WEEK6.PCA&KMeans_US Arrest.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 목차\n",
    "### Part1. PCA(Principal Component Analysis) on USArrest\n",
    "### Part2.K-means clustering on USArrest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part1. PCA(Principal Component Analysis) on USArrest\n",
    "\n",
    "이번 과제는 다음과 같은 순서로 정리하였습니다. \n",
    "    1. 데이터 준비하기(불러와서 표준화하기)\n",
    "    2. 싸이킷런의 PCA 활용하기\n",
    "    3. 직접 PCA 구해보기\n",
    "    4. 차원축소한 데이터 그래프에 그려보기\n",
    "    5. Scree Plot 그려보기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 170,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.preprocessing import StandardScaler \n",
    "from sklearn.decomposition import PCA\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA()\n",
    "scaler = StandardScaler()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 데이터 준비하기(불러와서 표준화하기)\n",
    "50개 주에 대한 Murder, Assault, Urbanpop, Rape 등의 데이터가 있는 USArrests.csv 파일을 가져옵니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>7.9</td>\n",
       "      <td>204</td>\n",
       "      <td>78</td>\n",
       "      <td>38.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>3.3</td>\n",
       "      <td>110</td>\n",
       "      <td>77</td>\n",
       "      <td>11.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>5.9</td>\n",
       "      <td>238</td>\n",
       "      <td>72</td>\n",
       "      <td>15.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>15.4</td>\n",
       "      <td>335</td>\n",
       "      <td>80</td>\n",
       "      <td>31.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>17.4</td>\n",
       "      <td>211</td>\n",
       "      <td>60</td>\n",
       "      <td>25.8</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Murder  Assault  UrbanPop  Rape\n",
       "Alabama        13.2      236        58  21.2\n",
       "Alaska         10.0      263        48  44.5\n",
       "Arizona         8.1      294        80  31.0\n",
       "Arkansas        8.8      190        50  19.5\n",
       "California      9.0      276        91  40.6\n",
       "Colorado        7.9      204        78  38.7\n",
       "Connecticut     3.3      110        77  11.1\n",
       "Delaware        5.9      238        72  15.8\n",
       "Florida        15.4      335        80  31.9\n",
       "Georgia        17.4      211        60  25.8"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "usarrests = pd.read_csv(\"USArrests.csv\", index_col=0)\n",
    "usarrests.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(50, 4)"
      ]
     },
     "execution_count": 196,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "usarrests.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Alabama</th>\n",
       "      <td>13.2</td>\n",
       "      <td>236</td>\n",
       "      <td>58</td>\n",
       "      <td>21.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alaska</th>\n",
       "      <td>10.0</td>\n",
       "      <td>263</td>\n",
       "      <td>48</td>\n",
       "      <td>44.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arizona</th>\n",
       "      <td>8.1</td>\n",
       "      <td>294</td>\n",
       "      <td>80</td>\n",
       "      <td>31.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Arkansas</th>\n",
       "      <td>8.8</td>\n",
       "      <td>190</td>\n",
       "      <td>50</td>\n",
       "      <td>19.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>California</th>\n",
       "      <td>9.0</td>\n",
       "      <td>276</td>\n",
       "      <td>91</td>\n",
       "      <td>40.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Colorado</th>\n",
       "      <td>7.9</td>\n",
       "      <td>204</td>\n",
       "      <td>78</td>\n",
       "      <td>38.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Connecticut</th>\n",
       "      <td>3.3</td>\n",
       "      <td>110</td>\n",
       "      <td>77</td>\n",
       "      <td>11.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Delaware</th>\n",
       "      <td>5.9</td>\n",
       "      <td>238</td>\n",
       "      <td>72</td>\n",
       "      <td>15.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Florida</th>\n",
       "      <td>15.4</td>\n",
       "      <td>335</td>\n",
       "      <td>80</td>\n",
       "      <td>31.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Georgia</th>\n",
       "      <td>17.4</td>\n",
       "      <td>211</td>\n",
       "      <td>60</td>\n",
       "      <td>25.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hawaii</th>\n",
       "      <td>5.3</td>\n",
       "      <td>46</td>\n",
       "      <td>83</td>\n",
       "      <td>20.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Idaho</th>\n",
       "      <td>2.6</td>\n",
       "      <td>120</td>\n",
       "      <td>54</td>\n",
       "      <td>14.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Illinois</th>\n",
       "      <td>10.4</td>\n",
       "      <td>249</td>\n",
       "      <td>83</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Indiana</th>\n",
       "      <td>7.2</td>\n",
       "      <td>113</td>\n",
       "      <td>65</td>\n",
       "      <td>21.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Iowa</th>\n",
       "      <td>2.2</td>\n",
       "      <td>56</td>\n",
       "      <td>57</td>\n",
       "      <td>11.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kansas</th>\n",
       "      <td>6.0</td>\n",
       "      <td>115</td>\n",
       "      <td>66</td>\n",
       "      <td>18.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kentucky</th>\n",
       "      <td>9.7</td>\n",
       "      <td>109</td>\n",
       "      <td>52</td>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Louisiana</th>\n",
       "      <td>15.4</td>\n",
       "      <td>249</td>\n",
       "      <td>66</td>\n",
       "      <td>22.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maine</th>\n",
       "      <td>2.1</td>\n",
       "      <td>83</td>\n",
       "      <td>51</td>\n",
       "      <td>7.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Maryland</th>\n",
       "      <td>11.3</td>\n",
       "      <td>300</td>\n",
       "      <td>67</td>\n",
       "      <td>27.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Massachusetts</th>\n",
       "      <td>4.4</td>\n",
       "      <td>149</td>\n",
       "      <td>85</td>\n",
       "      <td>16.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Michigan</th>\n",
       "      <td>12.1</td>\n",
       "      <td>255</td>\n",
       "      <td>74</td>\n",
       "      <td>35.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Minnesota</th>\n",
       "      <td>2.7</td>\n",
       "      <td>72</td>\n",
       "      <td>66</td>\n",
       "      <td>14.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Mississippi</th>\n",
       "      <td>16.1</td>\n",
       "      <td>259</td>\n",
       "      <td>44</td>\n",
       "      <td>17.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Missouri</th>\n",
       "      <td>9.0</td>\n",
       "      <td>178</td>\n",
       "      <td>70</td>\n",
       "      <td>28.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Montana</th>\n",
       "      <td>6.0</td>\n",
