E05_explained_variance-components_ and eigen_val-eigen_vec.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "cf112067",
   "metadata": {},
   "source": [
    "this experiment are intend for comparing the manual eigen value and eigen vector and the sklearn module in PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4e8df47e",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7614ec4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_boston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d523d563",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\users\\m477a\\appdata\\local\\programs\\python\\python39\\lib\\site-packages\\sklearn\\utils\\deprecation.py:87: FutureWarning: Function load_boston is deprecated; `load_boston` is deprecated in 1.0 and will be removed in 1.2.\n",
      "\n",
      "    The Boston housing prices dataset has an ethical problem. You can refer to\n",
      "    the documentation of this function for further details.\n",
      "\n",
      "    The scikit-learn maintainers therefore strongly discourage the use of this\n",
      "    dataset unless the purpose of the code is to study and educate about\n",
      "    ethical issues in data science and machine learning.\n",
      "\n",
      "    In this special case, you can fetch the dataset from the original\n",
      "    source::\n",
      "\n",
      "        import pandas as pd\n",
      "        import numpy as np\n",
      "\n",
      "\n",
      "        data_url = \"http://lib.stat.cmu.edu/datasets/boston\"\n",
      "        raw_df = pd.read_csv(data_url, sep=\"\\s+\", skiprows=22, header=None)\n",
      "        data = np.hstack([raw_df.values[::2, :], raw_df.values[1::2, :2]])\n",
      "        target = raw_df.values[1::2, 2]\n",
      "\n",
      "    Alternative datasets include the California housing dataset (i.e.\n",
      "    :func:`~sklearn.datasets.fetch_california_housing`) and the Ames housing\n",
      "    dataset. You can load the datasets as follows::\n",
      "\n",
      "        from sklearn.datasets import fetch_california_housing\n",
      "        housing = fetch_california_housing()\n",
      "\n",
      "    for the California housing dataset and::\n",
      "\n",
      "        from sklearn.datasets import fetch_openml\n",
      "        housing = fetch_openml(name=\"house_prices\", as_frame=True)\n",
      "\n",
      "    for the Ames housing dataset.\n",
      "    \n",
      "  warnings.warn(msg, category=FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "boston_dataset = load_boston()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "65d81228",
   "metadata": {},
   "outputs": [],
   "source": [
    "boston = pd.DataFrame(boston_dataset.data, columns=boston_dataset.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "61221260",
   "metadata": {},
   "outputs": [
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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",
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       "      <th>TAX</th>\n",
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       "      <th>LSTAT</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
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       "      <td>4.98</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\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",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
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       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>501</th>\n",
       "      <td>0.06263</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.593</td>\n",
       "      <td>69.1</td>\n",
       "      <td>2.4786</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>391.99</td>\n",
       "      <td>9.67</td>\n",
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       "    <tr>\n",
       "      <th>502</th>\n",
       "      <td>0.04527</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.120</td>\n",
       "      <td>76.7</td>\n",
       "      <td>2.2875</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>0.06076</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.976</td>\n",
       "      <td>91.0</td>\n",
       "      <td>2.1675</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.64</td>\n",
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       "    <tr>\n",
       "      <th>504</th>\n",
       "      <td>0.10959</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.794</td>\n",
       "      <td>89.3</td>\n",
       "      <td>2.3889</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>393.45</td>\n",
       "      <td>6.48</td>\n",
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       "    <tr>\n",
       "      <th>505</th>\n",
       "      <td>0.04741</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.93</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.573</td>\n",
       "      <td>6.030</td>\n",
       "      <td>80.8</td>\n",
       "      <td>2.5050</td>\n",
       "      <td>1.0</td>\n",
       "      <td>273.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>396.90</td>\n",
       "      <td>7.88</td>\n",
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       "<p>506 rows × 13 columns</p>\n",
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      "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",
       "501  0.06263   0.0  11.93   0.0  0.573  6.593  69.1  2.4786  1.0  273.0   \n",
       "502  0.04527   0.0  11.93   0.0  0.573  6.120  76.7  2.2875  1.0  273.0   \n",
       "503  0.06076   0.0  11.93   0.0  0.573  6.976  91.0  2.1675  1.0  273.0   \n",
       "504  0.10959   0.0  11.93   0.0  0.573  6.794  89.3  2.3889  1.0  273.0   \n",
       "505  0.04741   0.0  11.93   0.0  0.573  6.030  80.8  2.5050  1.0  273.0   \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  \n",
       "..       ...     ...    ...  \n",
       "501     21.0  391.99   9.67  \n",
       "502     21.0  396.90   9.08  \n",
       "503     21.0  396.90   5.64  \n",
       "504     21.0  393.45   6.48  \n",
       "505     21.0  396.90   7.88  \n",
       "\n",
       "[506 rows x 13 columns]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5165417f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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",
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       "      <th>LSTAT</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "      <td>506.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>3.613524</td>\n",
       "      <td>11.363636</td>\n",
       "      <td>11.136779</td>\n",
       "      <td>0.069170</td>\n",
       "      <td>0.554695</td>\n",
       "      <td>6.284634</td>\n",
       "      <td>68.574901</td>\n",
       "      <td>3.795043</td>\n",
       "      <td>9.549407</td>\n",
       "      <td>408.237154</td>\n",
       "      <td>18.455534</td>\n",
       "      <td>356.674032</td>\n",
       "      <td>12.653063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8.601545</td>\n",
       "      <td>23.322453</td>\n",
       "      <td>6.860353</td>\n",
       "      <td>0.253994</td>\n",
       "      <td>0.115878</td>\n",
       "      <td>0.702617</td>\n",
       "      <td>28.148861</td>\n",
       "      <td>2.105710</td>\n",
       "      <td>8.707259</td>\n",
       "      <td>168.537116</td>\n",
       "      <td>2.164946</td>\n",
       "      <td>91.294864</td>\n",
       "      <td>7.141062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.006320</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.460000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.385000</td>\n",
       "      <td>3.561000</td>\n",
       "      <td>2.900000</td>\n",
       "      <td>1.129600</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>187.000000</td>\n",
       "      <td>12.600000</td>\n",
       "      <td>0.320000</td>\n",
       "      <td>1.730000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.082045</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.190000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.449000</td>\n",
