Aula6-Classificao-Regressao-logistica.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regressão Logistica"
   ]
  },
  {
   "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": [
    "Vamos realizar a classificação em um conjunto de dados artificiais."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "from scipy.special import expit\n",
    "\n",
    "X = np.arange(12).reshape(-1, 1)\n",
    "y = np.array([0, 0, 0, 0,1,0, 1, 1, 1, 1, 1, 1])\n",
    "plt.plot(X, y, 'ko')\n",
    "\n",
    "# Ajusta o modelo de regressao logistica\n",
    "model = linear_model.LogisticRegression(C=1e5)\n",
    "model.fit(X, y)\n",
    "loss = expit(X * model.coef_ + model.intercept_).ravel()\n",
    "plt.plot(X, loss, color='red', linewidth=3)\n",
    "\n",
    "# Podemos obter uma curva mais suave\n",
    "#xx = np.arange(min(X), max(X), 0.01)\n",
    "#loss = expit(xx * model.coef_ + model.intercept_).ravel()\n",
    "#plt.plot(xx, loss, color='red', linewidth=3)\n",
    "\n",
    "# Ajusta um modelo de regressao linear\n",
    "linear = linear_model.LinearRegression()\n",
    "linear.fit(X, y)\n",
    "plt.plot(X, linear.coef_ * X + linear.intercept_, linewidth=2, linestyle='dashed')\n",
    "plt.axhline(.5, color='.5')\n",
    "plt.savefig('logistic.eps')\n",
    "plt.show(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[9.97194873e-01 2.80512708e-03]\n",
      " [9.89727807e-01 1.02721933e-02]\n",
      " [9.63119034e-01 3.68809657e-02]\n",
      " [8.76205038e-01 1.23794962e-01]\n",
      " [6.57340632e-01 3.42659368e-01]\n",
      " [3.42079153e-01 6.57920847e-01]\n",
      " [1.23515708e-01 8.76484292e-01]\n",
      " [3.67895382e-02 9.63210462e-01]\n",
      " [1.02460269e-02 9.89753973e-01]\n",
      " [2.79792780e-03 9.97202072e-01]\n",
      " [7.59885722e-04 9.99240114e-01]\n",
      " [2.06069640e-04 9.99793930e-01]]\n"
     ]
    }
   ],
   "source": [
    "p = model.predict_proba(X)\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Acurácia: 0.8333333333333334\n"
     ]
    }
   ],
   "source": [
    "print(\"Acurácia:\", model.score(X, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "O modelo de regressão logística usa a função logística."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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": [
    "import matplotlib.pyplot as plt \n",
    "import numpy as np \n",
    "import math \n",
    "  \n",
    "x = np.linspace(-10, 10, 100) \n",
    "z = 1/(1 + np.exp(-x)) \n",
    "  \n",
    "plt.figure(figsize=(6,4))\n",
    "plt.plot(x, z) \n",
    "plt.xlabel(\"x\", fontsize = 15) \n",
    "plt.ylabel(\"h(x)\", fontsize = 15) \n",
    "plt.savefig('logistic-function.eps')\n",
