Logistic Regression 多分类.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn import datasets\n",
    "\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data[:,:2]\n",
    "y = iris.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "log_reg = LogisticRegression()\n",
    "log_reg.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "multi_class='ovr' 意味着默认对于多分类问题使用的是ovr\n",
    "\n",
    "如果想使用ovo需要显示的指定LogisticRegression(multi_class=\"multinomial\", solver=\"newton-cg\")\n",
    "\n",
    "### 通常ovo效果好一些"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.65789473684210531"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg.score(X_test, y_test)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_decision_boundary(model, axis):\n",
    "    \n",
    "    x0, x1 = np.meshgrid(\n",
    "        np.linspace(axis[0], axis[1], int((axis[1]-axis[0])*100)).reshape(-1, 1),\n",
    "        np.linspace(axis[2], axis[3], int((axis[3]-axis[2])*100)).reshape(-1, 1),\n",
    "    )\n",
    "    X_new = np.c_[x0.ravel(), x1.ravel()]\n",
    "\n",
    "    y_predict = model.predict(X_new)\n",
    "    zz = y_predict.reshape(x0.shape)\n",
    "\n",
    "    from matplotlib.colors import ListedColormap\n",
    "    custom_cmap = ListedColormap(['#EF9A9A','#FFF59D','#90CAF9'])\n",
    "    \n",
    "    plt.contourf(x0, x1, zz, linewidth=5, cmap=custom_cmap)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda\\lib\\site-packages\\matplotlib\\contour.py:960: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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7iXbLdPeHAAs55jYgtzGCzAp9B2bpw7zryWs5d9cdmE/g1su2xVfx43NuyXpY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\nfyu9jtofpqGZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_decision_boundary(log_reg, axis=[4, 8.5, 1.5, 4.5])\n",
    "plt.scatter(X[y==0,0], X[y==0,1])\n",
    "plt.scatter(X[y==1,0], X[y==1,1])\n",
    "plt.scatter(X[y==2,0], X[y==2,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 使用OVO进行多分类"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_reg2 = LogisticRegression(multi_class=\"multinomial\", solver=\"newton-cg\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.78947368421052633"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg2.fit(X_train, y_train)\n",
