{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Análise Multivariada e Aprendizado Não-Supervisionado\n",
    "\n",
    "por Cibele Russo.\n",
    "\n",
    "ICMC USP São Carlos.\n",
    "\n",
    "\n",
    "## Aula 11d: Análise discriminante linear - Aplicação em Python\n",
    "\n",
    "Fonte e links recomendados: \n",
    "- https://scikit-learn.org/stable/modules/generated/sklearn.discriminant_analysis.LinearDiscriminantAnalysis.html\n",
    "\n",
    "- https://scikit-learn.org/stable/auto_examples/decomposition/plot_pca_vs_lda.html\n",
    "\n",
    "- https://www.kaggle.com/harshamodali/linear-discriminant-analysis-on-iris-dataset\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#!pip install sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "\n",
    "X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])\n",
    "y = np.array([1, 1, 1, 2, 2, 2])\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearDiscriminantAnalysis()"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf = LinearDiscriminantAnalysis()\n",
    "clf.fit(X, y)\n",
    "LinearDiscriminantAnalysis()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 2, 2, 2])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1]\n"
     ]
    }
   ],
   "source": [
    "print(clf.predict([[-0.8, -1]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[2]\n"
     ]
    }
   ],
   "source": [
    "print(clf.predict([[-1, 2]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dados iris, ver também a Aula 1c, disponível no link abaixo:\n",
    "# https://www.youtube.com/watch?v=R44jbSmpjgg&list=PLt7qVSwRVn5bg14OLl6dHTNnXVrEM6UiS&index=3\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn import datasets\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n",
    "\n",
    "iris = datasets.load_iris()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "        [4.9, 3. , 1.4, 0.2],\n",
       "        [4.7, 3.2, 1.3, 0.2],\n",
       "        [4.6, 3.1, 1.5, 0.2],\n",
       "        [5. , 3.6, 1.4, 0.2],\n",
       "        [5.4, 3.9, 1.7, 0.4],\n",
       "        [4.6, 3.4, 1.4, 0.3],\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",
       "        [4.8, 3.4, 1.6, 0.2],\n",
       "        [4.8, 3. , 1.4, 0.1],\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, 0.4],\n",
       "        [5.1, 3.5, 1.4, 0.3],\n",
       "        [5.7, 3.8, 1.7, 0.3],\n",
       "        [5.1, 3.8, 1.5, 0.3],\n",
       "        [5.4, 3.4, 1.7, 0.2],\n",
       "        [5.1, 3.7, 1.5, 0.4],\n",
       "        [4.6, 3.6, 1. , 0.2],\n",
       "        [5.1, 3.3, 1.7, 0.5],\n",
       "        [4.8, 3.4, 1.9, 0.2],\n",
       "        [5. , 3. , 1.6, 0.2],\n",
       "        [5. , 3.4, 1.6, 0.4],\n",
       "        [5.2, 3.5, 1.5, 0.2],\n",
       "        [5.2, 3.4, 1.4, 0.2],\n",
       "        [4.7, 3.2, 1.6, 0.2],\n",
       "        [4.8, 3.1, 1.6, 0.2],\n",
       "        [5.4, 3.4, 1.5, 0.4],\n",
       "        [5.2, 4.1, 1.5, 0.1],\n",
       "        [5.5, 4.2, 1.4, 0.2],\n",
       "        [4.9, 3.1, 1.5, 0.2],\n",
       "        [5. , 3.2, 1.2, 0.2],\n",
       "        [5.5, 3.5, 1.3, 0.2],\n",
       "        [4.9, 3.6, 1.4, 0.1],\n",
       "        [4.4, 3. , 1.3, 0.2],\n",
       "        [5.1, 3.4, 1.5, 0.2],\n",
       "        [5. , 3.5, 1.3, 0.3],\n",
       "        [4.5, 2.3, 1.3, 0.3],\n",
       "        [4.4, 3.2, 1.3, 0.2],\n",
       "        [5. , 3.5, 1.6, 0.6],\n",
       "        [5.1, 3.8, 1.9, 0.4],\n",
       "        [4.8, 3. , 1.4, 0.3],\n",
       "        [5.1, 3.8, 1.6, 0.2],\n",
       "        [4.6, 3.2, 1.4, 0.2],\n",
       "        [5.3, 3.7, 1.5, 0.2],\n",
       "        [5. , 3.3, 1.4, 0.2],\n",
       "        [7. , 3.2, 4.7, 1.4],\n",
