unsupervised-learning/PCA_titanic_dataset.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA applied to Titanic dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Library Import"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# some librarys\n",
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Collecting Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>PassengerId</th>\n",
       "      <th>Survived</th>\n",
       "      <th>Pclass</th>\n",
       "      <th>Name</th>\n",
       "      <th>Sex</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Ticket</th>\n",
       "      <th>Fare</th>\n",
       "      <th>Cabin</th>\n",
       "      <th>Embarked</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
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       "      <td>Braund, Mr. Owen Harris</td>\n",
       "      <td>male</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
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       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C85</td>\n",
       "      <td>C</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
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       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>C123</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>NaN</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "3            4         1       1   \n",
       "4            5         0       3   \n",
       "\n",
       "                                                Name     Sex   Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
       "\n",
       "   Parch            Ticket     Fare Cabin Embarked  \n",
       "0      0         A/5 21171   7.2500   NaN        S  \n",
       "1      0          PC 17599  71.2833   C85        C  \n",
       "2      0  STON/O2. 3101282   7.9250   NaN        S  \n",
       "3      0            113803  53.1000  C123        S  \n",
       "4      0            373450   8.0500   NaN        S  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# open database\n",
    "df = pd.read_csv(\"titanic/train.csv\")\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data Wrabling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PassengerId      0\n",
       "Survived         0\n",
       "Pclass           0\n",
       "Name             0\n",
       "Sex              0\n",
       "Age            177\n",
       "SibSp            0\n",
       "Parch            0\n",
       "Ticket           0\n",
       "Fare             0\n",
       "Cabin          687\n",
       "Embarked         2\n",
       "dtype: int64"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Survived</th>\n",
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       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
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       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>S</td>\n",
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       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
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       "      <td>5</td>\n",
       "      <td>0</td>\n",
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       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>S</td>\n",
       "    </tr>\n",
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      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "3            4         1       1   \n",
       "4            5         0       3   \n",
       "\n",