       "      <td>109</td>\n",
       "      <td>53</td>\n",
       "      <td>16.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nebraska</th>\n",
       "      <td>4.3</td>\n",
       "      <td>102</td>\n",
       "      <td>62</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nevada</th>\n",
       "      <td>12.2</td>\n",
       "      <td>252</td>\n",
       "      <td>81</td>\n",
       "      <td>46.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Hampshire</th>\n",
       "      <td>2.1</td>\n",
       "      <td>57</td>\n",
       "      <td>56</td>\n",
       "      <td>9.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Jersey</th>\n",
       "      <td>7.4</td>\n",
       "      <td>159</td>\n",
       "      <td>89</td>\n",
       "      <td>18.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New Mexico</th>\n",
       "      <td>11.4</td>\n",
       "      <td>285</td>\n",
       "      <td>70</td>\n",
       "      <td>32.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>New York</th>\n",
       "      <td>11.1</td>\n",
       "      <td>254</td>\n",
       "      <td>86</td>\n",
       "      <td>26.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Carolina</th>\n",
       "      <td>13.0</td>\n",
       "      <td>337</td>\n",
       "      <td>45</td>\n",
       "      <td>16.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>North Dakota</th>\n",
       "      <td>0.8</td>\n",
       "      <td>45</td>\n",
       "      <td>44</td>\n",
       "      <td>7.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ohio</th>\n",
       "      <td>7.3</td>\n",
       "      <td>120</td>\n",
       "      <td>75</td>\n",
       "      <td>21.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oklahoma</th>\n",
       "      <td>6.6</td>\n",
       "      <td>151</td>\n",
       "      <td>68</td>\n",
       "      <td>20.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Oregon</th>\n",
       "      <td>4.9</td>\n",
       "      <td>159</td>\n",
       "      <td>67</td>\n",
       "      <td>29.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Pennsylvania</th>\n",
       "      <td>6.3</td>\n",
       "      <td>106</td>\n",
       "      <td>72</td>\n",
       "      <td>14.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rhode Island</th>\n",
       "      <td>3.4</td>\n",
       "      <td>174</td>\n",
       "      <td>87</td>\n",
       "      <td>8.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Carolina</th>\n",
       "      <td>14.4</td>\n",
       "      <td>279</td>\n",
       "      <td>48</td>\n",
       "      <td>22.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>South Dakota</th>\n",
       "      <td>3.8</td>\n",
       "      <td>86</td>\n",
       "      <td>45</td>\n",
       "      <td>12.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Tennessee</th>\n",
       "      <td>13.2</td>\n",
       "      <td>188</td>\n",
       "      <td>59</td>\n",
       "      <td>26.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Texas</th>\n",
       "      <td>12.7</td>\n",
       "      <td>201</td>\n",
       "      <td>80</td>\n",
       "      <td>25.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Utah</th>\n",
       "      <td>3.2</td>\n",
       "      <td>120</td>\n",
       "      <td>80</td>\n",
       "      <td>22.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Vermont</th>\n",
       "      <td>2.2</td>\n",
       "      <td>48</td>\n",
       "      <td>32</td>\n",
       "      <td>11.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Virginia</th>\n",
       "      <td>8.5</td>\n",
       "      <td>156</td>\n",
       "      <td>63</td>\n",
       "      <td>20.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Washington</th>\n",
       "      <td>4.0</td>\n",
       "      <td>145</td>\n",
       "      <td>73</td>\n",
       "      <td>26.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>West Virginia</th>\n",
       "      <td>5.7</td>\n",
       "      <td>81</td>\n",
       "      <td>39</td>\n",
       "      <td>9.3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wisconsin</th>\n",
       "      <td>2.6</td>\n",
       "      <td>53</td>\n",
       "      <td>66</td>\n",
       "      <td>10.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Wyoming</th>\n",
       "      <td>6.8</td>\n",
       "      <td>161</td>\n",
       "      <td>60</td>\n",
       "      <td>15.6</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                Murder  Assault  UrbanPop  Rape\n",
       "Alabama           13.2      236        58  21.2\n",
       "Alaska            10.0      263        48  44.5\n",
       "Arizona            8.1      294        80  31.0\n",
       "Arkansas           8.8      190        50  19.5\n",
       "California         9.0      276        91  40.6\n",
       "Colorado           7.9      204        78  38.7\n",
       "Connecticut        3.3      110        77  11.1\n",
       "Delaware           5.9      238        72  15.8\n",
       "Florida           15.4      335        80  31.9\n",
       "Georgia           17.4      211        60  25.8\n",
       "Hawaii             5.3       46        83  20.2\n",
       "Idaho              2.6      120        54  14.2\n",
       "Illinois          10.4      249        83  24.0\n",
       "Indiana            7.2      113        65  21.0\n",
       "Iowa               2.2       56        57  11.3\n",
       "Kansas             6.0      115        66  18.0\n",
       "Kentucky           9.7      109        52  16.3\n",
       "Louisiana         15.4      249        66  22.2\n",
       "Maine              2.1       83        51   7.8\n",
       "Maryland          11.3      300        67  27.8\n",
       "Massachusetts      4.4      149        85  16.3\n",
       "Michigan          12.1      255        74  35.1\n",
       "Minnesota          2.7       72        66  14.9\n",
       "Mississippi       16.1      259        44  17.1\n",
       "Missouri           9.0      178        70  28.2\n",
       "Montana            6.0      109        53  16.4\n",
       "Nebraska           4.3      102        62  16.5\n",
       "Nevada            12.2      252        81  46.0\n",
       "New Hampshire      2.1       57        56   9.5\n",
       "New Jersey         7.4      159        89  18.8\n",
       "New Mexico        11.4      285        70  32.1\n",
       "New York          11.1      254        86  26.1\n",
       "North Carolina    13.0      337        45  16.1\n",
       "North Dakota       0.8       45        44   7.3\n",
       "Ohio               7.3      120        75  21.4\n",
       "Oklahoma           6.6      151        68  20.0\n",
       "Oregon             4.9      159        67  29.3\n",
       "Pennsylvania       6.3      106        72  14.9\n",
       "Rhode Island       3.4      174        87   8.3\n",
       "South Carolina    14.4      279        48  22.5\n",
       "South Dakota       3.8       86        45  12.8\n",
       "Tennessee         13.2      188        59  26.9\n",
       "Texas             12.7      201        80  25.5\n",
       "Utah               3.2      120        80  22.9\n",
       "Vermont            2.2       48        32  11.2\n",
       "Virginia           8.5      156        63  20.7\n",
