{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Análise Multivariada e Aprendizado Não-Supervisionado\n",
    "\n",
    "por Cibele Russo.\n",
    "\n",
    "ICMC USP São Carlos.\n",
    "\n",
    "## Análise de Componentes Principais - Introdução"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O conjunto de dados \"educacao.csv\" (Fonte: Ipeadata) mostra etatísticas educacionais por estado de acordo com a descrição a seguir.\n",
    "\n",
    "\n",
    "- Sigla (do estado)\n",
    "- Estado\n",
    "- X1: Frequência escolar de pessoas com 7 a 14 anos\n",
    "- X2: Defasagem escolar em mais de 1 ano de atraso de pessoas com 7 a 14 anos (2000)\n",
    "- X3: Média de anos de estudo de pessoas com 25 anos ou mais (2000)\n",
    "- X4: Taxa de analfabetos com 25 anos ou mais (2000)\n",
    "- X5: Taxa de evasão escolar de pessoas com 7 a 14 anos (2000)\n",
    "- X6: Taxa de evasão escolar de pessoas com 15 a 17 anos (2000)\n",
    "- X7: Frequência escolar de pessoas com 7 a 22 anos\n",
    "\n",
    "\n",
    "1. Deseja-se criar uma ordenação pela primeira componente principal da matriz de variâncias e covariâncias.\n",
    "2. Quanto da variabilidade total dos dados é explicado pela primeira componente principai?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "        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>Estado</th>\n",
       "      <th>Freq:7-14</th>\n",
       "      <th>Defasagem_escolar</th>\n",
       "      <th>Anos.estudo:25+</th>\n",
       "      <th>Analfabetos:25+</th>\n",
       "      <th>Evasão:7-14</th>\n",
       "      <th>Evasao:15-17</th>\n",
       "      <th>Freq:7-22</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sigla</th>\n",
       "      <th></th>\n",
       "      <th></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>AC</th>\n",
       "      <td>Acre</td>\n",
       "      <td>0.839</td>\n",
       "      <td>0.371</td>\n",
       "      <td>4.6</td>\n",
       "      <td>0.297</td>\n",
       "      <td>0.1608</td>\n",
       "      <td>0.3047</td>\n",
       "      <td>0.7602</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AL</th>\n",
       "      <td>Alagoas</td>\n",
       "      <td>0.890</td>\n",
       "      <td>0.470</td>\n",
       "      <td>4.1</td>\n",
       "      <td>0.382</td>\n",
       "      <td>0.1097</td>\n",
       "      <td>0.2722</td>\n",
       "      <td>0.7780</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AM</th>\n",
       "      <td>Amazonas</td>\n",
       "      <td>0.832</td>\n",
       "      <td>0.410</td>\n",
       "      <td>5.5</td>\n",
       "      <td>0.191</td>\n",
       "      <td>0.1680</td>\n",
       "      <td>0.2726</td>\n",
       "      <td>0.7495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AP</th>\n",
       "      <td>Amapá</td>\n",
       "      <td>0.934</td>\n",
       "      <td>0.287</td>\n",
       "      <td>6.1</td>\n",
       "      <td>0.160</td>\n",
       "      <td>0.0660</td>\n",
       "      <td>0.1706</td>\n",
       "      <td>0.8841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>Bahia</td>\n",
       "      <td>0.931</td>\n",
       "      <td>0.418</td>\n",
       "      <td>4.5</td>\n",
       "      <td>0.285</td>\n",
       "      <td>0.0687</td>\n",
       "      <td>0.2068</td>\n",
       "      <td>0.8168</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Estado  Freq:7-14  Defasagem_escolar  Anos.estudo:25+  \\\n",
       "Sigla                                                            \n",
       "AC         Acre      0.839              0.371              4.6   \n",
       "AL      Alagoas      0.890              0.470              4.1   \n",
       "AM     Amazonas      0.832              0.410              5.5   \n",
       "AP        Amapá      0.934              0.287              6.1   \n",
       "BA        Bahia      0.931              0.418              4.5   \n",
       "\n",
       "       Analfabetos:25+  Evasão:7-14  Evasao:15-17  Freq:7-22  \n",
       "Sigla                                                         \n",
       "AC               0.297       0.1608        0.3047     0.7602  \n",
       "AL               0.382       0.1097        0.2722     0.7780  \n",
       "AM               0.191       0.1680        0.2726     0.7495  \n",
       "AP               0.160       0.0660        0.1706     0.8841  \n",