    "log_reg2.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\Anaconda\\lib\\site-packages\\matplotlib\\contour.py:960: UserWarning: The following kwargs were not used by contour: 'linewidth'\n",
      "  s)\n"
     ]
    },
    {
     "data": {
      "image/png": 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D06ZuG5pW3l4jzaYfldMPOVq505HOocZIS7H0xSWdJCOOo86t7guR0klSc9qCv2v2XZUE\nWoOUTr20XsCdeeyXuOAZGqZ0jqscEyLV0ulI5z/MKe8LNUZaiqEvGj4kGxkcJW6ccFS0cvnGw3hw\n7/TJY5dM38uq+a8Gr7mbUhuR8K7FDRt8ljYfuoRd+x7EJ7awa8Zb2XzokslmHzV2Oc7QEx/j1tJj\nbB4cZO7+/Zw/cBITi340uT/qvve8dDOv79sEwOv7NrHnpZsnRzqHGiMtxdEXl3SSSDKKOOrcA83e\nJv88uHc6yzceFvpb6oo8TrisSuPSTjWquHNiM+CTUcWnt92R6H6HnvgYP+AJNg0N4WZsGhriBzzB\n0BMfiz33iX/7S+5/Yz0lMzCjZMb9b6zniX/7y0Q1Se9Qw48RKtJ5oNnXsikr/rzKa6NPU6io4q2l\nx9gzUPczMzDAraXHYs998I31YHU/U2bl7SKo4ccKFeksqqI0+9Cr/FBRxc2DTX5mmmyv1SwOrMHK\nUqWGHyNUpLNo8nwJJwuhoopz9zf5mWmyvVbImLD0Bv0sxAgV6VwyfS+NIp3l7flS1EYfcpUfKqp4\n/sBJzCjV/cyUSpw/cFLsuUsOORXqhyG6l7eLoIYfK8ko4qhzV81/tabpl//Up3Sy1gur+lBN/7g5\n5/Cn877IzKG5gDFzaC5/Ou+LiZMsE4t+xGUsYt7EBObOvIkJLmPRlJROM4uO/y6nHXIqA+7gzoA7\npx1yKouO/26imqR3xMYyzWwG8BtgeuX41e7+pbpjpgM/BE4FXgE+4u7Pdr3aGFERyCSTJ5PEIx/e\nPY0tlTEMWyYGeXj3tMn7umD2bja8OjRZ0wWzpz5GFtMyp+1az4zxOxjcvw2+3Tzv3tCdN8Kj94OX\nwAbg3afBBy4+sL/JxMtW3L52DSufH2PzgDG35Kw4ZiHnnl5+49Xtz42x8on72Pz6OHPfNMqKRUs5\n920LJ8/7+XNfbzjRMqmoqOKaZz7Ni7sfnLx95PASlh37rcnbUZMrt40cR2n8SQBKDLJt5Dhm1tx3\n1OTKRcd/l0Udfj+dTuEMKY81FVnsPHwzM2DE3Xea2TTgt8AKd7+/5pi/Bk5y90+Z2SXAf3L3j0Td\nb7fn4ddPl4Ty5ZMr37IdoOm+kA30mq2zpkzTLHMuHt3FKcP7ImuK+n5C1Txt13pGdq6eOqhsaBp8\n8M/iG/OdN8Ijaw/efvLp5aZfP/Gyjfu+fe0artowNiW9MqNU4qqjF8JRx3LV+l+zZ//EgX2DQ1x1\n6tnwwjMNzgv/QSb1zb6q2vTf8cLqKZMrofyu11//ydd56I0ny1M4awaz1dZcP7kSypeSkv52EXW/\nQJDHLGJNeZBkHn7sJR0v21m5Oa3yp/5fifOB6ytfrwbOqvxDkZqoCGRWkyejpmnG1ZRFzSOlX3Y+\nlfLR+6O3J5h4ufL5sYZRxZXPl1f2tc0eYM/+CVY+cV+T88oTLUNq1Oxrt0dNroyawgnh4qCdTuEM\nKY81FV1L1/DNbNDMHgG2Ar9y9wfqDjkK2ADg7hPAduDNDe5nuZmtM7N1L493dyZMVAQyq3hkVEwu\nrqa0a55z6WCyqZTe5Lutbk9w35sHGq8dNg8Ym19v/HO0+fXxpuc1m3SZlqjJlVFTOCFcHDTqfrOa\nlpnHmoqupYbv7vvd/WRgPrDEzOovEzb6m3XQtSJ3X+Xui9198eGj3V2pRkUgs4pHRsXk4mpKs+bJ\nF2ZbmErZlDX5bqvbE9z33FLjy45zS87cNzX+OZr7ptGm5zWbdJmWqMmVUVM4IVwctNMpnCHlsaai\nayul4+7bgHuAD9bt2ggcDWBmQ8BsINW4SVQEMqvJk1HTNONqSqvmKSmcFqdSNvTu06K3J7jvFccs\nbBhVXHHMQlYsWsqMwanZgxmDQ6xYtLTJeeWJliEdObwkcnvU5MqoKZwQLg7a6RTOkPJYU9G1ktJ5\nC7DP3beZ2TBwNvDVusNuAz4O/D/gIuAuT/nT0VuZLpl24qU6VC1qmmazmkJPy2wYt2xjKuVBqmmc\nZimdBPd97unLYC1NUzpA45TO2xY2PO/p2eFesAVYduy3IlM61TROo5TOTC5qOoUTwk2u7HQKZ0h5\nrKnoWknpnET5BdlByj3rZ+5+tZldDaxz99sq0c0fAadQXtlf4u7/HnW/3U7pxOmVDwTvhmDZ+rjY\nZYJYZseP22DfSv/G5KlR8ci42F+SDwVPcm4eKSKZniQpndiGH0qaDT+LiGNeBW32UbHLBLHMjh8X\nmu5b6d+IjEeuGRmJjP1FnRvXuJOcm0ehoqLSWNBYZi8o+geCd0Pwd83GxS5DfRB51P1G7Ftx4g2R\n8ci42F+SDwVPcm4eKSJZHH3xASi9OLWyHamMR4iLXYb6IPJO7reyb9bujQ13j+5+gZ1Nfjaqsb8k\nHwqe5Nw8UkSyOPpihd9LUyvbkeosnLjYZZLIZ6eP22FN48NHxcb+knwoeJJz80gRyeLoi4ZftA8E\n74bUh57FxS6TRD47fdwWamoWj4yL/SX5UPAk5+aRIpLF0ReXdIr0geBJZTbdMi52mSTymeRxY2qa\nBuz4P//3oLRM3AeRR0Ur4yQ5N4/0IefF0RcpnX5R9FHGWVr55EezLkGkJUlSOn2xwu8HeWj2UWOK\ngcjxybHndipmZPOBx/0nRobmtjV+974Xr+WpbTfjlDAGOGHOh1l65OVA2Jx90TL8oTL6yv63Tw2/\nB+Sl2deOKd70+jhXrf81QLlx149P9tLk7dvfuSj63E5FPCYfuPigmndObObeTV+ZPLw2W16777g5\n53Dfi9cytm31gbumNHn7L/z4KTn7Wbs3cvbjnwdI3JjrM/zdvO8Q6jP69c9j3u631/XFi7a9Kk+f\nSBU1phiIHJ8ce26nYkY2N3rcVsfvPrXt5oZ3/dS2m4Pm7IuW4c9inLM0pxV+QeWl0VdFjSkGIscn\nx57bqZiRzc3uPyo/Xt3nTYZfO6WgOfuiZfizGOcszWmFX0B5a/ZA5JhiIHJ8cuy5nYoZ2dzs/lsZ\nv2tN/uoYA0Fz9kXL8GcxzlmaU8MvkDxdwqkXNaYYiByfHHtup2JGNjd73C++5+TYbPkJcz7c8K5P\nmPPhoDn7omX4sxjnLM3pkk5B5LXRV1VfXG2atIkYn3xu5T66ntKJGdkcVfPTO6Oz5dU0TqOUzh8q\nDx8iSVO0DH+W45zlYMrh51xHjT7UGOKAj/uVW77DjW/smvzcgIsPGeGLF/xV8MeN8tn73hzZUBQL\nlCwoh9+jOm72tSOBd7xWvg1hm36Cx/3KLd/hp2/sgsrn3pegfPuW78Q3/UDf7+3PjXHvpnuaxv4U\nC5Qi0jX8nOr4Ek6oMcQBH/fGmmY/yay8PeDjRln5xH2RsT/FAqWItMLPmcTX6kONIQ74uE3Ck023\nd+txo8RFNhULlCLSCj9HuvLCbKgxxAEft9kPYUs/nIG+36jIZu1/m+0XySM1/JzoWgon1BjigI97\n8SEjUB8ecC9vD/i4URpFNmtjf4oFShHpkk4OdDVyGWoMccDH/eIFfwWdpnQCfb/1kc36wWqKBUoR\nKZaZobxn6xtKEoGMOjdQtLKbUzg1Qjlf+jUWq1hmARW22XcagYw6F4JFK7s5hXPFiTeo6eeEYrGd\n0TX8DBSy2UOyCGTUuQGjlUGmcErmFIvtjBp+ivI8C6clSSKQUeemHK1MMoVzxYk3dHyudI9isZ1R\nw09JoRt9VZIIZNS5KUcrk07hVNPPnmKxnVHDD6zwq/paSSKQUeemGK3syhROyZxisZ3Ri7YB9Uyj\nr0oSgWzl3MDRym5+Vq5ewM2WYrGdiW34ZnY08ENgLuV3u69y95V1x5wB3Ao8U9l0