       "      <td>5.885500</td>\n",
       "      <td>45.025000</td>\n",
       "      <td>2.100175</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>279.000000</td>\n",
       "      <td>17.400000</td>\n",
       "      <td>375.377500</td>\n",
       "      <td>6.950000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.256510</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.690000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.538000</td>\n",
       "      <td>6.208500</td>\n",
       "      <td>77.500000</td>\n",
       "      <td>3.207450</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>330.000000</td>\n",
       "      <td>19.050000</td>\n",
       "      <td>391.440000</td>\n",
       "      <td>11.360000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>3.677083</td>\n",
       "      <td>12.500000</td>\n",
       "      <td>18.100000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.624000</td>\n",
       "      <td>6.623500</td>\n",
       "      <td>94.075000</td>\n",
       "      <td>5.188425</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>666.000000</td>\n",
       "      <td>20.200000</td>\n",
       "      <td>396.225000</td>\n",
       "      <td>16.955000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>88.976200</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>27.740000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.871000</td>\n",
       "      <td>8.780000</td>\n",
       "      <td>100.000000</td>\n",
       "      <td>12.126500</td>\n",
       "      <td>24.000000</td>\n",
       "      <td>711.000000</td>\n",
       "      <td>22.000000</td>\n",
       "      <td>396.900000</td>\n",
       "      <td>37.970000</td>\n",
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       "             CRIM          ZN       INDUS        CHAS         NOX          RM  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean     3.613524   11.363636   11.136779    0.069170    0.554695    6.284634   \n",
       "std      8.601545   23.322453    6.860353    0.253994    0.115878    0.702617   \n",
       "min      0.006320    0.000000    0.460000    0.000000    0.385000    3.561000   \n",
       "25%      0.082045    0.000000    5.190000    0.000000    0.449000    5.885500   \n",
       "50%      0.256510    0.000000    9.690000    0.000000    0.538000    6.208500   \n",
       "75%      3.677083   12.500000   18.100000    0.000000    0.624000    6.623500   \n",
       "max     88.976200  100.000000   27.740000    1.000000    0.871000    8.780000   \n",
       "\n",
       "              AGE         DIS         RAD         TAX     PTRATIO           B  \\\n",
       "count  506.000000  506.000000  506.000000  506.000000  506.000000  506.000000   \n",
       "mean    68.574901    3.795043    9.549407  408.237154   18.455534  356.674032   \n",
       "std     28.148861    2.105710    8.707259  168.537116    2.164946   91.294864   \n",
       "min      2.900000    1.129600    1.000000  187.000000   12.600000    0.320000   \n",
       "25%     45.025000    2.100175    4.000000  279.000000   17.400000  375.377500   \n",
       "50%     77.500000    3.207450    5.000000  330.000000   19.050000  391.440000   \n",
       "75%     94.075000    5.188425   24.000000  666.000000   20.200000  396.225000   \n",
       "max    100.000000   12.126500   24.000000  711.000000   22.000000  396.900000   \n",
       "\n",
       "            LSTAT  \n",
       "count  506.000000  \n",
       "mean    12.653063  \n",
       "std      7.141062  \n",
       "min      1.730000  \n",
       "25%      6.950000  \n",
       "50%     11.360000  \n",
       "75%     16.955000  \n",
       "max     37.970000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boston.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d381fc65",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 506 entries, 0 to 505\n",
      "Data columns (total 13 columns):\n",
      " #   Column   Non-Null Count  Dtype  \n",
      "---  ------   --------------  -----  \n",
      " 0   CRIM     506 non-null    float64\n",
      " 1   ZN       506 non-null    float64\n",
      " 2   INDUS    506 non-null    float64\n",
      " 3   CHAS     506 non-null    float64\n",
      " 4   NOX      506 non-null    float64\n",
      " 5   RM       506 non-null    float64\n",
      " 6   AGE      506 non-null    float64\n",
      " 7   DIS      506 non-null    float64\n",
      " 8   RAD      506 non-null    float64\n",
      " 9   TAX      506 non-null    float64\n",
      " 10  PTRATIO  506 non-null    float64\n",
      " 11  B        506 non-null    float64\n",
      " 12  LSTAT    506 non-null    float64\n",
      "dtypes: float64(13)\n",
      "memory usage: 51.5 KB\n"
     ]
    }
   ],
   "source": [
    "boston.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e1bdd120",
   "metadata": {},
   "source": [
    "## Base on the Sklearn Model\n",
    "\n",
    "Standard scaler [here](https://stackoverflow.com/questions/40758562/can-anyone-explain-me-standardscaler)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "07241366",
   "metadata": {},
   "outputs": [],
   "source": [
    "# standardize the data\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "x = StandardScaler().fit_transform(boston)\n",
    "x = pd.DataFrame(x, columns=boston_dataset.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d8a74587",
   "metadata": {},
   "outputs": [],
   "source": [
    "## PCA\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA()\n",
    "pcat = pca.fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7eb4a71a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pcat.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "d8c71342",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2509514 , -0.25631454,  0.34667207,  0.00504243,  0.34285231,\n",
       "        -0.18924257,  0.3136706 , -0.32154387,  0.31979277,  0.33846915,\n",
       "         0.20494226, -0.20297261,  0.30975984],\n",
       "       [-0.31525237, -0.3233129 ,  0.11249291,  0.45482914,  0.21911553,\n",
       "         0.14933154,  0.31197778, -0.34907   , -0.27152094, -0.23945365,\n",
       "        -0.30589695,  0.23855944, -0.07432203],\n",
       "       [ 0.24656649,  0.29585782, -0.01594592,  0.28978082,  0.12096411,\n",
       "         0.59396117, -0.01767481, -0.04973627,  0.28725483,  0.22074447,\n",
       "        -0.32344627, -0.3001459 , -0.26700025],\n",
       "       [ 0.06177071,  0.12871159,  0.01714571,  0.81594136, -0.12822614,\n",
       "        -0.28059184, -0.17520603,  0.21543585,  0.13234996,  0.10333509,\n",
       "         0.28262198,  0.1684985 ,  0.06941441],\n",
       "       [ 0.08215692,  0.32061699, -0.00781119,  0.08653094,  0.13685356,\n",
       "        -0.4234472 ,  0.01669085,  0.09859225, -0.20413162, -0.13046057,\n",
       "        -0.58400223, -0.34560695,  0.39456113],\n",
       "       [-0.21965961, -0.3233881 , -0.0761379 ,  0.16749014, -0.15298267,\n",
       "         0.05926707, -0.07170914,  0.02343872, -0.14319401, -0.19293428,\n",
       "         0.2731533 , -0.80345454, -0.05321583],\n",
       "       [ 0.77760721, -0.27499628, -0.33957645,  0.07413621, -0.19963484,\n",
       "         0.06393992,  0.11601071, -0.10390044, -0.13794255, -0.31488683,\n",
       "         0.00232387,  0.07029476,  0.08701117],\n",
       "       [ 0.15335048, -0.40268031,  0.17393172, -0.02466215,  0.08012056,\n",
       "        -0.32675226, -0.60082292, -0.12181198,  0.08035831,  0.08277435,\n",
       "        -0.3178842 , -0.00492291, -0.42435293],\n",
       "       [ 0.26039028,  0.35813749,  0.64441615, -0.01372777, -0.01852201,\n",
       "         0.04789804, -0.06756218, -0.15329124, -0.47089067, -0.17656339,\n",
       "         0.25442836, -0.04489802, -0.19522139],\n",
       "       [ 0.01936913,  0.26752723, -0.36353226, -0.00618184,  0.23105645,\n",
       "        -0.43142019,  0.36277896, -0.17121314,  0.02190945, -0.03516835,\n",
       "         0.15343049, -0.09651512, -0.60071141],\n",
       "       [-0.10964435,  0.26275629, -0.30316943,  0.01392667,  0.11131888,\n",