       "        [6.4, 3.2, 4.5, 1.5],\n",
       "        [6.9, 3.1, 4.9, 1.5],\n",
       "        [5.5, 2.3, 4. , 1.3],\n",
       "        [6.5, 2.8, 4.6, 1.5],\n",
       "        [5.7, 2.8, 4.5, 1.3],\n",
       "        [6.3, 3.3, 4.7, 1.6],\n",
       "        [4.9, 2.4, 3.3, 1. ],\n",
       "        [6.6, 2.9, 4.6, 1.3],\n",
       "        [5.2, 2.7, 3.9, 1.4],\n",
       "        [5. , 2. , 3.5, 1. ],\n",
       "        [5.9, 3. , 4.2, 1.5],\n",
       "        [6. , 2.2, 4. , 1. ],\n",
       "        [6.1, 2.9, 4.7, 1.4],\n",
       "        [5.6, 2.9, 3.6, 1.3],\n",
       "        [6.7, 3.1, 4.4, 1.4],\n",
       "        [5.6, 3. , 4.5, 1.5],\n",
       "        [5.8, 2.7, 4.1, 1. ],\n",
       "        [6.2, 2.2, 4.5, 1.5],\n",
       "        [5.6, 2.5, 3.9, 1.1],\n",
       "        [5.9, 3.2, 4.8, 1.8],\n",
       "        [6.1, 2.8, 4. , 1.3],\n",
       "        [6.3, 2.5, 4.9, 1.5],\n",
       "        [6.1, 2.8, 4.7, 1.2],\n",
       "        [6.4, 2.9, 4.3, 1.3],\n",
       "        [6.6, 3. , 4.4, 1.4],\n",
       "        [6.8, 2.8, 4.8, 1.4],\n",
       "        [6.7, 3. , 5. , 1.7],\n",
       "        [6. , 2.9, 4.5, 1.5],\n",
       "        [5.7, 2.6, 3.5, 1. ],\n",
       "        [5.5, 2.4, 3.8, 1.1],\n",
       "        [5.5, 2.4, 3.7, 1. ],\n",
       "        [5.8, 2.7, 3.9, 1.2],\n",
       "        [6. , 2.7, 5.1, 1.6],\n",
       "        [5.4, 3. , 4.5, 1.5],\n",
       "        [6. , 3.4, 4.5, 1.6],\n",
       "        [6.7, 3.1, 4.7, 1.5],\n",
       "        [6.3, 2.3, 4.4, 1.3],\n",
       "        [5.6, 3. , 4.1, 1.3],\n",
       "        [5.5, 2.5, 4. , 1.3],\n",
       "        [5.5, 2.6, 4.4, 1.2],\n",
       "        [6.1, 3. , 4.6, 1.4],\n",
       "        [5.8, 2.6, 4. , 1.2],\n",
       "        [5. , 2.3, 3.3, 1. ],\n",
       "        [5.6, 2.7, 4.2, 1.3],\n",
       "        [5.7, 3. , 4.2, 1.2],\n",
       "        [5.7, 2.9, 4.2, 1.3],\n",
       "        [6.2, 2.9, 4.3, 1.3],\n",
       "        [5.1, 2.5, 3. , 1.1],\n",
       "        [5.7, 2.8, 4.1, 1.3],\n",
       "        [6.3, 3.3, 6. , 2.5],\n",
       "        [5.8, 2.7, 5.1, 1.9],\n",
       "        [7.1, 3. , 5.9, 2.1],\n",
       "        [6.3, 2.9, 5.6, 1.8],\n",
       "        [6.5, 3. , 5.8, 2.2],\n",
       "        [7.6, 3. , 6.6, 2.1],\n",
       "        [4.9, 2.5, 4.5, 1.7],\n",
       "        [7.3, 2.9, 6.3, 1.8],\n",
       "        [6.7, 2.5, 5.8, 1.8],\n",
       "        [7.2, 3.6, 6.1, 2.5],\n",
       "        [6.5, 3.2, 5.1, 2. ],\n",
       "        [6.4, 2.7, 5.3, 1.9],\n",
       "        [6.8, 3. , 5.5, 2.1],\n",
       "        [5.7, 2.5, 5. , 2. ],\n",
       "        [5.8, 2.8, 5.1, 2.4],\n",
       "        [6.4, 3.2, 5.3, 2.3],\n",
       "        [6.5, 3. , 5.5, 1.8],\n",
       "        [7.7, 3.8, 6.7, 2.2],\n",
       "        [7.7, 2.6, 6.9, 2.3],\n",
       "        [6. , 2.2, 5. , 1.5],\n",
       "        [6.9, 3.2, 5.7, 2.3],\n",
       "        [5.6, 2.8, 4.9, 2. ],\n",
       "        [7.7, 2.8, 6.7, 2. ],\n",
       "        [6.3, 2.7, 4.9, 1.8],\n",
       "        [6.7, 3.3, 5.7, 2.1],\n",
       "        [7.2, 3.2, 6. , 1.8],\n",
       "        [6.2, 2.8, 4.8, 1.8],\n",
       "        [6.1, 3. , 4.9, 1.8],\n",
       "        [6.4, 2.8, 5.6, 2.1],\n",
       "        [7.2, 3. , 5.8, 1.6],\n",
       "        [7.4, 2.8, 6.1, 1.9],\n",
       "        [7.9, 3.8, 6.4, 2. ],\n",
       "        [6.4, 2.8, 5.6, 2.2],\n",
       "        [6.3, 2.8, 5.1, 1.5],\n",
       "        [6.1, 2.6, 5.6, 1.4],\n",
       "        [7.7, 3. , 6.1, 2.3],\n",
       "        [6.3, 3.4, 5.6, 2.4],\n",
       "        [6.4, 3.1, 5.5, 1.8],\n",
       "        [6. , 3. , 4.8, 1.8],\n",
       "        [6.9, 3.1, 5.4, 2.1],\n",
       "        [6.7, 3.1, 5.6, 2.4],\n",
