03-07-Data Pre-processing.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Pre-Processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.16.5\n",
      "0.25.1\n",
      "3.7.4 (default, Aug 13 2019, 15:17:50) \n",
      "[Clang 4.0.1 (tags/RELEASE_401/final)]\n",
      "0.21.3\n"
     ]
    }
   ],
   "source": [
    "print(np.__version__)\n",
    "print(pd.__version__)\n",
    "import sys\n",
    "print(sys.version)\n",
    "import sklearn\n",
    "print(sklearn.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\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",
       "      <td>0</td>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\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",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\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",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      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  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.datasets import load_boston\n",
    "boston_data = load_boston()\n",
    "df = pd.DataFrame(boston_data.data, columns=boston_data.feature_names)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = df[['LSTAT']].values\n",
    "y = boston_data.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.scatter(X, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Without Pre-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.0001\n",
    "w_ = np.zeros(1 + X.shape[1])\n",
    "cost_ = []\n",
    "n_ = 100\n",
    "\n",
    "for i in range(n_):\n",
    "    y_pred = np.dot(X, w_[1:]) + w_[0]\n",
    "    errors = (y - y_pred)\n",
    "    \n",
    "    w_[1:] += alpha * X.T.dot(errors)\n",
    "    w_[0] += alpha * errors.sum()\n",
    "    \n",
    "    cost = (errors**2).sum() / 2.0\n",
    "    cost_.append(cost)\n",
    "    \n",
    "plt.figure(figsize=(8,6))\n",
    "plt.plot(range(1, n_ + 1), cost_);\n",
    "plt.ylabel('SSE');\n",
    "plt.xlabel('Epoch');    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# With Pre-processing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "sc_x = StandardScaler()\n",
    "sc_y = StandardScaler()\n",
    "X_std = sc_x.fit_transform(X)\n",
    "y_std = sc_y.fit_transform(y.reshape(-1,1)).flatten()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "alpha = 0.0001\n",
    "w_ = np.zeros(1 + X_std.shape[1])\n",
    "cost_ = []\n",
    "n_ = 100\n",
    "\n",
    "for i in range(n_):\n",
    "    y_pred = np.dot(X_std, w_[1:]) + w_[0]\n",
    "    errors = (y_std - y_pred)\n",
    "    \n",
    "    w_[1:] += alpha * X_std.T.dot(errors)\n",
    "    w_[0] += alpha * errors.sum()\n",
    "    \n",
    "    cost = (errors**2).sum() / 2.0\n",
    "    cost_.append(cost)\n",
    "plt.figure(figsize=(8,6))\n",
    "plt.plot(range(1, n_ + 1), cost_);\n",
    "plt.ylabel('SSE');\n",
    "plt.xlabel('Epoch');    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.hist(X);\n",
    "plt.xlim(-40, 40);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After Scaling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.hist(X_std);\n",
    "plt.xlim(-4, 4);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Data Pre-processing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Standardization / Mean Removal\n",
    "\n",
    "* Min-Max or Scaling Features to a Range\n",
    "\n",
    "* Normalization\n",
    "\n",
    "* Binarization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Assumptions**:\n",
    "\n",
    "* Implicit/explicit assumption of machine learning algorithms: The features follow a normal distribution.\n",
    "* Most method are based on linear assumptions\n",
    "* Most machine learning requires the data to be standard normally distributed. Gaussian with zero mean and unit variance.\n",
    "\n",
    "[scikit-learn:](http://scikit-learn.org/stable/modules/preprocessing.html) \n",
    "\n",
    "In practice we often ignore the shape of the distribution and just transform the data to center it by removing the mean value of each feature, then scale it by dividing non-constant features by their standard deviation.\n",
    "\n",
    "For instance, many elements used in the objective function of a learning algorithm (such as the RBF kernel of Support Vector Machines or the l1 and l2 regularizers of linear models) **assume that all features are centered around zero and have variance in the same order**. If a feature has a variance that is orders of magnitude larger than others, it might dominate the objective function and make the estimator unable to learn from other features correctly as expected.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import preprocessing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = np.array([[ 1., -1.,  2.],\n",
    "                    [ 2.,  0.,  0.],\n",
    "                    [ 0.,  1., -1.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 0.        , 0.33333333])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.mean(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Standardization / Mean Removal / Variance Scaling\n",