       "         0.05316154, -0.45915939, -0.69569257,  0.03654388, -0.10483575,\n",
       "         0.17450534,  0.0192749 ,  0.27138243],\n",
       "       [ 0.08676107, -0.07142528, -0.11319963, -0.00398268,  0.80432257,\n",
       "         0.15287286, -0.21193607,  0.39094113, -0.10702589, -0.21519113,\n",
       "         0.20959883,  0.04172316,  0.05522596],\n",
       "       [ 0.0459523 , -0.08091897, -0.25107654,  0.03592171,  0.04363045,\n",
       "         0.0455671 , -0.03855068, -0.01829854, -0.63348972,  0.72023345,\n",
       "         0.02339805, -0.00446307,  0.02443168]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen vectors\n",
    "pca.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d4edd306",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.1389812 , 1.43611329, 1.2450773 , 0.85927328, 0.83646904,\n",
       "       0.65870897, 0.5364162 , 0.39688167, 0.27749173, 0.22067394,\n",
       "       0.18638271, 0.16963823, 0.06363502])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen values\n",
    "pca.explained_variance_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "72bf03b6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13, 13)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.components_.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "55d5fc02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13,)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6581a3e",
   "metadata": {},
   "source": [
    "## Combine Methode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "adf1b859",
   "metadata": {},
   "outputs": [],
   "source": [
    "# manual normalization\n",
    "Xc = np.array((boston - boston.mean(axis=0))/boston.std(axis=0))\n",
    "Xc = pd.DataFrame(Xc, columns=boston_dataset.feature_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "bef22a08",
   "metadata": {},
   "outputs": [],
   "source": [
    "pca2 = PCA()\n",
    "pcat2 = pca2.fit_transform(Xc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7f4f5943",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(506, 13)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pcat2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "814e63a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.2509514 , -0.25631454,  0.34667207,  0.00504243,  0.34285231,\n",
       "        -0.18924257,  0.3136706 , -0.32154387,  0.31979277,  0.33846915,\n",
       "         0.20494226, -0.20297261,  0.30975984],\n",
       "       [-0.31525237, -0.3233129 ,  0.11249291,  0.45482914,  0.21911553,\n",
       "         0.14933154,  0.31197778, -0.34907   , -0.27152094, -0.23945365,\n",
       "        -0.30589695,  0.23855944, -0.07432203],\n",
       "       [ 0.24656649,  0.29585782, -0.01594592,  0.28978082,  0.12096411,\n",
       "         0.59396117, -0.01767481, -0.04973627,  0.28725483,  0.22074447,\n",
       "        -0.32344627, -0.3001459 , -0.26700025],\n",
       "       [ 0.06177071,  0.12871159,  0.01714571,  0.81594136, -0.12822614,\n",
       "        -0.28059184, -0.17520603,  0.21543585,  0.13234996,  0.10333509,\n",
       "         0.28262198,  0.1684985 ,  0.06941441],\n",
       "       [ 0.08215692,  0.32061699, -0.00781119,  0.08653094,  0.13685356,\n",
       "        -0.4234472 ,  0.01669085,  0.09859225, -0.20413162, -0.13046057,\n",
       "        -0.58400223, -0.34560695,  0.39456113],\n",
       "       [-0.21965961, -0.3233881 , -0.0761379 ,  0.16749014, -0.15298267,\n",
       "         0.05926707, -0.07170914,  0.02343872, -0.14319401, -0.19293428,\n",
       "         0.2731533 , -0.80345454, -0.05321583],\n",
       "       [ 0.77760721, -0.27499628, -0.33957645,  0.07413621, -0.19963484,\n",
       "         0.06393992,  0.11601071, -0.10390044, -0.13794255, -0.31488683,\n",
       "         0.00232387,  0.07029476,  0.08701117],\n",
       "       [ 0.15335048, -0.40268031,  0.17393172, -0.02466215,  0.08012056,\n",
       "        -0.32675226, -0.60082292, -0.12181198,  0.08035831,  0.08277435,\n",
       "        -0.3178842 , -0.00492291, -0.42435293],\n",
       "       [ 0.26039028,  0.35813749,  0.64441615, -0.01372777, -0.01852201,\n",
       "         0.04789804, -0.06756218, -0.15329124, -0.47089067, -0.17656339,\n",
       "         0.25442836, -0.04489802, -0.19522139],\n",
       "       [ 0.01936913,  0.26752723, -0.36353226, -0.00618184,  0.23105645,\n",
       "        -0.43142019,  0.36277896, -0.17121314,  0.02190945, -0.03516835,\n",
       "         0.15343049, -0.09651512, -0.60071141],\n",
       "       [-0.10964435,  0.26275629, -0.30316943,  0.01392667,  0.11131888,\n",
       "         0.05316154, -0.45915939, -0.69569257,  0.03654388, -0.10483575,\n",
       "         0.17450534,  0.0192749 ,  0.27138243],\n",
       "       [ 0.08676107, -0.07142528, -0.11319963, -0.00398268,  0.80432257,\n",
       "         0.15287286, -0.21193607,  0.39094113, -0.10702589, -0.21519113,\n",
       "         0.20959883,  0.04172316,  0.05522596],\n",
       "       [ 0.0459523 , -0.08091897, -0.25107654,  0.03592171,  0.04363045,\n",
       "         0.0455671 , -0.03855068, -0.01829854, -0.63348972,  0.72023345,\n",
       "         0.02339805, -0.00446307,  0.02443168]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen vectors combine methode\n",
    "pca2.components_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "48733e96",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.12684883, 1.43327512, 1.24261667, 0.85757511, 0.83481594,\n",
       "       0.65740718, 0.53535609, 0.39609731, 0.27694333, 0.22023782,\n",
       "       0.18601437, 0.16930298, 0.06350926])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen values combine methode\n",
    "pca2.explained_variance_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc746e8f",
   "metadata": {},
   "source": [
    "## Manual Methode"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "170cd35f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# normalize the data\n",
    "X = np.array((boston - boston.mean(axis=0))/boston.std(axis=0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "481427b5",
   "metadata": {},
   "outputs": [],
   "source": [
    "# X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9fc9f290",
   "metadata": {},
   "outputs": [],
   "source": [
    "# calculating the the covariance matrix of the data\n",
    "Cx = np.cov(X, rowvar=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "60577556",
   "metadata": {},
   "outputs": [],
   "source": [
    "L, P = np.linalg.eig(Cx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "5a3d4a60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.2509514 ,  0.31525237, -0.24656649, -0.06177071,  0.08215692,\n",
       "         0.21965961, -0.77760721, -0.15335048, -0.0459523 , -0.26039028,\n",
       "         0.08676107,  0.10964435, -0.01936913],\n",
       "       [ 0.25631454,  0.3233129 , -0.29585782, -0.12871159,  0.32061699,\n",
       "         0.3233881 ,  0.27499628,  0.40268031,  0.08091897, -0.35813749,\n",
       "        -0.07142528, -0.26275629, -0.26752723],\n",
       "       [-0.34667207, -0.11249291,  0.01594592, -0.01714571, -0.00781119,\n",
       "         0.0761379 ,  0.33957645, -0.17393172,  0.25107654, -0.64441615,\n",
       "        -0.11319963,  0.30316943,  0.36353226],\n",
       "       [-0.00504243, -0.45482914, -0.28978082, -0.81594136,  0.08653094,\n",
       "        -0.16749014, -0.07413621,  0.02466215, -0.03592171,  0.01372777,\n",
       "        -0.00398268, -0.01392667,  0.00618184],\n",
       "       [-0.34285231, -0.21911553, -0.12096411,  0.12822614,  0.13685356,\n",
       "         0.15298267,  0.19963484, -0.08012056, -0.04363045,  0.01852201,\n",
       "         0.80432257, -0.11131888, -0.23105645],\n",
       "       [ 0.18924257, -0.14933154, -0.59396117,  0.28059184, -0.4234472 ,\n",
       "        -0.05926707, -0.06393992,  0.32675226, -0.0455671 , -0.04789804,\n",
       "         0.15287286, -0.05316154,  0.43142019],\n",
       "       [-0.3136706 , -0.31197778,  0.01767481,  0.17520603,  0.01669085,\n",