       "Washington         4.0      145        73  26.2\n",
       "West Virginia      5.7       81        39   9.3\n",
       "Wisconsin          2.6       53        66  10.8\n",
       "Wyoming            6.8      161        60  15.6"
      ]
     },
     "execution_count": 273,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "usarrests"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 표준화하기"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PCA를 하기 위해서는 우선 데이터를 표준화(standardize)하여 단위(scale)를 맞춰줘야 합니다. 이 과정을 거치지 않으면, 값이 큰 Assult 같은 변수로 PCA 결과가 편향될 수 있습니다. 표준화를 쉽게 할 수 있는 StandardScaler를 활용하겠습니다. \n",
    "- StandardScaler: http://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "usarrests_scaled = scaler.fit_transform(usarrests)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
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       "        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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.255179</td>\n",
       "      <td>0.790787</td>\n",
       "      <td>-0.526195</td>\n",
       "      <td>-0.003451</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.513019</td>\n",
       "      <td>1.118060</td>\n",
       "      <td>-1.224067</td>\n",
       "      <td>2.509424</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.072361</td>\n",
       "      <td>1.493817</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.053466</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.234708</td>\n",
       "      <td>0.233212</td>\n",
       "      <td>-1.084492</td>\n",
       "      <td>-0.186794</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.281093</td>\n",
       "      <td>1.275635</td>\n",
       "      <td>1.776781</td>\n",
       "      <td>2.088814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.025976</td>\n",
       "      <td>0.402909</td>\n",
       "      <td>0.869548</td>\n",
       "      <td>1.883901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-1.040880</td>\n",
       "      <td>-0.736484</td>\n",
       "      <td>0.799761</td>\n",
       "      <td>-1.092723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-0.437875</td>\n",
       "      <td>0.815030</td>\n",
       "      <td>0.450825</td>\n",
       "      <td>-0.585834</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1.765415</td>\n",
       "      <td>1.990786</td>\n",
       "      <td>1.009122</td>\n",
       "      <td>1.150530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2.229265</td>\n",
       "      <td>0.487757</td>\n",
       "      <td>-0.386621</td>\n",
       "      <td>0.492653</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          0         1         2         3\n",
       "0  1.255179  0.790787 -0.526195 -0.003451\n",
       "1  0.513019  1.118060 -1.224067  2.509424\n",
       "2  0.072361  1.493817  1.009122  1.053466\n",
       "3  0.234708  0.233212 -1.084492 -0.186794\n",
       "4  0.281093  1.275635  1.776781  2.088814\n",
       "5  0.025976  0.402909  0.869548  1.883901\n",
       "6 -1.040880 -0.736484  0.799761 -1.092723\n",
       "7 -0.437875  0.815030  0.450825 -0.585834\n",
       "8  1.765415  1.990786  1.009122  1.150530\n",
       "9  2.229265  0.487757 -0.386621  0.492653"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(usarrests_scaled).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 싸이킷런의 PCA 활용하기 \n",
    "싸이킷런의 PCA를 활용하면 쉽게 PCA를 해볼 수 있습니다.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 197,
   "metadata": {},
   "outputs": [],
   "source": [
    "# from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca.fit(usarrests)\n",
    "usarrests_pca = pca.fit_transform(usarrests_scaled)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 204,
   "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>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>PC4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Murder</th>\n",
       "      <td>0.535899</td>\n",
       "      <td>0.418181</td>\n",
       "      <td>-0.341233</td>\n",
       "      <td>0.649228</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Assault</th>\n",
       "      <td>0.583184</td>\n",
       "      <td>0.187986</td>\n",
       "      <td>-0.268148</td>\n",
       "      <td>-0.743407</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UrbanPop</th>\n",
       "      <td>0.278191</td>\n",
       "      <td>-0.872806</td>\n",
       "      <td>-0.378016</td>\n",
       "      <td>0.133878</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rape</th>\n",
       "      <td>0.543432</td>\n",
       "      <td>-0.167319</td>\n",
       "      <td>0.817778</td>\n",
       "      <td>0.089024</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               PC1       PC2       PC3       PC4\n",
       "Murder    0.535899  0.418181 -0.341233  0.649228\n",
       "Assault   0.583184  0.187986 -0.268148 -0.743407\n",
       "UrbanPop  0.278191 -0.872806 -0.378016  0.133878\n",
       "Rape      0.543432 -0.167319  0.817778  0.089024"
      ]
     },
     "execution_count": 204,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(pca.components_.T,\n",
    "             index=usarrests.columns,\n",
    "             columns=['PC' + str(i+1) for i in range(len(pca.components_))])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 213,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        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",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.985566</td>\n",
       "      <td>1.133392</td>\n",
       "      <td>-0.444269</td>\n",
       "      <td>0.156267</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.950138</td>\n",
       "      <td>1.073213</td>\n",
       "      <td>2.040003</td>\n",
       "      <td>-0.438583</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.763164</td>\n",
       "      <td>-0.745957</td>\n",
       "      <td>0.054781</td>\n",
       "      <td>-0.834653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.141420</td>\n",
       "      <td>1.119797</td>\n",
       "      <td>0.114574</td>\n",
       "      <td>-0.182811</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.523980</td>\n",
       "      <td>-1.542934</td>\n",
       "      <td>0.598557</td>\n",
       "      <td>-0.341996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.514563</td>\n",
       "      <td>-0.987555</td>\n",
       "      <td>1.095007</td>\n",
       "      <td>0.001465</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-1.358647</td>\n",
       "      <td>-1.088928</td>\n",
       "      <td>-0.643258</td>\n",
       "      <td>-0.118469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.047709</td>\n",
       "      <td>-0.325359</td>\n",
       "      <td>-0.718633</td>\n",
       "      <td>-0.881978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.013042</td>\n",
       "      <td>0.039229</td>\n",
       "      <td>-0.576829</td>\n",
       "      <td>-0.096285</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.639283</td>\n",
       "      <td>1.278942</td>\n",
       "      <td>-0.342460</td>\n",
       "      <td>1.076797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.912657</td>\n",
       "      <td>-1.570460</td>\n",
