{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "1c1405f6",
   "metadata": {},
   "source": [
    "# PCA da Iris Flowers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4bb85991",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.linalg as la"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5cf72801",
   "metadata": {},
   "source": [
    "#### Tabela de dados com 5 campos\n",
    "##### 1. Comprimento da sépala em cm\n",
    "##### 2. Largura da sépala em cm\n",
    "##### 3. Comprimento da pétala em cm\n",
    "##### 4. Largura da pétala em cm\n",
    "##### 5. Classe: \n",
    "- 1 - Iris Setosa\n",
    "- 2 - Iris Versicolor\n",
    "- 3 - Iris Virginica"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fab44d66",
   "metadata": {},
   "source": [
    "### 1.Carregando a TABELA DE DADOS iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "d613db75",
   "metadata": {},
   "outputs": [],
   "source": [
    "iris=np.array([[5.1,3.5,1.4,0.2,1],\n",
    "[4.9,3.0,1.4,0.2,1],\n",
    "[4.7,3.2,1.3,0.2,1],\n",
    "[4.6,3.1,1.5,0.2,1],\n",
    "[5.0,3.6,1.4,0.2,1],\n",
    "[5.4,3.9,1.7,0.4,1],\n",
    "[4.6,3.4,1.4,0.3,1],\n",
    "[5.0,3.4,1.5,0.2,1],\n",
    "[4.4,2.9,1.4,0.2,1],\n",
    "[4.9,3.1,1.5,0.1,1],\n",
    "[5.4,3.7,1.5,0.2,1],\n",
    "[4.8,3.4,1.6,0.2,1],\n",
    "[4.8,3.0,1.4,0.1,1],\n",
    "[4.3,3.0,1.1,0.1,1],\n",
    "[5.8,4.0,1.2,0.2,1],\n",
    "[5.7,4.4,1.5,0.4,1],\n",
    "[5.4,3.9,1.3,0.4,1],\n",
    "[5.1,3.5,1.4,0.3,1],\n",
    "[5.7,3.8,1.7,0.3,1],\n",
    "[5.1,3.8,1.5,0.3,1],\n",
    "[5.4,3.4,1.7,0.2,1],\n",
    "[5.1,3.7,1.5,0.4,1],\n",
    "[4.6,3.6,1.0,0.2,1],\n",
    "[5.1,3.3,1.7,0.5,1],\n",
    "[4.8,3.4,1.9,0.2,1],\n",
    "[5.0,3.0,1.6,0.2,1],\n",
    "[5.0,3.4,1.6,0.4,1],\n",
    "[5.2,3.5,1.5,0.2,1],\n",
    "[5.2,3.4,1.4,0.2,1],\n",
    "[4.7,3.2,1.6,0.2,1],\n",
    "[4.8,3.1,1.6,0.2,1],\n",
    "[5.4,3.4,1.5,0.4,1],\n",
    "[5.2,4.1,1.5,0.1,1],\n",
    "[5.5,4.2,1.4,0.2,1],\n",
    "[4.9,3.1,1.5,0.1,1],\n",
    "[5.0,3.2,1.2,0.2,1],\n",
    "[5.5,3.5,1.3,0.2,1],\n",
    "[4.9,3.1,1.5,0.1,1],\n",
    "[4.4,3.0,1.3,0.2,1],\n",
    "[5.1,3.4,1.5,0.2,1],\n",
    "[5.0,3.5,1.3,0.3,1],\n",
    "[4.5,2.3,1.3,0.3,1],\n",
    "[4.4,3.2,1.3,0.2,1],\n",
    "[5.0,3.5,1.6,0.6,1],\n",
    "[5.1,3.8,1.9,0.4,1],\n",
    "[4.8,3.0,1.4,0.3,1],\n",
    "[5.1,3.8,1.6,0.2,1],\n",
    "[4.6,3.2,1.4,0.2,1],\n",
    "[5.3,3.7,1.5,0.2,1],\n",
    "[5.0,3.3,1.4,0.2,1],\n",
    "[7.0,3.2,4.7,1.4,2],\n",
    "[6.4,3.2,4.5,1.5,2],\n",
    "[6.9,3.1,4.9,1.5,2],\n",
    "[5.5,2.3,4.0,1.3,2],\n",
    "[6.5,2.8,4.6,1.5,2],\n",
    "[5.7,2.8,4.5,1.3,2],\n",
    "[6.3,3.3,4.7,1.6,2],\n",
    "[4.9,2.4,3.3,1.0,2],\n",
    "[6.6,2.9,4.6,1.3,2],\n",
    "[5.2,2.7,3.9,1.4,2],\n",
    "[5.0,2.0,3.5,1.0,2],\n",
    "[5.9,3.0,4.2,1.5,2],\n",
    "[6.0,2.2,4.0,1.0,2],\n",
    "[6.1,2.9,4.7,1.4,2],\n",
