Aula1-Preparacao-transformacao.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ciência de Dados<br> Aula 1: Preparação e transformação dos dados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Francisco Aparecido Rodrigues, francisco@icmc.usp.br.<br>\n",
    "Universidade de São Paulo, São Carlos, Brasil.<br>\n",
    "https://sites.icmc.usp.br/francisco <br>\n",
    "Copyright: Creative Commons"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um dos primeiros passos em Ciência de Dados é a preparação e transformação dos dados, de modo a prepará-los para etapas posteriores."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nessa aula, vamos considerar dados com elementos duplicados ou faltantes e realizar a sua limpeza. Também vamos considerar métodos básicos de pré-processamento e transformação de dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos ler um conjunto de dados com erros:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de linhas e colunas: (25, 5)\n"
     ]
    },
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>?</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>?</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.7</td>\n",
       "      <td>?</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length sepal_width  petal_length petal_width    species\n",
       "0           5.1         3.5           1.4         0.2  duplicada\n",
       "1           5.1         3.5           1.4         0.2  duplicada\n",
       "2             ?           3           1.4         0.2     setosa\n",
       "3           4.7         3.2           1.3         0.2     setosa\n",
       "4           5.1         3.5           1.4         0.2  duplicada\n",
       "5           NaN         3.1           1.5         0.2     setosa\n",
       "6             5         3.6           1.4         0.2     setosa\n",
       "7           5.4         3.9           1.7         0.4  duplicada\n",
       "8           5.4         3.9           1.7         0.4  duplicada\n",
       "9           4.6         3.4           1.4         NaN     setosa\n",
       "10            5         3.4           1.5         0.2     setosa\n",
       "11          4.4         2.9           1.4         0.2  duplicada\n",
       "12          4.9         3.1           1.5         0.1     setosa\n",
       "13          5.4         3.7           1.5         0.2     setosa\n",
       "14          4.4         2.9           1.4         0.2  duplicada\n",
       "15          4.8         3.4           1.6         0.2     setosa\n",
       "16          4.8           3           1.4         0.1     setosa\n",
       "17          4.4         2.9           1.4         0.2  duplicada\n",
       "18          4.3           3           1.1         0.1     setosa\n",
       "19          5.8           4           1.2         0.2     setosa\n",
       "20          5.7         4.4           1.5         0.4     setosa\n",
       "21          5.4         3.9           1.3           ?     setosa\n",
       "22          5.1         3.5           1.4         0.3     setosa\n",
       "23          5.7           ?           1.7         0.3     setosa\n",
       "24          NaN         3.8           1.5         0.3     setosa"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# gerador de números aleatórios\n",
    "import random\n",
    "random.seed(1) # inicia a semente do gerador de números aleatórios. Importante para reprodução dos resultados\n",
    "# Pandas is used for data manipulation\n",
    "import pandas as pd # bibliote Pandas é usada para manipulação de dados\n",
    "import matplotlib.pyplot as plt # biblioteca para visualização dos dados\n",
    "\n",
    "# CSV file\n",
    "data = pd.read_csv('data/iris-with-errors.csv', header=(0))\n",
    "print(\"Número de linhas e colunas:\",data.shape)\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Primeiramente, vamos remover os \"NaN\" (not a number, que representam valores desconhecidos) do arquivo, apagando as linhas que contém esse problema. Notem que algumas linhas serão removidas, tais como a 5 e 9."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>?</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>3.6</td>\n",
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       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>?</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.7</td>\n",
       "      <td>?</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length sepal_width  petal_length petal_width    species\n",
       "0           5.1         3.5           1.4         0.2  duplicada\n",
       "1           5.1         3.5           1.4         0.2  duplicada\n",
       "2             ?           3           1.4         0.2     setosa\n",
       "3           4.7         3.2           1.3         0.2     setosa\n",
       "4           5.1         3.5           1.4         0.2  duplicada\n",
       "6             5         3.6           1.4         0.2     setosa\n",
       "7           5.4         3.9           1.7         0.4  duplicada\n",
       "8           5.4         3.9           1.7         0.4  duplicada\n",
       "10            5         3.4           1.5         0.2     setosa\n",
       "11          4.4         2.9           1.4         0.2  duplicada\n",
       "12          4.9         3.1           1.5         0.1     setosa\n",
       "13          5.4         3.7           1.5         0.2     setosa\n",
       "14          4.4         2.9           1.4         0.2  duplicada\n",
       "15          4.8         3.4           1.6         0.2     setosa\n",
       "16          4.8           3           1.4         0.1     setosa\n",
       "17          4.4         2.9           1.4         0.2  duplicada\n",
       "18          4.3           3           1.1         0.1     setosa\n",
       "19          5.8           4           1.2         0.2     setosa\n",
       "20          5.7         4.4           1.5         0.4     setosa\n",
       "21          5.4         3.9           1.3           ?     setosa\n",
       "22          5.1         3.5           1.4         0.3     setosa\n",
       "23          5.7           ?           1.7         0.3     setosa"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# remove as linhas com NaN\n",
    "data = data.dropna() \n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Vamos remover as linhas duplicadas. Para isso, inicialmente verificamos se há a ocorrência dessas linhas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     False\n",
       "1      True\n",
       "2     False\n",
       "3     False\n",
       "4      True\n",
       "6     False\n",
       "7     False\n",
       "8      True\n",
       "10    False\n",
       "11    False\n",
       "12    False\n",
       "13    False\n",
       "14     True\n",
       "15    False\n",
       "16    False\n",
       "17     True\n",
       "18    False\n",
       "19    False\n",
       "20    False\n",
       "21    False\n",
       "22    False\n",
       "23    False\n",
       "dtype: bool"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Retorna True na posição em que há uma linha duplicada\n",
    "data.duplicated()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notem que indicamos nos dados originais, na última coluna, quais linhas estão duplicadas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para realizamos a remoção, usamos um método da biblioteca Pandas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>?</td>\n",
       "      <td>3</td>\n",
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       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
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       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
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       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>duplicada</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
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       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>?</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.7</td>\n",
       "      <td>?</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length sepal_width  petal_length petal_width    species\n",
       "0           5.1         3.5           1.4         0.2  duplicada\n",
       "2             ?           3           1.4         0.2     setosa\n",
       "3           4.7         3.2           1.3         0.2     setosa\n",
       "6             5         3.6           1.4         0.2     setosa\n",
       "7           5.4         3.9           1.7         0.4  duplicada\n",
       "10            5         3.4           1.5         0.2     setosa\n",
       "11          4.4         2.9           1.4         0.2  duplicada\n",
       "12          4.9         3.1           1.5         0.1     setosa\n",
       "13          5.4         3.7           1.5         0.2     setosa\n",
       "15          4.8         3.4           1.6         0.2     setosa\n",
       "16          4.8           3           1.4         0.1     setosa\n",
       "18          4.3           3           1.1         0.1     setosa\n",
       "19          5.8           4           1.2         0.2     setosa\n",
       "20          5.7         4.4           1.5         0.4     setosa\n",
       "21          5.4         3.9           1.3           ?     setosa\n",
       "22          5.1         3.5           1.4         0.3     setosa\n",
       "23          5.7           ?           1.7         0.3     setosa"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Remove as linhas duplicadas\n",
    "data = data.drop_duplicates()\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare essa tabela com a original (acima) e verifique se a remoção das linhas foi feita de forma correta. As linhas duplicadas são indicadas na última coluna."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Vamos remover as linhas que contenham \"?\" ou qualquer outro caracter que indique um erro ou entrada faltante."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Primeiramente, convertemos essas entradas para \"NaN\":"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>sepal_length</th>\n",
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       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
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       "      <th>6</th>\n",
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       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
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       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
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       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>13</th>\n",
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       "      <td>0.2</td>\n",
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       "      <th>15</th>\n",
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       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length sepal_width  petal_length petal_width    species\n",
       "0           5.1         3.5           1.4         0.2  duplicada\n",
       "2           NaN           3           1.4         0.2     setosa\n",
       "3           4.7         3.2           1.3         0.2     setosa\n",
       "6             5         3.6           1.4         0.2     setosa\n",
       "7           5.4         3.9           1.7         0.4  duplicada\n",
       "10            5         3.4           1.5         0.2     setosa\n",
       "11          4.4         2.9           1.4         0.2  duplicada\n",
       "12          4.9         3.1           1.5         0.1     setosa\n",
       "13          5.4         3.7           1.5         0.2     setosa\n",
       "15          4.8         3.4           1.6         0.2     setosa\n",
       "16          4.8           3           1.4         0.1     setosa\n",
       "18          4.3           3           1.1         0.1     setosa\n",
       "19          5.8           4           1.2         0.2     setosa\n",
       "20          5.7         4.4           1.5         0.4     setosa\n",
       "21          5.4         3.9           1.3         NaN     setosa\n",
       "22          5.1         3.5           1.4         0.3     setosa\n",
       "23          5.7         NaN           1.7         0.3     setosa"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Substitui Nan por um caracter desejado\n",
    "data = data.replace('?', np.nan)\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A seguir, fazemos a remoção, como anteriormente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>petal_length</th>\n",
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       "      <th>6</th>\n",