    "plt.show() "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Usamos o código abaixo para fazer a classificação completa."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/p2Z0b6OPgvMllf5IFhEnMBvoCyQDq0RksTFmQ6nZxgPvGWNeEZGOwGdATA3Uq5RnFRZat+9vKPp2DwyEhQvh3HPtrasK8goKmfP9DmZ9s5Xc/EIi6gcyaeD59LvAe7ZBucaV37G6AtuMMTsAROR/wECgdKAboEHR+zBgnzuLVMo2Tz1lXZJYbM4c6/FwXuStlUn844vNANzUJZLx13UkLMTf5qpUTXAl0FsAe0qNk4FLy8zzJPCliDwA1AP6lLcgERkODAeIioqqaq1KedaHH8LTT5eMH3kE7rrLvnrO0rBLo/huSwp/6dGKHrHaTMuXuXIMvbyzPqbM+DbgTWNMJNAfeFtETlu2MWaOMSbeGBMfEaHfWKoWW7v21PC+5hqYPt2+eqpg1a6j3P7aT5zIygMgyN/JW/d01TCvA1wJ9GSgZalxJKcfUrkXeA/AGLMSCAL0bIvyTocPWydBMzOtcdu28L//We1wa7H0nHyeWJTITa+uZMX2I7z2/Q67S1Ie5sp36CogVkRaAXuBW4Hby8yzG7gaeFNEOmAFeoo7C1XKI/Ly4OabYdcuaxwaah1DP+ccW8uqzLLNhxi3MJG9x7Pwcwh/69WGEVe1tbss5WGVBroxJl9ERgBfAE5grjFmvYg8DSQYYxYDjwKvicjDWIdj/mSMKXtYRqna79FHrUfIFZs/v1Y/ZehYRi6TPt3Agl/3AtCpRRjTh8TRsXmDSr5S+SKXfoc0xnyGdSli6c+eKPV+A3C5e0tTysNefx1efLFkPGkS3HCDffW4IHHfCRb8updAPwcP923Hn69ohZ8206qzavdBQaU8ZcWKU3ubFz/MuRbKzM0/eVdnj9gIxvY/jz4dmtI6Qptp1XX6o1yp5GSrt3medVUIcXHwxhu17rZ+YwzvJeyh+7RvWZ109OTnw69so2GuAN1DV3VdVpbV2/zgQWvcuLH1fNBa1tt8z9FMxixYx/JthwH4+Pf9dIluZHNVqrbRQFd1V3Fv84QEa1wLe5sXFBreWrmLGUs2k5VXwDkh/kwccD4DL2pud2mqFtJAV3XX88/DvHkl45kzoXdv++opY/eRTB56dw2/7j4OwIALmzNxQEfCQ72rKZjyHA10VTd9+SU8/njJ+N574f777aunHMEBTnYczqBpg0Am39iJvh2b2l2SquU00FXds3Xrqb3Nu3eH2bNrxUnQjftTadskFH+ng4j6gbz+x3jaNqlPWLA201KV06tcVN2Smmrd1n/cOoxBixZWEy6be5tn5xUw9fONXP/icl77oeSW/S7RjTTMlct0D13VHYWFcMcdsHGjNQ4Ksq5oadbM1rJ+3nGE0QvWsfNwBg6B9Ox8W+tR3ksDXdUdEyfCxx+XjF97DeLjbSsnLTuP6Us2Me+n3QDENgllxtA4OkfV7r4xqvbSQFd1w/vvw+TJJePHHrP21m2SfCyTm15dyf4T2fg5hPt7t+W+3m0I9HPaVpPyfhroyvf9/jv86U8l42uugWnTbCsHoHlYMFGNQoioH8iMoXGc10ybaanq00BXvq2i3uZOz+4JG2P4dN1+LoxsSMtGITgcwit3dKFBkJ8201Juo4GufFdeHtx0EyQlWeP69W3pbX4wNZvxHyXy1YaDXNE2nLfv7YqI0KhegEfrUL5PA135rkcegWXLrPciHu9tXtxMa/KnG0nLzqd+oB/9O53rsfWrukcDXfmmt96Cl14qGU+aBAMGeGz1u49kMnrBWlZsPwLA1ec1YfKgCzg3LNhjNai6RwNd+Z7jx62982I33QRjx3ps9anZeVz/4g+kZufTqF4AEwd05IYLmyO14E5U5ds00JXvmTIFjlh7xsTEeLy3eYMgf+6+vBW7jmTwxPUdaazNtJSHaKAr37J9O8yaVTKePh3q1avRVebmF/LKsu3ENg09eYz8oT6xukeuPE4DXfmWUaNKnjx02WXW4ZYa9Pue44z8YC2bD6YRHhpA7/ZNCA5wapgrW2igK9/xww9Wo61izz1XY4dasnILeO6rzby+fCeFBqIbhzBtcBzBAXqnp7KPBrryDYWFp54Ive026NatRla1cvsRRi9YS9KRTBwCw69szcN92mmYK9u5dIuaiPQTkc0isk1ERlcwz80iskFE1ovIf91bplKVmD+/5FFyQUE1dmt/fkEhYxeuI+lIJuc1q8/C+y5nbP8OGuaqVqh0D11EnMBsoC+QDKwSkcXGmA2l5okFxgCXG2OOiUiTmipYqdNkZsKYMSXjRx6BqCi3rqKg0OB0CH5OB1MHd+LnHUf5W682BPjpbfuq9nDlkEtXYJsxZgeAiPwPGAhsKDXPX4DZxphjAMaYQ+4uVKkK/fOfsHev9b5JExhd7i+RZ+VIeg5PfbyB0CA/nhnUCYBurRvTrXVjt61DKXdxZfeiBbCn1Di56LPS2gHtRORHEflJRPqVtyARGS4iCSKSkJKScnYVK1Xavn2nHl6ZPNnq2VJNxhgW/baXvs9/z+Lf9/HRmr0cSsuu9nKVqkmu7KGXd5mAKWc5sUAvIBL4QUQuMMYcP+WLjJkDzAGIj48vuwylqm78+JJOip06wT33VHuR+09kMX5hIt9ssn7RvLxtY6YOiqNJ/aBqL1upmuRKoCcDLUuNI4F95czzkzEmD9gpIpuxAn6VW6pUqjxr1sCbb5aMn3uu2m1x//vzbqZ+tpG0nHzqB/kx4bqO3BQfqdeVK6/gyiGXVUCsiLQSkQDgVmBxmXk+AnoDiEg41iGYHShVU4yBRx+1/gS47jro06fai03YdZS0nHz6dmzK14/05OZLWmqYK69R6R66MSZfREYAXwBOYK4xZr2IPA0kGGMWF027RkQ2AAXA48aYIzVZuKrjFi+GpUut904nPPvsWS0mv6CQlPSck10QJ1zfkT4dm/KHC5ppkCuvI8bYcyg7Pj7eJBRfN6xUVeTmwgUXwNat1njECHjxxSovZtOBVEZ9sJbM3AI+efAKfZ6n8goistoYU+7TzfVOUeV9XnmlJMzDwmDixCp9eU5+AbOXbuflpdvILzQ0Dwtiz9Es2jYJrYFilfIcDXTlXY4ehaeeKhlPmADh4S5/+Zrdxxj14Vq2HEwH4M5u0Yzs1576Qf7urlQpj9NAV97l6afh2DHrfZs21uEWF838eguzvtmKMdAqvB7TBnfiUr1BSPkQDXTlPbZsgdmzS8YzZkCg6w+PaNEwGIcIf7myNQ/1iSXIX4+ZK9+iga68x8iRkJ9vve/RAwYNOuPsJ7LyWLP7GL3aW62FhnaJpHPUOXqsXPks7SykvMPSpbBoUcm4kl7nX64/QN/nvuOvb69mR4p1vFxENMyVT9M9dFX7FRSc2uv8rrsgvtyrtkhJy+HJj9fz6dr9AFwc1VCvJ1d1hga6qv3eegt++816HxxsPQS6DGMMH/22l6c+3sDxzDxCApyMvLY9d10Wg8Ohga7qBg10Vbulp8O4cSXjxx+HyMjTZnv2y83MXrodgB6x4TwzqBMtG4V4qkqlagXbAv3IkSO8WbqxklLl2bULrr3Weh8QYD24opzvm9C8Am4ITqVloxAinCl8s3ijR8tUqjbQk6Kq9srJgT2lWvG3anWym2J2XgF7jmaenBTs7+SiqIZE1Hf9MkalfI32clG11113wdtvW+87d4aEBPIN/Hv5Tp7/ags5+YU8f8uFDOp8+iEYpXyV9nJR3ichoSTMAf75TzYcSGfkh7+TuDcVgCEXR9K7vT6+VqliGuiq9jHmlMsUs28czEu5zXn1peXkFxpaNAzmmcGd6NkuwsYilap9NNBV7bNgAfzwg/Xez495d47ipaXbEIE/dY/hsWvbExqo37pKlaX/K1TtkpMDI0diKHqY7YgR3HlDF35JX8PwK1sTH9PI5gKVqr30KhdVu7z0Et8XhjHozmc53iwSJkwg0M/JnLviNcyVqoTuoata40TyASb9cJAPbpkEwNz7n+GRRhriSrlKA13VCksS9zPhrRWknNeTgPxcHt70JX/+YKbdZSnlVTTQla0OpWUzcdF6Pk88AI4gLtmznmlLXqDNGy9DkN4kpFRVaKArW207mM7niQeoV5DL6G/+zbA1n+Po3QsGDLC7NKW8jga68rgTWXmEBVvP8OzeNpyn2zm56uG/EpmaYvU4r6TXuVKqfC5d5SIi/URks4hsE5HRZ5hvqIgYESm/WbWq0woLDW/+uJPLp33LLzuPWh8WFHDX849bYQ5w991w0UX2FamUF6t0D11EnMBsoC+QDKwSkcXGmA1l5qsPPAj8XBOFKu+27VA6oz9cS0KS9YDnrzcepGurRjB3LiQmWjPVqweTJtlYpVLezZVDLl2BbcaYHQAi8j9gILChzHyTgBnAY26tUHm1vIJC5ny/g1lfbyW3oJCI+oFMGngB/S5oBmlpMH58ycyjRkHz5vYVq5SXcyXQWwClepiSDFxaegYR6Qy0NMZ8IiIa6AqAnYczuH/+r2zYbzXTujk+knH9OxIWYh0/Z+pUOHTIeh8ZCY8+alOlSvkGVwK9vLNTJ3vuiogDeB74U6ULEhkODAeIiopyrULltRoE+XEgNZvIc4KZNjiOK2LDSyYmJVknP4tNnQoh+oQhparDlUBPBlqWGkcC+0qN6wMXAMuKHsbbDFgsIjcYY05peG6MmQPMAasfejXqVrXUmt3HOL95GAF+DhqHBvLm3ZfQJiKUemWbaY0ZY/VtAeuBz7ff7vlilfIxrlzlsgqIFZFWIhIA3AosLp5ojDlhjAk3xsQYY2KAn4DTwlz5tvScfJ5YlMigl1fwyrLtJz+Pi2x4epj/9BO8807J+LnnwKFthZSqrkr30I0x+SIyAvgCcAJzjTHrReRpIMEYs/jMS1C+btnmQ4xbmMje41n4OeTMl5CX6XXO0KHQo0eN16hUXeDSjUXGmM+Az8p89kQF8/aqflnKGxzLyGXSpxtY8OteADq1CGP6kDg6Nm9Q8Re99x6sXGm9DwiAadM8UKlSdYPeKarOyp6jmQx6+UcOp+cS6Ofgkb7tuPeKVvg5z3DoJDvbujSx2IMPQps2NV+sUnWEBro6K5HnBNO+WX1aFximDe5E64jQyr9o1izr6haA8HAYN65mi1SqjtFAVy4xxvD+6mS6xjQiJrweIsLLw7pQP9APh8OFviv798OUKSXjp56Chg1rrmCl6iANdFWpPUczGbNgHcu3HaZb60b898/dcDjkZIOtSuXkWCc/09KscYcOMHx4zRWsVB2lga4qVFBo+M+KXfzji81k5RVwTog/t14SVbVGiMbAAw/AihXW2OGAl14CP/3WU8rd9H+VKtfWg2mM+nAtv+4+DsCAC5szcUBHwkOr+NCJV1+F114rGU+fDldd5cZKlVLFNNDVaVKz8xj08grSc/Jp2iCQyTd2om/HplVf0HffWVeyFBs2TPu1KFWDNNDVaRoE+fO3Xm1IPpbJmP4daBDk4rHy0pKSrOPm+fnW+OKLrT11fXCFUjVGA12RnVfA819voeO5DRh4UQsA7uvVBjnb8M3IgBtvhMOHrXGTJvDRRxAc7KaKlVLl0UCv437ecYTRC9ax83AG4aEBXHt+M4L8nWcf5sbAvffCb79ZY39/+PBDaNnyzF+nlKo2DfQ6Ki07j+lLNjHvp90AtGsayvQhcQT5O6u34OnT4d13S8azZ8MVV1RvmUopl2ig10FLNx1i7MJ17D+Rjb9TuK9XW+7v3ZYAv2p2PPz0Uxg7tmR8333wl79Ub5lKKZdpoNcxeQWFTPp0A/tPZHNhZBjTh8ZxXrMzNNNy1aZNVk9zU9Tm/sorYebM6i9XKeUyDfQ6wBhDXoEhwM+Bv9PBjCFx/LbnOHdf3gqnK7ftV+b4cRg4EFKtR80RFQXvv28dP1dKeYwGuo87cCKb8R8l0rheANOHxgEQH9OI+JhG7llBQYG1Z75lizUODrauaGnSxD3LV0q5TAPdRxlj+N+qPTzz6UbScvKpH+THY9e2J6J+Fe/0rMz48fD55yXjN96Azp3duw6llEs00H1Q0pEMRn+4jpU7jgDQp0MTJt/Yyf1h/s47pz6gYswYuOUW965DKeUyDXQfYozh9eU7efbLzWTnFdKoXgBP3nA+A+LOPfvryivy66/W9ebFrrsOJk1y7zqUUlWigZLHsegAAA+xSURBVO5DRIQtB9PIzitk4EXNmTjgfBrVC3D/ig4dsu4Ezcqyxu3bw/z54KzmNexKqWrRQPdyufmFHEzNpmWjEADG9e/IHy44l97n1dBJydxcq0fLnj3WuEEDWLQIwsJqZn1KKZdV804SZaff9xxnwIvL+eMbv5CdVwBAWIh/zYU5wEMPwQ8/WO9FrOPo7dvX3PqUUi7TPXQvlJVbwHNfbeb15TspNBDTOIT9J7JpFV6vZlf8r3/BK6+UjKdOhf79a3adSimXaaB7mRXbDzP6w3XsPpqJQ+CvV7bmoT7tCA6o4ePXP/wAI0aUjG+9FUaOrNl1KqWqxKVAF5F+wCzACfzbGDOtzPRHgD8D+UAKcI8xJsnNtdZ50z7fxKvfbQfgvGb1mTE0jrhIDzxoefduGDKkpLd5587w+uva21ypWqbSQBcRJzAb6AskA6tEZLExZkOp2dYA8caYTBH5GzAD0AuS3ax9s1D8ncIDV8Xyfz3bVL+ZlisyM2HQIEhJscYREdadoCEhNb9upVSVuLKH3hXYZozZASAi/wMGAicD3RiztNT8PwF3uLPIuupIeg6rk45xzfnNALjxohbERzc6eUVLjTPG6pb466/W2M8PPvjA6tWilKp1XNnFawHsKTVOLvqsIvcCn5c3QUSGi0iCiCSkFO/xqdMYY1j02176PPcdI/67hm2H0gDrOnOPhTnAs8/Cf/9bMn7xRauLolKqVnJlD728A6Wm3BlF7gDigZ7lTTfGzAHmAMTHx5e7jLpu3/Esxn+UyLebDgFwedvGBPrZcMPOkiUwalTJ+K9/hf/7P8/XoZRymSuBngyUfn5YJLCv7Ewi0gcYB/Q0xuS4p7y6o7DQ8M6q3Uz9bBPpRc20JlzXkZviI91/235ltmyxrmIp7m1+xRXwwguerUEpVWWuBPoqIFZEWgF7gVuB20vPICKdgX8B/Ywxh9xeZR0wbckm5ny/A4C+HZsy+cYLaNogyPOFpKZavc1PnLDGkZHWcfOAGmghoJRyq0oD3RiTLyIjgC+wLluca4xZLyJPAwnGmMXAP4BQ4P2ivcndxpgbarBun3N71yg+W7efMX/oQP9OzTy/Vw5QWAjDhllPHwIICrKuaGna1PO1KKWqTIyx51B2fHy8SUhIsGXdtcHG/am8l7CHJ67veDK88wsK8XPa2I1h/HiYMqVkPH++9fAKpVStISKrjTHx5U3TO0U9LCe/gNnfbuPlZdvJLzR0ahHG4IsjAewN8/feOzXMR47UMFfKy2ige9Cvu48x6oO1bD2UDsBdl0WfvMbcVr/9BnffXTLu1w+eeca+epRSZ0UD3QMyc/N59ostvLFiJ8ZA6/B6TBsSR9dWbnquZ3WkpFi9zTMzrXFsrNVBUXubK+V1NNA94L8/72bujztxOoThPVvz96tjCfKvBYGZlwc33wxJRW136te3eps39EB/GKWU22mg1xBjzMmTnXddFsO6vSf4S4/WXNCiljwIIjkZHnsMli2zxiLWSdAOHWwtSyl19vQBFzXgi/UH6P/Cco5m5AIQ4Odg1q2da0eY79pl3fHZpg28+27J55Mnw4ABtpWllKo+3UN3o5S0HJ5cvJ5P1+0H4O2VSfy9T6zNVRXZts16IMVbb5W0wS12110wZow9dSml3EYD3Q2MMSxcs5enP9nA8cw8QgKcjOp3Hnd2i7a7NOsmoSlTrCZbhYWnTuveHSZMgGuv1d7mSvkADfRq2ns8i3EL17Fss9U9skdsOM8M6uTZrojlSUy0DqO8915JT5ZiPXvCE09A794a5Er5EA30ako+msmyzSk0CPJjwvUdGdrFhmZapa1ZA5MmwcKFp0/r29faI+/Rw/N1KaVqnAb6WTiSnkPj0EAALm3dmBlD4uh1XgRN6tvQTKvYL79YQf7JJ6dP69/fCvJu3Txfl1LKY/QqlyrILyjklWXb6T7tW1ZsO3zy85svaWlfmC9fbh0Dv/TS08P8xhshIQE+/VTDXKk6QPfQXbRhXyojP/ydxL2pAKzYfoTubcPtKcYY6/rxSZNg6dJTp4nA0KFWo624OFvKU0rZQwO9Etl5Bbz07TZe/c5qptWiYTBTB3fiynYRni/GGPjqK3j6afjxx1OnORxw220wdix07Oj52pRSttNAP4Nth9L469ur2Z6SgQj8qXsMj1/bnnqBHv5rM8Y6bDJpknWsvDSns+Q68thacs27UsoWGuhnEB4ayImsPFpH1GPGkDjiYzzcTKuw0HrAxOTJ1tUrpfn7Wx0SR4+GVq08W5dSqlbSQC9j5fYjXBzdkEA/Jw1DAnj73ktpFV7Ps820Cgqsx75NnmxdT15aYCD8+c/WA5xbtiz/65VSdZIGepHjmblM/nQjH6xO5sGr2vLINe0B6HBuA88UkJdn9Vn58UeYPr3kMXDFgoOtHiyPPw7nnuuZmpRSXkUDHfh83X4mLFrP4fQcAvwc1A/yr5kVGQMHD8LmzbBlS8mfW7bA9u2n91gBqFcPRoyARx6BJk1qpi6llE+o04F+KC2biYvW83niAQC6xjRi6pBOtIkIrd6C09Jg69ZTA7v4fVqaa8to0AAefBAeeggaN65ePUqpOqHOBvruI5kMeGk5J7LyqBfgZPQfzmPYpdE4HC7etp+XBzt3nr6nvXkz7N9/dkVFRlpXqvTpA/fdpw+aUEpVSZ0N9JaNgrmwZUMEeGZwJ1o0DC6ZmJsLGRnWY9kyMmDfvtODe8eO8g+RVCYsDNq3h3btrFfx+7ZtIbSavxkopeo0lwJdRPoBswAn8G9jzLQy0wOBt4AuwBHgFmPMLveWCvPnz2fcuHHsTUqifcuWPDVyJEP69Ts1fItfZcaFmZm8ld+EHqlJtDlxAMnI4JXsPELSjiNTy3zN2QR1af7+VkCXF9wRERV2OCzevt27dxMVFcWUKVMYNmxY9WqpgCfXZQdf3z6lymWMOeMLK8S3A62BAOB3oGOZee4DXi16fyvwbmXL7dKli6mKefPmmfZBQSbbOrVYpdfWxpFm8LAZJnrUJ2bo7dNN4Vkso9xXy5bGXH21MffdZ8zMmcZ89pkx27cbk5dXpW0r3r6QkBADnHyFhISYefPmVXlZtWlddvD17VN1G5BgKshVMWV7ZZchIpcBTxpjri0ajyn6QTC11DxfFM2zUkT8gANAhDnDwuPj401CQoLLP3hiYmLITErikMtfAXkOJ3O6DmbW5beT6+dPk7QjTPrqFa7d+tOZv9DPj9SCAtKNIQPrV44tRa+j4eG8/PXX1h54vXpVqObMYmJiSCp+WHMp0dHR7Nq1y23r8fS67ODr26fqNhFZbYyJL3eaC4E+FOhnjPlz0fhO4FJjzIhS8yQWzZNcNN5eNM/hMssaDgwHiIqK6lLef7qKOBwOgosCthDIKPVq06kThIRYAVv0SmzQnJFh8WxwWNeR3xJ0nLFNMghrUDRfmflP+SwgAIfDQXl/NyJCYdkn/7iBJ9fn6W3zNF/fPlW3nSnQXTmGXt4B37L/W1yZB2PMHGAOWHvoLqz7pKioKJKSkggCckp9Hh0dza61a0+Z90RWHrdM/YaM3AJaNgpm2uA4Lq9iZ8Ti9ZX3eU3w5Po8vW2e5uvbp1RFXOmHngyUvsc8EthX0TxFh1zCgKPuKLDYlClTCAkJOSXMQ0JCmDJlymnzhgX78/c+sdxzeSu+eOjKKod56fWVVtH63MGT6/P0tnmar2+fUhWq6OB68QtrL34H0IqSk6Lnl5nnfk49KfpeZcut6klRY6yTXdHR0UZETHR09MmTXGnZeWb8wnXmg4Q9VV7m2ayvpnhyfZ7eNk/z9e1TdRfVOSkKICL9gZlYV7zMNcZMEZGnixa8WESCgLeBzlh75rcaY3acaZlVPSlakaWbDzFuwTr2ncgmPDSA5aOu8mwjLaWU8qDqHkPHGPMZ8FmZz54o9T4buKk6RVbVsYxcJn2ygQVr9gIQFxnG9CFxGuZKqTrL6+4UNcbw2boDTFycyOH0XAL9HDx6TTvuubwVfk59RKpSqu7yukDPLzTM/HoLh9NzubRVI6YPiSMm3H3XgyullLfyukD3dzqYMTSODftTue2SKNebaSmllI/zukAH6Bx1Dp2jzrG7DKWUqlX0oLNSSvkIDXSllPIRGuhKKeUjNNCVUspHaKArpZSP0EBXSikfoYGulFI+QgNdKaV8hEvdFmtkxSIpgOuPLDpVOHC40rm8ly9vn26b9/Ll7fOmbYs2xkSUN8G2QK8OEUmoqH2kL/Dl7dNt816+vH2+sm16yEUppXyEBrpSSvkIbw30OXYXUMN8eft027yXL2+fT2ybVx5DV0opdTpv3UNXSilVhga6Ukr5CK8LdBHpJyKbRWSbiIy2ux53EZGWIrJURDaKyHoR+bvdNbmbiDhFZI2IfGJ3Le4mIg1F5AMR2VT0b3iZ3TW5i4g8XPQ9mSgi74hIkN01VYeIzBWRQyKSWOqzRiLylYhsLfrTK5+g41WBLiJOYDbwB6AjcJuIdLS3KrfJBx41xnQAugH3+9C2Ffs7sNHuImrILGCJMeY84EJ8ZDtFpAXwIBBvjLkAcAK32ltVtb0J9Cvz2WjgG2NMLPBN0djreFWgA12BbcaYHcaYXOB/wECba3ILY8x+Y8yvRe/TsAKhhb1VuY+IRALXAf+2uxZ3E5EGwJXA6wDGmFxjzHF7q3IrPyBYRPyAEGCfzfVUizHme+BomY8HAv8pev8f4EaPFuUm3hboLYA9pcbJ+FDoFRORGKAz8LO9lbjVTGAkUGh3ITWgNZACvFF0SOnfIlLP7qLcwRizF3gW2A3sB04YY760t6oa0dQYsx+snSugic31nBVvC3Qp5zOfuu5SREKBD4GHjDGpdtfjDiJyPXDIGLPa7lpqiB9wMfCKMaYzkIGX/speVtGx5IFAK6A5UE9E7rC3KlURbwv0ZKBlqXEkXv7rX2ki4o8V5vONMQvsrseNLgduEJFdWIfJrhKRefaW5FbJQLIxpvg3qg+wAt4X9AF2GmNSjDF5wAKgu8011YSDInIuQNGfh2yu56x4W6CvAmJFpJWIBGCdnFlsc01uISKCdQx2ozHmObvrcSdjzBhjTKQxJgbr3+xbY4zP7OUZYw4Ae0SkfdFHVwMbbCzJnXYD3UQkpOh79Gp85IRvGYuBPxa9/yOwyMZazpqf3QVUhTEmX0RGAF9gnW2fa4xZb3NZ7nI5cCewTkR+K/psrDHmMxtrUq57AJhftKOxA7jb5nrcwhjzs4h8APyKdSXWGrz8NnkReQfoBYSLSDIwEZgGvCci92L9ELvJvgrPnt76r5RSPsLbDrkopZSqgAa6Ukr5CA10pZTyERroSinlIzTQlVLKR2igK6WUj9BAV0opH/H/ER703ld7pCMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Acurácia: 0.8333333333333334\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import linear_model\n",
    "from scipy.special import expit\n",
    "\n",
    "X = np.arange(12).reshape(-1, 1)\n",
    "y = np.array([0, 0, 0, 0,1,0, 1, 1, 1, 1, 1, 1])\n",
    "plt.plot(X, y, 'ko')\n",
    "\n",
    "# Ajusta o modelo de regressao logistica\n",
    "model = linear_model.LogisticRegression(C=1e5)\n",
    "model.fit(X, y)\n",
    "loss = expit(X * model.coef_ + model.intercept_).ravel()\n",
    "plt.plot(X, loss, color='red', linewidth=3)\n",
    "\n",
    "# Para comparar, ajustamos um modelo de regressao linear\n",
    "linear = linear_model.LinearRegression()\n",
    "linear.fit(X, y)\n",
    "plt.plot(X, linear.coef_ * X + linear.intercept_, linewidth=2, linestyle='dashed')\n",
    "plt.axhline(.5, color='.5')\n",
    "plt.show(True)\n",
    "\n",
    "p = model.predict_proba(X)\n",
    "print(\"Acurácia:\", model.score(X, y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Classificação de dados "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos inicialmente ler os dados."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Número de linhas e colunas na matriz de atributos: (310, 7)\n"
     ]
    },
    {
     "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>pelvic_incidence</th>\n",
       "      <th>pelvic_tilt</th>\n",
       "      <th>lumbar_lordosis_angle</th>\n",
       "      <th>sacral_slope</th>\n",
       "      <th>pelvic_radius</th>\n",
       "      <th>degree_spondylolisthesis</th>\n",
       "      <th>class</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>63.027817</td>\n",
       "      <td>22.552586</td>\n",
       "      <td>39.609117</td>\n",
       "      <td>40.475232</td>\n",
       "      <td>98.672917</td>\n",
       "      <td>-0.254400</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>39.056951</td>\n",
       "      <td>10.060991</td>\n",
       "      <td>25.015378</td>\n",
       "      <td>28.995960</td>\n",
       "      <td>114.405425</td>\n",
       "      <td>4.564259</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>68.832021</td>\n",
       "      <td>22.218482</td>\n",
       "      <td>50.092194</td>\n",
       "      <td>46.613539</td>\n",
       "      <td>105.985135</td>\n",
       "      <td>-3.530317</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>69.297008</td>\n",
       "      <td>24.652878</td>\n",
       "      <td>44.311238</td>\n",
       "      <td>44.644130</td>\n",
       "      <td>101.868495</td>\n",
       "      <td>11.211523</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>49.712859</td>\n",
       "      <td>9.652075</td>\n",
       "      <td>28.317406</td>\n",
       "      <td>40.060784</td>\n",
       "      <td>108.168725</td>\n",
       "      <td>7.918501</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>40.250200</td>\n",
       "      <td>13.921907</td>\n",
       "      <td>25.124950</td>\n",
       "      <td>26.328293</td>\n",
       "      <td>130.327871</td>\n",
       "      <td>2.230652</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>53.432928</td>\n",
       "      <td>15.864336</td>\n",
       "      <td>37.165934</td>\n",
       "      <td>37.568592</td>\n",
       "      <td>120.567523</td>\n",
       "      <td>5.988551</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>45.366754</td>\n",
       "      <td>10.755611</td>\n",
       "      <td>29.038349</td>\n",
       "      <td>34.611142</td>\n",
       "      <td>117.270067</td>\n",
       "      <td>-10.675871</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>43.790190</td>\n",
       "      <td>13.533753</td>\n",
       "      <td>42.690814</td>\n",
       "      <td>30.256437</td>\n",
       "      <td>125.002893</td>\n",
       "      <td>13.289018</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>36.686353</td>\n",
       "      <td>5.010884</td>\n",
       "      <td>41.948751</td>\n",
       "      <td>31.675469</td>\n",
       "      <td>84.241415</td>\n",
       "      <td>0.664437</td>\n",
       "      <td>Hernia</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   pelvic_incidence  pelvic_tilt  lumbar_lordosis_angle  sacral_slope  \\\n",
       "0         63.027817    22.552586              39.609117     40.475232   \n",
       "1         39.056951    10.060991              25.015378     28.995960   \n",