       "      <td>0.050782</td>\n",
       "      <td>0.902807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-1.639800</td>\n",
       "      <td>0.210973</td>\n",
       "      <td>0.259801</td>\n",
       "      <td>-0.499104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.378911</td>\n",
       "      <td>-0.681841</td>\n",
       "      <td>-0.677496</td>\n",
       "      <td>-0.122021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-0.505461</td>\n",
       "      <td>-0.151563</td>\n",
       "      <td>0.228055</td>\n",
       "      <td>0.424666</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-2.253646</td>\n",
       "      <td>-0.104054</td>\n",
       "      <td>0.164564</td>\n",
       "      <td>0.017556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-0.796881</td>\n",
       "      <td>-0.270165</td>\n",
       "      <td>0.025553</td>\n",
       "      <td>0.206496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-0.750859</td>\n",
       "      <td>0.958440</td>\n",
       "      <td>-0.028369</td>\n",
       "      <td>0.670557</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.564818</td>\n",
       "      <td>0.871055</td>\n",
       "      <td>-0.783480</td>\n",
       "      <td>0.454728</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-2.396829</td>\n",
       "      <td>0.376392</td>\n",
       "      <td>-0.065682</td>\n",
       "      <td>-0.330460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.763369</td>\n",
       "      <td>0.427655</td>\n",
       "      <td>-0.157250</td>\n",
       "      <td>-0.559070</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-0.486166</td>\n",
       "      <td>-1.474496</td>\n",
       "      <td>-0.609497</td>\n",
       "      <td>-0.179599</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2.108441</td>\n",
       "      <td>-0.155397</td>\n",
       "      <td>0.384869</td>\n",
       "      <td>0.102372</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>-1.692682</td>\n",
       "      <td>-0.632261</td>\n",
       "      <td>0.153070</td>\n",
       "      <td>0.067317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.996494</td>\n",
       "      <td>2.393796</td>\n",
       "      <td>-0.740808</td>\n",
       "      <td>0.215508</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.696787</td>\n",
       "      <td>-0.263355</td>\n",
       "      <td>0.377444</td>\n",
       "      <td>0.225824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-1.185452</td>\n",
       "      <td>0.536874</td>\n",
       "      <td>0.246889</td>\n",
       "      <td>0.123742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>-1.265637</td>\n",
       "      <td>-0.193954</td>\n",
       "      <td>0.175574</td>\n",
       "      <td>0.015893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2.874395</td>\n",
       "      <td>-0.775600</td>\n",
       "      <td>1.163380</td>\n",
       "      <td>0.314515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-2.383915</td>\n",
       "      <td>-0.018082</td>\n",
       "      <td>0.036855</td>\n",
       "      <td>-0.033137</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.181566</td>\n",
       "      <td>-1.449506</td>\n",
       "      <td>-0.764454</td>\n",
       "      <td>0.243383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1.980024</td>\n",
       "      <td>0.142849</td>\n",
       "      <td>0.183692</td>\n",
       "      <td>-0.339534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1.682577</td>\n",
       "      <td>-0.823184</td>\n",
       "      <td>-0.643075</td>\n",
       "      <td>-0.013484</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1.123379</td>\n",
       "      <td>2.228003</td>\n",
       "      <td>-0.863572</td>\n",
       "      <td>-0.954382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>-2.992226</td>\n",
       "      <td>0.599119</td>\n",
       "      <td>0.301277</td>\n",
       "      <td>-0.253987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>-0.225965</td>\n",
       "      <td>-0.742238</td>\n",
       "      <td>-0.031139</td>\n",
       "      <td>0.473916</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>-0.311783</td>\n",
       "      <td>-0.287854</td>\n",
       "      <td>-0.015310</td>\n",
       "      <td>0.010332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.059122</td>\n",
       "      <td>-0.541411</td>\n",
       "      <td>0.939833</td>\n",
       "      <td>-0.237781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>-0.888416</td>\n",
       "      <td>-0.571100</td>\n",
       "      <td>-0.400629</td>\n",
       "      <td>0.359061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>-0.863772</td>\n",
       "      <td>-1.491978</td>\n",
       "      <td>-1.369946</td>\n",
       "      <td>-0.613569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.320724</td>\n",
       "      <td>1.933405</td>\n",
       "      <td>-0.300538</td>\n",
       "      <td>-0.131467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>-1.987775</td>\n",
       "      <td>0.823343</td>\n",
       "      <td>0.389293</td>\n",
       "      <td>-0.109572</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.999742</td>\n",
       "      <td>0.860251</td>\n",
       "      <td>0.188083</td>\n",
       "      <td>0.652864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1.355138</td>\n",
       "      <td>-0.412481</td>\n",
       "      <td>-0.492069</td>\n",
       "      <td>0.643195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>-0.550565</td>\n",
       "      <td>-1.471505</td>\n",
       "      <td>0.293728</td>\n",
       "      <td>-0.082314</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>-2.801412</td>\n",
       "      <td>1.402288</td>\n",
       "      <td>0.841263</td>\n",
       "      <td>-0.144890</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>-0.096335</td>\n",
       "      <td>0.199735</td>\n",
       "      <td>0.011713</td>\n",
       "      <td>0.211371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>-0.216903</td>\n",
       "      <td>-0.970124</td>\n",
       "      <td>0.624871</td>\n",
       "      <td>-0.220848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>-2.108585</td>\n",
       "      <td>1.424847</td>\n",
       "      <td>0.104775</td>\n",
       "      <td>0.131909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>-2.079714</td>\n",
       "      <td>-0.611269</td>\n",
       "      <td>-0.138865</td>\n",
       "      <td>0.184104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>-0.629427</td>\n",
       "      <td>0.321013</td>\n",
       "      <td>-0.240659</td>\n",
       "      <td>-0.166652</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0         1         2         3\n",
       "0   0.985566  1.133392 -0.444269  0.156267\n",
       "1   1.950138  1.073213  2.040003 -0.438583\n",
       "2   1.763164 -0.745957  0.054781 -0.834653\n",
       "3  -0.141420  1.119797  0.114574 -0.182811\n",
       "4   2.523980 -1.542934  0.598557 -0.341996\n",
       "5   1.514563 -0.987555  1.095007  0.001465\n",
       "6  -1.358647 -1.088928 -0.643258 -0.118469\n",
       "7   0.047709 -0.325359 -0.718633 -0.881978\n",
       "8   3.013042  0.039229 -0.576829 -0.096285\n",
