Feature Scaling.ipynb

{
 "cells": [
  {
   "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",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "from sklearn.preprocessing import StandardScaler"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is Normalization?\n",
    "\n",
    "#### Normalization is a scaling technique in which values are shifted and rescaled so that they end up ranging between 0 and 1. It is also known as Min-Max scaling.\n",
    "\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1. , 12.4,  3.9, 10.4])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=np.array([1.0,12.4,3.9,10.4])\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For [0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.        , 1.        , 0.25438596, 0.8245614 ])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#X-Xmin / Xmax-Xmin\n",
    "norm=(data-np.min(data))/(np.max(data)-np.min(data))\n",
    "norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For [a,b]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.        , 10.        ,  6.27192982,  9.12280702])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=5\n",
    "b=10\n",
    "norm=a+((data-np.min(data))* (b-a)/(np.max(data)-np.min(data)))\n",
    "norm"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MinMaxScaler for normalization of Data in range  between 0 and 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        ],\n",
       "       [1.        ],\n",
       "       [0.25438596],\n",
       "       [0.8245614 ]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mm=MinMaxScaler()\n",
    "#fit \n",
    "#transform\n",
    "#inverse transform\n",
    "#fit_transform\n",
    "mm.fit(data.reshape(-1,1))\n",
    "norm=mm.transform(data.reshape(-1,1))\n",
    "norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.89999994]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mm.inverse_transform([[0.25438596]]) #=> 3.9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        ],\n",
       "       [1.        ],\n",
       "       [0.25438596],\n",
       "       [0.8245614 ]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mm.fit_transform(data.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MinMaxScaler for normalization of Data in range  between a and b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.        ],\n",
       "       [10.        ],\n",
       "       [ 6.27192982],\n",
       "       [ 9.12280702]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a=5\n",
    "b=10\n",
    "mm=MinMaxScaler(feature_range=(a,b))\n",
    "mm.fit(data.reshape(-1,1))\n",
    "norm=mm.transform(data.reshape(-1,1))\n",
    "norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.        ],\n",
       "       [10.        ],\n",
       "       [ 6.27192982],\n",
       "       [ 9.12280702]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "norm=mm.fit_transform(data.reshape(-1,1))\n",
    "norm"
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## What is Standardization?\n",
    "\n",
    "#### Standardization is another scaling technique where the values are centered around the mean with a unit standard deviation. This means that the mean of the attribute becomes zero and the resultant distribution has a unit standard deviation.\n",
    "![image-2.png](attachment:image-2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1. , 12.4,  3.9, 10.4])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.27554   ,  1.17866354, -0.65122506,  0.74810152])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#scale_data =X -mean / std\n",
    "scaled_data=(data-np.mean(data))/np.std(data)\n",
    "scaled_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1.1102230246251565e-16"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## mean of scaled Data\n",
    "np.mean(scaled_data)\n",
    "#-1.11022 x 10^ -16"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999998"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.std(scaled_data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### StandardScaler z-scale normalization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.27554   ],\n",