       "                                                Name     Sex   Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
       "\n",
       "   Parch            Ticket     Fare Embarked  \n",
       "0      0         A/5 21171   7.2500        S  \n",
       "1      0          PC 17599  71.2833        C  \n",
       "2      0  STON/O2. 3101282   7.9250        S  \n",
       "3      0            113803  53.1000        S  \n",
       "4      0            373450   8.0500        S  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.drop(\"Cabin\", axis=1, inplace=True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PassengerId    0\n",
       "Survived       0\n",
       "Pclass         0\n",
       "Name           0\n",
       "Sex            0\n",
       "Age            0\n",
       "SibSp          0\n",
       "Parch          0\n",
       "Ticket         0\n",
       "Fare           0\n",
       "Embarked       0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.dropna(inplace=True)\n",
    "df.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "   male\n",
       "0     1\n",
       "1     0\n",
       "2     0\n",
       "3     0\n",
       "4     1"
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     "execution_count": 6,
     "metadata": {},
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   "source": [
    "sex = pd.get_dummies(df[\"Sex\"], drop_first=True)\n",
    "sex.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "   Q  S\n",
       "0  0  1\n",
       "1  0  0\n",
       "2  0  1\n",
       "3  0  1\n",
       "4  0  1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "embark = pd.get_dummies(df[\"Embarked\"], drop_first=True)\n",
    "embark.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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       "   2  3\n",
       "0  0  1\n",
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       "2  0  1\n",
       "3  0  0\n",
       "4  0  1"
      ]
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     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pclass = pd.get_dummies(df[\"Pclass\"], drop_first=True)\n",
    "Pclass.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "      <td>A/5 21171</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>S</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Cumings, Mrs. John Bradley (Florence Briggs Th...</td>\n",
       "      <td>female</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>PC 17599</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>C</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>Heikkinen, Miss. Laina</td>\n",
       "      <td>female</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>STON/O2. 3101282</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>S</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>Futrelle, Mrs. Jacques Heath (Lily May Peel)</td>\n",
       "      <td>female</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>113803</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>S</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>Allen, Mr. William Henry</td>\n",
       "      <td>male</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>373450</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>S</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PassengerId  Survived  Pclass  \\\n",
       "0            1         0       3   \n",
       "1            2         1       1   \n",
       "2            3         1       3   \n",
       "3            4         1       1   \n",