s7tf3d1Si6PV\nRp8oMpjVRMwENd0+MsLKo49k8+uj5e93ZGRyNDLvWhyk/nPftrDjBn/72jWsfH6MzQPG3JKz4piF\nnHt64Dew0b9xw3YdN+ccPS9tamWFPwH8vbs/ZGajwHoz+5W7/67uuHvd/UPdL7FY2mn2HUcG8zgR\nEyJr6nZEMrTb167hqg1j7BksX/XcNGhctWEM1jLZ9EOs8hU3lJBir+G7+yZ3f6jy9TgwBuTz89Qy\n1s4lnESRwTxOxIypqWgRyZXPj7FnYOpfjz0DA6x8fmzKtm6/gKu4oYTU1ou2ZrYAOAV4oMHu95rZ\no2Z2h5md2OT85Wa2zszWvTye8AOqc6bd6/WJIoN5nIgZU1OwDyoPZPOAtbW9WxQ3lJBabvhmNhO4\nCficu++o2/0Q8DZ3fzfwTeCWRvfh7qvcfbG7Lz58NOEHVOdIJy/OJooM5nEiZkxNwT6oPJC5pcYj\nRxpt7+YqX3FDCamlhm9m0yg3+39195vr97v7DnffWfl6DTDNzA7vaqU5lCRymSgymMeJmDE1FS0i\nueKYhcwoTZ3IP6NUYsUxYV9vUNxQQmolpWPA94Exd/96k2PmAlvc3c1sCeV/SF7paqU5kzRymSgy\nmOeJmE32hYxIhnDu6ctgLS2ndLr1Aq7ihhJS7LRMM/uPwL3A4xz4EKJ/BI4BcPdvm9lngE9TTvTs\nBj7v7muj7reo0zJ7LlsvXaNcvqQh6LRMd/8tEPlKlbtfB/R8jKDrzT6PWfo4d94Ij94PXgIbgHef\nBh+4OOuqckFvxpK802iFFgVp9r/82YF0SzW3/rt13X2cbrrzRnhkbbnZQ/m/j6wtbxdAc3Yk39Tw\nYwSbhZNVlj6JR+9vb7uI5IoafoSg1+uzytIn4aX2tvcprfIlrzQ8rYFUXpiddWjj5h46S5+EDTRu\n7qZ1g0gR6G9qndRSOFll6ZN492ntbe9jWuVLHqnh10g1cvmuxfDBPzuwop91aPl2nlM6H7gYTj79\nwIreBsq3ldJpSE1f8kaXdIA148P8y95ZvHj1AEfOLvEPZ+7kgj/ZE39iUnEjgfMY25x/LPz7WLmm\n0dnl270qj8+/SAJ9v8K/56QR/ttrs3lh+yCO8cL2QS7/xSi3PD4j/uSQ8hjbzGNNoXTpe9UqX/Kk\nrxv+nEsH+dpdM9m9b+rTsHvfAF+7a2ZGVVXkMbaZx5pC6eL3qqYvedG3Db96vf7F7Y2fgmbbU5PH\n2GYeawqln75X6Rt91/Dr30h15OzGGfJm21OT1QjkKHmsKZQuf69a5Use9FXDb5TC+YczdzI8bWpz\nH55WfuE2U3mMbeaxplACfK9q+pK1vkjpRMUtq2mcr901kxe3p5zSiZLVCOSi1RRKP32v0jdixyOH\nktZ4ZI0z7n23r13T8tz6g2QQvdRETUkiyXjknr6ko2bf+25fu4arNoyxaXAAN2PT4ABXbRjj9rUt\npGn6KWYqQo82/GATLiV3Vj4/xp6BqT/GewYGWPn8WPzJGcVMdS1fstJzDV+Nvr9sHmj82TzNtk+h\n6KX0mZ5q+Gr2/WduqfFrUM22T5FhzFSrfMlCzzR8Nfv+tOKYhcwoTY3VziiVWHFMCx+OnnHMVE1f\n0lb4hq/r9f3t3NOXcdXRC5m3v4S5M29/iauObjGlk4OJpWr6kqZC5/DV6AXKTb/lGGa9uImlIj2k\nsCt8NXsRkfYUruHrEo70Gl3WkbQUquGr0UuvUtOXNBTiGr4avYhIcrlf4avZS7/QKl9Cy+0KX41e\nRKS7Ylf4Zna0md1tZmNm9qSZrWhwjJnZP5vZ02b2mJm9J0lRavbSr7TKl5BaWeFPAH/v7g+Z2Siw\n3sx+5e6/qznmHOD4yp//AHyr8t+2qdnXyGB0r2RvxYk3aISyBBG7wnf3Te7+UOXrcWAMOKrusPOB\nH3rZ/cAcM5vXbjFq9jU0uldEuqytF23NbAFwCvBA3a6jgA01tzdy8D8KTSlb30BGo3slH3RpR0Jo\nueGb2UzgJuBz7r6jfneDUw4aV2hmy81snZmte3l8HNCqvimN7u17avrSbS01fDObRrnZ/6u739zg\nkI3A0TW35wMv1h/k7qvcfbG7Lz58dFTNPkqGo3tFpDe1ktIx4PvAmLt/vclhtwF/XknrnAZsd/dN\nUfc7eFjbtfaXjEf3Sj5olS/d1EpKZynwMeBxM3uksu0fgWMA3P3bwBpgGfA08DrwF90vtc9U0zhK\n6YhIl8Q2fHf/LY2v0dce48DfdKsoqdDoXkExTeme3I9WEBFd2pHuUMMXEekTavgiBaFVviSlhi8i\n0ifU8EUKRKt8SUINX6Rg1PSlU2r4IgWkpi+dUMMXEekTavgiIn1CDV+koHRZR9qlhi9SYGr60g41\nfJGCU9OXVqnhi4j0CTV8EZEvhpwGAAAFzklEQVQ+oYYv0gN0WUdaoYYv0iPU9CWOGr6ISJ9Qwxfp\nIVrlSxQ1fJEeo6Yvzajhi4j0CTV8kR6kVb40ooYvItIn1PBFepRW+VJPDV+kh6npSy01fBGRPqGG\nL9LjtMqXKjV8kT6gpi+ghi8i0jdiG76Z/Q8z22pmTzTZf4aZbTezRyp/rux+mSKSlFb50soK/wfA\nB2OOudfdT678uTp5WSISgpp+f4tt+O7+G+DVFGoREZGAhrp0P+81s0eBF4H/4u5PNjrIzJYDyys3\n99rIJxpeJsrQ4cDLWRfRQB7rUk2tyWFNn8hhTUAun6tc1vTOTk80d48/yGwB8At3X9Rg3yyg5O47\nzWwZsNLdj2/hPte5++L2Sw4njzVBPutSTa1RTa3LY129VlPilI6773D3nZWv1wDTzOzwpPcrIiLd\nlbjhm9lcM7PK10sq9/lK0vsVEZHuir2Gb2Y/Bs4ADjezjcCXgGkA7v5t4CLg02Y2AewGLvFWrhPB\nqk6LDiiPNUE+61JNrVFNrctjXT1VU0vX8EVEpPj0TlsRkT6hhi8i0idSafhmNmhmD5vZLxrsm25m\nPzWzp83sgUoENOuaLjOzl2rGRXwyhXqeNbPHK4+3rsF+M7N/rjxPj5nZe0LX1GJdqY/WMLM5Zrba\nzJ4yszEze2/d/tSfqxZqSvV5MrN31jzWI2a2w8w+V3dMqs9TizVlMqrFzP7OzJ40syfM7MdmNqNu\nf+p9qoWa2u9T7h78D/B54H9RzvLX7/tr4NuVry8BfpqDmi4DrkujjprHfBY4PGL/MuAOwIDTgAdy\nUtcZjZ7DwDVdD3yy8vUhwJysn6sWakr9eap57EFgM/C2rJ+nFmrK4ufpKOAZYLhy+2fAZXXHpNqn\nWqyp7T4VfIVvZvOBc4HvNTnkfMp/WQBWA2dVY54Z1pRH5wM/9LL7gTlmNi/rotJm5Tf6vQ/4PoC7\nv+Hu2+oOS/W5arGmLJ0F/NHdn6vbnuXPVLOasjIEDJvZEPAmylMDaqXep1qoqW1pXNL5BvAFoNRk\n/1HABgB3nwC2A2/OuCaACyu/5q42s6MD1wPgwJ1mtt7KIyjqTT5PFRsr27KuCyqjNczsDjM7MXA9\nbwdeAv5n5ZLc98xspO6YtJ+rVmqCdJ+nWpcAP26wPaufKWheE6T8PLn7C8B/B54HNgHb3f3OusNS\n7VMt1gRt9qmgDd/MPgRsdff1UYc12BYsK9piTT8HFrj7ScCvOfAve0hL3f09wDnA35jZ++r2p/o8\n1Yir6yHKv5a/G/gmcEvgeoaA9wDfcvdTgF3Af607Ju3nqpWa0n6eADCzQ4DzgBsb7W6wLfjPVExN\nqT9PZnYo5RX8scCRwIiZfbT+sAanhuxTrdTUdp8KvcJfCpxnZs8CPwHONLP6+awbgaMBKr+6zCbs\ndM7Ymtz9FXffW7n5XeDUgPVUH/PFyn+3Av8bWFJ3yOTzVDGfLvyKl7QuT3+0xkZgo7s/ULm9mnKz\nrT8mzecqtqYMnqeqc4CH3H1Lg32Z/ExF1ZTR83Q28Iy7v+Tu+4CbgdPrjkm7T8XW1EmfCtrw3f1y\nd5/v7gso/wp3l7vX/yt1G/DxytcXVY4J9i9nKzXVXcc8DxgLVU/l8UbMbLT6NfABoH6S6G3An1eS\nFadR/hVvU9Z1WcqjNdx9M7DBzKoTA88Cfld3WKrPVSs1pf081fjPNL90kvrPVFxNGT1PzwOnmdmb\nKo99Fgf/nU+1T7VSU0d9KuQrzXWvKJ9B5dV34GrgvMrXMyj/avc08CDw9hzUdC3wJPAocDdwQuA6\n3l55rEcrj3tFZfungE9VvjbgX4A/Ao8Di1N4flqp6zM1z9X9wOkp1HUysA54jPKv/Ifm4LmKqymL\n5+lNlJvl7JptWT9PcTWl/jxVHvfLwFOUFzQ/AqZn3adaqKntPqXRCiIifULvtBUR6RNq+CIifUIN\nX0SkT6jhi4j0CTV8EZE+oYYvItIn1PBFRPrE/weYt3fZv8ti/wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "plot_decision_boundary(log_reg2, axis=[4, 8.5, 1.5, 4.5])\n",
    "plt.scatter(X[y==0,0], X[y==0,1])\n",
    "plt.scatter(X[y==1,0], X[y==1,1])\n",
    "plt.scatter(X[y==2,0], X[y==2,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 使用所有的数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = iris.data\n",
    "y = iris.target\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=666)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.94736842105263153"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg = LogisticRegression()\n",
    "log_reg.fit(X_train, y_train)\n",
    "log_reg.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg2 = LogisticRegression(multi_class=\"multinomial\", solver=\"newton-cg\")\n",
    "log_reg2.fit(X_train, y_train)\n",
    "log_reg2.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### sklearn中的oVR和OVO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.multiclass import OneVsRestClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_reg_ovr = OneVsRestClassifier(log_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OneVsRestClassifier(estimator=LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False),\n",
       "          n_jobs=1)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg_ovr.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.94736842105263153"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg_ovr.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.multiclass import OneVsOneClassifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "log_reg_ovo = OneVsOneClassifier(log_reg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "OneVsOneClassifier(estimator=LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False),\n",
       "          n_jobs=1)"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg_ovo.fit(X_train,y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "log_reg_ovo.score(X_test,y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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