       "         0.07170914, -0.11601071,  0.60082292,  0.03855068,  0.06756218,\n",
       "        -0.21193607,  0.45915939, -0.36277896],\n",
       "       [ 0.32154387,  0.34907   ,  0.04973627, -0.21543585,  0.09859225,\n",
       "        -0.02343872,  0.10390044,  0.12181198,  0.01829854,  0.15329124,\n",
       "         0.39094113,  0.69569257,  0.17121314],\n",
       "       [-0.31979277,  0.27152094, -0.28725483, -0.13234996, -0.20413162,\n",
       "         0.14319401,  0.13794255, -0.08035831,  0.63348972,  0.47089067,\n",
       "        -0.10702589, -0.03654388, -0.02190945],\n",
       "       [-0.33846915,  0.23945365, -0.22074447, -0.10333509, -0.13046057,\n",
       "         0.19293428,  0.31488683, -0.08277435, -0.72023345,  0.17656339,\n",
       "        -0.21519113,  0.10483575,  0.03516835],\n",
       "       [-0.20494226,  0.30589695,  0.32344627, -0.28262198, -0.58400223,\n",
       "        -0.2731533 , -0.00232387,  0.3178842 , -0.02339805, -0.25442836,\n",
       "         0.20959883, -0.17450534, -0.15343049],\n",
       "       [ 0.20297261, -0.23855944,  0.3001459 , -0.1684985 , -0.34560695,\n",
       "         0.80345454, -0.07029476,  0.00492291,  0.00446307,  0.04489802,\n",
       "         0.04172316, -0.0192749 ,  0.09651512],\n",
       "       [-0.30975984,  0.07432203,  0.26700025, -0.06941441,  0.39456113,\n",
       "         0.05321583, -0.08701117,  0.42435293, -0.02443168,  0.19522139,\n",
       "         0.05522596, -0.27138243,  0.60071141]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen vector\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b22e9189",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.12684883, 1.43327512, 1.24261667, 0.85757511, 0.83481594,\n",
       "       0.65740718, 0.53535609, 0.39609731, 0.06350926, 0.27694333,\n",
       "       0.16930298, 0.18601437, 0.22023782])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen values\n",
    "L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "f19c3fb3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13, 13)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "9474da31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13,)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85febeb8",
   "metadata": {},
   "source": [
    "## Comparison of the result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "685c22bf",
   "metadata": {},
   "outputs": [],
   "source": [
    "ev1 = pd.DataFrame(pca.components_, columns=range(pca.components_.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3009665a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.250951</td>\n",
       "      <td>-0.256315</td>\n",
       "      <td>0.346672</td>\n",
       "      <td>0.005042</td>\n",
       "      <td>0.342852</td>\n",
       "      <td>-0.189243</td>\n",
       "      <td>0.313671</td>\n",
       "      <td>-0.321544</td>\n",
       "      <td>0.319793</td>\n",
       "      <td>0.338469</td>\n",
       "      <td>0.204942</td>\n",
       "      <td>-0.202973</td>\n",
       "      <td>0.309760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.315252</td>\n",
       "      <td>-0.323313</td>\n",
       "      <td>0.112493</td>\n",
       "      <td>0.454829</td>\n",
       "      <td>0.219116</td>\n",
       "      <td>0.149332</td>\n",
       "      <td>0.311978</td>\n",
       "      <td>-0.349070</td>\n",
       "      <td>-0.271521</td>\n",
       "      <td>-0.239454</td>\n",
       "      <td>-0.305897</td>\n",
       "      <td>0.238559</td>\n",
       "      <td>-0.074322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.246566</td>\n",
       "      <td>0.295858</td>\n",
       "      <td>-0.015946</td>\n",
       "      <td>0.289781</td>\n",
       "      <td>0.120964</td>\n",
       "      <td>0.593961</td>\n",
       "      <td>-0.017675</td>\n",
       "      <td>-0.049736</td>\n",
       "      <td>0.287255</td>\n",
       "      <td>0.220744</td>\n",
       "      <td>-0.323446</td>\n",
       "      <td>-0.300146</td>\n",
       "      <td>-0.267000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.061771</td>\n",
       "      <td>0.128712</td>\n",
       "      <td>0.017146</td>\n",
       "      <td>0.815941</td>\n",
       "      <td>-0.128226</td>\n",
       "      <td>-0.280592</td>\n",
       "      <td>-0.175206</td>\n",
       "      <td>0.215436</td>\n",
       "      <td>0.132350</td>\n",
       "      <td>0.103335</td>\n",
       "      <td>0.282622</td>\n",
       "      <td>0.168498</td>\n",
       "      <td>0.069414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.082157</td>\n",
       "      <td>0.320617</td>\n",
       "      <td>-0.007811</td>\n",
       "      <td>0.086531</td>\n",
       "      <td>0.136854</td>\n",
       "      <td>-0.423447</td>\n",
       "      <td>0.016691</td>\n",
       "      <td>0.098592</td>\n",
       "      <td>-0.204132</td>\n",
       "      <td>-0.130461</td>\n",
       "      <td>-0.584002</td>\n",
       "      <td>-0.345607</td>\n",
       "      <td>0.394561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.219660</td>\n",
       "      <td>-0.323388</td>\n",
       "      <td>-0.076138</td>\n",
       "      <td>0.167490</td>\n",
       "      <td>-0.152983</td>\n",
       "      <td>0.059267</td>\n",
       "      <td>-0.071709</td>\n",
       "      <td>0.023439</td>\n",
       "      <td>-0.143194</td>\n",
       "      <td>-0.192934</td>\n",
       "      <td>0.273153</td>\n",
       "      <td>-0.803455</td>\n",
       "      <td>-0.053216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.777607</td>\n",
       "      <td>-0.274996</td>\n",
       "      <td>-0.339576</td>\n",
       "      <td>0.074136</td>\n",
       "      <td>-0.199635</td>\n",
       "      <td>0.063940</td>\n",
       "      <td>0.116011</td>\n",
       "      <td>-0.103900</td>\n",
       "      <td>-0.137943</td>\n",
       "      <td>-0.314887</td>\n",
       "      <td>0.002324</td>\n",
       "      <td>0.070295</td>\n",
       "      <td>0.087011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.153350</td>\n",
       "      <td>-0.402680</td>\n",
       "      <td>0.173932</td>\n",
       "      <td>-0.024662</td>\n",
       "      <td>0.080121</td>\n",
       "      <td>-0.326752</td>\n",
       "      <td>-0.600823</td>\n",
       "      <td>-0.121812</td>\n",
       "      <td>0.080358</td>\n",
       "      <td>0.082774</td>\n",
       "      <td>-0.317884</td>\n",
       "      <td>-0.004923</td>\n",
       "      <td>-0.424353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.260390</td>\n",
       "      <td>0.358137</td>\n",
       "      <td>0.644416</td>\n",
       "      <td>-0.013728</td>\n",
       "      <td>-0.018522</td>\n",
       "      <td>0.047898</td>\n",
       "      <td>-0.067562</td>\n",
       "      <td>-0.153291</td>\n",
       "      <td>-0.470891</td>\n",
       "      <td>-0.176563</td>\n",
       "      <td>0.254428</td>\n",
       "      <td>-0.044898</td>\n",
       "      <td>-0.195221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.019369</td>\n",
       "      <td>0.267527</td>\n",
       "      <td>-0.363532</td>\n",
       "      <td>-0.006182</td>\n",
       "      <td>0.231056</td>\n",
       "      <td>-0.431420</td>\n",
       "      <td>0.362779</td>\n",
       "      <td>-0.171213</td>\n",
       "      <td>0.021909</td>\n",
       "      <td>-0.035168</td>\n",
       "      <td>0.153430</td>\n",
       "      <td>-0.096515</td>\n",
       "      <td>-0.600711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.109644</td>\n",
       "      <td>0.262756</td>\n",
       "      <td>-0.303169</td>\n",
       "      <td>0.013927</td>\n",
       "      <td>0.111319</td>\n",
       "      <td>0.053162</td>\n",
       "      <td>-0.459159</td>\n",
       "      <td>-0.695693</td>\n",
       "      <td>0.036544</td>\n",
       "      <td>-0.104836</td>\n",
       "      <td>0.174505</td>\n",
       "      <td>0.019275</td>\n",
       "      <td>0.271382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.086761</td>\n",
       "      <td>-0.071425</td>\n",