       "9   1.639283  1.278942 -0.342460  1.076797\n",
       "10 -0.912657 -1.570460  0.050782  0.902807\n",
       "11 -1.639800  0.210973  0.259801 -0.499104\n",
       "12  1.378911 -0.681841 -0.677496 -0.122021\n",
       "13 -0.505461 -0.151563  0.228055  0.424666\n",
       "14 -2.253646 -0.104054  0.164564  0.017556\n",
       "15 -0.796881 -0.270165  0.025553  0.206496\n",
       "16 -0.750859  0.958440 -0.028369  0.670557\n",
       "17  1.564818  0.871055 -0.783480  0.454728\n",
       "18 -2.396829  0.376392 -0.065682 -0.330460\n",
       "19  1.763369  0.427655 -0.157250 -0.559070\n",
       "20 -0.486166 -1.474496 -0.609497 -0.179599\n",
       "21  2.108441 -0.155397  0.384869  0.102372\n",
       "22 -1.692682 -0.632261  0.153070  0.067317\n",
       "23  0.996494  2.393796 -0.740808  0.215508\n",
       "24  0.696787 -0.263355  0.377444  0.225824\n",
       "25 -1.185452  0.536874  0.246889  0.123742\n",
       "26 -1.265637 -0.193954  0.175574  0.015893\n",
       "27  2.874395 -0.775600  1.163380  0.314515\n",
       "28 -2.383915 -0.018082  0.036855 -0.033137\n",
       "29  0.181566 -1.449506 -0.764454  0.243383\n",
       "30  1.980024  0.142849  0.183692 -0.339534\n",
       "31  1.682577 -0.823184 -0.643075 -0.013484\n",
       "32  1.123379  2.228003 -0.863572 -0.954382\n",
       "33 -2.992226  0.599119  0.301277 -0.253987\n",
       "34 -0.225965 -0.742238 -0.031139  0.473916\n",
       "35 -0.311783 -0.287854 -0.015310  0.010332\n",
       "36  0.059122 -0.541411  0.939833 -0.237781\n",
       "37 -0.888416 -0.571100 -0.400629  0.359061\n",
       "38 -0.863772 -1.491978 -1.369946 -0.613569\n",
       "39  1.320724  1.933405 -0.300538 -0.131467\n",
       "40 -1.987775  0.823343  0.389293 -0.109572\n",
       "41  0.999742  0.860251  0.188083  0.652864\n",
       "42  1.355138 -0.412481 -0.492069  0.643195\n",
       "43 -0.550565 -1.471505  0.293728 -0.082314\n",
       "44 -2.801412  1.402288  0.841263 -0.144890\n",
       "45 -0.096335  0.199735  0.011713  0.211371\n",
       "46 -0.216903 -0.970124  0.624871 -0.220848\n",
       "47 -2.108585  1.424847  0.104775  0.131909\n",
       "48 -2.079714 -0.611269 -0.138865  0.184104\n",
       "49 -0.629427  0.321013 -0.240659 -0.166652"
      ]
     },
     "execution_count": 213,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(usarrests_pca)\n",
    "# pca.components에 원본 데이터를 곱해서 subspace로 데이터를 옮긴 결과. "
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. 직접 PCA 구해보기\n",
    "1. 공분산 행렬 구하기\n",
    "2. 공분산 행렬의 고유값 및 고유벡터 구하기(Eigen Decomposition or SVD 이용)\n",
    "3. 고유값 보고 주성분 확인하기\n",
    "4. 고유벡터에 원데이터 사영(project)하기\n",
    "\n",
    "**Reference:**\n",
    " - http://rfriend.tistory.com/185\n",
    " - https://machinelearningmastery.com/calculate-principal-component-analysis-scratch-python/\n",
    " - https://ratsgo.github.io/machine%20learning/2017/04/24/PCA/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import array\n",
    "from numpy.linalg import eig, svd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = usarrests_scaled # scaled usarrests dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step1. 공분산 행렬 구하기"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.02040816 0.81823807 0.07099247 0.57508044]\n",
      " [0.81823807 1.02040816 0.2641548  0.67881758]\n",
      " [0.07099247 0.2641548  1.02040816 0.41973595]\n",
      " [0.57508044 0.67881758 0.41973595 1.02040816]]\n"
     ]
    }
   ],
   "source": [
    "cov_X = cov(X.T)\n",
    "print(V)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step2. 공분산 행렬의 고유값 및 고유벡터 구하기\n",
    "#### 방법1) np.linalg.eig 이용하기\n",
    "파이썬에서 고유값을 구하려면 numpy의 eig() 혹은 svd()를 이용해야 합니다. eig를 이용하면 행렬의 고유값과 고유벡터를 구할 수 있습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.53085875 1.00996444 0.17696948 0.36383998]\n",
      "[[ 0.53589947  0.41818087  0.6492278  -0.34123273]\n",
      " [ 0.58318363  0.1879856  -0.74340748 -0.26814843]\n",
      " [ 0.27819087 -0.87280619  0.13387773 -0.37801579]\n",
      " [ 0.54343209 -0.16731864  0.08902432  0.81777791]]\n"
     ]
    }
   ],
   "source": [
    "e_values, e_vectors = eig(cov_X)\n",
    "print(e_values)\n",
    "print(e_vectors)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 방법2) np.linalg.svd 이용하기"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "svd()를 이용하면 행렬A를 다음과 같은 세 가지 구성으로 분해해줍니다.\n",
    "\\begin{equation}\n",
    "A = U \\Sigma V^T\n",
    "\\end{equation}\n",
    "\n",
    "- U = AA^T 고유벡터\n",
    "- V^T = A^TA의 고유벡터 \n",
    "- Sigma = AA^T와 A^TA의 고유값의 제곱근(=특이값, singular value), 즉 A의 고유값을 대각원소로 가지고 나머지는 0인 대각행렬\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.53589947  0.41818087 -0.34123273  0.6492278 ]\n",
      " [-0.58318363  0.1879856  -0.26814843 -0.74340748]\n",
      " [-0.27819087 -0.87280619 -0.37801579  0.13387773]\n",
      " [-0.54343209 -0.16731864  0.81777791  0.08902432]]\n",
      "[2.53085875 1.00996444 0.36383998 0.17696948]\n",
      "[[-0.53589947 -0.58318363 -0.27819087 -0.54343209]\n",
      " [ 0.41818087  0.1879856  -0.87280619 -0.16731864]\n",
      " [-0.34123273 -0.26814843 -0.37801579  0.81777791]\n",
      " [ 0.6492278  -0.74340748  0.13387773  0.08902432]]\n"
     ]
    }
   ],
   "source": [
    "U, Sigma, V_t = svd(cov_X)\n",
    "print(U)\n",
    "print(Sigma)\n",
    "print(V_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step3. 고유값 보고 주성분 확인하기"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "고유값(eig의 e_values 또는 svd의 Sigma)를 확인해보면, 순서만 다르고, 똑같은 결과가 나옴을 확인할 수 있습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.53085875 1.00996444 0.17696948 0.36383998]\n",
      "[2.53085875 1.00996444 0.36383998 0.17696948]\n"
     ]
    }
   ],
   "source": [
    "print(e_values)\n",
    "print(Sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Step4. 로딩벡터에 원 데이터 곱하여 데이터 차원 축소하기 \n",
    "공분산행렬의 고유벡터는 원 데이터 X의 분산을 최대화해주는, PCA의 principal component loading값에 해당합니다. 로딩값 제곱의 합은 1로 제약을 두고 구해집니다. 확인해보겠습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1.0\n",
       "1    1.0\n",
       "2    1.0\n",
       "3    1.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(pd.DataFrame(e_vectors) ** 2).sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "또한, 위에서 pca()를 활용해 구한 pca.components_ 와 고유벡터가 같은 것을 확인할 수 있습니다. 고유값이 큰 상위 k개의 로딩 벡터를 선택하여, 여기에 원 데이터를 곱하게 되면(사영, projection)하게 되면, 차원이 축소된 데이터의 행렬을 구할 수 있습니다. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align*} \\overrightarrow { { \\alpha  }_{ p} } &= {eigen vector} \\\\\n",
    "\\overrightarrow { { z }_{ 11 } }, \\overrightarrow { { z }_{ 21 } }, ..., \\overrightarrow { { z }_{ n1 } } &= {PC1 scores} \\\\\n",
    "\\overrightarrow { { z }_{ 11 } } &={ \\alpha  }_{ 11 }\\overrightarrow { { x }_{ i1 } } +{ \\alpha  }_{ 21 }\\overrightarrow { { x }_{ i2 } } +...+{ \\alpha  }_{ p1 }\\overrightarrow { { x }_{ ip } } \\\\\n",
    "\\end{align*}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2.53085875 1.00996444 0.17696948 0.36383998]\n"
     ]
    }
   ],
   "source": [
    "print(e_values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 164,
   "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>PC2</th>\n",
       "      <th>PC3</th>\n",
       "      <th>PC4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Murder</th>\n",