       "4            5         0       3   \n",
       "\n",
       "                                                Name     Sex   Age  SibSp  \\\n",
       "0                            Braund, Mr. Owen Harris    male  22.0      1   \n",
       "1  Cumings, Mrs. John Bradley (Florence Briggs Th...  female  38.0      1   \n",
       "2                             Heikkinen, Miss. Laina  female  26.0      0   \n",
       "3       Futrelle, Mrs. Jacques Heath (Lily May Peel)  female  35.0      1   \n",
       "4                           Allen, Mr. William Henry    male  35.0      0   \n",
       "\n",
       "   Parch            Ticket     Fare Embarked  male  Q  S  2  3  \n",
       "0      0         A/5 21171   7.2500        S     1  0  1  0  1  \n",
       "1      0          PC 17599  71.2833        C     0  0  0  0  0  \n",
       "2      0  STON/O2. 3101282   7.9250        S     0  0  1  0  1  \n",
       "3      0            113803  53.1000        S     0  0  1  0  0  \n",
       "4      0            373450   8.0500        S     1  0  1  0  1  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.concat([df, sex, embark, Pclass], axis=1)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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>Survived</th>\n",
       "      <th>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>male</th>\n",
       "      <th>Q</th>\n",
       "      <th>S</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Survived   Age  SibSp  Parch     Fare  male  Q  S  2  3\n",
       "0         0  22.0      1      0   7.2500     1  0  1  0  1\n",
       "1         1  38.0      1      0  71.2833     0  0  0  0  0\n",
       "2         1  26.0      0      0   7.9250     0  0  1  0  1\n",
       "3         1  35.0      1      0  53.1000     0  0  1  0  0\n",
       "4         0  35.0      0      0   8.0500     1  0  1  0  1"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.drop([\"Sex\", \"Embarked\", \"PassengerId\", \"Name\", \"Ticket\", \"Pclass\"], axis=1, inplace=True)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Split features vectors and labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>Age</th>\n",
       "      <th>SibSp</th>\n",
       "      <th>Parch</th>\n",
       "      <th>Fare</th>\n",
       "      <th>male</th>\n",
       "      <th>Q</th>\n",
       "      <th>S</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>22.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>7.2500</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>71.2833</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>26.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>7.9250</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>35.0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>53.1000</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>35.0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8.0500</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Age  SibSp  Parch     Fare  male  Q  S  2  3\n",
       "0  22.0      1      0   7.2500     1  0  1  0  1\n",
       "1  38.0      1      0  71.2833     0  0  0  0  0\n",
       "2  26.0      0      0   7.9250     0  0  1  0  1\n",
       "3  35.0      1      0  53.1000     0  0  1  0  0\n",
       "4  35.0      0      0   8.0500     1  0  1  0  1"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = df.drop(\"Survived\", axis=1)\n",
    "y = df[\"Survived\"]\n",
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0\n",
       "1    1\n",