       "BA               0.285       0.0687        0.2068     0.8168  "
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "%matplotlib inline\n",
    "\n",
    "df = pd.read_csv(\"educacao.csv\", decimal=',', index_col=0)\n",
    "df.columns = ['Estado','Freq:7-14','Defasagem_escolar','Anos.estudo:25+', 'Analfabetos:25+', 'Evasão:7-14', 'Evasao:15-17', 'Freq:7-22']\n",
    "\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Freq:7-14</th>\n",
       "      <th>Defasagem_escolar</th>\n",
       "      <th>Anos.estudo:25+</th>\n",
       "      <th>Analfabetos:25+</th>\n",
       "      <th>Evasão:7-14</th>\n",
       "      <th>Evasao:15-17</th>\n",
       "      <th>Freq:7-22</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Freq:7-14</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.638089</td>\n",
       "      <td>0.505244</td>\n",
       "      <td>-0.477801</td>\n",
       "      <td>-0.999974</td>\n",
       "      <td>-0.559907</td>\n",
       "      <td>0.715964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Defasagem_escolar</th>\n",
       "      <td>-0.638089</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.816082</td>\n",
       "      <td>0.893044</td>\n",
       "      <td>0.639922</td>\n",
       "      <td>0.238947</td>\n",
       "      <td>-0.497443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Anos.estudo:25+</th>\n",
       "      <td>0.505244</td>\n",
       "      <td>-0.816082</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.900505</td>\n",
       "      <td>-0.506954</td>\n",
       "      <td>-0.497323</td>\n",
       "      <td>0.588444</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Analfabetos:25+</th>\n",
       "      <td>-0.477801</td>\n",
       "      <td>0.893044</td>\n",
       "      <td>-0.900505</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.479733</td>\n",
       "      <td>0.234025</td>\n",
       "      <td>-0.417379</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Evasão:7-14</th>\n",
       "      <td>-0.999974</td>\n",
       "      <td>0.639922</td>\n",
       "      <td>-0.506954</td>\n",
       "      <td>0.479733</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.560796</td>\n",
       "      <td>-0.717102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Evasao:15-17</th>\n",
       "      <td>-0.559907</td>\n",
       "      <td>0.238947</td>\n",
       "      <td>-0.497323</td>\n",
       "      <td>0.234025</td>\n",
       "      <td>0.560796</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.810542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Freq:7-22</th>\n",
       "      <td>0.715964</td>\n",
       "      <td>-0.497443</td>\n",
       "      <td>0.588444</td>\n",
       "      <td>-0.417379</td>\n",
       "      <td>-0.717102</td>\n",
       "      <td>-0.810542</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Freq:7-14  Defasagem_escolar  Anos.estudo:25+  \\\n",
       "Freq:7-14           1.000000          -0.638089         0.505244   \n",
       "Defasagem_escolar  -0.638089           1.000000        -0.816082   \n",
       "Anos.estudo:25+     0.505244          -0.816082         1.000000   \n",
       "Analfabetos:25+    -0.477801           0.893044        -0.900505   \n",
       "Evasão:7-14        -0.999974           0.639922        -0.506954   \n",
       "Evasao:15-17       -0.559907           0.238947        -0.497323   \n",
       "Freq:7-22           0.715964          -0.497443         0.588444   \n",
       "\n",
       "                   Analfabetos:25+  Evasão:7-14  Evasao:15-17  Freq:7-22  \n",
       "Freq:7-14                -0.477801    -0.999974     -0.559907   0.715964  \n",
       "Defasagem_escolar         0.893044     0.639922      0.238947  -0.497443  \n",
       "Anos.estudo:25+          -0.900505    -0.506954     -0.497323   0.588444  \n",
       "Analfabetos:25+           1.000000     0.479733      0.234025  -0.417379  \n",
       "Evasão:7-14               0.479733     1.000000      0.560796  -0.717102  \n",
       "Evasao:15-17              0.234025     0.560796      1.000000  -0.810542  \n",
       "Freq:7-22                -0.417379    -0.717102     -0.810542   1.000000  "
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Cálculo da matriz de correlações\n",
    "corr = df.corr()\n",