    "\n",
    "[scikit Scale](http://scikit-learn.org/stable/modules/preprocessing.html#standardization-or-mean-removal-and-variance-scaling)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean is removed. Data is centered on zero. This is to remove bias.\n",
    "\n",
    "Standardization of datasets is a common requirement for many machine learning estimators implemented in scikit-learn; they might behave badly if the individual features do not more or less look like standard normally distributed data: Gaussian with zero mean and unit variance. \"standard normal\" random variable with mean 0 and standard deviation 1.\n",
    "\n",
    "$$X'=\\frac{X-\\bar{X}}{\\sigma}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        , -1.22474487,  1.33630621],\n",
       "       [ 1.22474487,  0.        , -0.26726124],\n",
       "       [-1.22474487,  1.22474487, -1.06904497]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_scaled = preprocessing.scale(X_train)\n",
    "X_scaled"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scaled data has zero mean and unit variance (unit variance means variance = 1):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0.])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_scaled.mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1., 1., 1.])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_scaled.std(axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Keeping in mind that if you have scaled your training data, you must do likewise with your test data as well. However, your assumption is that the mean and variance must be invariant between your train and test data. `scikit-learn` assists with a built-in utility function `StandardScaler`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "StandardScaler(copy=True, with_mean=True, with_std=True)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler = preprocessing.StandardScaler().fit(X_train)\n",
    "scaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 0.        , 0.33333333])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler.mean_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.81649658, 0.81649658, 1.24721913])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler.scale_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        , -1.22474487,  1.33630621],\n",
       "       [ 1.22474487,  0.        , -0.26726124],\n",
       "       [-1.22474487,  1.22474487, -1.06904497]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler.transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8,6))\n",
    "plt.hist(X_train);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can now utilise the `transform` for new dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test = [[-1., 1., 0.]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.44948974,  1.22474487, -0.26726124]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Min-Max or Scaling Features to a Range\n",
    "\n",
    "Scaling features to lie between a given minimum and maximum value, often between zero and one, or so that the maximum absolute value of each feature is scaled to unit size.\n",
    "\n",
    "The motivation to use this scaling include robustness to very small standard deviations of features and preserving zero entries in sparse data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MinMaxScaler\n",
    "\n",
    "Scale a data to the `[0, 1]` range:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = np.array([[ 1., -1.,  2.],\n",
    "                    [ 2.,  0.,  0.],\n",
    "                    [ 0.,  1., -1.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "min_max_scaler = preprocessing.MinMaxScaler()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train_minmax = min_max_scaler.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.5       , 0.        , 1.        ],\n",
       "       [1.        , 0.5       , 0.33333333],\n",
       "       [0.        , 1.        , 0.        ]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_minmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to unseen data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test = np.array([[-3., -1.,  0.], [2., 1.5, 4.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_test_minmax = min_max_scaler.transform(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.5       ,  0.        ,  0.33333333],\n",
       "       [ 1.        ,  1.25      ,  1.66666667]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test_minmax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "doc:\n",
    "\n",
    "Init signature: preprocessing.MinMaxScaler(feature_range=(0, 1), copy=True)\n",
    "\n",
    "Transforms features by scaling each feature to a given range.\n",
    "\n",
    "This estimator scales and translates each feature individually such\n",