       "      <td>-0.113200</td>\n",
       "      <td>-0.003983</td>\n",
       "      <td>0.804323</td>\n",
       "      <td>0.152873</td>\n",
       "      <td>-0.211936</td>\n",
       "      <td>0.390941</td>\n",
       "      <td>-0.107026</td>\n",
       "      <td>-0.215191</td>\n",
       "      <td>0.209599</td>\n",
       "      <td>0.041723</td>\n",
       "      <td>0.055226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.045952</td>\n",
       "      <td>-0.080919</td>\n",
       "      <td>-0.251077</td>\n",
       "      <td>0.035922</td>\n",
       "      <td>0.043630</td>\n",
       "      <td>0.045567</td>\n",
       "      <td>-0.038551</td>\n",
       "      <td>-0.018299</td>\n",
       "      <td>-0.633490</td>\n",
       "      <td>0.720233</td>\n",
       "      <td>0.023398</td>\n",
       "      <td>-0.004463</td>\n",
       "      <td>0.024432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6   \\\n",
       "0   0.250951 -0.256315  0.346672  0.005042  0.342852 -0.189243  0.313671   \n",
       "1  -0.315252 -0.323313  0.112493  0.454829  0.219116  0.149332  0.311978   \n",
       "2   0.246566  0.295858 -0.015946  0.289781  0.120964  0.593961 -0.017675   \n",
       "3   0.061771  0.128712  0.017146  0.815941 -0.128226 -0.280592 -0.175206   \n",
       "4   0.082157  0.320617 -0.007811  0.086531  0.136854 -0.423447  0.016691   \n",
       "5  -0.219660 -0.323388 -0.076138  0.167490 -0.152983  0.059267 -0.071709   \n",
       "6   0.777607 -0.274996 -0.339576  0.074136 -0.199635  0.063940  0.116011   \n",
       "7   0.153350 -0.402680  0.173932 -0.024662  0.080121 -0.326752 -0.600823   \n",
       "8   0.260390  0.358137  0.644416 -0.013728 -0.018522  0.047898 -0.067562   \n",
       "9   0.019369  0.267527 -0.363532 -0.006182  0.231056 -0.431420  0.362779   \n",
       "10 -0.109644  0.262756 -0.303169  0.013927  0.111319  0.053162 -0.459159   \n",
       "11  0.086761 -0.071425 -0.113200 -0.003983  0.804323  0.152873 -0.211936   \n",
       "12  0.045952 -0.080919 -0.251077  0.035922  0.043630  0.045567 -0.038551   \n",
       "\n",
       "          7         8         9         10        11        12  \n",
       "0  -0.321544  0.319793  0.338469  0.204942 -0.202973  0.309760  \n",
       "1  -0.349070 -0.271521 -0.239454 -0.305897  0.238559 -0.074322  \n",
       "2  -0.049736  0.287255  0.220744 -0.323446 -0.300146 -0.267000  \n",
       "3   0.215436  0.132350  0.103335  0.282622  0.168498  0.069414  \n",
       "4   0.098592 -0.204132 -0.130461 -0.584002 -0.345607  0.394561  \n",
       "5   0.023439 -0.143194 -0.192934  0.273153 -0.803455 -0.053216  \n",
       "6  -0.103900 -0.137943 -0.314887  0.002324  0.070295  0.087011  \n",
       "7  -0.121812  0.080358  0.082774 -0.317884 -0.004923 -0.424353  \n",
       "8  -0.153291 -0.470891 -0.176563  0.254428 -0.044898 -0.195221  \n",
       "9  -0.171213  0.021909 -0.035168  0.153430 -0.096515 -0.600711  \n",
       "10 -0.695693  0.036544 -0.104836  0.174505  0.019275  0.271382  \n",
       "11  0.390941 -0.107026 -0.215191  0.209599  0.041723  0.055226  \n",
       "12 -0.018299 -0.633490  0.720233  0.023398 -0.004463  0.024432  "
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen vector model sklearn\n",
    "ev1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "042d08d3",
   "metadata": {},
   "outputs": [],
   "source": [
    "# eigen vector (combination)\n",
    "ev2 = pd.DataFrame(pca2.components_, columns=range(pca2.components_.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "6a2c4737",
   "metadata": {},
   "outputs": [
    {
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       "      <th>1</th>\n",
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       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.250951</td>\n",
       "      <td>-0.256315</td>\n",
       "      <td>0.346672</td>\n",
       "      <td>0.005042</td>\n",
       "      <td>0.342852</td>\n",
       "      <td>-0.189243</td>\n",
       "      <td>0.313671</td>\n",
       "      <td>-0.321544</td>\n",
       "      <td>0.319793</td>\n",
       "      <td>0.338469</td>\n",
       "      <td>0.204942</td>\n",
       "      <td>-0.202973</td>\n",
       "      <td>0.309760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.315252</td>\n",
       "      <td>-0.323313</td>\n",
       "      <td>0.112493</td>\n",
       "      <td>0.454829</td>\n",
       "      <td>0.219116</td>\n",
       "      <td>0.149332</td>\n",
       "      <td>0.311978</td>\n",
       "      <td>-0.349070</td>\n",
       "      <td>-0.271521</td>\n",
       "      <td>-0.239454</td>\n",
       "      <td>-0.305897</td>\n",
       "      <td>0.238559</td>\n",
       "      <td>-0.074322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.246566</td>\n",
       "      <td>0.295858</td>\n",
       "      <td>-0.015946</td>\n",
       "      <td>0.289781</td>\n",
       "      <td>0.120964</td>\n",
       "      <td>0.593961</td>\n",
       "      <td>-0.017675</td>\n",
       "      <td>-0.049736</td>\n",
       "      <td>0.287255</td>\n",
       "      <td>0.220744</td>\n",
       "      <td>-0.323446</td>\n",
       "      <td>-0.300146</td>\n",
       "      <td>-0.267000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.061771</td>\n",
       "      <td>0.128712</td>\n",
       "      <td>0.017146</td>\n",
       "      <td>0.815941</td>\n",
       "      <td>-0.128226</td>\n",
       "      <td>-0.280592</td>\n",
       "      <td>-0.175206</td>\n",
       "      <td>0.215436</td>\n",
       "      <td>0.132350</td>\n",
       "      <td>0.103335</td>\n",
       "      <td>0.282622</td>\n",
       "      <td>0.168498</td>\n",
       "      <td>0.069414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.082157</td>\n",
       "      <td>0.320617</td>\n",
       "      <td>-0.007811</td>\n",
       "      <td>0.086531</td>\n",
       "      <td>0.136854</td>\n",
       "      <td>-0.423447</td>\n",
       "      <td>0.016691</td>\n",
       "      <td>0.098592</td>\n",
       "      <td>-0.204132</td>\n",
       "      <td>-0.130461</td>\n",
       "      <td>-0.584002</td>\n",
       "      <td>-0.345607</td>\n",
       "      <td>0.394561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.219660</td>\n",
       "      <td>-0.323388</td>\n",
       "      <td>-0.076138</td>\n",
       "      <td>0.167490</td>\n",
       "      <td>-0.152983</td>\n",
       "      <td>0.059267</td>\n",
       "      <td>-0.071709</td>\n",
       "      <td>0.023439</td>\n",
       "      <td>-0.143194</td>\n",
       "      <td>-0.192934</td>\n",
       "      <td>0.273153</td>\n",
       "      <td>-0.803455</td>\n",
       "      <td>-0.053216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.777607</td>\n",
       "      <td>-0.274996</td>\n",
       "      <td>-0.339576</td>\n",
       "      <td>0.074136</td>\n",
       "      <td>-0.199635</td>\n",
       "      <td>0.063940</td>\n",
       "      <td>0.116011</td>\n",
       "      <td>-0.103900</td>\n",
       "      <td>-0.137943</td>\n",
       "      <td>-0.314887</td>\n",
       "      <td>0.002324</td>\n",
       "      <td>0.070295</td>\n",
       "      <td>0.087011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.153350</td>\n",
       "      <td>-0.402680</td>\n",
       "      <td>0.173932</td>\n",
       "      <td>-0.024662</td>\n",
       "      <td>0.080121</td>\n",
       "      <td>-0.326752</td>\n",
       "      <td>-0.600823</td>\n",
       "      <td>-0.121812</td>\n",
       "      <td>0.080358</td>\n",
       "      <td>0.082774</td>\n",
       "      <td>-0.317884</td>\n",
       "      <td>-0.004923</td>\n",
       "      <td>-0.424353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.260390</td>\n",
       "      <td>0.358137</td>\n",
       "      <td>0.644416</td>\n",
       "      <td>-0.013728</td>\n",
       "      <td>-0.018522</td>\n",
       "      <td>0.047898</td>\n",
       "      <td>-0.067562</td>\n",
       "      <td>-0.153291</td>\n",
       "      <td>-0.470891</td>\n",
       "      <td>-0.176563</td>\n",