    "[5.6,2.9,3.6,1.3,2],\n",
    "[6.7,3.1,4.4,1.4,2],\n",
    "[5.6,3.0,4.5,1.5,2],\n",
    "[5.8,2.7,4.1,1.0,2],\n",
    "[6.2,2.2,4.5,1.5,2],\n",
    "[5.6,2.5,3.9,1.1,2],\n",
    "[5.9,3.2,4.8,1.8,2],\n",
    "[6.1,2.8,4.0,1.3,2],\n",
    "[6.3,2.5,4.9,1.5,2],\n",
    "[6.1,2.8,4.7,1.2,2],\n",
    "[6.4,2.9,4.3,1.3,2],\n",
    "[6.6,3.0,4.4,1.4,2],\n",
    "[6.8,2.8,4.8,1.4,2],\n",
    "[6.7,3.0,5.0,1.7,2],\n",
    "[6.0,2.9,4.5,1.5,2],\n",
    "[5.7,2.6,3.5,1.0,2],\n",
    "[5.5,2.4,3.8,1.1,2],\n",
    "[5.5,2.4,3.7,1.0,2],\n",
    "[5.8,2.7,3.9,1.2,2],\n",
    "[6.0,2.7,5.1,1.6,2],\n",
    "[5.4,3.0,4.5,1.5,2],\n",
    "[6.0,3.4,4.5,1.6,2],\n",
    "[6.7,3.1,4.7,1.5,2],\n",
    "[6.3,2.3,4.4,1.3,2],\n",
    "[5.6,3.0,4.1,1.3,2],\n",
    "[5.5,2.5,4.0,1.3,2],\n",
    "[5.5,2.6,4.4,1.2,2],\n",
    "[6.1,3.0,4.6,1.4,2],\n",
    "[5.8,2.6,4.0,1.2,2],\n",
    "[5.0,2.3,3.3,1.0,2],\n",
    "[5.6,2.7,4.2,1.3,2],\n",
    "[5.7,3.0,4.2,1.2,2],\n",
    "[5.7,2.9,4.2,1.3,2],\n",
    "[6.2,2.9,4.3,1.3,2],\n",
    "[5.1,2.5,3.0,1.1,2],\n",
    "[5.7,2.8,4.1,1.3,2],\n",
    "[6.3,3.3,6.0,2.5,3],\n",
    "[5.8,2.7,5.1,1.9,3],\n",
    "[7.1,3.0,5.9,2.1,3],\n",
    "[6.3,2.9,5.6,1.8,3],\n",
    "[6.5,3.0,5.8,2.2,3],\n",
    "[7.6,3.0,6.6,2.1,3],\n",
    "[4.9,2.5,4.5,1.7,3],\n",
    "[7.3,2.9,6.3,1.8,3],\n",
    "[6.7,2.5,5.8,1.8,3],\n",
    "[7.2,3.6,6.1,2.5,3],\n",
    "[6.5,3.2,5.1,2.0,3],\n",
    "[6.4,2.7,5.3,1.9,3],\n",
    "[6.8,3.0,5.5,2.1,3],\n",
    "[5.7,2.5,5.0,2.0,3],\n",
    "[5.8,2.8,5.1,2.4,3],\n",
    "[6.4,3.2,5.3,2.3,3],\n",
    "[6.5,3.0,5.5,1.8,3],\n",
    "[7.7,3.8,6.7,2.2,3],\n",
    "[7.7,2.6,6.9,2.3,3],\n",
    "[6.0,2.2,5.0,1.5,3],\n",
    "[6.9,3.2,5.7,2.3,3],\n",
    "[5.6,2.8,4.9,2.0,3],\n",
    "[7.7,2.8,6.7,2.0,3],\n",
    "[6.3,2.7,4.9,1.8,3],\n",
    "[6.7,3.3,5.7,2.1,3],\n",
    "[7.2,3.2,6.0,1.8,3],\n",
    "[6.2,2.8,4.8,1.8,3],\n",
    "[6.1,3.0,4.9,1.8,3],\n",
    "[6.4,2.8,5.6,2.1,3],\n",
    "[7.2,3.0,5.8,1.6,3],\n",
    "[7.4,2.8,6.1,1.9,3],\n",
    "[7.9,3.8,6.4,2.0,3],\n",
    "[6.4,2.8,5.6,2.2,3],\n",
    "[6.3,2.8,5.1,1.5,3],\n",
    "[6.1,2.6,5.6,1.4,3],\n",
    "[7.7,3.0,6.1,2.3,3],\n",
    "[6.3,3.4,5.6,2.4,3],\n",
    "[6.4,3.1,5.5,1.8,3],\n",
    "[6.0,3.0,4.8,1.8,3],\n",
    "[6.9,3.1,5.4,2.1,3],\n",
    "[6.7,3.1,5.6,2.4,3],\n",
    "[6.9,3.1,5.1,2.3,3],\n",
    "[5.8,2.7,5.1,1.9,3],\n",
    "[6.8,3.2,5.9,2.3,3],\n",
    "[6.7,3.3,5.7,2.5,3],\n",
    "[6.7,3.0,5.2,2.3,3],\n",
    "[6.3,2.5,5.0,1.9,3],\n",
    "[6.5,3.0,5.2,2.0,3],\n",
    "[6.2,3.4,5.4,2.3,3],\n",
    "[5.9,3.0,5.1,1.8,3]],dtype=float)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0fc1fcce",
   "metadata": {},
   "source": [
    "### Retirando a tipo da classe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "33e9b9a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "classe=['Setosa','Versicolor','Verginica']\n",