    "that it is in the given range on the training set, i.e. between\n",
    "zero and one.\n",
    "\n",
    "The transformation is given by::\n",
    "\n",
    "    X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))\n",
    "    X_scaled = X_std * (max - min) + min\n",
    "    \n",
    "$$X_{std}=\\frac{X-X_{min}}{X_{max}-X_{min}}$$\n",
    "\n",
    "$$X'=X_{std} (\\text{max} - \\text{min}) + \\text{min}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "preprocessing.MinMaxScaler?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MaxAbsScaler\n",
    "\n",
    "Works in a very similar fashion, but scales in a way that the training data lies within the range `[-1, 1]` by dividing through the largest maximum value in each feature. It is meant for data that is already centered at zero or sparse data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train = np.array([[ 1., -1.,  2.],\n",
    "                    [ 2.,  0.,  0.],\n",
    "                    [ 0.,  1., -1.]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.5, -1. ,  1. ],\n",
       "       [ 1. ,  0. ,  0. ],\n",
       "       [ 0. ,  1. , -0.5]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_abs_scaler = preprocessing.MaxAbsScaler()\n",
    "X_train_maxabs = max_abs_scaler.fit_transform(X_train)\n",
    "X_train_maxabs "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.5, -0.5,  1. ],\n",
       "       [ 0. ,  0.5, -0.3]])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_test = np.array([[ -1., -0.5,  2.], [0., 0.5, -0.6]])\n",
    "X_test_maxabs = max_abs_scaler.transform(X_test)\n",
    "X_test_maxabs  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling sparse data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Centering sparse data would destroy the sparseness structure in the data, and thus rarely is a sensible thing to do. \n",
    "\n",
    "However, it can make sense to scale sparse inputs, especially if features are on different scales.\n",
    "\n",
    "`MaxAbsScaler` and `maxabs_scale` were specifically designed for scaling sparse data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Compare the effect of different scalers on data with outliers](http://scikit-learn.org/stable/auto_examples/preprocessing/plot_all_scaling.html#sphx-glr-auto-examples-preprocessing-plot-all-scaling-py)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Scaling vs Whitening\n",
    "\n",
    "It is sometimes not enough to center and scale the features independently, since a downstream model can further make some assumption on the linear independence of the features.\n",
    "\n",
    "To address this issue you can use `sklearn.decomposition.PCA` or `sklearn.decomposition.RandomizedPCA` with `whiten=True` to further remove the linear correlation across features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normalization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalization is the process of scaling individual samples to have unit norm. \n",
    "\n",
    "This process can be useful if you plan to use a quadratic form such as the dot-product or any other kernel to quantify the similarity of any pair of samples.\n",
    "\n",
    "$$X'=\\frac{X-X_{mean}}{X_{max}-X_{min}}$$\n",
    "\n",
    "This assumption is the base of the Vector Space Model often used in text classification and clustering contexts.\n",
    "\n",
    "There are two types of Normalization\n",
    "\n",
    "  1. **L1 normalization**, Least Absolute Deviations\n",
    "Ensure the sum of absolute values is 1 in each row. \n",
    "\n",
    "  2. **L2 normalization**, Least squares, \n",
    "Ensure that the sum of squares is 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.40824829, -0.40824829,  0.81649658],\n",
       "       [ 1.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.70710678, -0.70710678]])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [[ 1., -1.,  2.],\n",
    "     [ 2.,  0.,  0.],\n",
    "     [ 0.,  1., -1.]]\n",
    "X_normalized = preprocessing.normalize(X, norm='l2')\n",
    "\n",
    "X_normalized    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Alternatively\n",
    "\n",
    "The `preprocessing` module further provides a utility class `Normalizer` that implements the same operation using the `Transformer` API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Normalizer(copy=True, norm='l2')"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalizer = preprocessing.Normalizer().fit(X)  # fit does nothing\n",
    "normalizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.40824829, -0.40824829,  0.81649658],\n",
       "       [ 1.        ,  0.        ,  0.        ],\n",
       "       [ 0.        ,  0.70710678, -0.70710678]])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalizer.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.70710678,  0.70710678,  0.        ]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "normalizer.transform([[-1.,  1., 0.]])  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Binarization\n",