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       "      <th>7</th>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
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       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length sepal_width  petal_length petal_width    species\n",
       "0           5.1         3.5           1.4         0.2  duplicada\n",
       "3           4.7         3.2           1.3         0.2     setosa\n",
       "6             5         3.6           1.4         0.2     setosa\n",
       "7           5.4         3.9           1.7         0.4  duplicada\n",
       "10            5         3.4           1.5         0.2     setosa\n",
       "11          4.4         2.9           1.4         0.2  duplicada\n",
       "12          4.9         3.1           1.5         0.1     setosa\n",
       "13          5.4         3.7           1.5         0.2     setosa\n",
       "15          4.8         3.4           1.6         0.2     setosa\n",
       "16          4.8           3           1.4         0.1     setosa\n",
       "18          4.3           3           1.1         0.1     setosa\n",
       "19          5.8           4           1.2         0.2     setosa\n",
       "20          5.7         4.4           1.5         0.4     setosa\n",
       "22          5.1         3.5           1.4         0.3     setosa"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Remove as linhas com Nan\n",
    "data = data.dropna()\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Desse forma, temos um conjunto de dados sem erros e entradas duplicadas. É fundamental realizar essas operações em qualquer conjunto de dados antes de aplicarmos os métodos de aprendizado de máquina e estatística."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos também remover determinadas linhas e colunas dos dados. Para remover a segunda e quarta colunas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Atributos atuais: Index(['sepal_length', 'sepal_width', 'petal_length', 'petal_width',\n",
      "       'species'],\n",
      "      dtype='object')\n",
      "Colunas removidas: Index(['sepal_width', 'petal_width'], dtype='object')\n"
     ]
    },
    {
     "data": {
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       "    .dataframe tbody tr th {\n",
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>duplicada</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.7</td>\n",
       "      <td>1.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
       "      <td>1.7</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>1.6</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>1.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>1.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  petal_length    species\n",
       "0           5.1           1.4  duplicada\n",
       "3           4.7           1.3     setosa\n",
       "6             5           1.4     setosa\n",
       "7           5.4           1.7  duplicada\n",
       "10            5           1.5     setosa\n",
       "11          4.4           1.4  duplicada\n",
       "12          4.9           1.5     setosa\n",
       "13          5.4           1.5     setosa\n",
       "15          4.8           1.6     setosa\n",
       "16          4.8           1.4     setosa\n",
       "18          4.3           1.1     setosa\n",
       "19          5.8           1.2     setosa\n",
       "20          5.7           1.5     setosa\n",
       "22          5.1           1.4     setosa"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print(\"Atributos atuais:\",data.columns)\n",
    "print(\"Colunas removidas:\", data.columns[[1, 3]])\n",
    "# Remove as linhas especificadas\n",
    "data = data.drop(data.columns[[1, 3]], axis=1)\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para remover a primeira e terceira linhas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linhas Removidas: Int64Index([3, 10], dtype='int64')\n"
     ]
    },
    {
     "data": {
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       "\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>sepal_length</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.7</td>\n",
       "      <td>1.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
       "      <td>1.7</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>1.6</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>1.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>1.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>1.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length  petal_length    species\n",
       "3           4.7           1.3     setosa\n",
       "7           5.4           1.7  duplicada\n",
       "10            5           1.5     setosa\n",
       "11          4.4           1.4  duplicada\n",
       "12          4.9           1.5     setosa\n",
       "13          5.4           1.5     setosa\n",
       "15          4.8           1.6     setosa\n",
       "16          4.8           1.4     setosa\n",
       "18          4.3           1.1     setosa\n",
       "19          5.8           1.2     setosa\n",
       "20          5.7           1.5     setosa\n",
       "22          5.1           1.4     setosa"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = data.drop(data.index[[0, 2]], axis=0)\n",
    "print(\"Linhas Removidas:\", data.index[[0, 2]])\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Substituição de valores ausentes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Em muitas siutações, a matriz de atributos pode conter valores ausentes. Nesse caso, podemos usar diferentes métodos para substituir tais valores, como preenche-los com valores médios ou medianas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos ler os dados novamente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(25, 5)\n"
     ]
    },
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
       "      <th>petal_length</th>\n",
       "      <th>petal_width</th>\n",
       "      <th>species</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
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       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>?</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>5</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>?</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.7</td>\n",
       "      <td>?</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length sepal_width  petal_length petal_width    species\n",
       "0           5.1         3.5           1.4         0.2  duplicada\n",
       "1           5.1         3.5           1.4         0.2  duplicada\n",
       "2             ?           3           1.4         0.2     setosa\n",
       "3           4.7         3.2           1.3         0.2     setosa\n",
       "4           5.1         3.5           1.4         0.2  duplicada\n",
       "5           NaN         3.1           1.5         0.2     setosa\n",
       "6             5         3.6           1.4         0.2     setosa\n",
       "7           5.4         3.9           1.7         0.4  duplicada\n",
       "8           5.4         3.9           1.7         0.4  duplicada\n",
       "9           4.6         3.4           1.4         NaN     setosa\n",
       "10            5         3.4           1.5         0.2     setosa\n",
       "11          4.4         2.9           1.4         0.2  duplicada\n",
       "12          4.9         3.1           1.5         0.1     setosa\n",
       "13          5.4         3.7           1.5         0.2     setosa\n",
       "14          4.4         2.9           1.4         0.2  duplicada\n",
       "15          4.8         3.4           1.6         0.2     setosa\n",
       "16          4.8           3           1.4         0.1     setosa\n",
       "17          4.4         2.9           1.4         0.2  duplicada\n",
       "18          4.3           3           1.1         0.1     setosa\n",
       "19          5.8           4           1.2         0.2     setosa\n",
       "20          5.7         4.4           1.5         0.4     setosa\n",
       "21          5.4         3.9           1.3           ?     setosa\n",
       "22          5.1         3.5           1.4         0.3     setosa\n",
       "23          5.7           ?           1.7         0.3     setosa\n",
       "24          NaN         3.8           1.5         0.3     setosa"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/iris-with-errors.csv', header=(0))\n",
    "print(data.shape)\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos substituir os valores com 'NaN' e '?' pelos valores médios dos atributos. Primeiramente, mudamos as entradas '?' para 'NaN', como foi feito anteriormente."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>sepal_length</th>\n",
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       "      <th>petal_length</th>\n",
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       "      <th>species</th>\n",
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       "      <td>5.1</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
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       "      <td>3.6</td>\n",
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       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.4</td>\n",
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       "      <th>8</th>\n",
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       "      <td>0.4</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>NaN</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>duplicada</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>NaN</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.7</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>NaN</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal_length sepal_width  petal_length petal_width    species\n",
       "0           5.1         3.5           1.4         0.2  duplicada\n",
       "1           5.1         3.5           1.4         0.2  duplicada\n",
       "2           NaN           3           1.4         0.2     setosa\n",
       "3           4.7         3.2           1.3         0.2     setosa\n",
       "4           5.1         3.5           1.4         0.2  duplicada\n",
       "5           NaN         3.1           1.5         0.2     setosa\n",
       "6             5         3.6           1.4         0.2     setosa\n",
       "7           5.4         3.9           1.7         0.4  duplicada\n",
       "8           5.4         3.9           1.7         0.4  duplicada\n",
       "9           4.6         3.4           1.4         NaN     setosa\n",
       "10            5         3.4           1.5         0.2     setosa\n",
       "11          4.4         2.9           1.4         0.2  duplicada\n",
       "12          4.9         3.1           1.5         0.1     setosa\n",
       "13          5.4         3.7           1.5         0.2     setosa\n",
       "14          4.4         2.9           1.4         0.2  duplicada\n",
       "15          4.8         3.4           1.6         0.2     setosa\n",
       "16          4.8           3           1.4         0.1     setosa\n",
       "17          4.4         2.9           1.4         0.2  duplicada\n",
       "18          4.3           3           1.1         0.1     setosa\n",
       "19          5.8           4           1.2         0.2     setosa\n",
       "20          5.7         4.4           1.5         0.4     setosa\n",
       "21          5.4         3.9           1.3         NaN     setosa\n",
       "22          5.1         3.5           1.4         0.3     setosa\n",
       "23          5.7         NaN           1.7         0.3     setosa\n",
       "24          NaN         3.8           1.5         0.3     setosa"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "data = data.replace('?', np.nan)\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A seguir, inserimos a média de cada atributo nas entradas com valores 'NaN'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[5.1        3.5        1.4        0.2       ]\n",
      " [5.1        3.5        1.4        0.2       ]\n",
      " [5.02272727 3.         1.4        0.2       ]\n",
      " [4.7        3.2        1.3        0.2       ]\n",
      " [5.1        3.5        1.4        0.2       ]\n",
      " [5.02272727 3.1        1.5        0.2       ]\n",
      " [5.         3.6        1.4        0.2       ]\n",
      " [5.4        3.9        1.7        0.4       ]\n",
      " [5.4        3.9        1.7        0.4       ]\n",
      " [4.6        3.4        1.4        0.22608696]\n",
      " [5.         3.4        1.5        0.2       ]\n",
      " [4.4        2.9        1.4        0.2       ]\n",
      " [4.9        3.1        1.5        0.1       ]\n",
      " [5.4        3.7        1.5        0.2       ]\n",