    "X=iris[:,:-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ddde9a9",
   "metadata": {},
   "source": [
    "### 2.Calculando a Matriz de Covariância de um VETOR DE VARIÁVEIS ALEATÓRIAS $X'$, pois $X$ é TABELA DE DADOS\n",
    "- Também pode ser usado a Matriz de Correlação"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2462aa2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.68569351 -0.03926846  1.27368233  0.5169038 ]\n",
      " [-0.03926846  0.18800403 -0.32171275 -0.11798121]\n",
      " [ 1.27368233 -0.32171275  3.11317942  1.29638747]\n",
      " [ 0.5169038  -0.11798121  1.29638747  0.58241432]]\n"
     ]
    }
   ],
   "source": [
    "mCov = np.cov(X.T)\n",
    "print(mCov)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a24597a5",
   "metadata": {},
   "source": [
    "### 3. Calculando os autovalores decrescentes e autovetores correspondentes da Matriz de Covariância"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c63c376f",
   "metadata": {},
   "outputs": [],
   "source": [
    "[D,V]=la.eigh(mCov)    # autovalores e autovetores da matriz de covariância de X\n",
    "i=np.argsort(D)[::-1]  # Obtém índices para ordenação decrescente dos autovalores\n",
    "l=D[i]\n",
    "V=V[:,i]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "36fec7f5",
   "metadata": {},
   "source": [
    "#### Autovalores ordenados $\\lambda_0 \\geq \\lambda_1 \\geq \\lambda_2 \\geq \\lambda_3$, de $X$ com $4$ variáveis (campos)  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "20505e89",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.22484077 0.24224357 0.07852391 0.02368303]\n"
     ]
    }
   ],
   "source": [
    "print(l)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "471b942c",
   "metadata": {},
   "source": [
    "#### Autovetores $V$ relacionados "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d62221c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.36158968  0.65653988 -0.58099728  0.31725455]\n",
      " [-0.08226889  0.72971237  0.59641809 -0.32409435]\n",
      " [ 0.85657211 -0.1757674   0.07252408 -0.47971899]\n",
      " [ 0.35884393 -0.07470647  0.54906091  0.75112056]]\n"
     ]
    }
   ],
   "source": [
    "print(V)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6677eaba",
   "metadata": {},
   "source": [
    "### 4.Porcentagem explicativa acumulada das variáveis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "64b65fef",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.92461621 0.97763178 0.99481691 1.        ]\n"
     ]
    }
   ],
   "source": [
    "pe=np.cumsum(l)/np.sum(l) \n",
    "print(pe)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6fdc059",
   "metadata": {},
   "source": [
    "#### Os dois primeiros eixos (variáveis ou campos) já explicam $97\\%$ de $X$.\n",