       "      <td>0.535899</td>\n",
       "      <td>0.418181</td>\n",
       "      <td>0.649228</td>\n",
       "      <td>-0.341233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Assault</th>\n",
       "      <td>0.583184</td>\n",
       "      <td>0.187986</td>\n",
       "      <td>-0.743407</td>\n",
       "      <td>-0.268148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>UrbanPop</th>\n",
       "      <td>0.278191</td>\n",
       "      <td>-0.872806</td>\n",
       "      <td>0.133878</td>\n",
       "      <td>-0.378016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rape</th>\n",
       "      <td>0.543432</td>\n",
       "      <td>-0.167319</td>\n",
       "      <td>0.089024</td>\n",
       "      <td>0.817778</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               PC1       PC2       PC3       PC4\n",
       "Murder    0.535899  0.418181  0.649228 -0.341233\n",
       "Assault   0.583184  0.187986 -0.743407 -0.268148\n",
       "UrbanPop  0.278191 -0.872806  0.133878 -0.378016\n",
       "Rape      0.543432 -0.167319  0.089024  0.817778"
      ]
     },
     "execution_count": 164,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(e_vectors,\n",
    "             index=usarrests.columns,\n",
    "             columns=['PC' + str(i+1) for i in range(len(e_vectors))])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "첫번째, 두 번째 고유값이 가장 크게 나타남을 확인할 수 있습니다. 따라서 고유벡터에서 PC1, PC2에 해당하는 벡터만 가져와 데이터를 사영하면 데이터를 2차원으로 축소할 수 있을 것입니다."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.53589947,  0.41818087],\n",
       "       [ 0.58318363,  0.1879856 ],\n",
       "       [ 0.27819087, -0.87280619],\n",
       "       [ 0.54343209, -0.16731864]])"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pc1n2 = e_vectors[:,:2]\n",
    "pc1n2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 168,
   "metadata": {
    "scrolled": true
   },
   "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>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.985566</td>\n",
       "      <td>1.133392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.950138</td>\n",
       "      <td>1.073213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.763164</td>\n",
       "      <td>-0.745957</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.141420</td>\n",
       "      <td>1.119797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.523980</td>\n",
       "      <td>-1.542934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.514563</td>\n",
       "      <td>-0.987555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>-1.358647</td>\n",
       "      <td>-1.088928</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.047709</td>\n",
       "      <td>-0.325359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.013042</td>\n",
       "      <td>0.039229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1.639283</td>\n",
       "      <td>1.278942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>-0.912657</td>\n",
       "      <td>-1.570460</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>-1.639800</td>\n",
       "      <td>0.210973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.378911</td>\n",
       "      <td>-0.681841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>-0.505461</td>\n",
       "      <td>-0.151563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>-2.253646</td>\n",
       "      <td>-0.104054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>-0.796881</td>\n",
       "      <td>-0.270165</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-0.750859</td>\n",
       "      <td>0.958440</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1.564818</td>\n",
       "      <td>0.871055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-2.396829</td>\n",
       "      <td>0.376392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1.763369</td>\n",
       "      <td>0.427655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-0.486166</td>\n",
       "      <td>-1.474496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>2.108441</td>\n",
       "      <td>-0.155397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>-1.692682</td>\n",
       "      <td>-0.632261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.996494</td>\n",
       "      <td>2.393796</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.696787</td>\n",
       "      <td>-0.263355</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-1.185452</td>\n",
       "      <td>0.536874</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>-1.265637</td>\n",
       "      <td>-0.193954</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>2.874395</td>\n",
       "      <td>-0.775600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>-2.383915</td>\n",
       "      <td>-0.018082</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.181566</td>\n",
       "      <td>-1.449506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>1.980024</td>\n",
       "      <td>0.142849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>31</th>\n",
       "      <td>1.682577</td>\n",
       "      <td>-0.823184</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>32</th>\n",
       "      <td>1.123379</td>\n",
       "      <td>2.228003</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>33</th>\n",
       "      <td>-2.992226</td>\n",
       "      <td>0.599119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>34</th>\n",
       "      <td>-0.225965</td>\n",
       "      <td>-0.742238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>35</th>\n",
       "      <td>-0.311783</td>\n",
       "      <td>-0.287854</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36</th>\n",
       "      <td>0.059122</td>\n",
       "      <td>-0.541411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>37</th>\n",
       "      <td>-0.888416</td>\n",
       "      <td>-0.571100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>38</th>\n",
       "      <td>-0.863772</td>\n",
       "      <td>-1.491978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>39</th>\n",
       "      <td>1.320724</td>\n",
       "      <td>1.933405</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>40</th>\n",
       "      <td>-1.987775</td>\n",
       "      <td>0.823343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>41</th>\n",
       "      <td>0.999742</td>\n",
       "      <td>0.860251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>42</th>\n",
       "      <td>1.355138</td>\n",
       "      <td>-0.412481</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>43</th>\n",
       "      <td>-0.550565</td>\n",
       "      <td>-1.471505</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>44</th>\n",
       "      <td>-2.801412</td>\n",
       "      <td>1.402288</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>45</th>\n",
       "      <td>-0.096335</td>\n",
       "      <td>0.199735</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>46</th>\n",
       "      <td>-0.216903</td>\n",
       "      <td>-0.970124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>47</th>\n",
       "      <td>-2.108585</td>\n",
       "      <td>1.424847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>48</th>\n",
       "      <td>-2.079714</td>\n",