    "corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7fad9f745090>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Mapa de calor das correlações\n",
    "\n",
    "sns.heatmap(corr, \n",
    "        xticklabels=corr.columns,\n",
    "        yticklabels=corr.columns, cmap=\"YlGnBu\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.matrix(df.iloc[:,1:7])\n",
    "S = np.cov(np.transpose(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.25229345e-03, -2.74679915e-03,  1.83242165e-02,\n",
       "        -1.69881481e-03, -1.25257080e-03, -9.11138604e-04],\n",
       "       [-2.74679915e-03,  1.47974103e-02, -1.01741453e-01,\n",
       "         1.09146966e-02,  2.75537479e-03,  1.33662393e-03],\n",
       "       [ 1.83242165e-02, -1.01741453e-01,  1.05037037e+00,\n",
       "        -9.27263533e-02, -1.83907977e-02, -2.34382194e-02],\n",
       "       [-1.69881481e-03,  1.09146966e-02, -9.27263533e-02,\n",
       "         1.00946695e-02,  1.70610883e-03,  1.08124416e-03],\n",
       "       [-1.25257080e-03,  2.75537479e-03, -1.83907977e-02,\n",
       "         1.70610883e-03,  1.25291456e-03,  9.12810484e-04],\n",
       "       [-9.11138604e-04,  1.33662393e-03, -2.34382194e-02,\n",
       "         1.08124416e-03,  9.12810484e-04,  2.11461011e-03]])"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00125229, 0.01479741, 1.05037037, 0.01009467, 0.00125291,\n",
       "       0.00211461])"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# variâncias\n",
    "\n",
    "np.diagonal(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Análise de Componentes Principais\n",
    "\n",
    "# 1. Deseja-se criar uma ordenação pela primeira componente principal da matriz de variâncias e covariâncias.\n",
    "\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,\n",
       "    svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.01742178, -0.09659786,  0.99089297, -0.08778929, -0.01748487,\n",
       "        -0.02199475],\n",
       "       [-0.16251199,  0.84912059,  0.11956643,  0.40521502,  0.16282697,\n",
       "        -0.21811951]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Pesos das componentes principais\n",
    "\n",
    "pca.components_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.99054395, 0.00591768])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2. Quanto da variabilidade total dos dados é explicado pela primeira componente principai?\n",
    "\n",
    "# Variância das componentes principais\n",
    "\n",
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-0.80930053,  0.02415988],\n",
       "       [-1.31927548,  0.0733632 ],\n",
       "       [ 0.08849968,  0.13124416],\n",
       "       [ 0.70344242,  0.07504414],\n",
       "       [-0.90651001,  0.03865576],\n",
       "       [-0.99905428, -0.04256026],\n",
       "       [ 2.80892817,  0.15678382],\n",
       "       [ 0.51652076, -0.07844312],\n",
       "       [ 0.31310511, -0.04095023],\n",
       "       [-1.41152781,  0.02584695],\n",
       "       [ 0.21883525, -0.10447412],\n",
       "       [ 0.31501905, -0.07811325],\n",
       "       [ 0.1134638 , -0.07849148],\n",
       "       [-0.40905915,  0.08663115],\n",
       "       [-1.11158132,  0.03424346],\n",
       "       [-0.30842055,  0.0597159 ],\n",
       "       [-1.51427599,  0.04124559],\n",
       "       [ 0.62121959, -0.11047763],\n",
       "       [ 1.80750336,  0.10700596],\n",
       "       [-0.40310841,  0.02006428],\n",
       "       [-0.48877808, -0.12291928],\n",
       "       [ 0.31181926, -0.03207587],\n",
       "       [ 1.022639  , -0.07539528],\n",
       "       [ 0.82461933, -0.10764038],\n",
       "       [-0.71038253,  0.06238289],\n",
       "       [ 1.42342008, -0.04582494],\n",
       "       [-0.69776073, -0.0190213 ]])"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "PCA1 = pca.transform(X)[:,0]\n",
    "PCA2 = pca.transform(X)[:,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['PCA1'] = PCA1\n",
    "df['PCA2'] = PCA2\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estado</th>\n",
       "      <th>Freq:7-14</th>\n",
       "      <th>Defasagem_escolar</th>\n",
       "      <th>Anos.estudo:25+</th>\n",
       "      <th>Analfabetos:25+</th>\n",
       "      <th>Evasão:7-14</th>\n",
       "      <th>Evasao:15-17</th>\n",
       "      <th>Freq:7-22</th>\n",
       "      <th>PCA1</th>\n",