       "      <td>0.254428</td>\n",
       "      <td>-0.044898</td>\n",
       "      <td>-0.195221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.019369</td>\n",
       "      <td>0.267527</td>\n",
       "      <td>-0.363532</td>\n",
       "      <td>-0.006182</td>\n",
       "      <td>0.231056</td>\n",
       "      <td>-0.431420</td>\n",
       "      <td>0.362779</td>\n",
       "      <td>-0.171213</td>\n",
       "      <td>0.021909</td>\n",
       "      <td>-0.035168</td>\n",
       "      <td>0.153430</td>\n",
       "      <td>-0.096515</td>\n",
       "      <td>-0.600711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.109644</td>\n",
       "      <td>0.262756</td>\n",
       "      <td>-0.303169</td>\n",
       "      <td>0.013927</td>\n",
       "      <td>0.111319</td>\n",
       "      <td>0.053162</td>\n",
       "      <td>-0.459159</td>\n",
       "      <td>-0.695693</td>\n",
       "      <td>0.036544</td>\n",
       "      <td>-0.104836</td>\n",
       "      <td>0.174505</td>\n",
       "      <td>0.019275</td>\n",
       "      <td>0.271382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.086761</td>\n",
       "      <td>-0.071425</td>\n",
       "      <td>-0.113200</td>\n",
       "      <td>-0.003983</td>\n",
       "      <td>0.804323</td>\n",
       "      <td>0.152873</td>\n",
       "      <td>-0.211936</td>\n",
       "      <td>0.390941</td>\n",
       "      <td>-0.107026</td>\n",
       "      <td>-0.215191</td>\n",
       "      <td>0.209599</td>\n",
       "      <td>0.041723</td>\n",
       "      <td>0.055226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.045952</td>\n",
       "      <td>-0.080919</td>\n",
       "      <td>-0.251077</td>\n",
       "      <td>0.035922</td>\n",
       "      <td>0.043630</td>\n",
       "      <td>0.045567</td>\n",
       "      <td>-0.038551</td>\n",
       "      <td>-0.018299</td>\n",
       "      <td>-0.633490</td>\n",
       "      <td>0.720233</td>\n",
       "      <td>0.023398</td>\n",
       "      <td>-0.004463</td>\n",
       "      <td>0.024432</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6   \\\n",
       "0   0.250951 -0.256315  0.346672  0.005042  0.342852 -0.189243  0.313671   \n",
       "1  -0.315252 -0.323313  0.112493  0.454829  0.219116  0.149332  0.311978   \n",
       "2   0.246566  0.295858 -0.015946  0.289781  0.120964  0.593961 -0.017675   \n",
       "3   0.061771  0.128712  0.017146  0.815941 -0.128226 -0.280592 -0.175206   \n",
       "4   0.082157  0.320617 -0.007811  0.086531  0.136854 -0.423447  0.016691   \n",
       "5  -0.219660 -0.323388 -0.076138  0.167490 -0.152983  0.059267 -0.071709   \n",
       "6   0.777607 -0.274996 -0.339576  0.074136 -0.199635  0.063940  0.116011   \n",
       "7   0.153350 -0.402680  0.173932 -0.024662  0.080121 -0.326752 -0.600823   \n",
       "8   0.260390  0.358137  0.644416 -0.013728 -0.018522  0.047898 -0.067562   \n",
       "9   0.019369  0.267527 -0.363532 -0.006182  0.231056 -0.431420  0.362779   \n",
       "10 -0.109644  0.262756 -0.303169  0.013927  0.111319  0.053162 -0.459159   \n",
       "11  0.086761 -0.071425 -0.113200 -0.003983  0.804323  0.152873 -0.211936   \n",
       "12  0.045952 -0.080919 -0.251077  0.035922  0.043630  0.045567 -0.038551   \n",
       "\n",
       "          7         8         9         10        11        12  \n",
       "0  -0.321544  0.319793  0.338469  0.204942 -0.202973  0.309760  \n",
       "1  -0.349070 -0.271521 -0.239454 -0.305897  0.238559 -0.074322  \n",
       "2  -0.049736  0.287255  0.220744 -0.323446 -0.300146 -0.267000  \n",
       "3   0.215436  0.132350  0.103335  0.282622  0.168498  0.069414  \n",
       "4   0.098592 -0.204132 -0.130461 -0.584002 -0.345607  0.394561  \n",
       "5   0.023439 -0.143194 -0.192934  0.273153 -0.803455 -0.053216  \n",
       "6  -0.103900 -0.137943 -0.314887  0.002324  0.070295  0.087011  \n",
       "7  -0.121812  0.080358  0.082774 -0.317884 -0.004923 -0.424353  \n",
       "8  -0.153291 -0.470891 -0.176563  0.254428 -0.044898 -0.195221  \n",
       "9  -0.171213  0.021909 -0.035168  0.153430 -0.096515 -0.600711  \n",
       "10 -0.695693  0.036544 -0.104836  0.174505  0.019275  0.271382  \n",
       "11  0.390941 -0.107026 -0.215191  0.209599  0.041723  0.055226  \n",
       "12 -0.018299 -0.633490  0.720233  0.023398 -0.004463  0.024432  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ev2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "d256eb24",
   "metadata": {},
   "outputs": [],
   "source": [
    "# eigen vector manual\n",
    "ev3 = pd.DataFrame(P, columns=range(P.shape[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "e1695a5d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.250951</td>\n",
       "      <td>0.315252</td>\n",
       "      <td>-0.246566</td>\n",
       "      <td>-0.061771</td>\n",
       "      <td>0.082157</td>\n",
       "      <td>0.219660</td>\n",
       "      <td>-0.777607</td>\n",
       "      <td>-0.153350</td>\n",
       "      <td>-0.045952</td>\n",
       "      <td>-0.260390</td>\n",
       "      <td>0.086761</td>\n",
       "      <td>0.109644</td>\n",
       "      <td>-0.019369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.256315</td>\n",
       "      <td>0.323313</td>\n",
       "      <td>-0.295858</td>\n",
       "      <td>-0.128712</td>\n",
       "      <td>0.320617</td>\n",
       "      <td>0.323388</td>\n",
       "      <td>0.274996</td>\n",
       "      <td>0.402680</td>\n",
       "      <td>0.080919</td>\n",
       "      <td>-0.358137</td>\n",
       "      <td>-0.071425</td>\n",
       "      <td>-0.262756</td>\n",
       "      <td>-0.267527</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.346672</td>\n",
       "      <td>-0.112493</td>\n",
       "      <td>0.015946</td>\n",
       "      <td>-0.017146</td>\n",
       "      <td>-0.007811</td>\n",
       "      <td>0.076138</td>\n",
       "      <td>0.339576</td>\n",
       "      <td>-0.173932</td>\n",
       "      <td>0.251077</td>\n",
       "      <td>-0.644416</td>\n",
       "      <td>-0.113200</td>\n",
       "      <td>0.303169</td>\n",
       "      <td>0.363532</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.005042</td>\n",
       "      <td>-0.454829</td>\n",
       "      <td>-0.289781</td>\n",
       "      <td>-0.815941</td>\n",
       "      <td>0.086531</td>\n",
       "      <td>-0.167490</td>\n",
       "      <td>-0.074136</td>\n",
       "      <td>0.024662</td>\n",
       "      <td>-0.035922</td>\n",
       "      <td>0.013728</td>\n",
       "      <td>-0.003983</td>\n",
       "      <td>-0.013927</td>\n",
       "      <td>0.006182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.342852</td>\n",
       "      <td>-0.219116</td>\n",
       "      <td>-0.120964</td>\n",
       "      <td>0.128226</td>\n",
       "      <td>0.136854</td>\n",
       "      <td>0.152983</td>\n",
       "      <td>0.199635</td>\n",
       "      <td>-0.080121</td>\n",
       "      <td>-0.043630</td>\n",
       "      <td>0.018522</td>\n",
       "      <td>0.804323</td>\n",
       "      <td>-0.111319</td>\n",
       "      <td>-0.231056</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.189243</td>\n",
       "      <td>-0.149332</td>\n",
       "      <td>-0.593961</td>\n",
       "      <td>0.280592</td>\n",
       "      <td>-0.423447</td>\n",
       "      <td>-0.059267</td>\n",
       "      <td>-0.063940</td>\n",
       "      <td>0.326752</td>\n",
       "      <td>-0.045567</td>\n",
       "      <td>-0.047898</td>\n",
       "      <td>0.152873</td>\n",
       "      <td>-0.053162</td>\n",
       "      <td>0.431420</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-0.313671</td>\n",
       "      <td>-0.311978</td>\n",
       "      <td>0.017675</td>\n",
       "      <td>0.175206</td>\n",
       "      <td>0.016691</td>\n",
       "      <td>0.071709</td>\n",
       "      <td>-0.116011</td>\n",
       "      <td>0.600823</td>\n",
       "      <td>0.038551</td>\n",
       "      <td>0.067562</td>\n",
       "      <td>-0.211936</td>\n",
       "      <td>0.459159</td>\n",
