{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "195a411a",
   "metadata": {},
   "source": [
    "# PCA da Iris Flowers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "3d2e6546",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.linalg as la"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52b74349",
   "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": "af12b866",
   "metadata": {},
   "source": [
    "### Carregando a TABELA DE DADOS iris"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6b6db4de",
   "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": "b35e6c15",
   "metadata": {},
   "source": [
    "### Retirando a tipo da classe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "201e5600",
   "metadata": {},
   "outputs": [],
   "source": [
    "X=iris[:,:-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d48f2a5",
   "metadata": {},
   "source": [
    "### 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": 17,
   "id": "d58a0d26",
   "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": "416afe5b",
   "metadata": {},
   "source": [
    "### Calculando os autovalores decrescentes e autovetores correspondentes da Matriz de Covariância"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ce2315e9",
   "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": "72ec79aa",
   "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": 16,
   "id": "938636a5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.22484077 0.24224357 0.07852391 0.02368303]\n"
     ]
    }
   ],
   "source": [
    "print(l)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9db3d609",
   "metadata": {},
   "source": [
    "### Autovetores $V$ relacionados "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a702e0ca",
   "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": "e9bd415f",
   "metadata": {},
   "source": [
    "### Porcentagem explicativa acumulada das variáveis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "da4beda0",
   "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": "1da3e15a",
   "metadata": {},
   "source": [
    "#### Os dois primeiros eixos (variáveis ou campos) já explicam $97\\%$ de $X$.\n",
    "- Vamos reduzir para dois componentes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "49cebd3f",
   "metadata": {},
   "source": [
    "### $V$ é um conjunto de vetores ortogonais. Vamos tomar os dois primeiros "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6020c1e5",
   "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": "a4bb009a",
   "metadata": {},
   "source": [
    "### Se $X_v$ fosse um VETOR DE VARIÁVEIS ALEATÓRIAS obteríamos $Y_v=O'X_v$. \n",
    "### Um TABELA DE DADOS é um VETOR DE VARIÁVEIS ALEATÓRIAS transposto, isto é $Y_v'=(O'X_v)'= X_v'O$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "86851697",
   "metadata": {},
   "source": [
    "# Calculando a nova TABELA DE DADOS reduzida $Y=XO$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b5c66e31",
   "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": "e529fd3c",
   "metadata": {},
   "source": [
    "# Plotando a nova TABELA DE DADOS $Y$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "888d1176",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,6))\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": "256e0576",
   "metadata": {},
   "source": [
    "#### Para separar melhor os pontos, podemos usar Discriminante Linear de Fisher ou Discriminante canônico, que separa as classes para usando para isso PCA e outros conceitos\n",
    "- Procure por Discriminante Linear ou use scikit-learn do python"
   ]
  }
 ],
 "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",
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