       "      <th>PCA2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sigla</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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>AC</th>\n",
       "      <td>Acre</td>\n",
       "      <td>0.839</td>\n",
       "      <td>0.371</td>\n",
       "      <td>4.6</td>\n",
       "      <td>0.297</td>\n",
       "      <td>0.1608</td>\n",
       "      <td>0.3047</td>\n",
       "      <td>0.7602</td>\n",
       "      <td>-0.809301</td>\n",
       "      <td>0.024160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AL</th>\n",
       "      <td>Alagoas</td>\n",
       "      <td>0.890</td>\n",
       "      <td>0.470</td>\n",
       "      <td>4.1</td>\n",
       "      <td>0.382</td>\n",
       "      <td>0.1097</td>\n",
       "      <td>0.2722</td>\n",
       "      <td>0.7780</td>\n",
       "      <td>-1.319275</td>\n",
       "      <td>0.073363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AM</th>\n",
       "      <td>Amazonas</td>\n",
       "      <td>0.832</td>\n",
       "      <td>0.410</td>\n",
       "      <td>5.5</td>\n",
       "      <td>0.191</td>\n",
       "      <td>0.1680</td>\n",
       "      <td>0.2726</td>\n",
       "      <td>0.7495</td>\n",
       "      <td>0.088500</td>\n",
       "      <td>0.131244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AP</th>\n",
       "      <td>Amapá</td>\n",
       "      <td>0.934</td>\n",
       "      <td>0.287</td>\n",
       "      <td>6.1</td>\n",
       "      <td>0.160</td>\n",
       "      <td>0.0660</td>\n",
       "      <td>0.1706</td>\n",
       "      <td>0.8841</td>\n",
       "      <td>0.703442</td>\n",
       "      <td>0.075044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>Bahia</td>\n",
       "      <td>0.931</td>\n",
       "      <td>0.418</td>\n",
       "      <td>4.5</td>\n",
       "      <td>0.285</td>\n",
       "      <td>0.0687</td>\n",
       "      <td>0.2068</td>\n",
       "      <td>0.8168</td>\n",
       "      <td>-0.906510</td>\n",
       "      <td>0.038656</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         Estado  Freq:7-14  Defasagem_escolar  Anos.estudo:25+  \\\n",
       "Sigla                                                            \n",
       "AC         Acre      0.839              0.371              4.6   \n",
       "AL      Alagoas      0.890              0.470              4.1   \n",
       "AM     Amazonas      0.832              0.410              5.5   \n",
       "AP        Amapá      0.934              0.287              6.1   \n",
       "BA        Bahia      0.931              0.418              4.5   \n",
       "\n",
       "       Analfabetos:25+  Evasão:7-14  Evasao:15-17  Freq:7-22      PCA1  \\\n",
       "Sigla                                                                    \n",
       "AC               0.297       0.1608        0.3047     0.7602 -0.809301   \n",
       "AL               0.382       0.1097        0.2722     0.7780 -1.319275   \n",
       "AM               0.191       0.1680        0.2726     0.7495  0.088500   \n",
       "AP               0.160       0.0660        0.1706     0.8841  0.703442   \n",
       "BA               0.285       0.0687        0.2068     0.8168 -0.906510   \n",
       "\n",
       "           PCA2  \n",
       "Sigla            \n",
       "AC     0.024160  \n",
       "AL     0.073363  \n",
       "AM     0.131244  \n",
       "AP     0.075044  \n",
       "BA     0.038656  "
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Sigla\n",
       "AC   -0.809301\n",
       "AL   -1.319275\n",
       "AM    0.088500\n",
       "AP    0.703442\n",
       "BA   -0.906510\n",
       "Name: PCA1, dtype: float64"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['PCA1'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-1.51427599, -1.41152781, -1.31927548, -1.11158132, -0.99905428,\n",
       "       -0.90651001, -0.80930053, -0.71038253, -0.69776073, -0.48877808,\n",
       "       -0.40905915, -0.40310841, -0.30842055,  0.08849968,  0.1134638 ,\n",
       "        0.21883525,  0.31181926,  0.31310511,  0.31501905,  0.51652076,\n",
       "        0.62121959,  0.70344242,  0.82461933,  1.022639  ,  1.42342008,\n",