      " [4.4        2.9        1.4        0.2       ]\n",
      " [4.8        3.4        1.6        0.2       ]\n",
      " [4.8        3.         1.4        0.1       ]\n",
      " [4.4        2.9        1.4        0.2       ]\n",
      " [4.3        3.         1.1        0.1       ]\n",
      " [5.8        4.         1.2        0.2       ]\n",
      " [5.7        4.4        1.5        0.4       ]\n",
      " [5.4        3.9        1.3        0.22608696]\n",
      " [5.1        3.5        1.4        0.3       ]\n",
      " [5.7        3.4375     1.7        0.3       ]\n",
      " [5.02272727 3.8        1.5        0.3       ]]\n"
     ]
    }
   ],
   "source": [
    "# convertemos para o formato Numpy e ignoramos a última coluna (classe)\n",
    "X = np.array(data[data.columns[0:data.shape[1]-1]], dtype = float) \n",
    "# calculamos a média de cada atributo e armazenamos em um vetor\n",
    "# Usamos a função nanmean que calcula a média ignorando os Nan\n",
    "averages = np.nanmean(X, axis = 0) # veja https://docs.scipy.org/doc/numpy/reference/generated/numpy.nanmean.html\n",
    "for i in np.arange(0, X.shape[0]):\n",
    "    for j in np.arange(0, X.shape[1]):\n",
    "        if(np.isnan(X[i,j]) == True): # verificar se é uma entrada com Nan\n",
    "            X[i,j] = averages[j] # insere a média\n",
    "print(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assim como inserimos a média, poderíamos inserir a mediana ou qualquer outro valor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normalização e padronização"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos ler os dados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 5)\n"
     ]
    },
    {
     "data": {
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       "      <th></th>\n",
       "      <th>sepal_length</th>\n",
       "      <th>sepal_width</th>\n",
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       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
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       "      <th>3</th>\n",
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       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
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       "      <th>5</th>\n",
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       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>4.4</td>\n",
       "      <td>2.9</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.6</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>4.3</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.1</td>\n",
       "      <td>0.1</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>5.8</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>5.7</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>5.7</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.3</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.7</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.3</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.5</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>4.8</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.9</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    sepal_length  sepal_width  petal_length  petal_width species\n",
       "0            5.1          3.5           1.4          0.2  setosa\n",
       "1            4.9          3.0           1.4          0.2  setosa\n",
       "2            4.7          3.2           1.3          0.2  setosa\n",
       "3            4.6          3.1           1.5          0.2  setosa\n",
       "4            5.0          3.6           1.4          0.2  setosa\n",
       "5            5.4          3.9           1.7          0.4  setosa\n",
       "6            4.6          3.4           1.4          0.3  setosa\n",
       "7            5.0          3.4           1.5          0.2  setosa\n",
       "8            4.4          2.9           1.4          0.2  setosa\n",
       "9            4.9          3.1           1.5          0.1  setosa\n",
       "10           5.4          3.7           1.5          0.2  setosa\n",
       "11           4.8          3.4           1.6          0.2  setosa\n",
       "12           4.8          3.0           1.4          0.1  setosa\n",
       "13           4.3          3.0           1.1          0.1  setosa\n",
       "14           5.8          4.0           1.2          0.2  setosa\n",
       "15           5.7          4.4           1.5          0.4  setosa\n",
       "16           5.4          3.9           1.3          0.4  setosa\n",
       "17           5.1          3.5           1.4          0.3  setosa\n",
       "18           5.7          3.8           1.7          0.3  setosa\n",
       "19           5.1          3.8           1.5          0.3  setosa\n",
       "20           5.4          3.4           1.7          0.2  setosa\n",
       "21           5.1          3.7           1.5          0.4  setosa\n",
       "22           4.6          3.6           1.0          0.2  setosa\n",
       "23           5.1          3.3           1.7          0.5  setosa\n",
       "24           4.8          3.4           1.9          0.2  setosa"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "# CSV file\n",
    "data = pd.read_csv('data/iris.csv', header=(0))\n",
    "print(data.shape)\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Para normalizar os dados no intervalo [0,1]:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maior valor da coluna: 0 : 7.9\n",
      "Menor Valor da coluna: 0 : 4.3\n",
      "Maior valor da coluna: 1 : 4.4\n",
      "Menor Valor da coluna: 1 : 2.0\n",
      "Maior valor da coluna: 2 : 6.9\n",
      "Menor Valor da coluna: 2 : 1.0\n",
      "Maior valor da coluna: 3 : 2.5\n",
      "Menor Valor da coluna: 3 : 0.1\n",
      "[[0.22222222 0.625      0.06779661 0.04166667]\n",
      " [0.16666667 0.41666667 0.06779661 0.04166667]\n",
      " [0.11111111 0.5        0.05084746 0.04166667]\n",
      " [0.08333333 0.45833333 0.08474576 0.04166667]\n",
      " [0.19444444 0.66666667 0.06779661 0.04166667]\n",
      " [0.30555556 0.79166667 0.11864407 0.125     ]\n",
      " [0.08333333 0.58333333 0.06779661 0.08333333]\n",
      " [0.19444444 0.58333333 0.08474576 0.04166667]\n",
      " [0.02777778 0.375      0.06779661 0.04166667]\n",
      " [0.16666667 0.45833333 0.08474576 0.        ]\n",
      " [0.30555556 0.70833333 0.08474576 0.04166667]\n",
      " [0.13888889 0.58333333 0.10169492 0.04166667]\n",
      " [0.13888889 0.41666667 0.06779661 0.        ]\n",
      " [0.         0.41666667 0.01694915 0.        ]\n",
      " [0.41666667 0.83333333 0.03389831 0.04166667]\n",
      " [0.38888889 1.         0.08474576 0.125     ]\n",
      " [0.30555556 0.79166667 0.05084746 0.125     ]\n",
      " [0.22222222 0.625      0.06779661 0.08333333]\n",
      " [0.38888889 0.75       0.11864407 0.08333333]\n",
      " [0.22222222 0.75       0.08474576 0.08333333]\n",
      " [0.30555556 0.58333333 0.11864407 0.04166667]\n",
      " [0.22222222 0.70833333 0.08474576 0.125     ]\n",
      " [0.08333333 0.66666667 0.         0.04166667]\n",
      " [0.22222222 0.54166667 0.11864407 0.16666667]\n",
      " [0.13888889 0.58333333 0.15254237 0.04166667]\n",
      " [0.19444444 0.41666667 0.10169492 0.04166667]\n",
      " [0.19444444 0.58333333 0.10169492 0.125     ]\n",
      " [0.25       0.625      0.08474576 0.04166667]\n",
      " [0.25       0.58333333 0.06779661 0.04166667]\n",
      " [0.11111111 0.5        0.10169492 0.04166667]\n",
      " [0.13888889 0.45833333 0.10169492 0.04166667]\n",
      " [0.30555556 0.58333333 0.08474576 0.125     ]\n",
      " [0.25       0.875      0.08474576 0.        ]\n",
      " [0.33333333 0.91666667 0.06779661 0.04166667]\n",
      " [0.16666667 0.45833333 0.08474576 0.        ]\n",
      " [0.19444444 0.5        0.03389831 0.04166667]\n",
      " [0.33333333 0.625      0.05084746 0.04166667]\n",
      " [0.16666667 0.45833333 0.08474576 0.        ]\n",
      " [0.02777778 0.41666667 0.05084746 0.04166667]\n",
      " [0.22222222 0.58333333 0.08474576 0.04166667]\n",
      " [0.19444444 0.625      0.05084746 0.08333333]\n",
      " [0.05555556 0.125      0.05084746 0.08333333]\n",
      " [0.02777778 0.5        0.05084746 0.04166667]\n",
      " [0.19444444 0.625      0.10169492 0.20833333]\n",
      " [0.22222222 0.75       0.15254237 0.125     ]\n",
      " [0.13888889 0.41666667 0.06779661 0.08333333]\n",
      " [0.22222222 0.75       0.10169492 0.04166667]\n",
      " [0.08333333 0.5        0.06779661 0.04166667]\n",
      " [0.27777778 0.70833333 0.08474576 0.04166667]\n",
      " [0.19444444 0.54166667 0.06779661 0.04166667]\n",
      " [0.75       0.5        0.62711864 0.54166667]\n",
      " [0.58333333 0.5        0.59322034 0.58333333]\n",
      " [0.72222222 0.45833333 0.66101695 0.58333333]\n",
      " [0.33333333 0.125      0.50847458 0.5       ]\n",
      " [0.61111111 0.33333333 0.61016949 0.58333333]\n",
      " [0.38888889 0.33333333 0.59322034 0.5       ]\n",
      " [0.55555556 0.54166667 0.62711864 0.625     ]\n",
      " [0.16666667 0.16666667 0.38983051 0.375     ]\n",
      " [0.63888889 0.375      0.61016949 0.5       ]\n",
      " [0.25       0.29166667 0.49152542 0.54166667]\n",
      " [0.19444444 0.         0.42372881 0.375     ]\n",
      " [0.44444444 0.41666667 0.54237288 0.58333333]\n",
      " [0.47222222 0.08333333 0.50847458 0.375     ]\n",
      " [0.5        0.375      0.62711864 0.54166667]\n",
      " [0.36111111 0.375      0.44067797 0.5       ]\n",
      " [0.66666667 0.45833333 0.57627119 0.54166667]\n",
      " [0.36111111 0.41666667 0.59322034 0.58333333]\n",
      " [0.41666667 0.29166667 0.52542373 0.375     ]\n",
      " [0.52777778 0.08333333 0.59322034 0.58333333]\n",
      " [0.36111111 0.20833333 0.49152542 0.41666667]\n",
      " [0.44444444 0.5        0.6440678  0.70833333]\n",
      " [0.5        0.33333333 0.50847458 0.5       ]\n",
      " [0.55555556 0.20833333 0.66101695 0.58333333]\n",
      " [0.5        0.33333333 0.62711864 0.45833333]\n",
      " [0.58333333 0.375      0.55932203 0.5       ]\n",
      " [0.63888889 0.41666667 0.57627119 0.54166667]\n",
      " [0.69444444 0.33333333 0.6440678  0.54166667]\n",
      " [0.66666667 0.41666667 0.6779661  0.66666667]\n",
      " [0.47222222 0.375      0.59322034 0.58333333]\n",
      " [0.38888889 0.25       0.42372881 0.375     ]\n",
      " [0.33333333 0.16666667 0.47457627 0.41666667]\n",
      " [0.33333333 0.16666667 0.45762712 0.375     ]\n",
      " [0.41666667 0.29166667 0.49152542 0.45833333]\n",
      " [0.47222222 0.29166667 0.69491525 0.625     ]\n",
      " [0.30555556 0.41666667 0.59322034 0.58333333]\n",
      " [0.47222222 0.58333333 0.59322034 0.625     ]\n",
      " [0.66666667 0.45833333 0.62711864 0.58333333]\n",
      " [0.55555556 0.125      0.57627119 0.5       ]\n",
      " [0.36111111 0.41666667 0.52542373 0.5       ]\n",
      " [0.33333333 0.20833333 0.50847458 0.5       ]\n",
      " [0.33333333 0.25       0.57627119 0.45833333]\n",
      " [0.5        0.41666667 0.61016949 0.54166667]\n",
      " [0.41666667 0.25       0.50847458 0.45833333]\n",
      " [0.19444444 0.125      0.38983051 0.375     ]\n",
      " [0.36111111 0.29166667 0.54237288 0.5       ]\n",
      " [0.38888889 0.41666667 0.54237288 0.45833333]\n",
      " [0.38888889 0.375      0.54237288 0.5       ]\n",
      " [0.52777778 0.375      0.55932203 0.5       ]\n",
      " [0.22222222 0.20833333 0.33898305 0.41666667]\n",
      " [0.38888889 0.33333333 0.52542373 0.5       ]\n",
      " [0.55555556 0.54166667 0.84745763 1.        ]\n",
      " [0.41666667 0.29166667 0.69491525 0.75      ]\n",
      " [0.77777778 0.41666667 0.83050847 0.83333333]\n",
      " [0.55555556 0.375      0.77966102 0.70833333]\n",
      " [0.61111111 0.41666667 0.81355932 0.875     ]\n",
      " [0.91666667 0.41666667 0.94915254 0.83333333]\n",
      " [0.16666667 0.20833333 0.59322034 0.66666667]\n",
      " [0.83333333 0.375      0.89830508 0.70833333]\n",
      " [0.66666667 0.20833333 0.81355932 0.70833333]\n",
      " [0.80555556 0.66666667 0.86440678 1.        ]\n",
      " [0.61111111 0.5        0.69491525 0.79166667]\n",
      " [0.58333333 0.29166667 0.72881356 0.75      ]\n",
      " [0.69444444 0.41666667 0.76271186 0.83333333]\n",
      " [0.38888889 0.20833333 0.6779661  0.79166667]\n",
      " [0.41666667 0.33333333 0.69491525 0.95833333]\n",
      " [0.58333333 0.5        0.72881356 0.91666667]\n",
      " [0.61111111 0.41666667 0.76271186 0.70833333]\n",
      " [0.94444444 0.75       0.96610169 0.875     ]\n",
      " [0.94444444 0.25       1.         0.91666667]\n",
      " [0.47222222 0.08333333 0.6779661  0.58333333]\n",
      " [0.72222222 0.5        0.79661017 0.91666667]\n",
      " [0.36111111 0.33333333 0.66101695 0.79166667]\n",
