Aula4-Classificacao-Naive Bayes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classificador Naive Bayes"
   ]
  },
  {
   "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": [
    "No classificador Naive Bayes, podemos assumir que os atributos são normalmente distribuídos."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de linhas e colunas na matriz de atributos: (150, 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>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</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>3</th>\n",
       "      <td>4.6</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>4</th>\n",
       "      <td>5.0</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>5</th>\n",
       "      <td>5.4</td>\n",
       "      <td>3.9</td>\n",
       "      <td>1.7</td>\n",
       "      <td>0.4</td>\n",
       "      <td>setosa</td>\n",
       "    </tr>\n",
       "    <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",
       "  </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"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import random\n",
    "random.seed(42) # define the seed (important to reproduce the results)\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#data = pd.read_csv('data/vertebralcolumn-3C.csv', header=(0))\n",
    "data = pd.read_csv('data/Iris.csv', header=(0))\n",
    "\n",
    "data = data.dropna(axis='rows') #remove NaN\n",
    "# armazena os nomes das classes\n",
    "classes = np.array(pd.unique(data[data.columns[-1]]), dtype=str)  \n",
    "\n",
    "print(\"Número de linhas e colunas na matriz de atributos:\", data.shape)\n",
    "attributes = list(data.columns)\n",
    "data.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.to_numpy()\n",
    "nrow,ncol = data.shape\n",
    "y = data[:,-1]\n",
    "X = data[:,0:ncol-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Selecionando os conjuntos de treinamento e teste."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "p = 0.7 # fracao de elementos no conjunto de treinamento\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = p, random_state = 42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classificação: implementação do método"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inicialmente, definimos uma função para calcular a densidade de probabilidade conjunta: $$p(\\vec{x}|C_i) = \\prod_{j=1}^d p(x_j|C_i), \\quad i=1,\\ldots, k$$ \n",
    "onde $C_i$ são as classes. Se a distribuição for normal, temos que cada atributo $X_j$ tem a seguinte função densidade de probabilidade associada, para cada classe:\n",
    "$$\n",
    "p(x_j|C_i) = \\frac{1}{\\sqrt{2\\pi\\sigma_{C_i}}}\\exp \\left[ -\\frac{1}{2}\\left( \\frac{x_j-\\mu_{C_i}}{\\sigma_{C_i}}\\right)^2 \\right], \\quad i=1,2,\\ldots, k.\n",
    "$$\n",
    "Assim, definimos uma função para calcular a função de verossimilhança."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def likelyhood(y, Z):\n",
    "    def gaussian(x, mu, sig):\n",
    "        return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))\n",
    "    prob = 1\n",
    "    for j in np.arange(0, Z.shape[1]):\n",
    "        m = np.mean(Z[:,j])\n",
    "        s = np.std(Z[:,j])      \n",
    "        prob = prob*gaussian(y[j], m, s)\n",
    "    return prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A seguir, realizamos a estimação para cada classe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = pd.DataFrame(data=np.zeros((X_test.shape[0], len(classes))), columns = classes) \n",
    "for i in np.arange(0, len(classes)):\n",
    "    elements = tuple(np.where(y_train == classes[i]))\n",
    "    Z = X_train[elements,:][0]\n",
    "    for j in np.arange(0,X_test.shape[0]):\n",
    "        x = X_test[j,:]\n",
    "        pj = likelyhood(x,Z)\n",
    "        P[classes[i]][j] = pj*len(elements)/X_train.shape[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para as observações no conjunto de teste, a probabilidade pertencer a cada classe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>setosa</th>\n",
       "      <th>versicolor</th>\n",
       "      <th>virginica</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.824344e-90</td>\n",
       "      <td>4.440479e-03</td>\n",
       "      <td>4.107993e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.652256e-04</td>\n",
       "      <td>1.196823e-16</td>\n",
       "      <td>4.171552e-23</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6.741862e-287</td>\n",
       "      <td>3.100666e-17</td>\n",
       "      <td>2.363765e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.609452e-93</td>\n",
       "      <td>4.042876e-03</td>\n",
       "      <td>2.146958e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.453031e-106</td>\n",
       "      <td>8.057427e-04</td>\n",
       "      <td>3.352704e-04</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.491009e-03</td>\n",
       "      <td>5.335375e-15</td>\n",
       "      <td>1.159063e-22</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1.585589e-53</td>\n",
       "      <td>3.230445e-03</td>\n",
       "      <td>2.400042e-07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>5.666865e-172</td>\n",
       "      <td>6.868359e-10</td>\n",