       "      <td>-0.611269</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>49</th>\n",
       "      <td>-0.629427</td>\n",
       "      <td>0.321013</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0         1\n",
       "0   0.985566  1.133392\n",
       "1   1.950138  1.073213\n",
       "2   1.763164 -0.745957\n",
       "3  -0.141420  1.119797\n",
       "4   2.523980 -1.542934\n",
       "5   1.514563 -0.987555\n",
       "6  -1.358647 -1.088928\n",
       "7   0.047709 -0.325359\n",
       "8   3.013042  0.039229\n",
       "9   1.639283  1.278942\n",
       "10 -0.912657 -1.570460\n",
       "11 -1.639800  0.210973\n",
       "12  1.378911 -0.681841\n",
       "13 -0.505461 -0.151563\n",
       "14 -2.253646 -0.104054\n",
       "15 -0.796881 -0.270165\n",
       "16 -0.750859  0.958440\n",
       "17  1.564818  0.871055\n",
       "18 -2.396829  0.376392\n",
       "19  1.763369  0.427655\n",
       "20 -0.486166 -1.474496\n",
       "21  2.108441 -0.155397\n",
       "22 -1.692682 -0.632261\n",
       "23  0.996494  2.393796\n",
       "24  0.696787 -0.263355\n",
       "25 -1.185452  0.536874\n",
       "26 -1.265637 -0.193954\n",
       "27  2.874395 -0.775600\n",
       "28 -2.383915 -0.018082\n",
       "29  0.181566 -1.449506\n",
       "30  1.980024  0.142849\n",
       "31  1.682577 -0.823184\n",
       "32  1.123379  2.228003\n",
       "33 -2.992226  0.599119\n",
       "34 -0.225965 -0.742238\n",
       "35 -0.311783 -0.287854\n",
       "36  0.059122 -0.541411\n",
       "37 -0.888416 -0.571100\n",
       "38 -0.863772 -1.491978\n",
       "39  1.320724  1.933405\n",
       "40 -1.987775  0.823343\n",
       "41  0.999742  0.860251\n",
       "42  1.355138 -0.412481\n",
       "43 -0.550565 -1.471505\n",
       "44 -2.801412  1.402288\n",
       "45 -0.096335  0.199735\n",
       "46 -0.216903 -0.970124\n",
       "47 -2.108585  1.424847\n",
       "48 -2.079714 -0.611269\n",
       "49 -0.629427  0.321013"
      ]
     },
     "execution_count": 168,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Projected_X_2D = pc1n2.T.dot(X.T)\n",
    "pd.DataFrame(Projected_X_2D.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. 차원축소한 데이터 그래프에 그려보기\n",
    "이를 2차원 그래프에 표현하면 다음과 같이 나타납니다. \n",
    "- Reference: https://nbviewer.jupyter.org/github/emredjan/ISL-python/blob/master/labs/lab_10.4_principal_components_analysis.ipynb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "xvector = e_vectors.T[0] \n",
    "yvector = -e_vectors.T[1]\n",
    "pc1 = Projected_X_2D[0]\n",
    "pc2 = -Projected_X_2D[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 327,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2658b4f7f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('Biplot PC1 & PC2', size=16)    \n",
    "plt.xlabel('1st Principal Component')\n",
    "plt.ylabel('2nd Principal Component')\n",
    "m = 0.5\n",
    "plt.xlim(min(pc1) - m, max(pc1) + m)\n",
    "plt.ylim(min(pc2) - m, max(pc2) + m)\n",
    "\n",
    "for i in range(len(pc1)):\n",
    "    plt.text(pc1[i], pc2[i], usarrests.index[i], color='black', alpha=0.4)\n",
    "    \n",
    "for i in range(len(xvector)):\n",
    "# arrows project features (ie columns from csv) as vectors onto PC axes\n",
    "    plt.arrow(0, 0, xvector[i]*max(pc1), yvector[i]*max(pc2),\n",
    "              color='r', width=0.005, head_width=0.1)\n",
    "    plt.text(xvector[i]*max(pc1)*1.1, yvector[i]*max(pc2)*1.1,\n",
    "             usarrests.columns[i], color='r', size=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Scree Plot 그려보기\n",
    "지금은 변수가 많지 않아 (즉, 원본 데이터의 차원이 높지 않아) 적절한 수준으로 데이터의 차원을 축소할 수 있는 주성분의 수를 금방 알 수 있었지만, 변수가 많아지면 이런 방식으로 파악하기 어렵습니다. 각각의 주성분이 전체 분산에서 어느 정도를 설명하는지 보고, 설명량이 급격히 줄어드는 지점에서 주성분의 수를 결정하면 보다 정확한 결정을 할 수 있습니다. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "싸이킷런의 pca에서는 각각의 주성분이 설명하는 분산의 비율을 아래와 같이 계산해줍니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 218,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.62006039 0.24744129 0.0891408  0.04335752]\n"
     ]
    }
   ],
   "source": [
    "explained_variance = pca.explained_variance_ratio_\n",
    "print(explained_variance)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 226,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26588a76c50>]"
      ]
     },
     "execution_count": 226,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x26588f374a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Scree Plot', size=16)   \n",
    "plt.plot(explained_variance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "주성분이 2개가 되는 지점에서 설명량이 급격히 줄어드는 것을 알 수 있습니다. 누적 설명량과 누적 scree plot을 그려보면 아래와 같습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 219,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 62.01  86.75  95.66 100.  ]\n"
     ]
    }
   ],
   "source": [
    "cum_exp_var =np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)\n",
    "print(cum_exp_var)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 227,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x26588699f98>]"
      ]
     },
     "execution_count": 227,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x265886c7e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Cummulative Scree Plot', size=16)   \n",
    "plt.plot(cum_exp_var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Part2. K-means clustering on USArrest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "이 부분은 다음과 같은 순서로 정리하였습니다. \n",
    "    1. 4차원일 때 Kmeans를 통한 군집화\n",
    "    2. 2차원으로 축소한 후 다시 kmeans를 돌려 군집화"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2658ae9c128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "color_p = sns.color_palette(\"husl\", 4)\n",
    "sns.palplot(color_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. 4차원일 때 Kmeans를 통한 군집화"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "원본데이터를 표준화했던 usarrests_scaled 데이터는 변수가 4개인 4차원의 데이터입니다. 이 데이터를 가지고 k=2,3,4인 경우의 k-means 군집화를 각각 해보고 그래프를 그려보겠습니다. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "먼저, k=4로 정하여 군집화를 해보면 다음과 같은 결과가 나옵니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans_4 = KMeans(n_clusters=4, random_state=42, n_init=20)\n",
    "kmeans_4.fit(usarrests_scaled)\n",
    "k_4 = kmeans_4.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 349,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x265890d4f28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 8))\n",
    "plt.title('K-Means Clustering with K=4', size=16)\n",
    "plt.xlabel('1st Principal Component')\n",
    "plt.ylabel('2nd Principal Component')\n",
    "m = 0.5\n",
    "plt.xlim(min(pc1) - m, max(pc1) + m)\n",
    "plt.ylim(min(pc2) - m, max(pc2) + m)\n",
    "for i in range(len(pc1)):\n",
    "    plt.text(pc1[i], pc2[i], usarrests.index[i], color=color_p[k_4[i]], alpha=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "각 클러스터의 변수별 평균값을 정리해보면 다음과 같습니다.\n",
    "- 분홍색: 0번 그룹. 도시 규모는 큰 편에 속하며(PC2 상단에 위치), 규모가 비슷한 다른 도시 클러스터(2번, 청록색) 보다 범죄는 적게 일어난다(PC1 왼쪽에 위치)\n",
    "- 국방색: 1번 그룹. 도시 규모는 작은 편에 속하며(PC2 하단에 위치), 규모가 비슷한 다른 도시 클러스터(3번, 보라색)보다 범죄는 많이 일어난다(PC1 우측에 위치)\n",
    "- 청록색: 2번 그룹. 도시 규모는 큰 편에 속하며(PC2 상단에 위치), 규모가 비슷한 다른 도시 클러스터(0번, 분홍색) 보다 범죄는 많이 일어난다(PC1 우측에 위치)\n",