      " [0.94444444 0.33333333 0.96610169 0.79166667]\n",
      " [0.55555556 0.29166667 0.66101695 0.70833333]\n",
      " [0.66666667 0.54166667 0.79661017 0.83333333]\n",
      " [0.80555556 0.5        0.84745763 0.70833333]\n",
      " [0.52777778 0.33333333 0.6440678  0.70833333]\n",
      " [0.5        0.41666667 0.66101695 0.70833333]\n",
      " [0.58333333 0.33333333 0.77966102 0.83333333]\n",
      " [0.80555556 0.41666667 0.81355932 0.625     ]\n",
      " [0.86111111 0.33333333 0.86440678 0.75      ]\n",
      " [1.         0.75       0.91525424 0.79166667]\n",
      " [0.58333333 0.33333333 0.77966102 0.875     ]\n",
      " [0.55555556 0.33333333 0.69491525 0.58333333]\n",
      " [0.5        0.25       0.77966102 0.54166667]\n",
      " [0.94444444 0.41666667 0.86440678 0.91666667]\n",
      " [0.55555556 0.58333333 0.77966102 0.95833333]\n",
      " [0.58333333 0.45833333 0.76271186 0.70833333]\n",
      " [0.47222222 0.41666667 0.6440678  0.70833333]\n",
      " [0.72222222 0.45833333 0.74576271 0.83333333]\n",
      " [0.66666667 0.45833333 0.77966102 0.95833333]\n",
      " [0.72222222 0.45833333 0.69491525 0.91666667]\n",
      " [0.41666667 0.29166667 0.69491525 0.75      ]\n",
      " [0.69444444 0.5        0.83050847 0.91666667]\n",
      " [0.66666667 0.54166667 0.79661017 1.        ]\n",
      " [0.66666667 0.41666667 0.71186441 0.91666667]\n",
      " [0.55555556 0.20833333 0.6779661  0.75      ]\n",
      " [0.61111111 0.41666667 0.71186441 0.79166667]\n",
      " [0.52777778 0.58333333 0.74576271 0.91666667]\n",
      " [0.44444444 0.41666667 0.69491525 0.70833333]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "# considera somente os atributos, ignorando a última coluna, que contem a classe\n",
    "X = np.array(data[data.columns[0:data.shape[1]-1]])\n",
    "for i  in range(X.shape[1]):\n",
    "    print(\"Maior valor da coluna:\", i, \":\", max(X[:,i]))\n",
    "    print(\"Menor Valor da coluna:\", i, \":\", min(X[:,i]))\n",
    "# prepara a função para transformar os dados\n",
    "scaler = MinMaxScaler(feature_range=(0, 1))\n",
    "# Realiza a normalização e coloca em um novo vetor\n",
    "X_norm = scaler.fit_transform(X)\n",
    "print(X_norm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ou seja, o máximo e mínimo do novo conjunto de dados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mínimo dos atributos: [0. 0. 0. 0.]\n",
      "Máximo dos atributos: [1. 1. 1. 1.]\n"
     ]
    }
   ],
   "source": [
    "print('Mínimo dos atributos:', np.amin(X_norm, axis=0))\n",
    "print('Máximo dos atributos:', np.amax(X_norm, axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para realizarmos a padronização dos dados, de forma que os atributos apresentem média igual a zero e variância igual a 1, o procedimento é parecido."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-9.00681170e-01  1.03205722e+00 -1.34127240e+00 -1.31297673e+00]\n",
      " [-1.14301691e+00 -1.24957601e-01 -1.34127240e+00 -1.31297673e+00]\n",
      " [-1.38535265e+00  3.37848329e-01 -1.39813811e+00 -1.31297673e+00]\n",
      " [-1.50652052e+00  1.06445364e-01 -1.28440670e+00 -1.31297673e+00]\n",
      " [-1.02184904e+00  1.26346019e+00 -1.34127240e+00 -1.31297673e+00]\n",
      " [-5.37177559e-01  1.95766909e+00 -1.17067529e+00 -1.05003079e+00]\n",
      " [-1.50652052e+00  8.00654259e-01 -1.34127240e+00 -1.18150376e+00]\n",
      " [-1.02184904e+00  8.00654259e-01 -1.28440670e+00 -1.31297673e+00]\n",
      " [-1.74885626e+00 -3.56360566e-01 -1.34127240e+00 -1.31297673e+00]\n",
      " [-1.14301691e+00  1.06445364e-01 -1.28440670e+00 -1.44444970e+00]\n",
      " [-5.37177559e-01  1.49486315e+00 -1.28440670e+00 -1.31297673e+00]\n",
      " [-1.26418478e+00  8.00654259e-01 -1.22754100e+00 -1.31297673e+00]\n",
      " [-1.26418478e+00 -1.24957601e-01 -1.34127240e+00 -1.44444970e+00]\n",
      " [-1.87002413e+00 -1.24957601e-01 -1.51186952e+00 -1.44444970e+00]\n",
      " [-5.25060772e-02  2.18907205e+00 -1.45500381e+00 -1.31297673e+00]\n",
      " [-1.73673948e-01  3.11468391e+00 -1.28440670e+00 -1.05003079e+00]\n",
      " [-5.37177559e-01  1.95766909e+00 -1.39813811e+00 -1.05003079e+00]\n",
      " [-9.00681170e-01  1.03205722e+00 -1.34127240e+00 -1.18150376e+00]\n",
      " [-1.73673948e-01  1.72626612e+00 -1.17067529e+00 -1.18150376e+00]\n",
      " [-9.00681170e-01  1.72626612e+00 -1.28440670e+00 -1.18150376e+00]\n",
      " [-5.37177559e-01  8.00654259e-01 -1.17067529e+00 -1.31297673e+00]\n",
      " [-9.00681170e-01  1.49486315e+00 -1.28440670e+00 -1.05003079e+00]\n",
      " [-1.50652052e+00  1.26346019e+00 -1.56873522e+00 -1.31297673e+00]\n",
      " [-9.00681170e-01  5.69251294e-01 -1.17067529e+00 -9.18557817e-01]\n",
      " [-1.26418478e+00  8.00654259e-01 -1.05694388e+00 -1.31297673e+00]\n",
      " [-1.02184904e+00 -1.24957601e-01 -1.22754100e+00 -1.31297673e+00]\n",
      " [-1.02184904e+00  8.00654259e-01 -1.22754100e+00 -1.05003079e+00]\n",
      " [-7.79513300e-01  1.03205722e+00 -1.28440670e+00 -1.31297673e+00]\n",
      " [-7.79513300e-01  8.00654259e-01 -1.34127240e+00 -1.31297673e+00]\n",
      " [-1.38535265e+00  3.37848329e-01 -1.22754100e+00 -1.31297673e+00]\n",
      " [-1.26418478e+00  1.06445364e-01 -1.22754100e+00 -1.31297673e+00]\n",
      " [-5.37177559e-01  8.00654259e-01 -1.28440670e+00 -1.05003079e+00]\n",
      " [-7.79513300e-01  2.42047502e+00 -1.28440670e+00 -1.44444970e+00]\n",
      " [-4.16009689e-01  2.65187798e+00 -1.34127240e+00 -1.31297673e+00]\n",
      " [-1.14301691e+00  1.06445364e-01 -1.28440670e+00 -1.44444970e+00]\n",
      " [-1.02184904e+00  3.37848329e-01 -1.45500381e+00 -1.31297673e+00]\n",
      " [-4.16009689e-01  1.03205722e+00 -1.39813811e+00 -1.31297673e+00]\n",
      " [-1.14301691e+00  1.06445364e-01 -1.28440670e+00 -1.44444970e+00]\n",
      " [-1.74885626e+00 -1.24957601e-01 -1.39813811e+00 -1.31297673e+00]\n",
      " [-9.00681170e-01  8.00654259e-01 -1.28440670e+00 -1.31297673e+00]\n",
      " [-1.02184904e+00  1.03205722e+00 -1.39813811e+00 -1.18150376e+00]\n",
      " [-1.62768839e+00 -1.74477836e+00 -1.39813811e+00 -1.18150376e+00]\n",
      " [-1.74885626e+00  3.37848329e-01 -1.39813811e+00 -1.31297673e+00]\n",
      " [-1.02184904e+00  1.03205722e+00 -1.22754100e+00 -7.87084847e-01]\n",
      " [-9.00681170e-01  1.72626612e+00 -1.05694388e+00 -1.05003079e+00]\n",
      " [-1.26418478e+00 -1.24957601e-01 -1.34127240e+00 -1.18150376e+00]\n",
      " [-9.00681170e-01  1.72626612e+00 -1.22754100e+00 -1.31297673e+00]\n",
      " [-1.50652052e+00  3.37848329e-01 -1.34127240e+00 -1.31297673e+00]\n",
      " [-6.58345429e-01  1.49486315e+00 -1.28440670e+00 -1.31297673e+00]\n",
      " [-1.02184904e+00  5.69251294e-01 -1.34127240e+00 -1.31297673e+00]\n",
      " [ 1.40150837e+00  3.37848329e-01  5.35295827e-01  2.64698913e-01]\n",
      " [ 6.74501145e-01  3.37848329e-01  4.21564419e-01  3.96171883e-01]\n",
      " [ 1.28034050e+00  1.06445364e-01  6.49027235e-01  3.96171883e-01]\n",
      " [-4.16009689e-01 -1.74477836e+00  1.37235899e-01  1.33225943e-01]\n",
      " [ 7.95669016e-01 -5.87763531e-01  4.78430123e-01  3.96171883e-01]\n",
      " [-1.73673948e-01 -5.87763531e-01  4.21564419e-01  1.33225943e-01]\n",
      " [ 5.53333275e-01  5.69251294e-01  5.35295827e-01  5.27644853e-01]\n",
      " [-1.14301691e+00 -1.51337539e+00 -2.60824029e-01 -2.61192967e-01]\n",
      " [ 9.16836886e-01 -3.56360566e-01  4.78430123e-01  1.33225943e-01]\n",
      " [-7.79513300e-01 -8.19166497e-01  8.03701950e-02  2.64698913e-01]\n",
      " [-1.02184904e+00 -2.43898725e+00 -1.47092621e-01 -2.61192967e-01]\n",
      " [ 6.86617933e-02 -1.24957601e-01  2.50967307e-01  3.96171883e-01]\n",
      " [ 1.89829664e-01 -1.97618132e+00  1.37235899e-01 -2.61192967e-01]\n",
      " [ 3.10997534e-01 -3.56360566e-01  5.35295827e-01  2.64698913e-01]\n",
      " [-2.94841818e-01 -3.56360566e-01 -9.02269170e-02  1.33225943e-01]\n",
      " [ 1.03800476e+00  1.06445364e-01  3.64698715e-01  2.64698913e-01]\n",
      " [-2.94841818e-01 -1.24957601e-01  4.21564419e-01  3.96171883e-01]\n",
      " [-5.25060772e-02 -8.19166497e-01  1.94101603e-01 -2.61192967e-01]\n",
      " [ 4.32165405e-01 -1.97618132e+00  4.21564419e-01  3.96171883e-01]\n",
      " [-2.94841818e-01 -1.28197243e+00  8.03701950e-02 -1.29719997e-01]\n",
      " [ 6.86617933e-02  3.37848329e-01  5.92161531e-01  7.90590793e-01]\n",
      " [ 3.10997534e-01 -5.87763531e-01  1.37235899e-01  1.33225943e-01]\n",
      " [ 5.53333275e-01 -1.28197243e+00  6.49027235e-01  3.96171883e-01]\n",
      " [ 3.10997534e-01 -5.87763531e-01  5.35295827e-01  1.75297293e-03]\n",
      " [ 6.74501145e-01 -3.56360566e-01  3.07833011e-01  1.33225943e-01]\n",
      " [ 9.16836886e-01 -1.24957601e-01  3.64698715e-01  2.64698913e-01]\n",
      " [ 1.15917263e+00 -5.87763531e-01  5.92161531e-01  2.64698913e-01]\n",
      " [ 1.03800476e+00 -1.24957601e-01  7.05892939e-01  6.59117823e-01]\n",
      " [ 1.89829664e-01 -3.56360566e-01  4.21564419e-01  3.96171883e-01]\n",
      " [-1.73673948e-01 -1.05056946e+00 -1.47092621e-01 -2.61192967e-01]\n",
      " [-4.16009689e-01 -1.51337539e+00  2.35044910e-02 -1.29719997e-01]\n",
      " [-4.16009689e-01 -1.51337539e+00 -3.33612130e-02 -2.61192967e-01]\n",
      " [-5.25060772e-02 -8.19166497e-01  8.03701950e-02  1.75297293e-03]\n",
      " [ 1.89829664e-01 -8.19166497e-01  7.62758643e-01  5.27644853e-01]\n",
      " [-5.37177559e-01 -1.24957601e-01  4.21564419e-01  3.96171883e-01]\n",
      " [ 1.89829664e-01  8.00654259e-01  4.21564419e-01  5.27644853e-01]\n",
      " [ 1.03800476e+00  1.06445364e-01  5.35295827e-01  3.96171883e-01]\n",
      " [ 5.53333275e-01 -1.74477836e+00  3.64698715e-01  1.33225943e-01]\n",
      " [-2.94841818e-01 -1.24957601e-01  1.94101603e-01  1.33225943e-01]\n",
      " [-4.16009689e-01 -1.28197243e+00  1.37235899e-01  1.33225943e-01]\n",
      " [-4.16009689e-01 -1.05056946e+00  3.64698715e-01  1.75297293e-03]\n",
      " [ 3.10997534e-01 -1.24957601e-01  4.78430123e-01  2.64698913e-01]\n",
      " [-5.25060772e-02 -1.05056946e+00  1.37235899e-01  1.75297293e-03]\n",
      " [-1.02184904e+00 -1.74477836e+00 -2.60824029e-01 -2.61192967e-01]\n",
      " [-2.94841818e-01 -8.19166497e-01  2.50967307e-01  1.33225943e-01]\n",
      " [-1.73673948e-01 -1.24957601e-01  2.50967307e-01  1.75297293e-03]\n",
      " [-1.73673948e-01 -3.56360566e-01  2.50967307e-01  1.33225943e-01]\n",
      " [ 4.32165405e-01 -3.56360566e-01  3.07833011e-01  1.33225943e-01]\n",
      " [-9.00681170e-01 -1.28197243e+00 -4.31421141e-01 -1.29719997e-01]\n",
      " [-1.73673948e-01 -5.87763531e-01  1.94101603e-01  1.33225943e-01]\n",
      " [ 5.53333275e-01  5.69251294e-01  1.27454998e+00  1.71090158e+00]\n",
      " [-5.25060772e-02 -8.19166497e-01  7.62758643e-01  9.22063763e-01]\n",
      " [ 1.52267624e+00 -1.24957601e-01  1.21768427e+00  1.18500970e+00]\n",
      " [ 5.53333275e-01 -3.56360566e-01  1.04708716e+00  7.90590793e-01]\n",
      " [ 7.95669016e-01 -1.24957601e-01  1.16081857e+00  1.31648267e+00]\n",
      " [ 2.12851559e+00 -1.24957601e-01  1.61574420e+00  1.18500970e+00]\n",
      " [-1.14301691e+00 -1.28197243e+00  4.21564419e-01  6.59117823e-01]\n",
      " [ 1.76501198e+00 -3.56360566e-01  1.44514709e+00  7.90590793e-01]\n",
      " [ 1.03800476e+00 -1.28197243e+00  1.16081857e+00  7.90590793e-01]\n",
      " [ 1.64384411e+00  1.26346019e+00  1.33141568e+00  1.71090158e+00]\n",
      " [ 7.95669016e-01  3.37848329e-01  7.62758643e-01  1.05353673e+00]\n",
      " [ 6.74501145e-01 -8.19166497e-01  8.76490051e-01  9.22063763e-01]\n",
      " [ 1.15917263e+00 -1.24957601e-01  9.90221459e-01  1.18500970e+00]\n",
      " [-1.73673948e-01 -1.28197243e+00  7.05892939e-01  1.05353673e+00]\n",
      " [-5.25060772e-02 -5.87763531e-01  7.62758643e-01  1.57942861e+00]\n",
      " [ 6.74501145e-01  3.37848329e-01  8.76490051e-01  1.44795564e+00]\n",
      " [ 7.95669016e-01 -1.24957601e-01  9.90221459e-01  7.90590793e-01]\n",
      " [ 2.24968346e+00  1.72626612e+00  1.67260991e+00  1.31648267e+00]\n",
      " [ 2.24968346e+00 -1.05056946e+00  1.78634131e+00  1.44795564e+00]\n",
      " [ 1.89829664e-01 -1.97618132e+00  7.05892939e-01  3.96171883e-01]\n",
      " [ 1.28034050e+00  3.37848329e-01  1.10395287e+00  1.44795564e+00]\n",
      " [-2.94841818e-01 -5.87763531e-01  6.49027235e-01  1.05353673e+00]\n",
      " [ 2.24968346e+00 -5.87763531e-01  1.67260991e+00  1.05353673e+00]\n",
      " [ 5.53333275e-01 -8.19166497e-01  6.49027235e-01  7.90590793e-01]\n",
      " [ 1.03800476e+00  5.69251294e-01  1.10395287e+00  1.18500970e+00]\n",
      " [ 1.64384411e+00  3.37848329e-01  1.27454998e+00  7.90590793e-01]\n",
      " [ 4.32165405e-01 -5.87763531e-01  5.92161531e-01  7.90590793e-01]\n",
      " [ 3.10997534e-01 -1.24957601e-01  6.49027235e-01  7.90590793e-01]\n",
      " [ 6.74501145e-01 -5.87763531e-01  1.04708716e+00  1.18500970e+00]\n",