       "       [ 1.17866354],\n",
       "       [-0.65122506],\n",
       "       [ 0.74810152]])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc=StandardScaler()\n",
    "#fit\n",
    "#transform\n",
    "#inverse_transform\n",
    "#fit_transform\n",
    "data=data.reshape(-1,1)\n",
    "sc.fit(data)\n",
    "sc.transform(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.90000001]])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.inverse_transform([[-0.65122506]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.27554   ],\n",
       "       [ 1.17866354],\n",
       "       [-0.65122506],\n",
       "       [ 0.74810152]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc.fit_transform(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    " df=pd.read_csv(\"../Data/bodyfat.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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>Density</th>\n",
       "      <th>bodyfat</th>\n",
       "      <th>Age</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Height</th>\n",
       "      <th>Neck</th>\n",
       "      <th>Chest</th>\n",
       "      <th>Abdomen</th>\n",
       "      <th>Hip</th>\n",
       "      <th>Thigh</th>\n",
       "      <th>Knee</th>\n",
       "      <th>Ankle</th>\n",
       "      <th>Biceps</th>\n",
       "      <th>Forearm</th>\n",
       "      <th>Wrist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0708</td>\n",
       "      <td>12.3</td>\n",
       "      <td>23</td>\n",
       "      <td>154.25</td>\n",
       "      <td>67.75</td>\n",
       "      <td>36.2</td>\n",
       "      <td>93.1</td>\n",
       "      <td>85.2</td>\n",
       "      <td>94.5</td>\n",
       "      <td>59.0</td>\n",
       "      <td>37.3</td>\n",
       "      <td>21.9</td>\n",
       "      <td>32.0</td>\n",
       "      <td>27.4</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0853</td>\n",
       "      <td>6.1</td>\n",
       "      <td>22</td>\n",
       "      <td>173.25</td>\n",
       "      <td>72.25</td>\n",
       "      <td>38.5</td>\n",
       "      <td>93.6</td>\n",
       "      <td>83.0</td>\n",
       "      <td>98.7</td>\n",
       "      <td>58.7</td>\n",
       "      <td>37.3</td>\n",
       "      <td>23.4</td>\n",
       "      <td>30.5</td>\n",
       "      <td>28.9</td>\n",
       "      <td>18.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0414</td>\n",
       "      <td>25.3</td>\n",
       "      <td>22</td>\n",
       "      <td>154.00</td>\n",
       "      <td>66.25</td>\n",
       "      <td>34.0</td>\n",
       "      <td>95.8</td>\n",
       "      <td>87.9</td>\n",
       "      <td>99.2</td>\n",
       "      <td>59.6</td>\n",
       "      <td>38.9</td>\n",
       "      <td>24.0</td>\n",
       "      <td>28.8</td>\n",
       "      <td>25.2</td>\n",
       "      <td>16.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0751</td>\n",
       "      <td>10.4</td>\n",
       "      <td>26</td>\n",
       "      <td>184.75</td>\n",
       "      <td>72.25</td>\n",
       "      <td>37.4</td>\n",
       "      <td>101.8</td>\n",
       "      <td>86.4</td>\n",
       "      <td>101.2</td>\n",
       "      <td>60.1</td>\n",
       "      <td>37.3</td>\n",
       "      <td>22.8</td>\n",
       "      <td>32.4</td>\n",
       "      <td>29.4</td>\n",
       "      <td>18.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0340</td>\n",
       "      <td>28.7</td>\n",
       "      <td>24</td>\n",
       "      <td>184.25</td>\n",
       "      <td>71.25</td>\n",
       "      <td>34.4</td>\n",
       "      <td>97.3</td>\n",
       "      <td>100.0</td>\n",
       "      <td>101.9</td>\n",
       "      <td>63.2</td>\n",
       "      <td>42.2</td>\n",
       "      <td>24.0</td>\n",
       "      <td>32.2</td>\n",
       "      <td>27.7</td>\n",
       "      <td>17.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Density  bodyfat  Age  Weight  Height  Neck  Chest  Abdomen    Hip  Thigh  \\\n",