       "        [6.9, 3.1, 5.1, 2.3],\n",
       "        [5.8, 2.7, 5.1, 1.9],\n",
       "        [6.8, 3.2, 5.9, 2.3],\n",
       "        [6.7, 3.3, 5.7, 2.5],\n",
       "        [6.7, 3. , 5.2, 2.3],\n",
       "        [6.3, 2.5, 5. , 1.9],\n",
       "        [6.5, 3. , 5.2, 2. ],\n",
       "        [6.2, 3.4, 5.4, 2.3],\n",
       "        [5.9, 3. , 5.1, 1.8]]),\n",
       " 'target': array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "        0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "        2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2]),\n",
       " 'frame': None,\n",
       " 'target_names': array(['setosa', 'versicolor', 'virginica'], dtype='<U10'),\n",
       " 'DESCR': '.. _iris_dataset:\\n\\nIris plants dataset\\n--------------------\\n\\n**Data Set Characteristics:**\\n\\n    :Number of Instances: 150 (50 in each of three classes)\\n    :Number of Attributes: 4 numeric, predictive attributes and the class\\n    :Attribute Information:\\n        - sepal length in cm\\n        - sepal width in cm\\n        - petal length in cm\\n        - petal width in cm\\n        - class:\\n                - Iris-Setosa\\n                - Iris-Versicolour\\n                - Iris-Virginica\\n                \\n    :Summary Statistics:\\n\\n    ============== ==== ==== ======= ===== ====================\\n                    Min  Max   Mean    SD   Class Correlation\\n    ============== ==== ==== ======= ===== ====================\\n    sepal length:   4.3  7.9   5.84   0.83    0.7826\\n    sepal width:    2.0  4.4   3.05   0.43   -0.4194\\n    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\\n    petal width:    0.1  2.5   1.20   0.76    0.9565  (high!)\\n    ============== ==== ==== ======= ===== ====================\\n\\n    :Missing Attribute Values: None\\n    :Class Distribution: 33.3% for each of 3 classes.\\n    :Creator: R.A. Fisher\\n    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\\n    :Date: July, 1988\\n\\nThe famous Iris database, first used by Sir R.A. Fisher. The dataset is taken\\nfrom Fisher\\'s paper. Note that it\\'s the same as in R, but not as in the UCI\\nMachine Learning Repository, which has two wrong data points.\\n\\nThis is perhaps the best known database to be found in the\\npattern recognition literature.  Fisher\\'s paper is a classic in the field and\\nis referenced frequently to this day.  (See Duda & Hart, for example.)  The\\ndata set contains 3 classes of 50 instances each, where each class refers to a\\ntype of iris plant.  One class is linearly separable from the other 2; the\\nlatter are NOT linearly separable from each other.\\n\\n.. topic:: References\\n\\n   - Fisher, R.A. \"The use of multiple measurements in taxonomic problems\"\\n     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\\n     Mathematical Statistics\" (John Wiley, NY, 1950).\\n   - Duda, R.O., & Hart, P.E. (1973) Pattern Classification and Scene Analysis.\\n     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\\n   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\\n     Structure and Classification Rule for Recognition in Partially Exposed\\n     Environments\".  IEEE Transactions on Pattern Analysis and Machine\\n     Intelligence, Vol. PAMI-2, No. 1, 67-71.\\n   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\\n     on Information Theory, May 1972, 431-433.\\n   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\\n     conceptual clustering system finds 3 classes in the data.\\n   - Many, many more ...',\n",
       " 'feature_names': ['sepal length (cm)',\n",
       "  'sepal width (cm)',\n",
       "  'petal length (cm)',\n",
       "  'petal width (cm)'],\n",