       "        1.80750336,  2.80892817])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sort(df['PCA1'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como propor uma ordenação dos dados usando a primeira componente principal?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estado</th>\n",
       "      <th>Freq:7-14</th>\n",
       "      <th>Defasagem_escolar</th>\n",
       "      <th>Anos.estudo:25+</th>\n",
       "      <th>Analfabetos:25+</th>\n",
       "      <th>Evasão:7-14</th>\n",
       "      <th>Evasao:15-17</th>\n",
       "      <th>Freq:7-22</th>\n",
       "      <th>PCA1</th>\n",
       "      <th>PCA2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sigla</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></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>DF</th>\n",
       "      <td>Distrito_Federal</td>\n",
       "      <td>0.976</td>\n",
       "      <td>0.136</td>\n",
       "      <td>8.2</td>\n",
       "      <td>0.072</td>\n",
       "      <td>0.0238</td>\n",
       "      <td>0.1329</td>\n",
       "      <td>0.9198</td>\n",
       "      <td>2.808928</td>\n",
       "      <td>0.156784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RJ</th>\n",
       "      <td>Rio_de_Janeiro</td>\n",
       "      <td>0.961</td>\n",
       "      <td>0.224</td>\n",
       "      <td>7.2</td>\n",
       "      <td>0.076</td>\n",
       "      <td>0.0389</td>\n",
       "      <td>0.1854</td>\n",
       "      <td>0.8378</td>\n",
       "      <td>1.807503</td>\n",
       "      <td>0.107006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SP</th>\n",
       "      <td>São_Paulo</td>\n",
       "      <td>0.968</td>\n",
       "      <td>0.099</td>\n",
       "      <td>6.8</td>\n",
       "      <td>0.079</td>\n",
       "      <td>0.0320</td>\n",
       "      <td>0.1754</td>\n",
       "      <td>0.8351</td>\n",
       "      <td>1.423420</td>\n",
       "      <td>-0.045825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RS</th>\n",
       "      <td>Rio_Grande_do_Sul</td>\n",
       "      <td>0.973</td>\n",
       "      <td>0.136</td>\n",
       "      <td>6.4</td>\n",
       "      <td>0.078</td>\n",
       "      <td>0.0267</td>\n",
       "      <td>0.2262</td>\n",
       "      <td>0.8460</td>\n",
       "      <td>1.022639</td>\n",
       "      <td>-0.075395</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SC</th>\n",
       "      <td>Santa_Catarina</td>\n",
       "      <td>0.967</td>\n",
       "      <td>0.131</td>\n",
       "      <td>6.2</td>\n",
       "      <td>0.074</td>\n",
       "      <td>0.0333</td>\n",
       "      <td>0.2469</td>\n",
       "      <td>0.8436</td>\n",
       "      <td>0.824619</td>\n",
       "      <td>-0.107640</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AP</th>\n",
       "      <td>Amapá</td>\n",
       "      <td>0.934</td>\n",
       "      <td>0.287</td>\n",
       "      <td>6.1</td>\n",
       "      <td>0.160</td>\n",
       "      <td>0.0660</td>\n",
       "      <td>0.1706</td>\n",
       "      <td>0.8841</td>\n",
       "      <td>0.703442</td>\n",
       "      <td>0.075044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PR</th>\n",
       "      <td>Paraná</td>\n",
       "      <td>0.956</td>\n",
       "      <td>0.137</td>\n",
       "      <td>6.0</td>\n",
       "      <td>0.117</td>\n",
       "      <td>0.0436</td>\n",
       "      <td>0.2694</td>\n",
       "      <td>0.8288</td>\n",
       "      <td>0.621220</td>\n",
       "      <td>-0.110478</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ES</th>\n",
       "      <td>Espírito_Santo</td>\n",
       "      <td>0.944</td>\n",
       "      <td>0.170</td>\n",
       "      <td>5.9</td>\n",
       "      <td>0.142</td>\n",
       "      <td>0.0557</td>\n",
       "      <td>0.2606</td>\n",
       "      <td>0.7975</td>\n",
       "      <td>0.516521</td>\n",
       "      <td>-0.078443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MS</th>\n",
       "      <td>Mato_Grosso_do_Sul</td>\n",
       "      <td>0.952</td>\n",
       "      <td>0.206</td>\n",
       "      <td>5.7</td>\n",
       "      <td>0.140</td>\n",
       "      <td>0.0479</td>\n",
       "      <td>0.2741</td>\n",
       "      <td>0.8153</td>\n",
       "      <td>0.315019</td>\n",
       "      <td>-0.078113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GO</th>\n",
       "      <td>Goiás</td>\n",
       "      <td>0.960</td>\n",
       "      <td>0.233</td>\n",