       "2         68.832021    22.218482              50.092194     46.613539   \n",
       "3         69.297008    24.652878              44.311238     44.644130   \n",
       "4         49.712859     9.652075              28.317406     40.060784   \n",
       "5         40.250200    13.921907              25.124950     26.328293   \n",
       "6         53.432928    15.864336              37.165934     37.568592   \n",
       "7         45.366754    10.755611              29.038349     34.611142   \n",
       "8         43.790190    13.533753              42.690814     30.256437   \n",
       "9         36.686353     5.010884              41.948751     31.675469   \n",
       "\n",
       "   pelvic_radius  degree_spondylolisthesis   class  \n",
       "0      98.672917                 -0.254400  Hernia  \n",
       "1     114.405425                  4.564259  Hernia  \n",
       "2     105.985135                 -3.530317  Hernia  \n",
       "3     101.868495                 11.211523  Hernia  \n",
       "4     108.168725                  7.918501  Hernia  \n",
       "5     130.327871                  2.230652  Hernia  \n",
       "6     120.567523                  5.988551  Hernia  \n",
       "7     117.270067                -10.675871  Hernia  \n",
       "8     125.002893                 13.289018  Hernia  \n",
       "9      84.241415                  0.664437  Hernia  "
      ]
     },
     "execution_count": 11,
     "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/winequality-red.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": "markdown",
   "metadata": {},
   "source": [
    "Convertendo para o formato Numpy e normalizando:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = data.to_numpy()\n",
    "nrow,ncol = data.shape\n",
    "y = data[:,-1]\n",
    "X = data[:,0:ncol-1]\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "scaler = StandardScaler().fit(X)\n",
    "X = scaler.transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Selecionamos os conjunto de treinamento e teste usando o método hold-out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "p = 0.2 # fraction of elements in the test set\n",
    "x_train, x_test, y_train, y_test = train_test_split(X, y, test_size = p, random_state = 42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Realizando a classificação por regressão logística:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Acurácia:  0.8548387096774194\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import metrics\n",
    "\n",
    "model = LogisticRegression(solver = 'lbfgs', multi_class = 'auto', max_iter = 1000)\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y_pred = model.predict(x_test)\n",
    "print('Acurácia: ', model.score(x_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Código completo:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Acurácia:  1.0\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn import metrics\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "#data = pd.read_csv('data/vertebralcolumn-3C.csv', header=(0))\n",
    "#data = pd.read_csv('data/winequality-red.csv', header=(0))\n",