       "2    1\n",
       "3    1\n",
       "4    0\n",
       "Name: Survived, dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Rescaling feature vector to all have the same scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "X_std = StandardScaler().fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.52766856,  0.52251079, -0.50678737, ...,  0.53403984,\n",
       "        -0.56653751,  1.00281295],\n",
       "       [ 0.57709388,  0.52251079, -0.50678737, ..., -1.87251946,\n",
       "        -0.56653751, -0.99719495],\n",
       "       [-0.25147795, -0.55271372, -0.50678737, ...,  0.53403984,\n",
       "        -0.56653751,  1.00281295],\n",
       "       ...,\n",
       "       [-0.73481151, -0.55271372, -0.50678737, ...,  0.53403984,\n",
       "        -0.56653751, -0.99719495],\n",
       "       [-0.25147795, -0.55271372, -0.50678737, ..., -1.87251946,\n",
       "        -0.56653751, -0.99719495],\n",
       "       [ 0.16280796, -0.55271372, -0.50678737, ..., -1.87251946,\n",
       "        -0.56653751,  1.00281295]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_std"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Covariance Matrix of features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1.00140647 -0.30778322 -0.18816076  0.09327352  0.09917652 -0.0217234\n",
      "  -0.02546714  0.00922673 -0.31038021]\n",
      " [-0.30778322  1.00140647  0.38387668  0.1400572  -0.10644562  0.05140316\n",
      "   0.01899424 -0.05264358  0.07716859]\n",
      " [-0.18816076  0.38387668  1.00140647  0.20691428 -0.2498937  -0.00942982\n",
      "   0.01327725 -0.01858366  0.02778932]\n",
      " [ 0.09327352  0.1400572   0.20691428  1.00140647 -0.18271345 -0.06243393\n",
      "  -0.25134748 -0.14044296 -0.40278453]\n",
      " [ 0.09917652 -0.10644562 -0.2498937  -0.18271345  1.00140647 -0.02729398\n",
      "   0.10923139 -0.07545279  0.15866923]\n",
      " [-0.0217234   0.05140316 -0.00942982 -0.06243393 -0.02729398  1.00140647\n",
      "  -0.37939159 -0.08104234  0.14529129]\n",
      " [-0.02546714  0.01899424  0.01327725 -0.25134748  0.10923139 -0.37939159\n",
      "   1.00140647  0.16881438  0.09327123]\n",
      " [ 0.00922673 -0.05264358 -0.01858366 -0.14044296 -0.07545279 -0.08104234\n",
      "   0.16881438  1.00140647 -0.56574292]\n",
      " [-0.31038021  0.07716859  0.02778932 -0.40278453  0.15866923  0.14529129\n",
      "   0.09327123 -0.56574292  1.00140647]]\n"
     ]
    }
   ],
   "source": [
    "features = X_std.T\n",
    "covariance_matrix = np.cov(features)\n",
    "print(covariance_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigen Vectors and Eigen Values from Covariance Matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eig(covariance_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Eigenvector \n",
      "[[-0.42549744  0.1394993   0.28667546 -0.20079376 -0.29547624  0.24164493\n",
      "  -0.2210482  -0.69424943 -0.02116256]\n",
      " [ 0.32524147 -0.39675153 -0.2396664  -0.02254068  0.02048875  0.2988928\n",
      "  -0.59593585 -0.07186357 -0.47832787]\n",
      " [ 0.22326197 -0.477692   -0.23241727  0.08288772 -0.08232349  0.04728662\n",
      "   0.63216684 -0.501769   -0.0256136 ]\n",
      " [-0.1700155  -0.4941996   0.22598462 -0.38691513 -0.46420169 -0.4776237\n",
      "  -0.01195451  0.24956426 -0.14162019]\n",
      " [ 0.02503839  0.43948292  0.03331133  0.03222906 -0.18180031 -0.03141219\n",
      "   0.32798115  0.06414191 -0.81139114]\n",