      " [ 1.64384411e+00 -1.24957601e-01  1.16081857e+00  5.27644853e-01]\n",
      " [ 1.88617985e+00 -5.87763531e-01  1.33141568e+00  9.22063763e-01]\n",
      " [ 2.49201920e+00  1.72626612e+00  1.50201279e+00  1.05353673e+00]\n",
      " [ 6.74501145e-01 -5.87763531e-01  1.04708716e+00  1.31648267e+00]\n",
      " [ 5.53333275e-01 -5.87763531e-01  7.62758643e-01  3.96171883e-01]\n",
      " [ 3.10997534e-01 -1.05056946e+00  1.04708716e+00  2.64698913e-01]\n",
      " [ 2.24968346e+00 -1.24957601e-01  1.33141568e+00  1.44795564e+00]\n",
      " [ 5.53333275e-01  8.00654259e-01  1.04708716e+00  1.57942861e+00]\n",
      " [ 6.74501145e-01  1.06445364e-01  9.90221459e-01  7.90590793e-01]\n",
      " [ 1.89829664e-01 -1.24957601e-01  5.92161531e-01  7.90590793e-01]\n",
      " [ 1.28034050e+00  1.06445364e-01  9.33355755e-01  1.18500970e+00]\n",
      " [ 1.03800476e+00  1.06445364e-01  1.04708716e+00  1.57942861e+00]\n",
      " [ 1.28034050e+00  1.06445364e-01  7.62758643e-01  1.44795564e+00]\n",
      " [-5.25060772e-02 -8.19166497e-01  7.62758643e-01  9.22063763e-01]\n",
      " [ 1.15917263e+00  3.37848329e-01  1.21768427e+00  1.44795564e+00]\n",
      " [ 1.03800476e+00  5.69251294e-01  1.10395287e+00  1.71090158e+00]\n",
      " [ 1.03800476e+00 -1.24957601e-01  8.19624347e-01  1.44795564e+00]\n",
      " [ 5.53333275e-01 -1.28197243e+00  7.05892939e-01  9.22063763e-01]\n",
      " [ 7.95669016e-01 -1.24957601e-01  8.19624347e-01  1.05353673e+00]\n",
      " [ 4.32165405e-01  8.00654259e-01  9.33355755e-01  1.44795564e+00]\n",
      " [ 6.86617933e-02 -1.24957601e-01  7.62758643e-01  7.90590793e-01]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "X = np.array(data[data.columns[0:data.shape[1]-1]])\n",
    "# prepara a função para transformar os dados\n",
    "scaler = StandardScaler().fit(X)\n",
    "# realiza a padronização (média=0, variância = 1)\n",
    "rescaledX = scaler.transform(X)\n",
    "print(rescaledX)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos verificar se cada coluna apresenta média igual a zero e desvio padrão igual a um."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Media da coluna 0 é igual a:  -4.736951571734001e-16\n",
      "Desvio padrão da coluna 0 é igual a:  1.0 \n",
      "\n",
      "Media da coluna 1 é igual a:  -6.631732200427602e-16\n",
      "Desvio padrão da coluna 1 é igual a:  0.9999999999999999 \n",
      "\n",
      "Media da coluna 2 é igual a:  3.315866100213801e-16\n",
      "Desvio padrão da coluna 2 é igual a:  0.9999999999999998 \n",
      "\n",
      "Media da coluna 3 é igual a:  -2.842170943040401e-16\n",
      "Desvio padrão da coluna 3 é igual a:  1.0 \n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in np.arange(0,rescaledX.shape[1]):\n",
    "    print('Media da coluna', i, 'é igual a: ', np.mean(rescaledX[:,i]))\n",
    "    print('Desvio padrão da coluna', i, 'é igual a: ', np.std(rescaledX[:,i]),'\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binarização dos dados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A binarização dos dados resulta em valores zero ou um, de acordo com um dado limiar. Ou seja, se o valor em X for maior do que o limiar, o valor resultante será 1, caso contrário será zero.\n",
    "$$\n",
    "X_{novo}(i,j) = \n",
    "\\begin{cases} 1, & \\mbox{se } X(i,j) \\geq T \\\\ 0, & \\mbox{se } X(i,j) < T \\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Limiar: 0.2\n",
      "---------------------\n",
      "Antes: [0.22222222 0.625      0.06779661 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.16666667 0.41666667 0.06779661 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.11111111 0.5        0.05084746 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.08333333 0.45833333 0.08474576 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.66666667 0.06779661 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.30555556 0.79166667 0.11864407 0.125     ]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.08333333 0.58333333 0.06779661 0.08333333]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.58333333 0.08474576 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.02777778 0.375      0.06779661 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.16666667 0.45833333 0.08474576 0.        ]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.30555556 0.70833333 0.08474576 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.13888889 0.58333333 0.10169492 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.13888889 0.41666667 0.06779661 0.        ]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.         0.41666667 0.01694915 0.        ]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.41666667 0.83333333 0.03389831 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.38888889 1.         0.08474576 0.125     ]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.30555556 0.79166667 0.05084746 0.125     ]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.625      0.06779661 0.08333333]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.38888889 0.75       0.11864407 0.08333333]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.75       0.08474576 0.08333333]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.30555556 0.58333333 0.11864407 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.70833333 0.08474576 0.125     ]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.08333333 0.66666667 0.         0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.54166667 0.11864407 0.16666667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.13888889 0.58333333 0.15254237 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.41666667 0.10169492 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.58333333 0.10169492 0.125     ]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.25       0.625      0.08474576 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.25       0.58333333 0.06779661 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.11111111 0.5        0.10169492 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.13888889 0.45833333 0.10169492 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.30555556 0.58333333 0.08474576 0.125     ]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.25       0.875      0.08474576 0.        ]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.33333333 0.91666667 0.06779661 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.16666667 0.45833333 0.08474576 0.        ]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.5        0.03389831 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.33333333 0.625      0.05084746 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.16666667 0.45833333 0.08474576 0.        ]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.02777778 0.41666667 0.05084746 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.58333333 0.08474576 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.625      0.05084746 0.08333333]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.05555556 0.125      0.05084746 0.08333333]\n",
      "Depois: [0. 0. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.02777778 0.5        0.05084746 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.625      0.10169492 0.20833333]\n",
      "Depois: [0. 1. 0. 1.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.75       0.15254237 0.125     ]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.13888889 0.41666667 0.06779661 0.08333333]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.75       0.10169492 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.08333333 0.5        0.06779661 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.27777778 0.70833333 0.08474576 0.04166667]\n",
      "Depois: [1. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.54166667 0.06779661 0.04166667]\n",
      "Depois: [0. 1. 0. 0.]\n",
      "---------------------\n",
      "Antes: [0.75       0.5        0.62711864 0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.58333333 0.5        0.59322034 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.72222222 0.45833333 0.66101695 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.33333333 0.125      0.50847458 0.5       ]\n",
      "Depois: [1. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.61111111 0.33333333 0.61016949 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.38888889 0.33333333 0.59322034 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.54166667 0.62711864 0.625     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.16666667 0.16666667 0.38983051 0.375     ]\n",
      "Depois: [0. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.63888889 0.375      0.61016949 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.25       0.29166667 0.49152542 0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.         0.42372881 0.375     ]\n",
      "Depois: [0. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.44444444 0.41666667 0.54237288 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.47222222 0.08333333 0.50847458 0.375     ]\n",
      "Depois: [1. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.5        0.375      0.62711864 0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.36111111 0.375      0.44067797 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.45833333 0.57627119 0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.36111111 0.41666667 0.59322034 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.41666667 0.29166667 0.52542373 0.375     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.52777778 0.08333333 0.59322034 0.58333333]\n",
      "Depois: [1. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.36111111 0.20833333 0.49152542 0.41666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.44444444 0.5        0.6440678  0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.5        0.33333333 0.50847458 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.20833333 0.66101695 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.5        0.33333333 0.62711864 0.45833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.58333333 0.375      0.55932203 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.63888889 0.41666667 0.57627119 0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.69444444 0.33333333 0.6440678  0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.41666667 0.6779661  0.66666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.47222222 0.375      0.59322034 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.38888889 0.25       0.42372881 0.375     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.33333333 0.16666667 0.47457627 0.41666667]\n",
      "Depois: [1. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.33333333 0.16666667 0.45762712 0.375     ]\n",
      "Depois: [1. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.41666667 0.29166667 0.49152542 0.45833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.47222222 0.29166667 0.69491525 0.625     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.30555556 0.41666667 0.59322034 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.47222222 0.58333333 0.59322034 0.625     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.45833333 0.62711864 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Antes: [0.55555556 0.125      0.57627119 0.5       ]\n",
      "Depois: [1. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.36111111 0.41666667 0.52542373 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.33333333 0.20833333 0.50847458 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.33333333 0.25       0.57627119 0.45833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.5        0.41666667 0.61016949 0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.41666667 0.25       0.50847458 0.45833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.19444444 0.125      0.38983051 0.375     ]\n",
      "Depois: [0. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.36111111 0.29166667 0.54237288 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.38888889 0.41666667 0.54237288 0.45833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.38888889 0.375      0.54237288 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.52777778 0.375      0.55932203 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.22222222 0.20833333 0.33898305 0.41666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.38888889 0.33333333 0.52542373 0.5       ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.54166667 0.84745763 1.        ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.41666667 0.29166667 0.69491525 0.75      ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.77777778 0.41666667 0.83050847 0.83333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.375      0.77966102 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.61111111 0.41666667 0.81355932 0.875     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.91666667 0.41666667 0.94915254 0.83333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.16666667 0.20833333 0.59322034 0.66666667]\n",