       " 'filename': '/home/cibele/anaconda3/lib/python3.7/site-packages/sklearn/datasets/data/iris.csv'}"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.data\n",
    "y = iris.target\n",
    "target_names = iris.target_names\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "X_r = pca.fit(X).transform(X)\n",
    "\n",
    "lda = LinearDiscriminantAnalysis(n_components=2)\n",
    "X_r2 = lda.fit(X, y).transform(X)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "       [ 8.31444876e+00,  6.44953177e-01],\n",
       "       [ 7.67196741e+00, -1.34893840e-01],\n",
       "       [-1.45927545e+00,  2.85437643e-02],\n",
       "       [-1.79770574e+00,  4.84385502e-01],\n",
       "       [-2.41694888e+00, -9.27840307e-02],\n",
       "       [-2.26247349e+00, -1.58725251e+00],\n",
       "       [-2.54867836e+00, -4.72204898e-01],\n",
       "       [-2.42996725e+00, -9.66132066e-01],\n",
       "       [-2.44848456e+00,  7.95961954e-01],\n",
       "       [-2.22666513e-01, -1.58467318e+00],\n",
       "       [-1.75020123e+00, -8.21180130e-01],\n",
       "       [-1.95842242e+00, -3.51563753e-01],\n",
       "       [-1.19376031e+00, -2.63445570e+00],\n",
       "       [-1.85892567e+00,  3.19006544e-01],\n",
       "       [-1.15809388e+00, -2.64340991e+00],\n",
       "       [-2.66605725e+00, -6.42504540e-01],\n",
       "       [-3.78367218e-01,  8.66389312e-02],\n",
       "       [-1.20117255e+00,  8.44373592e-02],\n",
       "       [-2.76810246e+00,  3.21995363e-02],\n",
       "       [-7.76854039e-01, -1.65916185e+00],\n",
       "       [-3.49805433e+00, -1.68495616e+00],\n",
       "       [-1.09042788e+00, -1.62658350e+00],\n",
       "       [-3.71589615e+00,  1.04451442e+00],\n",
       "       [-9.97610366e-01, -4.90530602e-01],\n",
       "       [-3.83525931e+00, -1.40595806e+00],\n",
       "       [-2.25741249e+00, -1.42679423e+00],\n",
       "       [-1.25571326e+00, -5.46424197e-01],\n",
       "       [-1.43755762e+00, -1.34424979e-01],\n",
       "       [-2.45906137e+00, -9.35277280e-01],\n",
       "       [-3.51848495e+00,  1.60588866e-01],\n",
       "       [-2.58979871e+00, -1.74611728e-01],\n",
       "       [ 3.07487884e-01, -1.31887146e+00],\n",
       "       [-1.10669179e+00, -1.75225371e+00],\n",
       "       [-6.05524589e-01, -1.94298038e+00],\n",
       "       [-8.98703769e-01, -9.04940034e-01],\n",
       "       [-4.49846635e+00, -8.82749915e-01],\n",
       "       [-2.93397799e+00,  2.73791065e-02],\n",
       "       [-2.10360821e+00,  1.19156767e+00],\n",
       "       [-2.14258208e+00,  8.87797815e-02],\n",
       "       [-2.47945603e+00, -1.94073927e+00],\n",
       "       [-1.32552574e+00, -1.62869550e-01],\n",
       "       [-1.95557887e+00, -1.15434826e+00],\n",
       "       [-2.40157020e+00, -1.59458341e+00],\n",
       "       [-2.29248878e+00, -3.32860296e-01],\n",
       "       [-1.27227224e+00, -1.21458428e+00],\n",
       "       [-2.93176055e-01, -1.79871509e+00],\n",
       "       [-2.00598883e+00, -9.05418042e-01],\n",
       "       [-1.18166311e+00, -5.37570242e-01],\n",
       "       [-1.61615645e+00, -4.70103580e-01],\n",
       "       [-1.42158879e+00, -5.51244626e-01],\n",
       "       [ 4.75973788e-01, -7.99905482e-01],\n",
       "       [-1.54948259e+00, -5.93363582e-01],\n",
       "       [-7.83947399e+00,  2.13973345e+00],\n",
       "       [-5.50747997e+00, -3.58139892e-02],\n",
       "       [-6.29200850e+00,  4.67175777e-01],\n",
       "       [-5.60545633e+00, -3.40738058e-01],\n",
       "       [-6.85055995e+00,  8.29825394e-01],\n",
       "       [-7.41816784e+00, -1.73117995e-01],\n",
       "       [-4.67799541e+00, -4.99095015e-01],\n",
       "       [-6.31692685e+00, -9.68980756e-01],\n",