    "- Vamos reduzir para dois componentes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b34f69c",
   "metadata": {},
   "source": [
    "#### $V$ é um conjunto de vetores ortogonais. Vamos tomar os dois primeiros "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "0f9eac6c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0.36158968  0.65653988]\n",
      " [-0.08226889  0.72971237]\n",
      " [ 0.85657211 -0.1757674 ]\n",
      " [ 0.35884393 -0.07470647]]\n"
     ]
    }
   ],
   "source": [
    "O=V[:,:2]\n",
    "print(O)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "841194f7",
   "metadata": {},
   "source": [
    "### 5.Calculando a nova TABELA DE DADOS reduzida $Y=XO$\n",
    "- Se $X_v$ fosse um VETOR DE VARIÁVEIS ALEATÓRIAS obteríamos $Y_v=O'X_v$. \n",
    "- Uma TABELA DE DADOS é um VETOR DE VARIÁVEIS ALEATÓRIAS transposto, isto é $Y_v'=(O'X_v)'= X_v'O$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "e3c5e8fd",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2.82713597 5.64133105]\n",
      " [2.79595248 5.14516688]\n",
      " [2.62152356 5.17737812]\n",
      " [2.7649059  5.00359942]\n",
      " [2.78275012 5.64864829]\n",
      " [3.23144574 6.06250644]\n",
      " [2.69045242 5.23261922]\n",
      " [2.8848611  5.48512908]\n",
      " [2.62338453 4.7439257 ]\n",
      " [2.83749841 5.20803203]\n",
      " [3.00481631 5.96665874]\n",
      " [2.89820038 5.33624436]\n",
      " [2.72390912 5.08698354]\n",
      " [2.28614265 4.81144382]\n",
      " [2.86779988 6.50091863]\n",
      " [3.12747377 6.65947808]\n",
      " [2.88881689 6.13281341]\n",
      " [2.86302037 5.6338604 ]\n",
      " [3.31226514 6.19396782]\n",
      " [2.92399691 5.83519737]\n",
      " [3.2008114  5.71259155]\n",
      " [2.96810819 5.75475549]\n",
      " [2.2954854  5.4563393 ]\n",
      " [3.20821456 5.42024641]\n",
      " [3.15517201 5.28351414]\n",
      " [3.00342587 5.17566739]\n",
      " [3.0422871  5.45261105]\n",
      " [2.94895215 5.68940829]\n",
      " [2.87152183 5.6340138 ]\n",
      " [2.87849519 5.1246479 ]\n",
      " [2.92288105 5.11733065]\n",
      " [3.10126576 5.73280374]\n",
      " [2.86370642 6.13470636]\n",
      " [2.91418362 6.41474566]\n",
      " [2.83749841 5.20803203]\n",
      " [2.64434325 5.39191683]\n",
      " [2.88611463 5.92152374]\n",
      " [2.83749841 5.20803203]\n",
      " [2.52950043 4.83447368]\n",
      " [2.92102007 5.55078307]\n",
      " [2.74120419 5.58578315]\n",
      " [2.65913202 4.38185836]\n",
      " [2.51304665 4.98041616]\n",
      " [3.105829   5.51064099]\n",
      " [3.30251014 5.75741976]\n",
      " [2.79567791 5.07204225]\n",
      " [2.97376973 5.82509128]\n",
      " [2.6710218  5.09414739]\n",
      " [2.96865734 5.90100476]\n",
      " [2.80743078 5.42973458]\n",
      " [6.79613769 6.00016292]\n",
      " [6.44375385 5.63392182]\n",
      " [6.97540442 5.81891356]\n",