       "      <td>-0.362779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.321544</td>\n",
       "      <td>0.349070</td>\n",
       "      <td>0.049736</td>\n",
       "      <td>-0.215436</td>\n",
       "      <td>0.098592</td>\n",
       "      <td>-0.023439</td>\n",
       "      <td>0.103900</td>\n",
       "      <td>0.121812</td>\n",
       "      <td>0.018299</td>\n",
       "      <td>0.153291</td>\n",
       "      <td>0.390941</td>\n",
       "      <td>0.695693</td>\n",
       "      <td>0.171213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.319793</td>\n",
       "      <td>0.271521</td>\n",
       "      <td>-0.287255</td>\n",
       "      <td>-0.132350</td>\n",
       "      <td>-0.204132</td>\n",
       "      <td>0.143194</td>\n",
       "      <td>0.137943</td>\n",
       "      <td>-0.080358</td>\n",
       "      <td>0.633490</td>\n",
       "      <td>0.470891</td>\n",
       "      <td>-0.107026</td>\n",
       "      <td>-0.036544</td>\n",
       "      <td>-0.021909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-0.338469</td>\n",
       "      <td>0.239454</td>\n",
       "      <td>-0.220744</td>\n",
       "      <td>-0.103335</td>\n",
       "      <td>-0.130461</td>\n",
       "      <td>0.192934</td>\n",
       "      <td>0.314887</td>\n",
       "      <td>-0.082774</td>\n",
       "      <td>-0.720233</td>\n",
       "      <td>0.176563</td>\n",
       "      <td>-0.215191</td>\n",
       "      <td>0.104836</td>\n",
       "      <td>0.035168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.204942</td>\n",
       "      <td>0.305897</td>\n",
       "      <td>0.323446</td>\n",
       "      <td>-0.282622</td>\n",
       "      <td>-0.584002</td>\n",
       "      <td>-0.273153</td>\n",
       "      <td>-0.002324</td>\n",
       "      <td>0.317884</td>\n",
       "      <td>-0.023398</td>\n",
       "      <td>-0.254428</td>\n",
       "      <td>0.209599</td>\n",
       "      <td>-0.174505</td>\n",
       "      <td>-0.153430</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.202973</td>\n",
       "      <td>-0.238559</td>\n",
       "      <td>0.300146</td>\n",
       "      <td>-0.168498</td>\n",
       "      <td>-0.345607</td>\n",
       "      <td>0.803455</td>\n",
       "      <td>-0.070295</td>\n",
       "      <td>0.004923</td>\n",
       "      <td>0.004463</td>\n",
       "      <td>0.044898</td>\n",
       "      <td>0.041723</td>\n",
       "      <td>-0.019275</td>\n",
       "      <td>0.096515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>-0.309760</td>\n",
       "      <td>0.074322</td>\n",
       "      <td>0.267000</td>\n",
       "      <td>-0.069414</td>\n",
       "      <td>0.394561</td>\n",
       "      <td>0.053216</td>\n",
       "      <td>-0.087011</td>\n",
       "      <td>0.424353</td>\n",
       "      <td>-0.024432</td>\n",
       "      <td>0.195221</td>\n",
       "      <td>0.055226</td>\n",
       "      <td>-0.271382</td>\n",
       "      <td>0.600711</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6   \\\n",
       "0  -0.250951  0.315252 -0.246566 -0.061771  0.082157  0.219660 -0.777607   \n",
       "1   0.256315  0.323313 -0.295858 -0.128712  0.320617  0.323388  0.274996   \n",
       "2  -0.346672 -0.112493  0.015946 -0.017146 -0.007811  0.076138  0.339576   \n",
       "3  -0.005042 -0.454829 -0.289781 -0.815941  0.086531 -0.167490 -0.074136   \n",
       "4  -0.342852 -0.219116 -0.120964  0.128226  0.136854  0.152983  0.199635   \n",
       "5   0.189243 -0.149332 -0.593961  0.280592 -0.423447 -0.059267 -0.063940   \n",
       "6  -0.313671 -0.311978  0.017675  0.175206  0.016691  0.071709 -0.116011   \n",
       "7   0.321544  0.349070  0.049736 -0.215436  0.098592 -0.023439  0.103900   \n",
       "8  -0.319793  0.271521 -0.287255 -0.132350 -0.204132  0.143194  0.137943   \n",
       "9  -0.338469  0.239454 -0.220744 -0.103335 -0.130461  0.192934  0.314887   \n",
       "10 -0.204942  0.305897  0.323446 -0.282622 -0.584002 -0.273153 -0.002324   \n",
       "11  0.202973 -0.238559  0.300146 -0.168498 -0.345607  0.803455 -0.070295   \n",
       "12 -0.309760  0.074322  0.267000 -0.069414  0.394561  0.053216 -0.087011   \n",
       "\n",
       "          7         8         9         10        11        12  \n",
       "0  -0.153350 -0.045952 -0.260390  0.086761  0.109644 -0.019369  \n",
       "1   0.402680  0.080919 -0.358137 -0.071425 -0.262756 -0.267527  \n",
       "2  -0.173932  0.251077 -0.644416 -0.113200  0.303169  0.363532  \n",
       "3   0.024662 -0.035922  0.013728 -0.003983 -0.013927  0.006182  \n",
       "4  -0.080121 -0.043630  0.018522  0.804323 -0.111319 -0.231056  \n",
       "5   0.326752 -0.045567 -0.047898  0.152873 -0.053162  0.431420  \n",
       "6   0.600823  0.038551  0.067562 -0.211936  0.459159 -0.362779  \n",
       "7   0.121812  0.018299  0.153291  0.390941  0.695693  0.171213  \n",
       "8  -0.080358  0.633490  0.470891 -0.107026 -0.036544 -0.021909  \n",
       "9  -0.082774 -0.720233  0.176563 -0.215191  0.104836  0.035168  \n",
       "10  0.317884 -0.023398 -0.254428  0.209599 -0.174505 -0.153430  \n",
       "11  0.004923  0.004463  0.044898  0.041723 -0.019275  0.096515  \n",
       "12  0.424353 -0.024432  0.195221  0.055226 -0.271382  0.600711  "
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ev3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "498e9cdb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.250951</td>\n",
       "      <td>-0.256315</td>\n",
       "      <td>0.346672</td>\n",
       "      <td>0.005042</td>\n",
       "      <td>0.342852</td>\n",
       "      <td>-0.189243</td>\n",
       "      <td>0.313671</td>\n",
       "      <td>-0.321544</td>\n",
       "      <td>0.319793</td>\n",
       "      <td>0.338469</td>\n",
       "      <td>0.204942</td>\n",
       "      <td>-0.202973</td>\n",
       "      <td>0.309760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.315252</td>\n",
       "      <td>-0.323313</td>\n",
       "      <td>0.112493</td>\n",
       "      <td>0.454829</td>\n",
       "      <td>0.219116</td>\n",
       "      <td>0.149332</td>\n",
       "      <td>0.311978</td>\n",
       "      <td>-0.349070</td>\n",
       "      <td>-0.271521</td>\n",
       "      <td>-0.239454</td>\n",
       "      <td>-0.305897</td>\n",
       "      <td>0.238559</td>\n",
       "      <td>-0.074322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.246566</td>\n",
       "      <td>0.295858</td>\n",
       "      <td>-0.015946</td>\n",
       "      <td>0.289781</td>\n",
       "      <td>0.120964</td>\n",
       "      <td>0.593961</td>\n",
       "      <td>-0.017675</td>\n",
       "      <td>-0.049736</td>\n",
       "      <td>0.287255</td>\n",
       "      <td>0.220744</td>\n",
       "      <td>-0.323446</td>\n",
       "      <td>-0.300146</td>\n",
       "      <td>-0.267000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.061771</td>\n",
       "      <td>0.128712</td>\n",
       "      <td>0.017146</td>\n",
       "      <td>0.815941</td>\n",
       "      <td>-0.128226</td>\n",
       "      <td>-0.280592</td>\n",
       "      <td>-0.175206</td>\n",
       "      <td>0.215436</td>\n",
       "      <td>0.132350</td>\n",
       "      <td>0.103335</td>\n",
       "      <td>0.282622</td>\n",
       "      <td>0.168498</td>\n",
       "      <td>0.069414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.082157</td>\n",
       "      <td>-0.320617</td>\n",
       "      <td>0.007811</td>\n",
       "      <td>-0.086531</td>\n",
       "      <td>-0.136854</td>\n",
       "      <td>0.423447</td>\n",
       "      <td>-0.016691</td>\n",
       "      <td>-0.098592</td>\n",
       "      <td>0.204132</td>\n",
       "      <td>0.130461</td>\n",
       "      <td>0.584002</td>\n",
       "      <td>0.345607</td>\n",
       "      <td>-0.394561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>-0.219660</td>\n",
       "      <td>-0.323388</td>\n",
       "      <td>-0.076138</td>\n",
       "      <td>0.167490</td>\n",
       "      <td>-0.152983</td>\n",