       "       [-6.32773684e+00, -1.38328993e+00],\n",
       "       [-6.85281335e+00,  2.71758963e+00],\n",
       "       [-4.44072512e+00,  1.34723692e+00],\n",
       "       [-5.45009572e+00, -2.07736942e-01],\n",
       "       [-5.66033713e+00,  8.32713617e-01],\n",
       "       [-5.95823722e+00, -9.40175447e-02],\n",
       "       [-6.75926282e+00,  1.60023206e+00],\n",
       "       [-5.80704331e+00,  2.01019882e+00],\n",
       "       [-5.06601233e+00, -2.62733839e-02],\n",
       "       [-6.60881882e+00,  1.75163587e+00],\n",
       "       [-9.17147486e+00, -7.48255067e-01],\n",
       "       [-4.76453569e+00, -2.15573720e+00],\n",
       "       [-6.27283915e+00,  1.64948141e+00],\n",
       "       [-5.36071189e+00,  6.46120732e-01],\n",
       "       [-7.58119982e+00, -9.80722934e-01],\n",
       "       [-4.37150279e+00, -1.21297458e-01],\n",
       "       [-5.72317531e+00,  1.29327553e+00],\n",
       "       [-5.27915920e+00, -4.24582377e-02],\n",
       "       [-4.08087208e+00,  1.85936572e-01],\n",
       "       [-4.07703640e+00,  5.23238483e-01],\n",
       "       [-6.51910397e+00,  2.96976389e-01],\n",
       "       [-4.58371942e+00, -8.56815813e-01],\n",
       "       [-6.22824009e+00, -7.12719638e-01],\n",
       "       [-5.22048773e+00,  1.46819509e+00],\n",
       "       [-6.80015000e+00,  5.80895175e-01],\n",
       "       [-3.81515972e+00, -9.42985932e-01],\n",
       "       [-5.10748966e+00, -2.13059000e+00],\n",
       "       [-6.79671631e+00,  8.63090395e-01],\n",
       "       [-6.52449599e+00,  2.44503527e+00],\n",
       "       [-4.99550279e+00,  1.87768525e-01],\n",
       "       [-3.93985300e+00,  6.14020389e-01],\n",
       "       [-5.20383090e+00,  1.14476808e+00],\n",
       "       [-6.65308685e+00,  1.80531976e+00],\n",
       "       [-5.10555946e+00,  1.99218201e+00],\n",
       "       [-5.50747997e+00, -3.58139892e-02],\n",
       "       [-6.79601924e+00,  1.46068695e+00],\n",
       "       [-6.84735943e+00,  2.42895067e+00],\n",
       "       [-5.64500346e+00,  1.67771734e+00],\n",
       "       [-5.17956460e+00, -3.63475041e-01],\n",
       "       [-4.96774090e+00,  8.21140550e-01],\n",
       "       [-5.88614539e+00,  2.34509051e+00],\n",
       "       [-4.68315426e+00,  3.32033811e-01]])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_r2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda.classes_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
       "       0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,\n",
       "       2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lda.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "plt.figure()\n",
    "colors = ['navy', 'turquoise', 'darkorange']\n",
    "lw = 2\n",
    "\n",
    "\n",
    "for color, i, target_name in zip(colors, [0, 1, 2], target_names):\n",
    "    plt.scatter(X_r[y == i, 0], X_r[y == i, 1], color=color, alpha=.8, lw=lw,\n",
    "                label=target_name)\n",
    "plt.legend(loc='best', shadow=False, scatterpoints=1)\n",
    "plt.title('PCA of IRIS dataset')\n",
    "\n",
    "plt.figure()\n",
    "for color, i, target_name in zip(colors, [0, 1, 2], target_names):\n",
    "    plt.scatter(X_r2[y == i, 0], X_r2[y == i, 1], alpha=.8, color=color,\n",
    "                label=target_name)\n",
    "plt.legend(loc='best', shadow=False, scatterpoints=1)\n",
    "plt.title('LDA of IRIS dataset')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercício: Separe 80% da base para treino e 20% para teste, e utilize os discriminantes lineares para predizer a classificação das observações da base de teste. Verifique os percentuais de acerto.**"
   ]
  }
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