      " [ 0.20963984 -0.05289622  0.48646434  0.08451545  0.54614063 -0.50929061\n",
      "  -0.10808559 -0.33274866 -0.17149939]\n",
      " [-0.0388967   0.24129342 -0.63214676  0.10294309 -0.17567924 -0.60037716\n",
      "  -0.24501548 -0.27617463  0.04936388]\n",
      " [-0.45165025 -0.07397492 -0.34316696 -0.55505412  0.56586743  0.02815336\n",
      "   0.12658996  0.01448673 -0.1657036 ]\n",
      " [ 0.61995326  0.30177347  0.01265212 -0.6897363  -0.08731299  0.01736119\n",
      "   0.03014318 -0.08649135  0.17994487]]\n"
     ]
    }
   ],
   "source": [
    "print(\"Eigenvector \\n{}\".format(eig_vecs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "EigenValues \n",
      "[1.83722751 1.79097298 1.49087017 0.18987533 1.09350437 0.47446778\n",
      " 0.56583156 0.73145821 0.83845033]\n"
     ]
    }
   ],
   "source": [
    "print(\"\\nEigenValues \\n{}\".format(eig_vals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20384968135225123"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "''' We reduce dimension to 1 dimension, since 1\n",
    "eigenvector has 20% (enough) variances '''\n",
    "\n",
    "eig_vals[0] / sum(eig_vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Project Data Point onto selected Eigen Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "       -3.02206331e-01,  1.42649400e+00, -2.44004877e-01,  8.21399576e-01,\n",
       "        9.66864855e-01, -4.77770972e-01,  8.77561049e-01,  4.00658079e-01,\n",
       "        9.09310837e-01, -1.27444612e+00, -6.56994143e-01,  5.81694402e-01,\n",
       "        9.95079447e-01,  2.64164829e-01,  5.62317896e-01, -1.43775306e+00,\n",
       "        3.22629043e+00, -6.76705463e-01,  1.86178664e+00, -1.04723913e-01,\n",
       "       -1.84922743e+00,  1.17300344e+00, -1.01025146e+00, -1.30122547e+00,\n",
       "        1.58160779e+00,  9.71882465e-01, -1.07485033e+00, -1.26313753e+00,\n",
       "       -1.51751745e+00, -2.09839624e+00, -1.21714586e+00, -7.90590847e-01,\n",
       "        1.98034024e+00,  7.33127083e-01, -7.08059062e-01, -7.03134964e-01,\n",
       "        1.12606800e-01, -1.27911900e+00,  1.10001972e+00,  9.03137741e-01,\n",
       "        9.38784280e-01, -1.32693176e+00, -1.37916355e+00,  5.27469887e-01,\n",
       "        7.90176397e-01, -1.62700131e+00,  7.65224928e-01,  2.71088830e+00,\n",
       "       -1.60565625e+00, -4.24211942e-01, -4.84215933e-01,  1.72949134e+00])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "projected_X = X_std.dot(eig_vecs.T[0])\n",
    "projected_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "result = pd.DataFrame(projected_X, columns=['PC1'])\n",
    "result['y-axis'] = 0.0\n",
    "result['label'] = y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>PC1</th>\n",
       "      <th>y-axis</th>\n",
       "      <th>label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1.202429</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>-0.671786</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.680987</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>-0.618817</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.468215</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        PC1  y-axis  label\n",
       "0  1.202429     0.0    0.0\n",
       "1 -0.671786     0.0    1.0\n",
       "2  0.680987     0.0    1.0\n",
       "3 -0.618817     0.0    1.0\n",