       "0   1.0708     12.3   23  154.25   67.75  36.2   93.1     85.2   94.5   59.0   \n",
       "1   1.0853      6.1   22  173.25   72.25  38.5   93.6     83.0   98.7   58.7   \n",
       "2   1.0414     25.3   22  154.00   66.25  34.0   95.8     87.9   99.2   59.6   \n",
       "3   1.0751     10.4   26  184.75   72.25  37.4  101.8     86.4  101.2   60.1   \n",
       "4   1.0340     28.7   24  184.25   71.25  34.4   97.3    100.0  101.9   63.2   \n",
       "\n",
       "   Knee  Ankle  Biceps  Forearm  Wrist  \n",
       "0  37.3   21.9    32.0     27.4   17.1  \n",
       "1  37.3   23.4    30.5     28.9   18.2  \n",
       "2  38.9   24.0    28.8     25.2   16.6  \n",
       "3  37.3   22.8    32.4     29.4   18.2  \n",
       "4  42.2   24.0    32.2     27.7   17.7  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.boxplot(figsize=(10,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df[\"bodyfat\"].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "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>Density</th>\n",
       "      <th>bodyfat</th>\n",
       "      <th>Age</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Height</th>\n",
       "      <th>Neck</th>\n",
       "      <th>Chest</th>\n",
       "      <th>Abdomen</th>\n",
       "      <th>Hip</th>\n",
       "      <th>Thigh</th>\n",
       "      <th>Knee</th>\n",
       "      <th>Ankle</th>\n",
       "      <th>Biceps</th>\n",
       "      <th>Forearm</th>\n",
       "      <th>Wrist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.665496</td>\n",
       "      <td>0.258947</td>\n",
       "      <td>0.016949</td>\n",
       "      <td>0.146127</td>\n",
       "      <td>0.792746</td>\n",
       "      <td>0.253731</td>\n",
       "      <td>0.242531</td>\n",
       "      <td>0.200762</td>\n",
       "      <td>0.151515</td>\n",
       "      <td>0.294264</td>\n",
       "      <td>0.267081</td>\n",
       "      <td>0.189189</td>\n",
       "      <td>0.356436</td>\n",
       "      <td>0.460432</td>\n",
       "      <td>0.232143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.792801</td>\n",
       "      <td>0.128421</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.223789</td>\n",
       "      <td>0.886010</td>\n",
       "      <td>0.368159</td>\n",
       "      <td>0.251318</td>\n",
       "      <td>0.172808</td>\n",
       "      <td>0.218501</td>\n",
       "      <td>0.286783</td>\n",
       "      <td>0.267081</td>\n",
       "      <td>0.290541</td>\n",
       "      <td>0.282178</td>\n",
       "      <td>0.568345</td>\n",
       "      <td>0.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.407375</td>\n",
       "      <td>0.532632</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.145105</td>\n",
       "      <td>0.761658</td>\n",
       "      <td>0.144279</td>\n",
       "      <td>0.289982</td>\n",
       "      <td>0.235070</td>\n",
       "      <td>0.226475</td>\n",
       "      <td>0.309227</td>\n",
       "      <td>0.366460</td>\n",
       "      <td>0.331081</td>\n",
       "      <td>0.198020</td>\n",
       "      <td>0.302158</td>\n",
       "      <td>0.142857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.703248</td>\n",
       "      <td>0.218947</td>\n",
       "      <td>0.067797</td>\n",
       "      <td>0.270795</td>\n",
       "      <td>0.886010</td>\n",
       "      <td>0.313433</td>\n",
       "      <td>0.395431</td>\n",
       "      <td>0.216010</td>\n",
       "      <td>0.258373</td>\n",
       "      <td>0.321696</td>\n",
       "      <td>0.267081</td>\n",
       "      <td>0.250000</td>\n",
       "      <td>0.376238</td>\n",
       "      <td>0.604317</td>\n",
       "      <td>0.428571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.342406</td>\n",
       "      <td>0.604211</td>\n",
       "      <td>0.033898</td>\n",
       "      <td>0.268751</td>\n",
       "      <td>0.865285</td>\n",
       "      <td>0.164179</td>\n",
       "      <td>0.316344</td>\n",
       "      <td>0.388818</td>\n",
       "      <td>0.269537</td>\n",
       "      <td>0.399002</td>\n",
       "      <td>0.571429</td>\n",