    "\n",
    "$$f(x)={0,1}$$\n",
    "\n",
    "Feature binarization is the process of thresholding numerical features to get boolean values. This can be useful for downstream probabilistic estimators that make assumption that the input data is distributed according to a multi-variate Bernoulli distribution\n",
    "\n",
    "\n",
    "It is also common among the text processing community to use binary feature values (probably to simplify the probabilistic reasoning) even if normalized counts (a.k.a. term frequencies) or TF-IDF valued features often perform slightly better in practice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Binarizer(copy=True, threshold=0.0)"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = [[ 1., -1.,  2.],\n",
    "     [ 2.,  0.,  0.],\n",
    "     [ 0.,  1., -1.]]\n",
    "\n",
    "binarizer = preprocessing.Binarizer().fit(X)  # fit does nothing\n",
    "binarizer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 1.],\n",
       "       [1., 0., 0.],\n",
       "       [0., 1., 0.]])"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binarizer.transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Modifying the threshold"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "binarizer = preprocessing.Binarizer(threshold=-0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 0.]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binarizer.transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Encoding categorical features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[LabelEncoder](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.LabelEncoder.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "source = ['australia', 'singapore', 'new zealand', 'hong kong']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "label_enc = preprocessing.LabelEncoder()\n",
    "src = label_enc.fit_transform(source)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "country to code mapping:\n",
      "\n",
      "australia \t 0\n",
      "hong kong \t 1\n",
      "new zealand \t 2\n",
      "singapore \t 3\n"
     ]
    }
   ],
   "source": [
    "print(\"country to code mapping:\\n\") \n",
    "for k, v in enumerate(label_enc.classes_): \n",
    "    print(v,'\\t', k) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "test_data = ['hong kong', 'singapore', 'australia', 'new zealand']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = label_enc.transform(test_data) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 3 0 2]\n"
     ]
    }
   ],
   "source": [
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One Hot / One-of-K Encoding\n",
    "\n",
    "* Useful for dealing with sparse matrix\n",
    "* uses [one-of-k scheme](http://code-factor.blogspot.sg/2012/10/one-hotone-of-k-data-encoder-for.html)\n",
    "\n",
    "\n",
    "The process of turning a series of categorical responses into a set of binary result (0 or 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[One Hot Encoder](http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.OneHotEncoder.html#sklearn.preprocessing.OneHotEncoder)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['australia', 'singapore', 'new zealand', 'hong kong']"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "source"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 3, 2, 1])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "src"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import OneHotEncoder"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 0.]\n",
      " [0. 0. 0. 1.]\n",
      " [0. 0. 1. 0.]\n",
      " [0. 1. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "one_hot_enc = OneHotEncoder(sparse=False, categories='auto')\n",
    "src = src.reshape(len(src), 1)\n",
    "one_hot = one_hot_enc.fit_transform(src)\n",
    "print(one_hot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['australia']\n"
     ]
    }
   ],
   "source": [
    "invert_res = label_enc.inverse_transform([np.argmax(one_hot[0, :])])\n",
    "print(invert_res)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['hong kong']\n"
     ]
    }
   ],
   "source": [
    "invert_res = label_enc.inverse_transform([np.argmax(one_hot[3, :])])\n",
    "print(invert_res)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# References\n",
    "\n",
    "* [Section - Should I normalize/standardize/rescale the data?](http://www.faqs.org/faqs/ai-faq/neural-nets/part2/section-16.html)\n",
    "* [Colleen Farrelly - Machine Learning by Analogy](https://www.slideshare.net/ColleenFarrelly/machine-learning-by-analogy-59094152)\n",
    "* [Lior Rokach - Introduction to Machine Learning](https://www.slideshare.net/liorrokach/introduction-to-machine-learning-13809045)\n",
    "* [Ritchie Ng](http://www.ritchieng.com/machinelearning-one-hot-encoding/)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}