       "      <td>0.059267</td>\n",
       "      <td>-0.071709</td>\n",
       "      <td>0.023439</td>\n",
       "      <td>-0.143194</td>\n",
       "      <td>-0.192934</td>\n",
       "      <td>0.273153</td>\n",
       "      <td>-0.803455</td>\n",
       "      <td>-0.053216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.777607</td>\n",
       "      <td>-0.274996</td>\n",
       "      <td>-0.339576</td>\n",
       "      <td>0.074136</td>\n",
       "      <td>-0.199635</td>\n",
       "      <td>0.063940</td>\n",
       "      <td>0.116011</td>\n",
       "      <td>-0.103900</td>\n",
       "      <td>-0.137943</td>\n",
       "      <td>-0.314887</td>\n",
       "      <td>0.002324</td>\n",
       "      <td>0.070295</td>\n",
       "      <td>0.087011</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.153350</td>\n",
       "      <td>-0.402680</td>\n",
       "      <td>0.173932</td>\n",
       "      <td>-0.024662</td>\n",
       "      <td>0.080121</td>\n",
       "      <td>-0.326752</td>\n",
       "      <td>-0.600823</td>\n",
       "      <td>-0.121812</td>\n",
       "      <td>0.080358</td>\n",
       "      <td>0.082774</td>\n",
       "      <td>-0.317884</td>\n",
       "      <td>-0.004923</td>\n",
       "      <td>-0.424353</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.045952</td>\n",
       "      <td>-0.080919</td>\n",
       "      <td>-0.251077</td>\n",
       "      <td>0.035922</td>\n",
       "      <td>0.043630</td>\n",
       "      <td>0.045567</td>\n",
       "      <td>-0.038551</td>\n",
       "      <td>-0.018299</td>\n",
       "      <td>-0.633490</td>\n",
       "      <td>0.720233</td>\n",
       "      <td>0.023398</td>\n",
       "      <td>-0.004463</td>\n",
       "      <td>0.024432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.260390</td>\n",
       "      <td>0.358137</td>\n",
       "      <td>0.644416</td>\n",
       "      <td>-0.013728</td>\n",
       "      <td>-0.018522</td>\n",
       "      <td>0.047898</td>\n",
       "      <td>-0.067562</td>\n",
       "      <td>-0.153291</td>\n",
       "      <td>-0.470891</td>\n",
       "      <td>-0.176563</td>\n",
       "      <td>0.254428</td>\n",
       "      <td>-0.044898</td>\n",
       "      <td>-0.195221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.086761</td>\n",
       "      <td>0.071425</td>\n",
       "      <td>0.113200</td>\n",
       "      <td>0.003983</td>\n",
       "      <td>-0.804323</td>\n",
       "      <td>-0.152873</td>\n",
       "      <td>0.211936</td>\n",
       "      <td>-0.390941</td>\n",
       "      <td>0.107026</td>\n",
       "      <td>0.215191</td>\n",
       "      <td>-0.209599</td>\n",
       "      <td>-0.041723</td>\n",
       "      <td>-0.055226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-0.109644</td>\n",
       "      <td>0.262756</td>\n",
       "      <td>-0.303169</td>\n",
       "      <td>0.013927</td>\n",
       "      <td>0.111319</td>\n",
       "      <td>0.053162</td>\n",
       "      <td>-0.459159</td>\n",
       "      <td>-0.695693</td>\n",
       "      <td>0.036544</td>\n",
       "      <td>-0.104836</td>\n",
       "      <td>0.174505</td>\n",
       "      <td>0.019275</td>\n",
       "      <td>0.271382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.019369</td>\n",
       "      <td>0.267527</td>\n",
       "      <td>-0.363532</td>\n",
       "      <td>-0.006182</td>\n",
       "      <td>0.231056</td>\n",
       "      <td>-0.431420</td>\n",
       "      <td>0.362779</td>\n",
       "      <td>-0.171213</td>\n",
       "      <td>0.021909</td>\n",
       "      <td>-0.035168</td>\n",
       "      <td>0.153430</td>\n",
       "      <td>-0.096515</td>\n",
       "      <td>-0.600711</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3         4         5         6   \\\n",
       "0   0.250951 -0.256315  0.346672  0.005042  0.342852 -0.189243  0.313671   \n",
       "1  -0.315252 -0.323313  0.112493  0.454829  0.219116  0.149332  0.311978   \n",
       "2   0.246566  0.295858 -0.015946  0.289781  0.120964  0.593961 -0.017675   \n",
       "3   0.061771  0.128712  0.017146  0.815941 -0.128226 -0.280592 -0.175206   \n",
       "4  -0.082157 -0.320617  0.007811 -0.086531 -0.136854  0.423447 -0.016691   \n",
       "5  -0.219660 -0.323388 -0.076138  0.167490 -0.152983  0.059267 -0.071709   \n",
       "6   0.777607 -0.274996 -0.339576  0.074136 -0.199635  0.063940  0.116011   \n",
       "7   0.153350 -0.402680  0.173932 -0.024662  0.080121 -0.326752 -0.600823   \n",
       "8   0.045952 -0.080919 -0.251077  0.035922  0.043630  0.045567 -0.038551   \n",
       "9   0.260390  0.358137  0.644416 -0.013728 -0.018522  0.047898 -0.067562   \n",
       "10 -0.086761  0.071425  0.113200  0.003983 -0.804323 -0.152873  0.211936   \n",
       "11 -0.109644  0.262756 -0.303169  0.013927  0.111319  0.053162 -0.459159   \n",
       "12  0.019369  0.267527 -0.363532 -0.006182  0.231056 -0.431420  0.362779   \n",
       "\n",
       "          7         8         9         10        11        12  \n",
       "0  -0.321544  0.319793  0.338469  0.204942 -0.202973  0.309760  \n",
       "1  -0.349070 -0.271521 -0.239454 -0.305897  0.238559 -0.074322  \n",
       "2  -0.049736  0.287255  0.220744 -0.323446 -0.300146 -0.267000  \n",
       "3   0.215436  0.132350  0.103335  0.282622  0.168498  0.069414  \n",
       "4  -0.098592  0.204132  0.130461  0.584002  0.345607 -0.394561  \n",
       "5   0.023439 -0.143194 -0.192934  0.273153 -0.803455 -0.053216  \n",
       "6  -0.103900 -0.137943 -0.314887  0.002324  0.070295  0.087011  \n",
       "7  -0.121812  0.080358  0.082774 -0.317884 -0.004923 -0.424353  \n",
       "8  -0.018299 -0.633490  0.720233  0.023398 -0.004463  0.024432  \n",
       "9  -0.153291 -0.470891 -0.176563  0.254428 -0.044898 -0.195221  \n",
       "10 -0.390941  0.107026  0.215191 -0.209599 -0.041723 -0.055226  \n",
       "11 -0.695693  0.036544 -0.104836  0.174505  0.019275  0.271382  \n",
       "12 -0.171213  0.021909 -0.035168  0.153430 -0.096515 -0.600711  "
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "-(ev3.T)\n",
    "# so actually the sklearn pca has same result if we do transpose and \n",
    "# multiple it with minus(subrraction)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "32188726",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.1389812 , 1.43611329, 1.2450773 , 0.85927328, 0.83646904,\n",
       "       0.65870897, 0.5364162 , 0.39688167, 0.27749173, 0.22067394,\n",
       "       0.18638271, 0.16963823, 0.06363502])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen values model sklearn\n",
    "pca.explained_variance_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "9442fb31",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.12684883, 1.43327512, 1.24261667, 0.85757511, 0.83481594,\n",
       "       0.65740718, 0.53535609, 0.39609731, 0.27694333, 0.22023782,\n",
       "       0.18601437, 0.16930298, 0.06350926])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen values model sklearn with manual normalization (combination)\n",
    "pca2.explained_variance_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "0401f098",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.12684883, 1.43327512, 1.24261667, 0.85757511, 0.83481594,\n",
       "       0.65740718, 0.53535609, 0.39609731, 0.06350926, 0.27694333,\n",
       "       0.16930298, 0.18601437, 0.22023782])"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# eigen values manual\n",
    "L"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d261f11",
   "metadata": {},
   "source": [
    "### Conclusion\n",
    "so from the experiment we can get several conclusion which,\n",
    "- the sklearn preprocessing standardization making the the sklearn pca resulting different with the manual process\n",
    "- even the result of combination of eigen values are same with manual process the eigen vector are not the same with the manual process and it's more look like with the sklearn pca "
   ]
  }
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