       "      <td>0.331081</td>\n",
       "      <td>0.366337</td>\n",
       "      <td>0.482014</td>\n",
       "      <td>0.339286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>247</th>\n",
       "      <td>0.690079</td>\n",
       "      <td>0.231579</td>\n",
       "      <td>0.813559</td>\n",
       "      <td>0.064378</td>\n",
       "      <td>0.777202</td>\n",
       "      <td>0.189055</td>\n",
       "      <td>0.173989</td>\n",
       "      <td>0.180432</td>\n",
       "      <td>0.060606</td>\n",
       "      <td>0.059850</td>\n",
       "      <td>0.111801</td>\n",
       "      <td>0.162162</td>\n",
       "      <td>0.039604</td>\n",
       "      <td>0.338129</td>\n",
       "      <td>0.482143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>0.251097</td>\n",
       "      <td>0.707368</td>\n",
       "      <td>0.847458</td>\n",
       "      <td>0.337216</td>\n",
       "      <td>0.834197</td>\n",
       "      <td>0.487562</td>\n",
       "      <td>0.513181</td>\n",
       "      <td>0.452351</td>\n",
       "      <td>0.311005</td>\n",
       "      <td>0.309227</td>\n",
       "      <td>0.484472</td>\n",
       "      <td>0.277027</td>\n",
       "      <td>0.514851</td>\n",
       "      <td>0.546763</td>\n",
       "      <td>0.767857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>249</th>\n",
       "      <td>0.331870</td>\n",
       "      <td>0.616842</td>\n",
       "      <td>0.847458</td>\n",
       "      <td>0.278970</td>\n",
       "      <td>0.756477</td>\n",
       "      <td>0.388060</td>\n",
       "      <td>0.558875</td>\n",
       "      <td>0.534943</td>\n",
       "      <td>0.266348</td>\n",
       "      <td>0.326683</td>\n",
       "      <td>0.267081</td>\n",
       "      <td>0.162162</td>\n",
       "      <td>0.321782</td>\n",
       "      <td>0.446043</td>\n",
       "      <td>0.392857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>0.394205</td>\n",
       "      <td>0.547368</td>\n",
       "      <td>0.847458</td>\n",
       "      <td>0.295320</td>\n",
       "      <td>0.849741</td>\n",
       "      <td>0.388060</td>\n",
       "      <td>0.509666</td>\n",
       "      <td>0.405337</td>\n",
       "      <td>0.204147</td>\n",
       "      <td>0.219451</td>\n",
       "      <td>0.534161</td>\n",
       "      <td>0.243243</td>\n",
       "      <td>0.282178</td>\n",
       "      <td>0.604317</td>\n",
       "      <td>0.714286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>251</th>\n",
       "      <td>0.281826</td>\n",
       "      <td>0.671579</td>\n",
       "      <td>0.881356</td>\n",
       "      <td>0.363785</td>\n",
       "      <td>0.839378</td>\n",
       "      <td>0.482587</td>\n",
       "      <td>0.581722</td>\n",
       "      <td>0.496823</td>\n",
       "      <td>0.352472</td>\n",
       "      <td>0.301746</td>\n",
       "      <td>0.571429</td>\n",
       "      <td>0.371622</td>\n",
       "      <td>0.440594</td>\n",
       "      <td>0.647482</td>\n",
       "      <td>0.910714</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>252 rows × 15 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Density   bodyfat       Age    Weight    Height      Neck     Chest  \\\n",
       "0    0.665496  0.258947  0.016949  0.146127  0.792746  0.253731  0.242531   \n",
       "1    0.792801  0.128421  0.000000  0.223789  0.886010  0.368159  0.251318   \n",
       "2    0.407375  0.532632  0.000000  0.145105  0.761658  0.144279  0.289982   \n",
       "3    0.703248  0.218947  0.067797  0.270795  0.886010  0.313433  0.395431   \n",
       "4    0.342406  0.604211  0.033898  0.268751  0.865285  0.164179  0.316344   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "247  0.690079  0.231579  0.813559  0.064378  0.777202  0.189055  0.173989   \n",
       "248  0.251097  0.707368  0.847458  0.337216  0.834197  0.487562  0.513181   \n",
       "249  0.331870  0.616842  0.847458  0.278970  0.756477  0.388060  0.558875   \n",
       "250  0.394205  0.547368  0.847458  0.295320  0.849741  0.388060  0.509666   \n",
