Scaling and Normalization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Collecting mlxtend\n",
      "  Using cached mlxtend-0.17.3-py2.py3-none-any.whl (1.3 MB)\n",
      "Requirement already satisfied: numpy>=1.16.2 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from mlxtend) (1.18.1)\n",
      "Requirement already satisfied: setuptools in c:\\users\\riya\\anaconda3\\lib\\site-packages (from mlxtend) (45.2.0.post20200210)\n",
      "Requirement already satisfied: scikit-learn>=0.20.3 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from mlxtend) (0.22.1)\n",
      "Requirement already satisfied: matplotlib>=3.0.0 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from mlxtend) (3.2.1)\n",
      "Requirement already satisfied: joblib>=0.13.2 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from mlxtend) (0.13.2)\n",
      "Requirement already satisfied: pandas>=0.24.2 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from mlxtend) (0.24.2)\n",
      "Requirement already satisfied: scipy>=1.2.1 in c:\\users\\riya\\appdata\\roaming\\python\\python37\\site-packages (from mlxtend) (1.4.1)\n",
      "Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in c:\\users\\riya\\appdata\\roaming\\python\\python37\\site-packages (from matplotlib>=3.0.0->mlxtend) (2.4.2)\n",
      "Requirement already satisfied: kiwisolver>=1.0.1 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from matplotlib>=3.0.0->mlxtend) (1.1.0)\n",
      "Requirement already satisfied: cycler>=0.10 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from matplotlib>=3.0.0->mlxtend) (0.10.0)\n",
      "Requirement already satisfied: python-dateutil>=2.1 in c:\\users\\riya\\anaconda3\\lib\\site-packages (from matplotlib>=3.0.0->mlxtend) (2.8.1)\n",
      "Requirement already satisfied: pytz>=2011k in c:\\users\\riya\\anaconda3\\lib\\site-packages (from pandas>=0.24.2->mlxtend) (2019.3)\n",
      "Requirement already satisfied: six in c:\\users\\riya\\appdata\\roaming\\python\\python37\\site-packages (from cycler>=0.10->matplotlib>=3.0.0->mlxtend) (1.12.0)\n",
      "Installing collected packages: mlxtend\n",
      "Successfully installed mlxtend-0.17.3\n"
     ]
    }
   ],
   "source": [
    "import sys\n",
    "!{sys.executable} -m pip install mlxtend"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# for Box-Cox Transformation\n",
    "# A Box Cox transformation is a way \n",
    "# to transform non-normal dependent variables into a normal shape.\n",
    "from scipy import stats\n",
    "\n",
    "# for min_max scaling\n",
    "from mlxtend.preprocessing import minmax_scaling\n",
    "\n",
    "# plotting modules\n",
    "import seaborn as sb\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# set seed for reproducibility\n",
    "np.random.seed(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scaling vs. Normalization\n",
    "# What is the difference?\n",
    "\n",
    "# Both transforms the values of numeric variables \n",
    "# for the transformed data points to have specific helpful properties.\n",
    "\n",
    "# Scaling is changing the range of data\n",
    "# Normalizing is changing shape of the distribution of data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Scaling fits the data in a range\n",
    "# Useful when using methods that are based on measures of how far the data points are.\n",
    "# E.g., SVM and KNN."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Scaled data')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate 1000 data points randomly drawn from an exponential distribution\n",
    "original_data = np.random.exponential(size=1000)\n",
    "\n",
    "# min-max scale the data between 0 and 1\n",
    "scaled_data = minmax_scaling(original_data, columns=[0])\n",
    "\n",
    "# plot both together to compare\n",
    "fig, ax = plt.subplots(1,2)\n",
    "sb.distplot(original_data, ax=ax[0])\n",
    "ax[0].set_title(\"Original Data\")\n",
    "sb.distplot(scaled_data, ax=ax[1])\n",
    "ax[1].set_title(\"Scaled data\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# The point of normalization is to change your observations\n",
    "# so that they can be described as a normal distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Normalized data')"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# normalize the exponential data with box-cox\n",
    "normalized_data = stats.boxcox(original_data)\n",
    "\n",
    "# plot both together to compare\n",
    "fig, ax=plt.subplots(1,2)\n",
    "sb.distplot(original_data, ax=ax[0])\n",
    "ax[0].set_title(\"Original Data\")\n",
    "sb.distplot(normalized_data[0], ax=ax[1])\n",
    "ax[1].set_title(\"Normalized data\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}