       "      <td>5.7</td>\n",
       "      <td>0.150</td>\n",
       "      <td>0.0398</td>\n",
       "      <td>0.2154</td>\n",
       "      <td>0.8364</td>\n",
       "      <td>0.313105</td>\n",
       "      <td>-0.040950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RR</th>\n",
       "      <td>Roraima</td>\n",
       "      <td>0.943</td>\n",
       "      <td>0.221</td>\n",
       "      <td>5.7</td>\n",
       "      <td>0.175</td>\n",
       "      <td>0.0568</td>\n",
       "      <td>0.1998</td>\n",
       "      <td>0.8639</td>\n",
       "      <td>0.311819</td>\n",
       "      <td>-0.032076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MG</th>\n",
       "      <td>Minas_Gerais</td>\n",
       "      <td>0.959</td>\n",
       "      <td>0.179</td>\n",
       "      <td>5.6</td>\n",
       "      <td>0.148</td>\n",
       "      <td>0.0411</td>\n",
       "      <td>0.2396</td>\n",
       "      <td>0.7893</td>\n",
       "      <td>0.218835</td>\n",
       "      <td>-0.104474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MT</th>\n",
       "      <td>Mato_Grosso</td>\n",
       "      <td>0.936</td>\n",
       "      <td>0.221</td>\n",
       "      <td>5.5</td>\n",
       "      <td>0.155</td>\n",
       "      <td>0.0640</td>\n",
       "      <td>0.2764</td>\n",
       "      <td>0.8273</td>\n",
       "      <td>0.113464</td>\n",
       "      <td>-0.078491</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AM</th>\n",
       "      <td>Amazonas</td>\n",
       "      <td>0.832</td>\n",
       "      <td>0.410</td>\n",
       "      <td>5.5</td>\n",
       "      <td>0.191</td>\n",
       "      <td>0.1680</td>\n",
       "      <td>0.2726</td>\n",
       "      <td>0.7495</td>\n",
       "      <td>0.088500</td>\n",
       "      <td>0.131244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PE</th>\n",
       "      <td>Pernambuco</td>\n",
       "      <td>0.921</td>\n",
       "      <td>0.368</td>\n",
       "      <td>5.1</td>\n",
       "      <td>0.283</td>\n",
       "      <td>0.0795</td>\n",
       "      <td>0.2563</td>\n",
       "      <td>0.7950</td>\n",
       "      <td>-0.308421</td>\n",
       "      <td>0.059716</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RN</th>\n",
       "      <td>Rio_Grande_do_Norte</td>\n",
       "      <td>0.948</td>\n",
       "      <td>0.328</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.298</td>\n",
       "      <td>0.0523</td>\n",
       "      <td>0.2150</td>\n",
       "      <td>0.8465</td>\n",
       "      <td>-0.403108</td>\n",
       "      <td>0.020064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PA</th>\n",
       "      <td>Pará</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.445</td>\n",
       "      <td>5.0</td>\n",
       "      <td>0.206</td>\n",
       "      <td>0.0992</td>\n",
       "      <td>0.2644</td>\n",
       "      <td>0.7791</td>\n",
       "      <td>-0.409059</td>\n",
       "      <td>0.086631</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RO</th>\n",
       "      <td>Rondônia</td>\n",
       "      <td>0.907</td>\n",
       "      <td>0.257</td>\n",
       "      <td>4.9</td>\n",
       "      <td>0.170</td>\n",
       "      <td>0.0932</td>\n",
       "      <td>0.3626</td>\n",
       "      <td>0.7569</td>\n",
       "      <td>-0.488778</td>\n",
       "      <td>-0.122919</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>TO</th>\n",
       "      <td>Tocantins</td>\n",
       "      <td>0.932</td>\n",
       "      <td>0.347</td>\n",
       "      <td>4.7</td>\n",
       "      <td>0.240</td>\n",
       "      <td>0.0676</td>\n",
       "      <td>0.2193</td>\n",
       "      <td>0.8541</td>\n",
       "      <td>-0.697761</td>\n",
       "      <td>-0.019021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SE</th>\n",
       "      <td>Sergipe</td>\n",
       "      <td>0.933</td>\n",
       "      <td>0.422</td>\n",
       "      <td>4.7</td>\n",
       "      <td>0.296</td>\n",
       "      <td>0.0674</td>\n",
       "      <td>0.2412</td>\n",
       "      <td>0.8149</td>\n",
       "      <td>-0.710383</td>\n",
       "      <td>0.062383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AC</th>\n",
       "      <td>Acre</td>\n",
       "      <td>0.839</td>\n",
       "      <td>0.371</td>\n",
       "      <td>4.6</td>\n",