       "251  0.281826  0.671579  0.881356  0.363785  0.839378  0.482587  0.581722   \n",
       "\n",
       "      Abdomen       Hip     Thigh      Knee     Ankle    Biceps   Forearm  \\\n",
       "0    0.200762  0.151515  0.294264  0.267081  0.189189  0.356436  0.460432   \n",
       "1    0.172808  0.218501  0.286783  0.267081  0.290541  0.282178  0.568345   \n",
       "2    0.235070  0.226475  0.309227  0.366460  0.331081  0.198020  0.302158   \n",
       "3    0.216010  0.258373  0.321696  0.267081  0.250000  0.376238  0.604317   \n",
       "4    0.388818  0.269537  0.399002  0.571429  0.331081  0.366337  0.482014   \n",
       "..        ...       ...       ...       ...       ...       ...       ...   \n",
       "247  0.180432  0.060606  0.059850  0.111801  0.162162  0.039604  0.338129   \n",
       "248  0.452351  0.311005  0.309227  0.484472  0.277027  0.514851  0.546763   \n",
       "249  0.534943  0.266348  0.326683  0.267081  0.162162  0.321782  0.446043   \n",
       "250  0.405337  0.204147  0.219451  0.534161  0.243243  0.282178  0.604317   \n",
       "251  0.496823  0.352472  0.301746  0.571429  0.371622  0.440594  0.647482   \n",
       "\n",
       "        Wrist  \n",
       "0    0.232143  \n",
       "1    0.428571  \n",
       "2    0.142857  \n",
       "3    0.428571  \n",
       "4    0.339286  \n",
       "..        ...  \n",
       "247  0.482143  \n",
       "248  0.767857  \n",
       "249  0.392857  \n",
       "250  0.714286  \n",
       "251  0.910714  \n",
       "\n",
       "[252 rows x 15 columns]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#min max scaler \n",
    "mm=MinMaxScaler()\n",
    "mdf=mm.fit_transform(df)\n",
    "mdf=pd.DataFrame(mdf,columns=df.columns)\n",
    "mdf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mdf[\"bodyfat\"].hist()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mdf.boxplot(figsize=(10,5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Standard Scaler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "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>Density</th>\n",
       "      <th>bodyfat</th>\n",
       "      <th>Age</th>\n",
       "      <th>Weight</th>\n",
       "      <th>Height</th>\n",
       "      <th>Neck</th>\n",
       "      <th>Chest</th>\n",
       "      <th>Abdomen</th>\n",
       "      <th>Hip</th>\n",
       "      <th>Thigh</th>\n",
       "      <th>Knee</th>\n",
       "      <th>Ankle</th>\n",
       "      <th>Biceps</th>\n",
       "      <th>Forearm</th>\n",
       "      <th>Wrist</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.801647</td>\n",
       "      <td>-0.820246</td>\n",
       "      <td>-1.740073</td>\n",
       "      <td>-0.841246</td>\n",
       "      <td>-0.656205</td>\n",
       "      <td>-0.738665</td>\n",
       "      <td>-0.918048</td>\n",
       "      <td>-0.683533</td>\n",
       "      <td>-0.755929</td>\n",
       "      <td>-0.077479</td>\n",
       "      <td>-0.536131</td>\n",
       "      <td>-0.710826</td>\n",
       "      <td>-0.090676</td>\n",
       "      <td>-0.626718</td>\n",
       "      <td>-1.212541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.565061</td>\n",
       "      <td>-1.562573</td>\n",
       "      <td>-1.819583</td>\n",
       "      <td>-0.193462</td>\n",
       "      <td>0.574790</td>\n",
       "      <td>0.209365</td>\n",
       "      <td>-0.858621</td>\n",
       "      <td>-0.887963</td>\n",
       "      <td>-0.168502</td>\n",
       "      <td>-0.134736</td>\n",
       "      <td>-0.536131</td>\n",
       "      <td>0.175947</td>\n",
       "      <td>-0.588143</td>\n",
       "      <td>0.117079</td>\n",
       "      <td>-0.031943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.746240</td>\n",
       "      <td>0.736245</td>\n",
       "      <td>-1.819583</td>\n",
       "      <td>-0.849769</td>\n",
       "      <td>-1.066536</td>\n",
       "      <td>-1.645475</td>\n",
       "      <td>-0.597144</td>\n",
       "      <td>-0.432643</td>\n",
       "      <td>-0.098570</td>\n",
       "      <td>0.037035</td>\n",