      "Depois: [0. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.83333333 0.375      0.89830508 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.20833333 0.81355932 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.80555556 0.66666667 0.86440678 1.        ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.61111111 0.5        0.69491525 0.79166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.58333333 0.29166667 0.72881356 0.75      ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.69444444 0.41666667 0.76271186 0.83333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.38888889 0.20833333 0.6779661  0.79166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.41666667 0.33333333 0.69491525 0.95833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.58333333 0.5        0.72881356 0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.61111111 0.41666667 0.76271186 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.94444444 0.75       0.96610169 0.875     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.94444444 0.25       1.         0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.47222222 0.08333333 0.6779661  0.58333333]\n",
      "Depois: [1. 0. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.72222222 0.5        0.79661017 0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.36111111 0.33333333 0.66101695 0.79166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.94444444 0.33333333 0.96610169 0.79166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.29166667 0.66101695 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.54166667 0.79661017 0.83333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.80555556 0.5        0.84745763 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.52777778 0.33333333 0.6440678  0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.5        0.41666667 0.66101695 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.58333333 0.33333333 0.77966102 0.83333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.80555556 0.41666667 0.81355932 0.625     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.86111111 0.33333333 0.86440678 0.75      ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [1.         0.75       0.91525424 0.79166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.58333333 0.33333333 0.77966102 0.875     ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.33333333 0.69491525 0.58333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.5        0.25       0.77966102 0.54166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.94444444 0.41666667 0.86440678 0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.58333333 0.77966102 0.95833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.58333333 0.45833333 0.76271186 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.47222222 0.41666667 0.6440678  0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.72222222 0.45833333 0.74576271 0.83333333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.45833333 0.77966102 0.95833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.72222222 0.45833333 0.69491525 0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.41666667 0.29166667 0.69491525 0.75      ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.69444444 0.5        0.83050847 0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.54166667 0.79661017 1.        ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.66666667 0.41666667 0.71186441 0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.55555556 0.20833333 0.6779661  0.75      ]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.61111111 0.41666667 0.71186441 0.79166667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.52777778 0.58333333 0.74576271 0.91666667]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n",
      "Antes: [0.44444444 0.41666667 0.69491525 0.70833333]\n",
      "Depois: [1. 1. 1. 1.]\n",
      "---------------------\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import Binarizer\n",
    "from sklearn.preprocessing import MinMaxScaler\n",
    "\n",
    "# considera apenas os atributos, ignorando a última coluna das classes\n",
    "X = np.array(data[data.columns[0:data.shape[1]-1]], dtype = float)\n",
    "T = 0.2 # valor do limiar\n",
    "print('Limiar:', T)\n",
    "print('---------------------')\n",
    "\n",
    "# prepara a normalização dos dados\n",
    "scaler = MinMaxScaler(feature_range=(0, 1))\n",
    "# realiza a normalização\n",
    "X_pad = scaler.fit_transform(X)\n",
    "# faz a binarização considerando o limiar (threshold)\n",
    "binarizer = Binarizer(threshold=T).fit(X_pad)\n",
    "binaryX = binarizer.transform(X_pad)\n",
    "for i in np.arange(0,X_pad.shape[0]):\n",
    "    print(\"Antes:\", X_pad[i,])\n",
    "    print('Depois:',binaryX[i,])\n",
    "    print('---------------------')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conversão de variáveis nominais em inteiros"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quando temos dados nominais e ordinais, podemos convertê-los para variáveis numéricas. Vamos fazer isso com as classes dos dados, mudando os valores nominais para inteiros."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de linhas e colunas: (150, 5)\n",
      "Coluna com as classes:\n",
      " 0         setosa\n",
      "1         setosa\n",
      "2         setosa\n",
      "3         setosa\n",
      "4         setosa\n",
      "         ...    \n",
      "145    virginica\n",
      "146    virginica\n",
      "147    virginica\n",
      "148    virginica\n",
      "149    virginica\n",
      "Name: species, Length: 150, dtype: object\n"
     ]
    }
   ],
   "source": [
    "# leitura dos dados\n",
    "data = pd.read_csv('data/iris.csv', header=(0))\n",
    "print('Número de linhas e colunas:', data.shape)\n",
    "# mostramos a última coluna\n",
    "print('Coluna com as classes:\\n', data[data.columns[-1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Novos dados:\n",
      "0      0\n",
      "1      0\n",
      "2      0\n",
      "3      0\n",
      "4      0\n",
      "      ..\n",
      "145    2\n",
      "146    2\n",
      "147    2\n",
      "148    2\n",
      "149    2\n",
      "Name: species, Length: 150, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "# armazena o nome das classes\n",
    "classes = np.unique(data[data.columns[-1]])\n",
    "number = 0 # valor que será usado para representar a clases\n",
    "for i in classes:\n",
    "    data = data.replace(i, number) # substitui cada valor da classe por number\n",
    "    number = number + 1\n",
    "print('Novos dados:')\n",
    "print(data[data.columns[-1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esse mesmo procedimento pode ser usado em qualquer uma das colunas da matriz de atributos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One-hot encoding"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quando temos variáveis nominais e precisamos transformá-las para numéricas, uma maneira simples é usar o método one-hot encoding. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>A</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>c</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>a</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A\n",
       "0  a\n",
       "1  b\n",
       "2  a\n",
       "3  c\n",
       "4  a"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# cria um dataframe do Pandas\n",
    "df = pd.DataFrame({\n",
    "          'A':['a','b','a', 'c', 'a', 'b'],\n",
    "        })\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usando one-hot enconding, obtemos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>A_a</th>\n",
       "      <th>A_b</th>\n",
       "      <th>A_c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   A_a  A_b  A_c\n",
       "0    1    0    0\n",
       "1    0    1    0\n",
       "2    1    0    0\n",
       "3    0    0    1\n",
       "4    1    0    0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.get_dummies(df)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note que foi usado um código binário para cada valor nominal."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dados correlacionados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos identificar as colunas em que a correlação entre elas é maior do que $|p|$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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>crim</th>\n",
       "      <th>zn</th>\n",
       "      <th>indus</th>\n",
       "      <th>chas</th>\n",
       "      <th>nox</th>\n",
       "      <th>rm</th>\n",
       "      <th>age</th>\n",
       "      <th>dis</th>\n",
       "      <th>rad</th>\n",
       "      <th>tax</th>\n",
       "      <th>ptratio</th>\n",
       "      <th>b</th>\n",
       "      <th>lstat</th>\n",
       "      <th>medv</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1</td>\n",
       "      <td>296</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2</td>\n",
       "      <td>242</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.02985</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.430</td>\n",
       "      <td>58.7</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3</td>\n",
       "      <td>222</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.12</td>\n",
       "      <td>5.21</td>\n",
       "      <td>28.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.08829</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.012</td>\n",
       "      <td>66.6</td>\n",
       "      <td>5.5605</td>\n",
       "      <td>5</td>\n",
       "      <td>311</td>\n",
       "      <td>15.2</td>\n",
       "      <td>395.60</td>\n",
       "      <td>12.43</td>\n",
       "      <td>22.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.14455</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.172</td>\n",
       "      <td>96.1</td>\n",
       "      <td>5.9505</td>\n",
       "      <td>5</td>\n",
       "      <td>311</td>\n",
       "      <td>15.2</td>\n",
       "      <td>396.90</td>\n",
       "      <td>19.15</td>\n",
       "      <td>27.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.21124</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>5.631</td>\n",
       "      <td>100.0</td>\n",
       "      <td>6.0821</td>\n",
       "      <td>5</td>\n",
       "      <td>311</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.63</td>\n",
       "      <td>29.93</td>\n",
       "      <td>16.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.17004</td>\n",
       "      <td>12.5</td>\n",
       "      <td>7.87</td>\n",
       "      <td>0</td>\n",
       "      <td>0.524</td>\n",
       "      <td>6.004</td>\n",
       "      <td>85.9</td>\n",
       "      <td>6.5921</td>\n",
       "      <td>5</td>\n",
       "      <td>311</td>\n",
       "      <td>15.2</td>\n",
       "      <td>386.71</td>\n",
       "      <td>17.10</td>\n",
       "      <td>18.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      crim    zn  indus  chas    nox     rm    age     dis  rad  tax  ptratio  \\\n",
       "0  0.00632  18.0   2.31     0  0.538  6.575   65.2  4.0900    1  296     15.3   \n",
       "1  0.02731   0.0   7.07     0  0.469  6.421   78.9  4.9671    2  242     17.8   \n",
       "2  0.02729   0.0   7.07     0  0.469  7.185   61.1  4.9671    2  242     17.8   \n",
       "3  0.03237   0.0   2.18     0  0.458  6.998   45.8  6.0622    3  222     18.7   \n",
       "4  0.06905   0.0   2.18     0  0.458  7.147   54.2  6.0622    3  222     18.7   \n",
       "5  0.02985   0.0   2.18     0  0.458  6.430   58.7  6.0622    3  222     18.7   \n",
       "6  0.08829  12.5   7.87     0  0.524  6.012   66.6  5.5605    5  311     15.2   \n",
       "7  0.14455  12.5   7.87     0  0.524  6.172   96.1  5.9505    5  311     15.2   \n",
       "8  0.21124  12.5   7.87     0  0.524  5.631  100.0  6.0821    5  311     15.2   \n",
       "9  0.17004  12.5   7.87     0  0.524  6.004   85.9  6.5921    5  311     15.2   \n",
       "\n",
       "        b  lstat  medv  \n",
       "0  396.90   4.98  24.0  \n",
       "1  396.90   9.14  21.6  \n",
       "2  392.83   4.03  34.7  \n",
       "3  394.63   2.94  33.4  \n",
       "4  396.90   5.33  36.2  \n",
       "5  394.12   5.21  28.7  \n",
       "6  395.60  12.43  22.9  \n",
       "7  396.90  19.15  27.1  \n",
       "8  386.63  29.93  16.5  \n",