       "      <td>0.297</td>\n",
       "      <td>0.1608</td>\n",
       "      <td>0.3047</td>\n",
       "      <td>0.7602</td>\n",
       "      <td>-0.809301</td>\n",
       "      <td>0.024160</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BA</th>\n",
       "      <td>Bahia</td>\n",
       "      <td>0.931</td>\n",
       "      <td>0.418</td>\n",
       "      <td>4.5</td>\n",
       "      <td>0.285</td>\n",
       "      <td>0.0687</td>\n",
       "      <td>0.2068</td>\n",
       "      <td>0.8168</td>\n",
       "      <td>-0.906510</td>\n",
       "      <td>0.038656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CE</th>\n",
       "      <td>Ceará</td>\n",
       "      <td>0.944</td>\n",
       "      <td>0.328</td>\n",
       "      <td>4.4</td>\n",
       "      <td>0.314</td>\n",
       "      <td>0.0563</td>\n",
       "      <td>0.2089</td>\n",
       "      <td>0.8481</td>\n",
       "      <td>-0.999054</td>\n",
       "      <td>-0.042560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PB</th>\n",
       "      <td>Paraíba</td>\n",
       "      <td>0.939</td>\n",
       "      <td>0.425</td>\n",
       "      <td>4.3</td>\n",
       "      <td>0.348</td>\n",
       "      <td>0.0613</td>\n",
       "      <td>0.2502</td>\n",
       "      <td>0.8039</td>\n",
       "      <td>-1.111581</td>\n",
       "      <td>0.034243</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>AL</th>\n",
       "      <td>Alagoas</td>\n",
       "      <td>0.890</td>\n",
       "      <td>0.470</td>\n",
       "      <td>4.1</td>\n",
       "      <td>0.382</td>\n",
       "      <td>0.1097</td>\n",
       "      <td>0.2722</td>\n",
       "      <td>0.7780</td>\n",
       "      <td>-1.319275</td>\n",
       "      <td>0.073363</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MA</th>\n",
       "      <td>Maranhão</td>\n",
       "      <td>0.916</td>\n",
       "      <td>0.445</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.350</td>\n",
       "      <td>0.0840</td>\n",
       "      <td>0.2399</td>\n",
       "      <td>0.7819</td>\n",
       "      <td>-1.411528</td>\n",
       "      <td>0.025847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PI</th>\n",
       "      <td>Piauí</td>\n",
       "      <td>0.937</td>\n",
       "      <td>0.476</td>\n",
       "      <td>3.9</td>\n",
       "      <td>0.367</td>\n",
       "      <td>0.0631</td>\n",
       "      <td>0.2355</td>\n",
       "      <td>0.8005</td>\n",
       "      <td>-1.514276</td>\n",
       "      <td>0.041246</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Estado  Freq:7-14  Defasagem_escolar  Anos.estudo:25+  \\\n",
       "Sigla                                                                       \n",
       "DF        Distrito_Federal      0.976              0.136              8.2   \n",
       "RJ          Rio_de_Janeiro      0.961              0.224              7.2   \n",
       "SP               São_Paulo      0.968              0.099              6.8   \n",
       "RS       Rio_Grande_do_Sul      0.973              0.136              6.4   \n",
       "SC          Santa_Catarina      0.967              0.131              6.2   \n",
       "AP                   Amapá      0.934              0.287              6.1   \n",
       "PR                  Paraná      0.956              0.137              6.0   \n",
       "ES          Espírito_Santo      0.944              0.170              5.9   \n",
       "MS      Mato_Grosso_do_Sul      0.952              0.206              5.7   \n",
       "GO                   Goiás      0.960              0.233              5.7   \n",
       "RR                 Roraima      0.943              0.221              5.7   \n",
       "MG            Minas_Gerais      0.959              0.179              5.6   \n",
       "MT             Mato_Grosso      0.936              0.221              5.5   \n",
       "AM                Amazonas      0.832              0.410              5.5   \n",
       "PE              Pernambuco      0.921              0.368              5.1   \n",
       "RN     Rio_Grande_do_Norte      0.948              0.328              5.0   \n",
       "PA                    Pará      0.901              0.445              5.0   \n",
       "RO                Rondônia      0.907              0.257              4.9   \n",