       "4  0.468215     0.0    0.0"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "result.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1, 'PCA Applied To Titanic Dataset')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 411.875x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot('PC1', 'y-axis', data=result, fit_reg=False, \n",
    "           scatter_kws={\"s\":50}, hue=\"label\")\n",
    "# set title\n",
    "plt.title(\"PCA Applied To Titanic Dataset\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using PCA of Sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.20242856, -1.03277067, -0.47912886, ..., -0.41141451,\n",
       "        -0.0114627 ,  0.06300828],\n",
       "       [-0.67178641,  1.50907444,  1.53786887, ..., -0.82249007,\n",
       "        -1.17571042, -0.3115767 ],\n",
       "       [ 0.68098724, -0.57805984, -0.20861567, ..., -0.5136111 ,\n",
       "         0.18397347,  0.16615908],\n",
       "       ...,\n",
       "       [-0.42421194,  0.29913639, -0.27817982, ..., -0.47204612,\n",
       "         0.53479644, -1.14891533],\n",
       "       [-0.48421593, -0.10113179,  1.45092125, ...,  0.69251559,\n",
       "        -0.96154699, -0.87111918],\n",
       "       [ 1.72949134, -0.69818752,  4.00273083, ...,  0.11016858,\n",
       "         1.32296011, -0.00600855]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA()\n",
    "# This is where we do all of the PCA math(i.e \n",
    "# calculate loading scores and the variation\n",
    "# each PC accounts for)\n",
    "pca.fit(X_std)\n",
    "# Generate coordinates for a PCA graph based on the\n",
    "# loading scores and the scaled data\n",
    "pca_data = pca.transform(X_std)\n",
    "pca_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate the percentage of variation that each PC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iovvqdJRrvFo4q42xRERED2maICQtoZxmdKCoXBdg22u1ObaIiOiioTrKtayDXERELH9qdZSTtD0wjeIK4nrbv2prVBER0XXDNlJL+keKtoc3UAz9faakL7U7sIiI6K46VxAfBba1/XsASSdRTD/6f9oZWEREdFedx1wfoWEMJoqxlB5uTzgREdEr6lxBPA3MlTSDog1iT2CmpG8B2P7LNsYXERFdUidBXFi+Bvy8PaFEREQvqZMgflpO3PMHkrayfVebYoqIiB5Qpw3iOkkfHliR9DlefUUREREroDpXELsD0yV9iGIyn3lkCtCIiBXesFcQth+lGKRvV6APOMv2M3VOLukMSQslzWkoW1fSDEn3lO/rNDn2sHKfeyQdVuuniYiIlqnTUe4qYGdgG2A/4BuSvlbz/GcCew8qOw642vaWwNXl+uA616WYonRniquV45slkoiIaI86bRAn2/647ads3wHsRvHo67BsXws8Maj4AF4ZFfYs4MCKQ98LzLD9hO0ngRm8NtFEREQbNU0Qkt4EYPsiSasMlNteSvEHe7TWK29bAfyWol1jsI2AhxrWF5RlVXEeLWmWpFmLFi0aQ1gREdFoqCuI7zcs3zBo23+0onLb5tVDio/mHNNt99vunzJlSivCiogIhk4QarJctT4Sj0naAKB8X1ixz8PA1Ib1jcnwHhERHTVUgnCT5ar1kbgEGHgq6TDg4op9rgD2krRO2Ti9V1kWEREdMlQ/iI3L8ZbUsEy5XtkeMJikcyn6UUyWtIDiyaSTgPMkHQk8CHy43LcfOMb2UbafkPRl4ObyVCfaHtzYHRERbTRUgvh8w/KsQdsGr1eyfWiTTXtU7DsLOKph/QzgjDr1RERE6w015ehZzbZFRMSKr9aUoxFR6Dvu0o7WN/+k/TpaX0SjOh3lIiJiHBqqo9xXy/cPdS6ciIjoFUNdQewrScAXOhVMRET0jqHaIC4HngTWkLSY4vFWD7zbXqsD8UVERJc0vYKw/XnbawOX2l7L9pqN7x2MMSIiumDYp5hsHyBpPWDHsugm2xkVLyJiBVdnPogPATOBD1H0ep4p6aB2BxYREd1Vpx/El4AdbS8EkDQFuAr4UTsDi4iI7qrTD2LCQHIoPV7zuIiIWI7VuYK4XNIVwLnl+sHAZe0LKSIiekGdRurPS/pTYFpZNN32he0NKyIiuq3WWEy2LwAuaHMsERHRQzJYX8RyqpMDB2bQwPEpjc0REVGpVoKQtJqkrdodTERE9I46HeXeD8ymGJsJSdtJumS0FUraStLshtdiSccO2md3SU837POPo60vIiJGp04bxAnATsDPAWzPlrTZaCu0fRewHYCkicDDQNVTUdfZft9o64mIiLGpc4vpJdtPDypzi+rfA7jP9oMtOl9ERLRInQQxV9JHgImStpT0beCXLar/EF7pgDfYrpJuk/RTSW9udgJJR0uaJWnWokUZQzAiolXqJIi/AN4MvEDxx3wxcOyQR9QgaWVgf+D8is23Apva3hb4NnBRs/PYnm6733b/lClTxhpWRESU6vSkfg74YvlqpX2AW20/VlHn4oblyyT9h6TJtn/X4hgiIqKJYROEpJ/w2jaHp4FZwKm2fz/Kug+lye0lSesDj9m2pJ0ornQeH2U9ERExCnVuMd0PPAN8t3wtBpYAbyzXR0zS6sCeNAzfIekYSceUqwcBcyTdBnwLOMR2qxrGIyKihjqPue5me8eG9Z9Iutn2jpLmjqZS288CbxhUdkrD8snAyaM5d0REtEadK4g1JG0ysFIur1GuvtiWqCIiouvqXEF8Drhe0n2AgM2AT5e3ic5qZ3AREdE9dZ5iukzSlsCbyqK7Ghqmv9G2yCIioqvqDve9JbAVsCqwrSRsn92+sCIiotvqPOZ6PLA7sDXFVKP7ANcDSRARESuwOo3UB1GMmfRb20cA2wKvb2tUERHRdXVuMT1v+2VJSyWtBSwEprY5rohYTnRyZjvI7HadVCdBzJK0NkWnuFsoOs3d0NaoIiKi6+o8xfTpcvEUSZcDa9m+vb1hRUREt9WZUe7qgWXb823f3lgWERErpqZXEJJWBV4HTJa0DkUnOYC1gI06EFtERHTRULeYPkkx78OGFG0PAwliMRknKSJihdc0Qdj+JvBNSX9h+9sdjCkiInpAnUbqb0vaDehr3D89qSMiVmx1elJ/D9gcmA0sK4tNelJHRKzQ6vSD6Ae2zoQ9ERHjS50EMQdYH3i0lRVLmk8xM90yYKnt/kHbBXwT2Bd4Djjc9q2tjCEiVizp1d1adRLEZOBOSTOBFwYKbe/fgvrfZft3TbbtQzGK7JbAzsB/lu8REdEBdRLECe0OookDgLPLW1s3Slpb0ga2W3olExER1YbtSW37GmA+sFK5fDPQils9Bq6UdIukoyu2bwQ81LC+gIoOepKOljRL0qxFixa1IKyIiIB6Q218AvgRcGpZtBFwUQvqnmZ7e4pbSZ+R9CejOYnt6bb7bfdPmTKlBWFFRATUmw/iM8DbKXpQY/se4I/GWrHth8v3hcCFwE6DdnmYVw8rvnFZFhERHVAnQbxg+8WBFUmTKG4PjZqk1SWtObAM7EXxtFSjS4CPq7AL8HTaHyIiOqdOI/U1kv4BWE3SnsCngZ+Msd71gAuLJ1mZBHzf9uWSjgGwfQrF9Kb7AvdSPOZ6xBjrjIiIEaiTII4DjgTuoBjA7zLgtLFUavt+iqlLB5ef0rBsittbERHRBXUSxGrAGba/CyBpYln2XDsDi4iI7qrTBnE1RUIYsBpwVXvCiYiIXlEnQaxq+5mBlXL5de0LKSIiekGdBPGspO0HViTtADzfvpAiIqIX1GmD+CvgfEmPUMwqtz5wcFujioiIrhsyQUiaAKwMvAnYqiy+y/ZL7Q4sIiK6a8gEYftlSd+x/TZe25EtIiJWYLWeYpL0wXJ+hoiIGCfqJIhPAucDL0paLGmJpMVtjisiIrps2EZq22t2IpCIiOgtdYb7lqQ/k/S/y/WpkgaPvBoRESuYOreY/gPYFfhIuf4M8J22RRQRET2hTj+InW1vL+lXALaflLRym+OKiIguq3MF8VI5QJ8BJE0BXm5rVBER0XV1EsS3KGZ8+yNJXwGuB/65rVFFRETX1XmK6RxJtwB7UAy1caDteW2PLCIiuqppgpC0KnAMsAXFZEGn2l461golTQXOpphVzsB0298ctM/uwMXAA2XRBbZPHGvdERFR31BXEGcBLwHXAfsAfwwc24I6lwKfs31rOS/1LZJm2L5z0H7X2X5fC+qLiIhRGCpBbG37LQCSTgdmtqJC248Cj5bLSyTNAzYCBieIiIjooqEaqf8wYmsrbi1VkdQHvA24qWLzrpJuk/RTSW8e4hxHS5oladaiRYvaEWZExLg01BXEtg1jLglYrVwXYNtrjaViSWsAPwaOtT14bKdbgU1tPyNpX+AiYMuq89ieDkwH6O/v91hiioiIVzS9grA90fZa5WtN25MalseaHFaiSA7n2L6gou7FA9Oc2r4MWEnS5LHUGRERI1OnH0RLlcOGnw7Ms/1vTfZZf2B48XLcpwnA452LMiIi6gy10WpvBz4G3CFpdln2D8AmALZPAQ4CPiVpKcX814fYzu2jiFgu9B13aUfrm3/Sfm05b8cThO3rKdoxhtrnZODkzkQUERFVOn6LKSIilg9JEBERUSkJIiIiKiVBREREpSSIiIiolAQRERGVkiAiIqJSEkRERFRKgoiIiEpJEBERUSkJIiIiKiVBREREpSSIiIiolAQRERGVkiAiIqJSEkRERFRKgoiIiEpdSRCS9pZ0l6R7JR1XsX0VST8st98kqa/zUUZEjG8dTxCSJgLfAfYBtgYOlbT1oN2OBJ60vQXw78BXOxtlRER04wpiJ+Be2/fbfhH4AXDAoH0OAM4ql38E7CFpyHmsIyKitWS7sxVKBwF72z6qXP8YsLPtzzbsM6fcZ0G5fl+5z+8qznc0cHS5uhVwV5t/hMEmA6+Jqwt6JQ7onVh6JQ5ILFV6JQ7onVi6EcemtqdUbZjU4UBazvZ0YHq36pc0y3Z/t+rvtTigd2LplTggsfRyHNA7sfRKHAO6cYvpYWBqw/rGZVnlPpImAa8HHu9IdBERAXQnQdwMbClpM0krA4cAlwza5xLgsHL5IOB/3Ol7YRER41zHbzHZXirps8AVwETgDNtzJZ0IzLJ9CXA68D1J9wJPUCSRXtW121uD9Eoc0Dux9EockFiq9Eoc0Dux9EocQBcaqSMiYvmQntQREVEpCSIiIiolQQxB0jJJsyXNkXS+pNeV5etL+oGk+yTdIukySW8st10u6SlJ/93NWCRtJ+kGSXMl3S7p4C7FsamkW8tj5ko6phVxjCaWhuPWkrRA0sndiqPhmNmSBj+k0elYNpF0paR5ku5s1dA2o/isvKvhdzJb0u8lHdjpOMpt/1J+XudJ+pbUmo66o4zlq+X+c1r1/7g223k1eQHPNCyfA/wNIOAG4JiGbdsC7yiX9wDeD/x3N2MB3ghsWZZtCDwKrN2FOFYGVinL1gDmAxt269+nXP8m8H3g5C5+Tp5pRd0tiuXnwJ4N/0av6+a/T1m2LsUDKmOOZRSf2d2AX1A8RDOx3G/3bvxOgP2AGRQPFK1O8RToWu347FS9lvuOch10HfBW4F3AS7ZPGdhg+7aG5asl7d4LsTSUPSJpITAFeKpbcQCr0L6r1lqxSNoBWA+4HGhHh6SR/k7aadhYVIyDNsn2jLL8mW7FMshBwE9tP9fpOCTtCqxK8eVGwErAYy2Oo24snweutb0UWCrpdmBv4Lw2xPMaucVUg4rOevsAdwDbALcsT7FI2oniw35fN+KQNLX8YD8EfNX2I62KYySxSJoAfB3421bWP9I4SqtKmiXpxlbcRhlDLG8EnpJ0gaRfSfpXFQNqdiOWRocA53YjDts3AD+juOp+FLjC9rxuxALcBuwt6XWSJlMkk6lN9m25JIihrSZpNjAL+A1F/4zlKhZJGwDfA46w/XI34rD9kO23AlsAh0larwVxjCaWTwOXuRzjq4VG82+zqYshFT4CfEPS5l2KZRLFrYy/BXYE/hdweJdiAf7wmX0LRV+pjschaQvgjylGedgIeLekd3QjFttXApcBv6RImDcAy1oUy7Byi2loz9verrFA0lyKy9+ej0XSWsClwBdt39itOAaUt7rmUPxB+lEXYtkVeIekT1Pca19Z0jO2XzMnSZvjwPbD5fv9kn4OvI3WXOGNNJYFwGzb95f7XgTsQmu+DI32s/Jh4ELbL7UghtHE8QHgxoHbbZJ+SvHZua4LsWD7K8BXyn2/D9zdgjhqyRXEyP0PsIqKUWQBkPTWFn7DaEksKoYxuRA423Yr/hiPNo6NJa1Wlq0DTKO9I+42jcX2R21vYruP4hvz2S1IDiOOQ9I6klYpyyYDbwfubFMcQ8ZC0ei5tqSB0Tzf3cVYBhxKi28vjTCO3wDvlDRJ0krAO4GW3mKqG4ukiZLeMFBG0WZxZRtjebVOtYYvjy+aPGlC8VTQeRTf+OZSfEsfeGLoOmAR8DzFt7P3diMW4M+Al4DZDa/tuhDHnsDtFPdSbweO7ua/T8M+h9OGp5hq/k52o7j3fFv5fmSXP7MD/0Z3AGcCK3cxlj6KwTondOt3QvHk0qkUSeFO4N+6GMuqZQx3Aje24v/wSF4ZaiMiIirlFlNERFRKgoiIiEpJEBERUSkJIiIiKiVBREREpSSI6FnNRr6s2O8ySWuP4vwbShp1HxFJ88t+DIPL15B0asPInD+XtPNo6+kFKkYH3rfbcURnJUFEL3ve9na2twFeBF41VLgKE2zva3vEgxDafsR2O3rFn0YxEumWtncAjgBek0iWM9sBSRDjTBJELC+uA7aQ1CfpLklnA3OAqQPf5Mtt8yR9V8VY/lc29OLeQtJVkm5TMT/F5uX+c8rth0u6uPy2f4+k4wcqlnRReSUwt7G3a5VyTKWdgS+5HPvK9gO2Ly23/41eGdv/2LKsT9KvJZ0p6W5J50h6j6RflLHsVO53gqTvqZjn4x5JnyjLpWKQvTmS7lA5Z4Ck3cuf50fl+c+RinkNJO0g6Zry57pCxfhHlPt/VdLMMpaBXvknAgeXV3SdnZMgujOel2MAAALbSURBVKeTvfLyymskL8pepxRjhl0MfIqip+3LwC4N+82n+IbeByyl7G1K0TP1z8rlm4APlMurAq8r959Tlh1OMXLnG4DVKJJPf7lt3fJ9oPwNjfUOinl/inGEqn6eHSh6K69OMRbUXIoxmAbifgvFl7ZbgDMohpo+ALioPP4Eit7Xq5U/70MUPXA/SDFnwESKocx/A2wA7A48TTHo3ASKgd6mUQxf/UtgSnneg4EzyuWfA18vl/cFrmr4/bSk53ley88rg/VFLxsY+RKKK4jTKf4gPujmgw8+YHvgmFuAPklrAhvZvhDA9u8B9NpJwmbYfrzcdgHFH9NZwF9K+kC5z1SKIRAeH8XPM40ieTzbUMc7gEvKuO8oy+cCV9u2pDsoEsiAi20/Dzwv6WfATuV5z7W9DHhM0jUUI7MuBma6HL22/F32UcwJsg0wo/wdTKRIjgMuKN9vGVR3jDNJENHLqka+BHh2iGNeaFheRvFtu67B485YxeRP7wF2tf2cipFXVx3iHHOBbSVNLP9g19UY98sN6y/z6v+nr4lxBOddVp5LwFzbuw5zzMD+MU6lDSJWeLaXAAtUTswjaZUmT0TtKWndst3iQIppJ18PPFkmhzdRDIU9VF33UVx1/FPD/f4+SftRXAUdqGLyl9UphpUe6RDSB0haVcUIn7tTjMZ6HUX7wEQVo7L+CTBziHPcBUxRMXMaklaS9OZh6l0CrDnCWGM5lwQR48XHKG4V3U5x/339in1mAj+mGNn0x7ZnUUxNOknSPOAkihE1h3MURVvAvWUj+JnAQtu3lsszKdpETrP9qxH+HLdTzHZ2I/BlF7PzXcgrI+b+D/B3tn/b7AS2X6SYf+Crkm6jGOl3t2Hq/RmwdRqpx5eM5hpB8RQTRaP0Z7sdSzOSTqBouP9at2OJ8SFXEBERUSlXEBERUSlXEBERUSkJIiIiKiVBREREpSSIiIiolAQRERGV/j9G9wfeiZAM+gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "per_var = np.round(pca.explained_variance_ratio_*100, decimals=1)\n",
    "labels = ['PC'+str(x) for x in range(1, len(per_var)+1)]\n",
    "\n",
    "plt.bar(x=range(1, len(per_var)+1), height=per_var, tick_label= labels)\n",
    "plt.ylabel(\"Percentage of Explained Variance\")\n",
    "plt.xlabel(\"Principal Component\")\n",
    "plt.title(\"Scree Plot\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### To draw a PCA Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "# first put the new coordinates into a nice matrix where the rows\n",
    "# have sample labels and the columns have PC labels.\n",
    "pca_df = pd.DataFrame(pca_data, index=[X.index], columns=labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(-0.6717864110378873, -0.6981875170379409, '(1,)')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.pyplot import figure\n",
    "figure(num=None, figsize=(10, 10), dpi=80, facecolor='w', edgecolor='k')\n",
    "\n",
    "plt.scatter(pca_df.PC1, pca_df.PC2)\n",
    "plt.title(\"My PCA Graph\")\n",
    "plt.xlabel(\"PC1 - {0}%\".format(per_var[0]))\n",
    "plt.ylabel(\"PC2 - {0}%\".format(per_var[1]))\n",
    "\n",
    "# This loop adds sample names to the Graph\n",
    "# for sample in pca_df.index:\n",
    "#     plt.annotate(sample, (pca_df.PC1.loc[sample], pca_df.PC2.loc[sample]))\n",
    "plt.annotate(pca_df.index[0], (pca_df.PC1.loc[pca_df.index[0]], pca_df.PC2.loc[sample]))\n",
    "plt.annotate(pca_df.index[1], (pca_df.PC1.loc[pca_df.index[1]], pca_df.PC2.loc[sample]))\n",
    "                "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "language": "python",
   "name": "venv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}