       "9  386.71  17.10  18.9  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/BostonHousing.csv', header=(0))\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A matriz de correlação entre as variáveis:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# obtem a matriz de correlação dos dados\n",
    "corr = data.corr()\n",
    "# Mostra a matriz\n",
    "plt.figure(figsize=(7, 7))\n",
    "# imshow é usado para mostrar imagens\n",
    "plt.imshow(corr, cmap='Blues', interpolation='none', aspect='auto')\n",
    "# mostra a barra lateral de cores\n",
    "plt.colorbar()\n",
    "# inclui o nome das variáveis\n",
    "plt.xticks(range(len(corr)), corr.columns, rotation='vertical')\n",
    "plt.yticks(range(len(corr)), corr.columns);\n",
    "plt.suptitle('Correlation between variables', fontsize=15, fontweight='bold')\n",
    "plt.grid(False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Os dados estão armazenados na matriz:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "             crim        zn     indus      chas       nox        rm       age  \\\n",
      "crim     1.000000 -0.200469  0.406583 -0.055892  0.420972 -0.219247  0.352734   \n",
      "zn      -0.200469  1.000000 -0.533828 -0.042697 -0.516604  0.311991 -0.569537   \n",
      "indus    0.406583 -0.533828  1.000000  0.062938  0.763651 -0.391676  0.644779   \n",
      "chas    -0.055892 -0.042697  0.062938  1.000000  0.091203  0.091251  0.086518   \n",
      "nox      0.420972 -0.516604  0.763651  0.091203  1.000000 -0.302188  0.731470   \n",
      "rm      -0.219247  0.311991 -0.391676  0.091251 -0.302188  1.000000 -0.240265   \n",
      "age      0.352734 -0.569537  0.644779  0.086518  0.731470 -0.240265  1.000000   \n",
      "dis     -0.379670  0.664408 -0.708027 -0.099176 -0.769230  0.205246 -0.747881   \n",
      "rad      0.625505 -0.311948  0.595129 -0.007368  0.611441 -0.209847  0.456022   \n",
      "tax      0.582764 -0.314563  0.720760 -0.035587  0.668023 -0.292048  0.506456   \n",
      "ptratio  0.289946 -0.391679  0.383248 -0.121515  0.188933 -0.355501  0.261515   \n",
      "b       -0.385064  0.175520 -0.356977  0.048788 -0.380051  0.128069 -0.273534   \n",
      "lstat    0.455621 -0.412995  0.603800 -0.053929  0.590879 -0.613808  0.602339   \n",
      "medv    -0.388305  0.360445 -0.483725  0.175260 -0.427321  0.695360 -0.376955   \n",
      "\n",
      "              dis       rad       tax   ptratio         b     lstat      medv  \n",
      "crim    -0.379670  0.625505  0.582764  0.289946 -0.385064  0.455621 -0.388305  \n",
      "zn       0.664408 -0.311948 -0.314563 -0.391679  0.175520 -0.412995  0.360445  \n",
      "indus   -0.708027  0.595129  0.720760  0.383248 -0.356977  0.603800 -0.483725  \n",
      "chas    -0.099176 -0.007368 -0.035587 -0.121515  0.048788 -0.053929  0.175260  \n",
      "nox     -0.769230  0.611441  0.668023  0.188933 -0.380051  0.590879 -0.427321  \n",
      "rm       0.205246 -0.209847 -0.292048 -0.355501  0.128069 -0.613808  0.695360  \n",
      "age     -0.747881  0.456022  0.506456  0.261515 -0.273534  0.602339 -0.376955  \n",
      "dis      1.000000 -0.494588 -0.534432 -0.232471  0.291512 -0.496996  0.249929  \n",
      "rad     -0.494588  1.000000  0.910228  0.464741 -0.444413  0.488676 -0.381626  \n",
      "tax     -0.534432  0.910228  1.000000  0.460853 -0.441808  0.543993 -0.468536  \n",
      "ptratio -0.232471  0.464741  0.460853  1.000000 -0.177383  0.374044 -0.507787  \n",
      "b        0.291512 -0.444413 -0.441808 -0.177383  1.000000 -0.366087  0.333461  \n",
      "lstat   -0.496996  0.488676  0.543993  0.374044 -0.366087  1.000000 -0.737663  \n",
      "medv     0.249929 -0.381626 -0.468536 -0.507787  0.333461 -0.737663  1.000000  \n"
     ]
    }
   ],
   "source": [
    "print(corr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assim, para identificarmos as variáveis correlacionadas, usamos um laço for:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variáveis mais correlacionadas:\n",
      " [['indus', 'nox'], ['nox', 'indus'], ['nox', 'dis'], ['dis', 'nox'], ['rad', 'tax'], ['tax', 'rad']]\n"
     ]
    }
   ],
   "source": [
    "p = 0.75 # correlação mínima\n",
    "var = []\n",
    "for i in corr.columns:\n",
    "    for j in corr.columns:\n",
    "        if(i != j):\n",
    "            if np.abs(corr[i][j]) > p: # se maior do que |p|\n",
    "                var.append([i,j])\n",
    "print('Variáveis mais correlacionadas:\\n', var)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Com isso, podemos remover as variáveis mais correlacionadas de modo a reduzir a redundância nos dados."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dados desbalanceados"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Muitas vezes, o número de observações difere em cada classe, de modo que os dados são desbalanceados. Podemos verificar o número de elementos em cada classe criando um histograma."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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>Comp</th>\n",
       "      <th>Circ</th>\n",
       "      <th>D.Circ</th>\n",
       "      <th>Rad.Ra</th>\n",
       "      <th>Pr.Axis.Ra</th>\n",
       "      <th>Max.L.Ra</th>\n",
       "      <th>Scat.Ra</th>\n",
       "      <th>Elong</th>\n",
       "      <th>Pr.Axis.Rect</th>\n",
       "      <th>Max.L.Rect</th>\n",
       "      <th>Sc.Var.Maxis</th>\n",
       "      <th>Sc.Var.maxis</th>\n",
       "      <th>Ra.Gyr</th>\n",
       "      <th>Skew.Maxis</th>\n",
       "      <th>Skew.maxis</th>\n",
       "      <th>Kurt.maxis</th>\n",
       "      <th>Kurt.Maxis</th>\n",
       "      <th>Holl.Ra</th>\n",
       "      <th>Class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>95</td>\n",
       "      <td>48</td>\n",
       "      <td>83</td>\n",
       "      <td>178</td>\n",
       "      <td>72</td>\n",
       "      <td>10</td>\n",
       "      <td>162</td>\n",
       "      <td>42</td>\n",
       "      <td>20</td>\n",
       "      <td>159</td>\n",
       "      <td>176</td>\n",
       "      <td>379</td>\n",
       "      <td>184</td>\n",
       "      <td>70</td>\n",
       "      <td>6</td>\n",
       "      <td>16</td>\n",
       "      <td>187</td>\n",
       "      <td>197</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>91</td>\n",
       "      <td>41</td>\n",
       "      <td>84</td>\n",
       "      <td>141</td>\n",
       "      <td>57</td>\n",
       "      <td>9</td>\n",
       "      <td>149</td>\n",
       "      <td>45</td>\n",
       "      <td>19</td>\n",
       "      <td>143</td>\n",
       "      <td>170</td>\n",
       "      <td>330</td>\n",
       "      <td>158</td>\n",
       "      <td>72</td>\n",
       "      <td>9</td>\n",
       "      <td>14</td>\n",
       "      <td>189</td>\n",
       "      <td>199</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>104</td>\n",
       "      <td>50</td>\n",
       "      <td>106</td>\n",
       "      <td>209</td>\n",
       "      <td>66</td>\n",
       "      <td>10</td>\n",
       "      <td>207</td>\n",
       "      <td>32</td>\n",
       "      <td>23</td>\n",
       "      <td>158</td>\n",
       "      <td>223</td>\n",
       "      <td>635</td>\n",
       "      <td>220</td>\n",
       "      <td>73</td>\n",
       "      <td>14</td>\n",
       "      <td>9</td>\n",
       "      <td>188</td>\n",
       "      <td>196</td>\n",
       "      <td>saab</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>93</td>\n",
       "      <td>41</td>\n",
       "      <td>82</td>\n",
       "      <td>159</td>\n",
       "      <td>63</td>\n",
       "      <td>9</td>\n",
       "      <td>144</td>\n",
       "      <td>46</td>\n",
       "      <td>19</td>\n",
       "      <td>143</td>\n",
       "      <td>160</td>\n",
       "      <td>309</td>\n",
       "      <td>127</td>\n",
       "      <td>63</td>\n",
       "      <td>6</td>\n",
       "      <td>10</td>\n",
       "      <td>199</td>\n",
       "      <td>207</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>85</td>\n",
       "      <td>44</td>\n",
       "      <td>70</td>\n",
       "      <td>205</td>\n",
       "      <td>103</td>\n",
       "      <td>52</td>\n",
       "      <td>149</td>\n",
       "      <td>45</td>\n",
       "      <td>19</td>\n",
       "      <td>144</td>\n",
       "      <td>241</td>\n",
       "      <td>325</td>\n",
       "      <td>188</td>\n",
       "      <td>127</td>\n",
       "      <td>9</td>\n",
       "      <td>11</td>\n",
       "      <td>180</td>\n",
       "      <td>183</td>\n",
       "      <td>bus</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>107</td>\n",
       "      <td>57</td>\n",
       "      <td>106</td>\n",
       "      <td>172</td>\n",
       "      <td>50</td>\n",
       "      <td>6</td>\n",
       "      <td>255</td>\n",
       "      <td>26</td>\n",
       "      <td>28</td>\n",
       "      <td>169</td>\n",
       "      <td>280</td>\n",
       "      <td>957</td>\n",
       "      <td>264</td>\n",
       "      <td>85</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>181</td>\n",
       "      <td>183</td>\n",
       "      <td>bus</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>97</td>\n",
       "      <td>43</td>\n",
       "      <td>73</td>\n",
       "      <td>173</td>\n",
       "      <td>65</td>\n",
       "      <td>6</td>\n",
       "      <td>153</td>\n",
       "      <td>42</td>\n",
       "      <td>19</td>\n",
       "      <td>143</td>\n",
       "      <td>176</td>\n",
       "      <td>361</td>\n",
       "      <td>172</td>\n",
       "      <td>66</td>\n",
       "      <td>13</td>\n",
       "      <td>1</td>\n",
       "      <td>200</td>\n",
       "      <td>204</td>\n",
       "      <td>bus</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>90</td>\n",
       "      <td>43</td>\n",
       "      <td>66</td>\n",
       "      <td>157</td>\n",
       "      <td>65</td>\n",
       "      <td>9</td>\n",
       "      <td>137</td>\n",
       "      <td>48</td>\n",
       "      <td>18</td>\n",
       "      <td>146</td>\n",
       "      <td>162</td>\n",
       "      <td>281</td>\n",
       "      <td>164</td>\n",
       "      <td>67</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>193</td>\n",
       "      <td>202</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>86</td>\n",
       "      <td>34</td>\n",
       "      <td>62</td>\n",
       "      <td>140</td>\n",
       "      <td>61</td>\n",
       "      <td>7</td>\n",
       "      <td>122</td>\n",
       "      <td>54</td>\n",
       "      <td>17</td>\n",
       "      <td>127</td>\n",
       "      <td>141</td>\n",
       "      <td>223</td>\n",
       "      <td>112</td>\n",
       "      <td>64</td>\n",
       "      <td>2</td>\n",
       "      <td>14</td>\n",
       "      <td>200</td>\n",
       "      <td>208</td>\n",
       "      <td>van</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>93</td>\n",
       "      <td>44</td>\n",
       "      <td>98</td>\n",
       "      <td>197</td>\n",
       "      <td>62</td>\n",
       "      <td>11</td>\n",
       "      <td>183</td>\n",
       "      <td>36</td>\n",
       "      <td>22</td>\n",
       "      <td>146</td>\n",
       "      <td>202</td>\n",
       "      <td>505</td>\n",
       "      <td>152</td>\n",
       "      <td>64</td>\n",
       "      <td>4</td>\n",
       "      <td>14</td>\n",
       "      <td>195</td>\n",
       "      <td>204</td>\n",
       "      <td>saab</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Comp  Circ  D.Circ  Rad.Ra  Pr.Axis.Ra  Max.L.Ra  Scat.Ra  Elong  \\\n",
       "0    95    48      83     178          72        10      162     42   \n",
       "1    91    41      84     141          57         9      149     45   \n",
       "2   104    50     106     209          66        10      207     32   \n",
       "3    93    41      82     159          63         9      144     46   \n",
       "4    85    44      70     205         103        52      149     45   \n",
       "5   107    57     106     172          50         6      255     26   \n",
       "6    97    43      73     173          65         6      153     42   \n",
       "7    90    43      66     157          65         9      137     48   \n",
       "8    86    34      62     140          61         7      122     54   \n",
       "9    93    44      98     197          62        11      183     36   \n",
       "\n",
       "   Pr.Axis.Rect  Max.L.Rect  Sc.Var.Maxis  Sc.Var.maxis  Ra.Gyr  Skew.Maxis  \\\n",
       "0            20         159           176           379     184          70   \n",
       "1            19         143           170           330     158          72   \n",
       "2            23         158           223           635     220          73   \n",
       "3            19         143           160           309     127          63   \n",
       "4            19         144           241           325     188         127   \n",