      " [5.6923103  4.48911979]\n",
      " [6.59847758 5.39011412]\n",
      " [6.15177985 4.89740025]\n",
      " [6.60656681 5.59861494]\n",
      " [4.75987596 4.31361622]\n",
      " [6.55464088 5.54368064]\n",
      " [5.50115303 4.59414886]\n",
      " [5.0002569  4.05223178]\n",
      " [6.02244116 5.21243963]\n",
      " [5.77367885 4.76683043]\n",
      " [6.49538764 5.19036331]\n",
      " [5.3364791  5.06290816]\n",
      " [6.43891604 5.78295994]\n",
      " [6.17093589 4.96274744]\n",
      " [5.74588368 4.9828019 ]\n",
      " [6.45370481 4.77290147]\n",
      " [5.5545895  4.73323428]\n",
      " [6.62758382 5.23050972]\n",
      " [5.86812967 5.2478999 ]\n",
      " [6.80781195 4.98716221]\n",
      " [6.43184575 5.13233337]\n",
      " [6.22535131 5.46510288]\n",
      " [6.41098396 5.64433471]\n",
      " [6.84238452 5.55939325]\n",
      " [7.06873937 5.58211632]\n",
      " [6.32379865 5.15239216]\n",
      " [5.20400834 4.94963712]\n",
      " [5.44100021 4.6121858 ]\n",
      " [5.31945861 4.63723319]\n",
      " [5.64633805 5.00301409]\n",
      " [6.89008008 4.89351859]\n",
      " [6.09861795 4.83143946]\n",
      " [6.31854859 5.50977769]\n",
      " [6.73177206 5.72275907]\n",
      " [6.32421089 4.94404473]\n",
      " [5.75653826 5.0479957 ]\n",
      " [5.67585653 4.63506226]\n",
      " [5.97437409 4.64519718]\n",
      " [6.40150354 5.28091129]\n",
      " [5.74022215 4.91246611]\n",
      " [4.80426181 4.30629897]\n",
      " [5.86687614 4.81150524]\n",
      " [5.84247005 5.10354359]\n",
      " [5.88658133 5.02310171]\n",
      " [6.15303338 5.33379491]\n",
      " [4.60287976 4.56315501]\n",
      " [5.80915101 4.96770721]\n",
      " [8.04307008 5.30288149]\n",
      " [6.92541532 4.73979867]\n",
      " [8.12782771 5.65665902]\n",
      " [7.48215804 5.13359804]\n",
      " [7.86110108 5.27284118]\n",
      " [8.90822302 5.86189178]\n",
      " [6.03072634 4.12337204]\n",
      " [8.44334819 5.66710074]\n",
      " [7.83101589 5.06917556]\n",
      " [8.42947733 6.09510436]\n",
      " [7.17327804 5.55676213]\n",
      " [7.31368355 5.09856912]\n",
      " [7.67672196 5.53000401]\n",
      " [6.85593732 4.53830831]\n",
      " [7.0966104  4.77541668]\n",
      " [7.41608668 5.43354272]\n",
      " [7.46059188 5.35545399]\n",
      " [9.00010848 6.48626828]\n",
      " [9.30602996 5.5679893 ]\n",
      " [6.80967292 4.55370979]\n",
      " [7.93951036 5.6915057 ]\n",
      " [6.70944047 4.70914477]\n",
      " [9.01060858 5.7714972 ]\n",
      " [6.89901135 5.11069274]\n",
      " [7.78719675 5.64811026]\n",
      " [8.12553693 5.87309068]\n",
      " [6.76896828 5.13558673]\n",
      " [6.80201275 5.19829848]\n",
      " [7.63419708 5.10386885]\n",
      " [7.8989075  5.77724298]\n",
      " [8.35230402 5.68746632]\n",
      " [8.743686   6.68524777]\n",
      " [7.67008147 5.0963982 ]\n",