       "      <td>3.319537e-03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>3.375351e-96</td>\n",
       "      <td>8.399067e-04</td>\n",
       "      <td>1.117962e-05</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>7.866680e-60</td>\n",
       "      <td>6.780257e-03</td>\n",
       "      <td>6.579053e-07</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          setosa    versicolor     virginica\n",
       "0   1.824344e-90  4.440479e-03  4.107993e-05\n",
       "1   1.652256e-04  1.196823e-16  4.171552e-23\n",
       "2  6.741862e-287  3.100666e-17  2.363765e-05\n",
       "3   1.609452e-93  4.042876e-03  2.146958e-04\n",
       "4  2.453031e-106  8.057427e-04  3.352704e-04\n",
       "5   1.491009e-03  5.335375e-15  1.159063e-22\n",
       "6   1.585589e-53  3.230445e-03  2.400042e-07\n",
       "7  5.666865e-172  6.868359e-10  3.319537e-03\n",
       "8   3.375351e-96  8.399067e-04  1.117962e-05\n",
       "9   7.866680e-60  6.780257e-03  6.579053e-07"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9555555555555556\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "y_pred = []\n",
    "for i in np.arange(0, P.shape[0]):\n",
    "    c = np.argmax(np.array(P.iloc[[i]]))\n",
    "    y_pred.append(P.columns[c])\n",
    "y_pred = np.array(y_pred, dtype=str)\n",
    "\n",
    "score = accuracy_score(y_pred, y_test)\n",
    "print('Accuracy:', score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Classificação: usando a biblioteca scikit-learn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos realizar a classificação usando a função disponível na biblioteca scikit-learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.9777777777777777\n"
     ]
    }
   ],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn import metrics\n",
    "\n",
    "model = GaussianNB()\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "y_pred = model.predict(X_test)\n",
    "score = accuracy_score(y_pred, y_test)\n",
    "print('Accuracy:', score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Outra maneira de efetuarmos a classificação é assumirmos que os atributos possuem distribuição diferente da normal. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uma possibilidade é assumirmos que os dados possuem distribuição de Bernoulli. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 0.28888888888888886\n"
     ]
    }
   ],
   "source": [
    "from sklearn.naive_bayes import BernoulliNB\n",
    "\n",
    "model = BernoulliNB()\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "y_pred = model.predict(X_test)\n",
    "score = accuracy_score(y_pred, y_test)\n",
    "print('Accuracy:', score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Código completo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Acuracia: 1.0\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "random.seed(42) \n",
    "\n",
    "data = pd.read_csv('data/Iris.csv', header=(0))\n",
    "\n",
    "classes = np.array(pd.unique(data[data.columns[-1]]), dtype=str)  \n",
    "\n",
    "# Converte para matriz e vetor do numpy\n",
    "data = data.to_numpy()\n",
    "nrow,ncol = data.shape\n",
    "y = data[:,-1]\n",
    "X = data[:,0:ncol-1]\n",
    "\n",
    "# Transforma os dados para terem media igual a zero e variancia igual a 1\n",
    "#scaler = StandardScaler().fit(X)\n",
    "#X = scaler.transform(X)\n",
    "\n",
    "# Seleciona os conjuntos de treinamento e teste\n",
    "p = 0.8 # fraction of elements in the test set\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, \n",
    "                                                    train_size = p, random_state = 42)\n",
    "\n",
    "# ajusta o classificador Naive-Bayes de acordo com os dados\n",
    "model = GaussianNB()\n",
    "model.fit(X_train, y_train)\n",
    "# realiza a predicao\n",
    "y_pred = model.predict(X_test)\n",
    "# calcula a acuracia\n",
    "score = accuracy_score(y_pred, y_test)\n",
    "print('Acuracia:', score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Região de decisão"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Selecionando dois atributos, podemos visualizar a região de decisão. Para graficar a região de separação, precisamos instalar a bibliteca mlxtend: http://rasbt.github.io/mlxtend/installation/<br>\n",
    "Pode ser usado: conda install -c conda-forge mlxtend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para o classificador Naive Bayes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from mlxtend.plotting import plot_decision_regions\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "import sklearn.datasets as skdata\n",
    "from matplotlib import pyplot\n",
    "from pandas import DataFrame\n",
    "\n",
    "# Gera os dados em duas dimensões\n",
    "n_samples = 100 # número de observações\n",
    "# centro dos grupos\n",
    "centers = [(-4, 0), (0, 0), (3, 3)]\n",
    "X, y = skdata.make_blobs(n_samples=100, n_features=2, cluster_std=1.0, centers=centers, \n",
    "                         shuffle=False, random_state=42)\n",
    "\n",
    "# monta a matrix de atributos\n",
    "d = np.column_stack((X,np.transpose(y)))\n",
    "# converte para o formato dataframe do Pandas\n",
    "data = DataFrame(data = d, columns=['X1', 'X2', 'y'])\n",
    "features_names = ['X1', 'X2']\n",