    "- 보라색: 3번 그룹. 도시 규모는 작은 편에 속하며(PC2 하단에 위치), 규모가 비슷한 다른 도시 클러스터(1번, 국방색)보다 범죄는 적게 일어난다(PC1 좌측에 위치)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2658a6c0c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.palplot(color_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 347,
   "metadata": {
    "scrolled": true
   },
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K_4</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.656250</td>\n",
       "      <td>138.875000</td>\n",
       "      <td>73.875000</td>\n",
       "      <td>18.781250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>13.937500</td>\n",
       "      <td>243.625000</td>\n",
       "      <td>53.750000</td>\n",
       "      <td>21.412500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10.815385</td>\n",
       "      <td>257.384615</td>\n",
       "      <td>76.000000</td>\n",
       "      <td>33.192308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.600000</td>\n",
       "      <td>78.538462</td>\n",
       "      <td>52.076923</td>\n",
       "      <td>12.176923</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Murder     Assault   UrbanPop       Rape\n",
       "K_4                                             \n",
       "0     5.656250  138.875000  73.875000  18.781250\n",
       "1    13.937500  243.625000  53.750000  21.412500\n",
       "2    10.815385  257.384615  76.000000  33.192308\n",
       "3     3.600000   78.538462  52.076923  12.176923"
      ]
     },
     "execution_count": 347,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "usarrests[\"K_4\"] = k_4\n",
    "usarrests.groupby(['K_4']).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 350,
   "metadata": {},
   "outputs": [],
   "source": [
    "# usarrests"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 276,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "kmeans_3 = KMeans(n_clusters=3, random_state=42, n_init=20)\n",
    "kmeans_3.fit(usarrests_scaled)\n",
    "k_3 = kmeans_3.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 361,
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "      <th>K_4</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K_3</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.656250</td>\n",
       "      <td>138.875</td>\n",
       "      <td>73.875000</td>\n",
       "      <td>18.78125</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.165000</td>\n",
       "      <td>255.250</td>\n",
       "      <td>68.400000</td>\n",
       "      <td>29.16500</td>\n",
       "      <td>1.650000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3.971429</td>\n",
       "      <td>86.500</td>\n",
       "      <td>51.928571</td>\n",
       "      <td>12.70000</td>\n",
       "      <td>2.857143</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Murder  Assault   UrbanPop      Rape       K_4\n",
       "K_3                                                   \n",
       "0     5.656250  138.875  73.875000  18.78125  0.000000\n",
       "1    12.165000  255.250  68.400000  29.16500  1.650000\n",
       "2     3.971429   86.500  51.928571  12.70000  2.857143"
      ]
     },
     "execution_count": 361,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "usarrests[\"K_3\"] = k_3\n",
    "usarrests.groupby(['K_3']).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 305,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2658a9b30f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "plt.title('K-Means Clustering with K=3', size=16)\n",
    "plt.xlabel('1st Principal Component')\n",
    "plt.ylabel('2nd Principal Component')\n",
    "m = 0.5\n",
    "plt.xlim(min(pc1) - m, max(pc1) + m)\n",
    "plt.ylim(min(pc2) - m, max(pc2) + m)\n",
    "for i in range(len(pc1)):\n",
    "    plt.text(pc1[i], pc2[i], usarrests.index[i], color=color_p[k_3[i]], alpha=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "클러스터를 2로 놓게 되면 인구규모는 비슷하지만, 범죄율에 있어서 차이가 나타나는 두 그룹으로 클러스터링 되었습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 277,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans_2 = KMeans(n_clusters=2, random_state=42, n_init=20)\n",
    "kmeans_2.fit(usarrests_scaled)\n",
    "k_2 = kmeans_2.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 362,
   "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>Murder</th>\n",
       "      <th>Assault</th>\n",
       "      <th>UrbanPop</th>\n",
       "      <th>Rape</th>\n",
       "      <th>K_4</th>\n",
       "      <th>K_3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>K_2</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.870</td>\n",
       "      <td>114.433333</td>\n",
       "      <td>63.633333</td>\n",
       "      <td>15.943333</td>\n",
       "      <td>1.333333</td>\n",
       "      <td>0.933333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.165</td>\n",
       "      <td>255.250000</td>\n",
       "      <td>68.400000</td>\n",
       "      <td>29.165000</td>\n",
       "      <td>1.650000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Murder     Assault   UrbanPop       Rape       K_4       K_3\n",
       "K_2                                                              \n",
       "0     4.870  114.433333  63.633333  15.943333  1.333333  0.933333\n",
       "1    12.165  255.250000  68.400000  29.165000  1.650000  1.000000"
      ]
     },
     "execution_count": 362,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "usarrests[\"K_2\"] = k_2\n",
    "usarrests.groupby(['K_2']).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 306,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2658a7e57b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "plt.title('K-Means Clustering with K=2', size=16)\n",
    "plt.xlabel('1st Principal Component')\n",
    "plt.ylabel('2nd Principal Component')\n",
    "m = 0.5\n",
    "plt.xlim(min(pc1) - m, max(pc1) + m)\n",
    "plt.ylim(min(pc2) - m, max(pc2) + m)\n",
    "for i in range(len(pc1)):\n",
    "    plt.text(pc1[i], pc2[i], usarrests.index[i], color=color_p[k_2[i]], alpha=0.8)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. 2차원으로 축소한 후 다시 kmeans를 돌려 군집화\n",
    "2차원으로 축소했던 데이터 Projected_X_2D를 두고 k=2로 설정하여 군집화한 결과, 4차원 데이터에서 k=2로 두고 군집화한 결과와 동일한 결과가 나왔습니다. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 316,
   "metadata": {},
   "outputs": [],
   "source": [
    "kmeans_X2D = KMeans(n_clusters=2, random_state=42, n_init=20)\n",
    "kmeans_X2D.fit(Projected_X_2D.T)\n",
    "k_X2D = kmeans_X2D.labels_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 317,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1,\n",
       "       0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0,\n",
       "       0, 0, 0, 0, 0, 0])"
      ]
     },
     "execution_count": 317,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k_X2D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x2658a6f30f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5, 5))\n",
    "plt.title('K-Means Clustering on 2D data', size=16)\n",
    "plt.xlabel('1st Principal Component')\n",
    "plt.ylabel('2nd Principal Component')\n",
    "m = .5\n",
    "plt.xlim(min(pc1) - m, max(pc1) + m)\n",
    "plt.ylim(min(pc2) - m, max(pc2) + m)\n",
    "for i in range(len(pc1)):\n",
    "    plt.text(pc1[i], pc2[i], usarrests.index[i], color=color_p[k_X2D[i]], alpha=0.8)"
   ]
  }
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