "      <td>0.010982</td>\n",
       "      <td>0.000463</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>0.002718</td>\n",
       "      <td>0.048931</td>\n",
       "      <td>0.004588</td>\n",
       "      <td>0.010624</td>\n",
       "      <td>0.152037</td>\n",
       "      <td>0.006168</td>\n",
       "      <td>0.203917</td>\n",
       "      <td>0.011661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000013</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000963</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000681</td>\n",
       "      <td>0.004682</td>\n",
       "      <td>0.006431</td>\n",
       "      <td>0.001499</td>\n",
       "      <td>0.001911</td>\n",
       "      <td>0.425977</td>\n",
       "      <td>0.024238</td>\n",
       "      <td>0.000475</td>\n",
       "      <td>0.003099</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000148</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.010430</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000883</td>\n",
       "      <td>0.009432</td>\n",
       "      <td>0.088582</td>\n",
       "      <td>0.003363</td>\n",
       "      <td>0.007875</td>\n",
       "      <td>0.565434</td>\n",
       "      <td>0.027163</td>\n",
       "      <td>0.507064</td>\n",
       "      <td>0.013486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.000515</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.016919</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000979</td>\n",
       "      <td>0.012099</td>\n",
       "      <td>0.126282</td>\n",
       "      <td>0.006399</td>\n",
       "      <td>0.010027</td>\n",
       "      <td>0.639890</td>\n",
       "      <td>0.033567</td>\n",
       "      <td>0.753246</td>\n",
       "      <td>0.019929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.004750</td>\n",
       "      <td>0.041516</td>\n",
       "      <td>0.023812</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.001060</td>\n",
       "      <td>0.013580</td>\n",
       "      <td>0.158637</td>\n",
       "      <td>0.010516</td>\n",
       "      <td>0.030581</td>\n",
       "      <td>0.850914</td>\n",
       "      <td>0.038620</td>\n",
       "      <td>0.809355</td>\n",
       "      <td>0.027524</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.113081</td>\n",
       "      <td>0.207644</td>\n",
       "      <td>0.061249</td>\n",
       "      <td>0.002282</td>\n",
       "      <td>0.002053</td>\n",
       "      <td>0.018156</td>\n",
       "      <td>0.237626</td>\n",
       "      <td>0.027624</td>\n",
       "      <td>0.035766</td>\n",
       "      <td>0.992514</td>\n",
       "      <td>0.053097</td>\n",
       "      <td>0.889808</td>\n",
       "      <td>0.070063</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean     0.004688    0.024027    0.018758    0.000120    0.000997    0.011640   \n",
       "std      0.011049    0.048105    0.010982    0.000463    0.000187    0.002718   \n",
       "min      0.000013    0.000000    0.000963    0.000000    0.000681    0.004682   \n",
       "25%      0.000148    0.000000    0.010430    0.000000    0.000883    0.009432   \n",
       "50%      0.000515    0.000000    0.016919    0.000000    0.000979    0.012099   \n",
       "75%      0.004750    0.041516    0.023812    0.000000    0.001060    0.013580   \n",
       "max      0.113081    0.207644    0.061249    0.002282    0.002053    0.018156   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  354.000000  354.000000  354.000000  354.000000  354.000000  354.000000   \n",
       "mean     0.122166    0.007251    0.014647    0.682156    0.033589    0.668592   \n",
       "std      0.048931    0.004588    0.010624    0.152037    0.006168    0.203917   \n",
       "min      0.006431    0.001499    0.001911    0.425977    0.024238    0.000475   \n",
       "25%      0.088582    0.003363    0.007875    0.565434    0.027163    0.507064   \n",
       "50%      0.126282    0.006399    0.010027    0.639890    0.033567    0.753246   \n",
       "75%      0.158637    0.010516    0.030581    0.850914    0.038620    0.809355   \n",
       "max      0.237626    0.027624    0.035766    0.992514    0.053097    0.889808   \n",
       "\n",
       "            LSTAT  \n",
       "count  354.000000  \n",
       "mean     0.021765  \n",
       "std      0.011661  \n",
       "min      0.003099  \n",
       "25%      0.013486  \n",
       "50%      0.019929  \n",
       "75%      0.027524  \n",
       "max      0.070063  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_scaled.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "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 Unit Norm 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": 20,
   "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": [
    "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 Unit Norm 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": "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,
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