    "class_labels = np.unique(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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"
    },
    {
     "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": [
    "from mlxtend.plotting import plot_decision_regions\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.naive_bayes import GaussianNB\n",
    "\n",
    "\n",
    "# mostra os dados e colori de acordo com as classes\n",
    "colors = ['red', 'blue', 'green', 'black']\n",
    "aux = 0\n",
    "for c in class_labels:\n",
    "    ind = np.where(y == c)\n",
    "    plt.scatter(X[ind,0][0], X[ind,1][0], color = colors[aux], label = c)\n",
    "    aux = aux + 1\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Training a classifier\n",
    "model = GaussianNB()\n",
    "model.fit(X, y)\n",
    "\n",
    "# Plotting decision regions\n",
    "plot_decision_regions(X, y, clf=model, legend=2)\n",
    "\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('X2')\n",
    "plt.title('Decision Regions')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercícios de fixação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1 - Repita todos os passos acima para a base de dados BreastCancer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2 - Considere a base vertebralcolumn-3C e compare o classificadores: Naive Bayes, Classificador Bayesiano paramétrico e o classiificador Bayesiano não-paramétrico."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3 - Considerando a base de dados Vehicle, projete os dados em duas dimensões usando PCA e mostre as regiões de separação como feito acima."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4 - Faça a classificação dos dados gerados artificialmente com o código abaixo. Compare os resultados para os métodos Naive Bayes, Classificador Bayesiano paramétrico e o classiificador Bayesiano não-paramétrico."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "from sklearn import datasets\n",
    "plt.figure(figsize=(6,4))\n",
    "\n",
    "n_samples = 1000\n",
    "\n",
    "data  = datasets.make_moons(n_samples=n_samples, noise=.05)\n",
    "X = data[0]\n",
    "y = data[1]\n",
    "plt.scatter(X[:,0], X[:,1], c=y, cmap='viridis', s=50, alpha=0.7)\n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "5 - Encontre a região de separação dos dados do exercício anterior usando o método Naive Bayes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "6 - (Facultativo) Escolha outras distribuições de probabilidade e implemente um algoritmo Naive Bayes geral. Ou seja, o algoritmo faz a classificação usando várias distribuições e obtém o melhor resultado, mostrando também qual a distribuição mais adequada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "7 - (Para pensar) É possível implementar o Naive Bayes heterogêneo, ou seja, com diferentes distribuições para cada atributo?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8 - (Desafio) Gere dados com diferentes níveis de correlação entre as variáveis e verifique se a perfomance do algoritmo muda com a correlação."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Código completo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy: 1.0\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.metrics import accuracy_score\n",
    "\n",
    "random.seed(42) \n",
    "data = pd.read_csv('data/Iris.csv', header=(0))\n",
    "# classes: setosa, virginica e versicolor\n",
    "classes = pd.unique(data[data.columns[-1]])\n",
    "classes = np.array(classes, dtype=str)  \n",
    "# converte para matrizes do numpy\n",
    "data = data.to_numpy()\n",
    "nrow,ncol = data.shape\n",
    "y = data[:,-1]\n",
    "X = data[:,0:ncol-1]\n",
    "# Seleciona o conjunto de teste e treinamento\n",
    "p = 0.7 \n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size = p)\n",
    "\n",
    "# funcao para calcular a verossimilhanca\n",
    "def likelyhood(y, Z):\n",
    "    def gaussian(x, mu, sig):\n",
    "        return np.exp(-np.power(x - mu, 2.) / (2 * np.power(sig, 2.)))\n",
    "    prob = 1\n",
    "    for j in np.arange(0, Z.shape[1]):\n",
    "        m = np.mean(Z[:,j])\n",
    "        s = np.std(Z[:,j])      \n",
    "        prob = prob*gaussian(y[j], m, s)\n",
    "    return prob\n",
    "\n",
    "# matriz que armazena o produto da verossimilhanca pela priori\n",
    "P = pd.DataFrame(data=np.zeros((X_test.shape[0], len(classes))), columns = classes) \n",
    "for i in np.arange(0, len(classes)):\n",
    "    elements = tuple(np.where(y_train == classes[i]))\n",
    "    Z = X_train[elements,:][0]\n",
    "    for j in np.arange(0,X_test.shape[0]):\n",
    "        x = X_test[j,:]\n",
    "        pj = likelyhood(x,Z) #verossimilhanca\n",
    "        pc = len(elements)/X_train.shape[0] # priori\n",
    "        P[classes[i]][j] = pj*pc\n",
    "        \n",
    "# realiza a classificao seguindo a regra de Bayes\n",
    "y_pred = []\n",
    "for i in np.arange(0, P.shape[0]):\n",
    "    c = np.argmax(np.array(P.iloc[[i]]))\n",
    "    y_pred.append(P.columns[c])\n",
    "y_pred = np.array(y_pred, dtype=str)\n",
    "# calcula a acuracia na classificacao\n",
    "score = accuracy_score(y_pred, y_test)\n",
    "print('Accuracy:', score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
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