       "      <td>0.128592</td>\n",
       "      <td>0.530656</td>\n",
       "      <td>-1.151940</td>\n",
       "      <td>-1.717621</td>\n",
       "      <td>-1.749177</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.028039</td>\n",
       "      <td>-1.047733</td>\n",
       "      <td>-1.501543</td>\n",
       "      <td>0.198617</td>\n",
       "      <td>0.574790</td>\n",
       "      <td>-0.244041</td>\n",
       "      <td>0.115976</td>\n",
       "      <td>-0.572026</td>\n",
       "      <td>0.181157</td>\n",
       "      <td>0.132464</td>\n",
       "      <td>-0.536131</td>\n",
       "      <td>-0.178762</td>\n",
       "      <td>0.041982</td>\n",
       "      <td>0.365012</td>\n",
       "      <td>-0.031943</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-1.135844</td>\n",
       "      <td>1.143327</td>\n",
       "      <td>-1.660563</td>\n",
       "      <td>0.181570</td>\n",
       "      <td>0.301235</td>\n",
       "      <td>-1.480601</td>\n",
       "      <td>-0.418864</td>\n",
       "      <td>0.691719</td>\n",
       "      <td>0.279061</td>\n",
       "      <td>0.724121</td>\n",
       "      <td>1.499585</td>\n",
       "      <td>0.530656</td>\n",
       "      <td>-0.024347</td>\n",
       "      <td>-0.477959</td>\n",
       "      <td>-0.568578</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Density   bodyfat       Age    Weight    Height      Neck     Chest  \\\n",
       "0  0.801647 -0.820246 -1.740073 -0.841246 -0.656205 -0.738665 -0.918048   \n",
       "1  1.565061 -1.562573 -1.819583 -0.193462  0.574790  0.209365 -0.858621   \n",
       "2 -0.746240  0.736245 -1.819583 -0.849769 -1.066536 -1.645475 -0.597144   \n",
       "3  1.028039 -1.047733 -1.501543  0.198617  0.574790 -0.244041  0.115976   \n",
       "4 -1.135844  1.143327 -1.660563  0.181570  0.301235 -1.480601 -0.418864   \n",
       "\n",
       "    Abdomen       Hip     Thigh      Knee     Ankle    Biceps   Forearm  \\\n",
       "0 -0.683533 -0.755929 -0.077479 -0.536131 -0.710826 -0.090676 -0.626718   \n",
       "1 -0.887963 -0.168502 -0.134736 -0.536131  0.175947 -0.588143  0.117079   \n",
       "2 -0.432643 -0.098570  0.037035  0.128592  0.530656 -1.151940 -1.717621   \n",
       "3 -0.572026  0.181157  0.132464 -0.536131 -0.178762  0.041982  0.365012   \n",
       "4  0.691719  0.279061  0.724121  1.499585  0.530656 -0.024347 -0.477959   \n",
       "\n",
       "      Wrist  \n",
       "0 -1.212541  \n",
       "1 -0.031943  \n",
       "2 -1.749177  \n",
       "3 -0.031943  \n",
       "4 -0.568578  "
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sc=StandardScaler()\n",
    "scaled_data=sc.fit_transform(df)\n",
    "scaled_data=pd.DataFrame(scaled_data,columns=df.columns)\n",
    "scaled_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Density    5.719411e-15\n",
       "bodyfat   -1.603655e-16\n",
       "Age        1.920862e-16\n",
       "Weight     2.757935e-16\n",
       "Height     1.475396e-15\n",
       "Neck      -7.586524e-16\n",
       "Chest     -3.524518e-17\n",
       "Abdomen    3.665498e-16\n",
       "Hip        8.132824e-16\n",
       "Thigh     -8.426626e-16\n",
       "Knee       8.564578e-16\n",
       "Ankle      7.361836e-16\n",
       "Biceps    -8.304644e-17\n",
       "Forearm   -2.977336e-15\n",
       "Wrist      2.854859e-16\n",
       "dtype: float64"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaled_data.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Density    1.00199\n",
       "bodyfat    1.00199\n",
       "Age        1.00199\n",
       "Weight     1.00199\n",
       "Height     1.00199\n",
       "Neck       1.00199\n",
       "Chest      1.00199\n",
       "Abdomen    1.00199\n",
       "Hip        1.00199\n",
       "Thigh      1.00199\n",
       "Knee       1.00199\n",
       "Ankle      1.00199\n",
       "Biceps     1.00199\n",
       "Forearm    1.00199\n",
       "Wrist      1.00199\n",
       "dtype: float64"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scaled_data.std()"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}