      " [6.9544457  5.17092244]\n",
      " [7.2909832  4.81325894]\n",
      " [8.58786472 6.00048817]\n",
      " [7.65632995 5.45363034]\n",
      " [7.41620602 5.36277124]\n",
      " [6.68019657 5.15022123]\n",
      " [7.61899683 5.68620598]\n",
      " [7.82564649 5.49733258]\n",
      " [7.43379398 5.72399491]\n",
      " [6.92541532 4.73979867]\n",
      " [8.07466581 5.59069823]\n",
      " [7.93073432 5.61822767]\n",
      " [7.45536015 5.50213895]\n",
      " [7.03700673 4.93970288]\n",
      " [7.27538903 5.39324292]\n",
      " [7.41297217 5.43060048]\n",
      " [6.90100923 5.03183702]]\n"
     ]
    }
   ],
   "source": [
    "Y=X@O\n",
    "print(Y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8fda5edd",
   "metadata": {},
   "source": [
    "### 6.Plotando a nova TABELA DE DADOS $Y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e8c865f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "plt.plot(Y[0:50,0],Y[0:50,1],'or',Y[50:100,0],Y[50:100,1],'og',Y[100:150,0],Y[100:150,1],'ob')\n",
    "\n",
    "plt.title(\"Rotação dos eixos principais de X. Ou seja, gerar um Y=XO\") #título do gráfico\n",
    "plt.xlabel('Eixo 1') #nome para eixo x\n",
    "plt.ylabel('Eixo 2') #nome para eixo y\n",
    "plt.legend(['Setosa','Versicolor', 'Virginica'],loc='best') #coloca legendas no gráfico\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28f724cd",
   "metadata": {},
   "source": [
    "#### Para separar melhor os pontos, podemos usar Discriminante Linear de Fisher ou Discriminante canônico, que separa as classes usando para isso PCA e outros conceitos. Ou seja, precisa fazer PCA e mais algumas coisas.\n",
    "- Procure por Discriminante Linear ou use scikit-learn do python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "857f1566",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,5))\n",
    "plt.axis([-3,5,-3,3])\n",
    "plt.arrow(0,-3,0,6)\n",
    "plt.arrow(-3,0,8,0)\n",
    "#plt.grid('on')\n",
    "plt.title('Cargas dos atributos e suas contribuições')\n",
    "cores=['r','g','b','c']\n",
    "medida = ['Comprimento Pétala','Largura Pétala','Comprimento Sépala','Largura Sépala']\n",
    "for i,cor in enumerate(cores):\n",
    "    plt.scatter(O[i,0],O[i,1],marker='+',c=cores[i])\n",
    "    plt.text(O[i,0]+0.1,O[i,1],medida[i], c=cores[i])\n",
    "    plt.arrow(0,0,O[i,0],O[i,1],color=cores[i])\n",
    "\n",
    "plt.xlabel('PCA1')\n",
    "plt.ylabel('PCA2')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e72b572e",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "2b401036",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "98e80dcf",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c0315f90",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cfa2f853",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "246135c6",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}