       "TO               Tocantins      0.932              0.347              4.7   \n",
       "SE                 Sergipe      0.933              0.422              4.7   \n",
       "AC                    Acre      0.839              0.371              4.6   \n",
       "BA                   Bahia      0.931              0.418              4.5   \n",
       "CE                   Ceará      0.944              0.328              4.4   \n",
       "PB                 Paraíba      0.939              0.425              4.3   \n",
       "AL                 Alagoas      0.890              0.470              4.1   \n",
       "MA                Maranhão      0.916              0.445              4.0   \n",
       "PI                   Piauí      0.937              0.476              3.9   \n",
       "\n",
       "       Analfabetos:25+  Evasão:7-14  Evasao:15-17  Freq:7-22      PCA1  \\\n",
       "Sigla                                                                    \n",
       "DF               0.072       0.0238        0.1329     0.9198  2.808928   \n",
       "RJ               0.076       0.0389        0.1854     0.8378  1.807503   \n",
       "SP               0.079       0.0320        0.1754     0.8351  1.423420   \n",
       "RS               0.078       0.0267        0.2262     0.8460  1.022639   \n",
       "SC               0.074       0.0333        0.2469     0.8436  0.824619   \n",
       "AP               0.160       0.0660        0.1706     0.8841  0.703442   \n",
       "PR               0.117       0.0436        0.2694     0.8288  0.621220   \n",
       "ES               0.142       0.0557        0.2606     0.7975  0.516521   \n",
       "MS               0.140       0.0479        0.2741     0.8153  0.315019   \n",
       "GO               0.150       0.0398        0.2154     0.8364  0.313105   \n",
       "RR               0.175       0.0568        0.1998     0.8639  0.311819   \n",
       "MG               0.148       0.0411        0.2396     0.7893  0.218835   \n",
       "MT               0.155       0.0640        0.2764     0.8273  0.113464   \n",
       "AM               0.191       0.1680        0.2726     0.7495  0.088500   \n",
       "PE               0.283       0.0795        0.2563     0.7950 -0.308421   \n",
       "RN               0.298       0.0523        0.2150     0.8465 -0.403108   \n",
       "PA               0.206       0.0992        0.2644     0.7791 -0.409059   \n",
       "RO               0.170       0.0932        0.3626     0.7569 -0.488778   \n",
       "TO               0.240       0.0676        0.2193     0.8541 -0.697761   \n",
       "SE               0.296       0.0674        0.2412     0.8149 -0.710383   \n",
       "AC               0.297       0.1608        0.3047     0.7602 -0.809301   \n",
       "BA               0.285       0.0687        0.2068     0.8168 -0.906510   \n",
       "CE               0.314       0.0563        0.2089     0.8481 -0.999054   \n",
       "PB               0.348       0.0613        0.2502     0.8039 -1.111581   \n",
       "AL               0.382       0.1097        0.2722     0.7780 -1.319275   \n",
       "MA               0.350       0.0840        0.2399     0.7819 -1.411528   \n",
       "PI               0.367       0.0631        0.2355     0.8005 -1.514276   \n",
       "\n",
       "           PCA2  \n",
       "Sigla            \n",
       "DF     0.156784  \n",
       "RJ     0.107006  \n",
       "SP    -0.045825  \n",
       "RS    -0.075395  \n",
       "SC    -0.107640  \n",
       "AP     0.075044  \n",
       "PR    -0.110478  \n",
       "ES    -0.078443  \n",
       "MS    -0.078113  \n",
       "GO    -0.040950  \n",
       "RR    -0.032076  \n",
       "MG    -0.104474  \n",
       "MT    -0.078491  \n",
       "AM     0.131244  \n",
       "PE     0.059716  \n",
       "RN     0.020064  \n",
       "PA     0.086631  \n",
       "RO    -0.122919  \n",
       "TO    -0.019021  \n",
       "SE     0.062383  \n",
       "AC     0.024160  \n",
       "BA     0.038656  \n",
       "CE    -0.042560  \n",
       "PB     0.034243  \n",
       "AL     0.073363  \n",
       "MA     0.025847  \n",
       "PI     0.041246  "
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.sort_values(by='PCA1', ascending=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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