       "5            28         169           280           957     264          85   \n",
       "6            19         143           176           361     172          66   \n",
       "7            18         146           162           281     164          67   \n",
       "8            17         127           141           223     112          64   \n",
       "9            22         146           202           505     152          64   \n",
       "\n",
       "   Skew.maxis  Kurt.maxis  Kurt.Maxis  Holl.Ra Class  \n",
       "0           6          16         187      197   van  \n",
       "1           9          14         189      199   van  \n",
       "2          14           9         188      196  saab  \n",
       "3           6          10         199      207   van  \n",
       "4           9          11         180      183   bus  \n",
       "5           5           9         181      183   bus  \n",
       "6          13           1         200      204   bus  \n",
       "7           3           3         193      202   van  \n",
       "8           2          14         200      208   van  \n",
       "9           4          14         195      204  saab  "
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('data/Vehicle.csv', header=(0))\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0       van\n",
      "1       van\n",
      "2      saab\n",
      "3       van\n",
      "4       bus\n",
      "       ... \n",
      "841    saab\n",
      "842     van\n",
      "843    saab\n",
      "844    saab\n",
      "845     van\n",
      "Name: Class, Length: 846, dtype: object\n"
     ]
    }
   ],
   "source": [
    "classes = data[data.columns[-1]]\n",
    "print(classes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O histograma do número de elementos em cada classe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[218. 212. 217. 199.]\n"
     ]
    }
   ],
   "source": [
    "# armazena os nomes das classes\n",
    "cl = np.unique(classes)\n",
    "# armazena o número de elementos em cada classe\n",
    "ncl = np.zeros(len(cl))\n",
    "for i in np.arange(0, len(cl)):\n",
    "    a = classes == cl[i]\n",
    "    ncl[i] = len(classes[a])\n",
    "print(ncl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Em um gráfico de barras:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# número de classes\n",
    "numbers = np.arange(0, len(cl))\n",
    "plt.bar(numbers, ncl,  alpha=.75)\n",
    "# mostra o nome das classes ao invés dos números\n",
    "plt.xticks(numbers, cl)\n",
    "plt.title('Número de elementos em cada classe')\n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos redistribuir os dados de modo que cada classes contenha o mesmo número de elementos."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos balancear os dados de forma que cada classe contenha $N$ elementos. Escolhermos $N$ elementos de forma aleatória, sem reposição, de cada classe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dados obtidos a partir da amostragem\n",
      "[[[94 37 73 186 71 7 154 42 19 127 171 362 132 67 2 8 197 206 'bus']\n",
      "  [86 46 73 125 57 6 151 45 19 147 170 334 188 82 9 11 180 184 'bus']\n",
      "  [87 39 74 165 66 6 145 45 19 134 173 318 139 70 3 21 195 200 'bus']]\n",
      "\n",
      " [[103 56 105 183 59 10 210 32 24 173 217 648 218 72 13 22 188 196\n",
      "   'opel']\n",
      "  [89 36 77 172 62 8 157 42 19 125 174 367 126 63 5 22 198 205 'opel']\n",
      "  [106 55 96 196 60 12 221 30 25 173 225 717 214 72 9 13 186 196 'opel']]\n",
      "\n",
      " [[109 54 109 225 68 11 214 31 24 169 226 675 212 68 11 32 189 202\n",
      "   'saab']\n",
      "  [86 41 64 148 61 5 150 45 19 138 165 333 173 80 5 8 182 185 'saab']\n",
      "  [101 48 85 191 60 11 175 38 21 153 192 458 187 62 5 22 197 210 'saab']]\n",
      "\n",
      " [[90 43 81 231 97 46 150 45 19 149 200 332 164 91 5 9 186 196 'van']\n",
      "  [84 37 70 145 62 9 136 48 18 134 159 280 140 68 11 9 194 202 'van']\n",
      "  [88 42 64 151 62 8 130 51 18 142 150 253 161 63 3 2 203 210 'van']]]\n"
     ]
    }
   ],
   "source": [
    "N = 3\n",
    "# classes\n",
    "cl = np.unique(classes)\n",
    "X = np.array(data)\n",
    "Xnew = []\n",
    "cls = np.array(data[data.columns[-1]])\n",
    "for i in np.arange(0, len(cl)):\n",
    "    a = np.argwhere(cls == cl[i])\n",
    "    # seleciona os índices nos dados de forma aleatória\n",
    "    inds = np.random.choice(a[:,0],N,replace=False)\n",
    "    Xnew.append(X[inds,:])\n",
    "Xnew = np.array(Xnew)\n",
    "print('Dados obtidos a partir da amostragem')\n",
    "print(Xnew)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Outliers - Box plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Em muitos casos, temos a presença de outliers nos dados. Uma maneira simples de identificar outliers é criando um boxplot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lembrem-se, um boxplot:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://cdn-images-1.medium.com/max/1600/1*2c21SkzJMf3frPXPAR_gZA.png\" style=\"height:300px\"> "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/franciscoaparecidorodrigues/Anaconda3/anaconda3/lib/python3.7/site-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
      "  import pandas.util.testing as tm\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# biblioteca para mostrar os gráficos\n",
    "import seaborn as sns\n",
    "data = pd.read_csv('data/iris.csv', header=(0))\n",
    "plt.figure(figsize=(8, 8))\n",
    "# mostra o boxplot\n",
    "sns.boxplot(x=\"species\", y=\"petal_length\", data=data)\n",
    "plt.xlabel('Espécie', fontsize=18)\n",
    "plt.ylabel('Comprimento da pétala', fontsize=16)\n",
    "plt.xticks(fontsize=14)\n",
    "plt.yticks(fontsize=14)\n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos ainda usar a distância interquantil (Q3 - Q1) para encontrar os outliers de uma forma simples. Vamos considerar um exemplo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       a     b     c\n",
      "0     96   112   100\n",
      "1     12   137    29\n",
      "2     82   116    64\n",
      "3     71  1580     8\n",
      "4     64   116   139\n",
      "5     88    60  1810\n",
      "6     76  1630  1850\n",
      "7    138    45   104\n",
      "8     41    73    39\n",
      "9    133    20    74\n",
      "10    64   127  1810\n",
      "11  1690   139   147\n",
      "12    61    77    72\n",
      "13  1930   108   104\n",
      "14   111    88   144\n",
      "15     6   129    45\n",
      "16   141   106     1\n",
      "17    41     9   117\n",
      "18    50    63   107\n",
      "19    84  1650   141\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(101)\n",
    "# geramos os dados de forma aleatória e colocamos em um dataframe\n",
    "data = pd.DataFrame({'a': np.random.randint(1, 200, 20), \n",
    "                          'b': np.random.randint(1, 200, 20),\n",
    "                          'c': np.random.randint(1, 200, 20)})\n",
    "\n",
    "# geramos os outliers, aumentando em 10 vezes o valor dos atributos\n",
    "data[data > 150] = data[data > 150]*10\n",
    "# mostramos os dados\n",
    "print (data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualizando os dados:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 540x540 with 12 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.pairplot(data)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para encontrarmos os outliers:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "        a      b      c\n",
      "0   False  False  False\n",
      "1   False  False  False\n",
      "2   False  False  False\n",
      "3   False   True  False\n",
      "4   False  False  False\n",
      "5   False  False   True\n",
      "6   False   True   True\n",
      "7   False  False  False\n",
      "8   False  False  False\n",
      "9   False  False  False\n",
      "10  False  False   True\n",
      "11   True  False  False\n",
      "12  False  False  False\n",
      "13   True  False  False\n",
      "14  False  False  False\n",
      "15  False  False  False\n",
      "16  False  False  False\n",
      "17  False  False  False\n",
      "18  False  False  False\n",
      "19  False   True  False\n"
     ]
    }
   ],
   "source": [
    "Q1 = data.quantile(0.25)\n",
    "Q3 = data.quantile(0.75)\n",
    "IQR = Q3 - Q1\n",
    "\n",
    "print (((data < (Q1 - 1.5 * IQR)) | (data > (Q3 + 1.5 * IQR))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos dizer que uma observação é um outlier se ao menos uma das variáveis está fora dos limites máximos do boxplot. Ou seja, se o valor é menor do que (Q1 - 1.5 * IQR) ou maior do que (Q3 + 1.5 * IQR).\n",
    "Outliers são indicados como True abaixo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0     False\n",
      "1     False\n",
      "2     False\n",
      "3      True\n",
      "4     False\n",
      "5      True\n",
      "6      True\n",
      "7     False\n",
      "8     False\n",
      "9     False\n",
      "10     True\n",
      "11     True\n",
      "12    False\n",
      "13     True\n",
      "14    False\n",
      "15    False\n",
      "16    False\n",
      "17    False\n",
      "18    False\n",
      "19     True\n",
      "dtype: bool\n"
     ]
    }
   ],
   "source": [
    "print (((data < (Q1 - 1.5 * IQR)) | (data > (Q3 + 1.5 * IQR))).any(axis=1))#~is used to invert the answer"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A partir dessa informação, podemos fazer a retirada dos outliers no dados originais."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\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>a</th>\n",
       "      <th>b</th>\n",
       "      <th>c</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>96</td>\n",
       "      <td>112</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12</td>\n",
       "      <td>137</td>\n",
       "      <td>29</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>82</td>\n",
       "      <td>116</td>\n",
       "      <td>64</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>64</td>\n",
       "      <td>116</td>\n",
       "      <td>139</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>138</td>\n",
       "      <td>45</td>\n",
       "      <td>104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>41</td>\n",
       "      <td>73</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>133</td>\n",
       "      <td>20</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>61</td>\n",
       "      <td>77</td>\n",
       "      <td>72</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>111</td>\n",
       "      <td>88</td>\n",
       "      <td>144</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>6</td>\n",
       "      <td>129</td>\n",
       "      <td>45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>141</td>\n",
       "      <td>106</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>41</td>\n",
       "      <td>9</td>\n",
       "      <td>117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>50</td>\n",
       "      <td>63</td>\n",
       "      <td>107</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      a    b    c\n",
       "0    96  112  100\n",
       "1    12  137   29\n",
       "2    82  116   64\n",
       "4    64  116  139\n",
       "7   138   45  104\n",
       "8    41   73   39\n",
       "9   133   20   74\n",
       "12   61   77   72\n",
       "14  111   88  144\n",
       "15    6  129   45\n",
       "16  141  106    1\n",
       "17   41    9  117\n",
       "18   50   63  107"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v = ((data < (Q1 - 1.5 * IQR)) | (data > (Q3 + 1.5 * IQR))).any(axis=1)\n",
    "#v = np.invert(v)\n",
    "data = data.drop(data.index[list(v)], axis=0)\n",
    "data.head(25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercícios de fixação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1 - Leia os dados com erro novamente, faça a limpeza e remova as duas últimas colunas."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2 - Leia os dados com erro novamente e insira a mediana de cada atributo onde for encontrada NaN."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3 - Conside os dados da Iris e mostre a distribuição de probabilidades de cada uma das variáveis após a normalização e padronização."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4 - Reamostre os dados da Iris e selecione 10 elementos em cada classe."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5 - Monte um boxplot para cada variável dos dados da Iris."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6 - Encontre os outliers nos dados das bases Iris e BostonHouse."
   ]
  }
 ],
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