    "data = pd.read_csv('data/iris.csv', header=(0))\n",
    "\n",
    "data = data.dropna(axis='rows') #remove NaN\n",
    "classes = np.array(pd.unique(data[data.columns[-1]]), dtype=str)  \n",
    "\n",
    "data = data.to_numpy()\n",
    "nrow,ncol = data.shape\n",
    "y = data[:,-1]\n",
    "X = data[:,0:ncol-1]\n",
    "\n",
    "p = 0.8 # fracao de elementos no conjunto de treinamento\n",
    "x_train, x_test, y_train, y_test = train_test_split(X, y, train_size = p)\n",
    "\n",
    "model = LogisticRegression(solver = 'lbfgs', multi_class = 'auto', max_iter = 1000)\n",
    "model.fit(x_train, y_train)\n",
    "\n",
    "y_pred = model.predict(x_test)\n",
    "print('Acurácia: ', model.score(x_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Região de separação"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para graficar a região de separação, precisamos instalar a bibliteca mlxtend: http://rasbt.github.io/mlxtend/installation/\n",
    "Pode ser usado: conda install -c conda-forge mlxtend"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uma propriedade importante da regressão logística é que a superfície de separação são hiperplanos (retas em duas dimensões, ou planos, em duas dimensões). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "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 numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.linear_model import LogisticRegression\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 = [(0, 0), (-2, -2), (2,0)]\n",
    "centers = [(0, 0), (-2, -2)]\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)\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.savefig('plot_ex.eps')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Training a classifier\n",
    "model = LogisticRegression(solver = 'lbfgs', multi_class = 'auto', max_iter = 1000)\n",
    "model.fit(X, y)\n",
    "# Plotting decision regions\n",
    "plot_decision_regions(X, y, clf=model, legend=2)\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('X2')\n",
    "#plt.savefig('logistic-region.eps')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para três classes:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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 numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "from sklearn.linear_model import LogisticRegression\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 = [(0, 0), (-2, -2), (2,0)]\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)\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.savefig('plot_ex.eps')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# Training a classifier\n",
    "model = LogisticRegression(solver = 'lbfgs', multi_class = 'auto', max_iter = 1000)\n",
    "model.fit(X, y)\n",
    "# Plotting decision regions\n",
    "plot_decision_regions(X, y, clf=model, legend=2)\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('X2')\n",
    "#plt.savefig('logistic-region.eps')\n",
    "plt.show()"
   ]
  },
  {
   "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",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}