第5.4节_分类（逻辑回归）.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-4-1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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",
    "\n",
    "# 读入学习数据\n",
    "train = np.loadtxt('images2.csv', delimiter=',', skiprows=1)\n",
    "train_x = train[:,0:2]\n",
    "train_y = train[:,2]\n",
    "\n",
    "# 初始化参数\n",
    "theta = np.random.rand(3)\n",
    "\n",
    "# 标准化\n",
    "mu = train_x.mean(axis=0)\n",
    "sigma = train_x.std(axis=0)\n",
    "def standardize(x):\n",
    "    return (x - mu) / sigma\n",
    "\n",
    "train_z = standardize(train_x)\n",
    "\n",
    "# 增加x0\n",
    "def to_matrix(x):\n",
    "    x0 = np.ones([x.shape[0], 1])\n",
    "    return np.hstack([x0, x])\n",
    "\n",
    "X = to_matrix(train_z)\n",
    "\n",
    "# 将标准化后的学习数据画成图形\n",
    "plt.plot(train_z[train_y == 1, 0], train_z[train_y == 1, 1], 'o')\n",
    "plt.plot(train_z[train_y == 0, 0], train_z[train_y == 0, 1], 'x')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-4-2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# sigmoid函数\n",
    "def f(x):\n",
    "    return 1 / (1 + np.exp(-np.dot(x, theta)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-4-3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "第1次: theta = [-0.30222713  4.53917982 -3.38661847]\n",
      "第2次: theta = [-0.30227415  4.53951923 -3.38691935]\n",
      "第3次: theta = [-0.30232115  4.53985859 -3.38722019]\n",
      "第4次: theta = [-0.30236815  4.5401979  -3.38752098]\n",
      "第5次: theta = [-0.30241513  4.54053716 -3.38782172]\n",
      "第6次: theta = [-0.3024621   4.54087637 -3.38812242]\n",
      "第7次: theta = [-0.30250906  4.54121552 -3.38842307]\n",
      "第8次: theta = [-0.30255601  4.54155463 -3.38872367]\n",
      "第9次: theta = [-0.30260295  4.54189368 -3.38902423]\n",
      "第10次: theta = [-0.30264988  4.54223268 -3.38932474]\n",
      "第11次: theta = [-0.30269679  4.54257163 -3.38962521]\n",
      "第12次: theta = [-0.3027437   4.54291053 -3.38992563]\n",
      "第13次: theta = [-0.30279059  4.54324937 -3.39022601]\n",
      "第14次: theta = [-0.30283747  4.54358817 -3.39052633]\n",
      "第15次: theta = [-0.30288435  4.54392691 -3.39082662]\n",
      "第16次: theta = [-0.30293121  4.5442656  -3.39112685]\n",
      "第17次: theta = [-0.30297805  4.54460424 -3.39142704]\n",
      "第18次: theta = [-0.30302489  4.54494283 -3.39172719]\n",
      "第19次: theta = [-0.30307172  4.54528137 -3.39202729]\n",
      "第20次: theta = [-0.30311854  4.54561986 -3.39232734]\n",
      "第21次: theta = [-0.30316534  4.54595829 -3.39262735]\n",
      "第22次: theta = [-0.30321213  4.54629668 -3.39292731]\n",
      "第23次: theta = [-0.30325892  4.54663501 -3.39322722]\n",
      "第24次: theta = [-0.30330569  4.54697329 -3.39352709]\n",
      "第25次: theta = [-0.30335245  4.54731152 -3.39382691]\n",
      "第26次: theta = [-0.3033992   4.5476497  -3.39412669]\n",
      "第27次: theta = [-0.30344594  4.54798783 -3.39442642]\n",
      "第28次: theta = [-0.30349266  4.5483259  -3.39472611]\n",
      "第29次: theta = [-0.30353938  4.54866393 -3.39502575]\n",
      "第30次: theta = [-0.30358608  4.5490019  -3.39532534]\n",
      "第31次: theta = [-0.30363278  4.54933983 -3.39562489]\n",
      "第32次: theta = [-0.30367946  4.5496777  -3.39592439]\n",
      "第33次: theta = [-0.30372613  4.55001552 -3.39622385]\n",
      "第34次: theta = [-0.30377279  4.55035329 -3.39652326]\n",
      "第35次: theta = [-0.30381944  4.55069101 -3.39682263]\n",
      "第36次: theta = [-0.30386608  4.55102867 -3.39712195]\n",
      "第37次: theta = [-0.30391271  4.55136629 -3.39742122]\n",
      "第38次: theta = [-0.30395933  4.55170385 -3.39772045]\n",
      "第39次: theta = [-0.30400593  4.55204137 -3.39801963]\n",
      "第40次: theta = [-0.30405253  4.55237883 -3.39831877]\n",
      "第41次: theta = [-0.30409911  4.55271624 -3.39861786]\n",
      "第42次: theta = [-0.30414569  4.55305361 -3.39891691]\n",
      "第43次: theta = [-0.30419225  4.55339092 -3.39921591]\n",
      "第44次: theta = [-0.3042388   4.55372817 -3.39951487]\n",
      "第45次: theta = [-0.30428534  4.55406538 -3.39981378]\n",
      "第46次: theta = [-0.30433187  4.55440254 -3.40011264]\n",
      "第47次: theta = [-0.30437838  4.55473965 -3.40041146]\n",
      "第48次: theta = [-0.30442489  4.5550767  -3.40071023]\n",
      "第49次: theta = [-0.30447139  4.55541371 -3.40100896]\n",
      "第50次: theta = [-0.30451787  4.55575066 -3.40130764]\n",
      "第51次: theta = [-0.30456435  4.55608756 -3.40160628]\n",
      "第52次: theta = [-0.30461081  4.55642441 -3.40190487]\n",
      "第53次: theta = [-0.30465726  4.55676122 -3.40220342]\n",
      "第54次: theta = [-0.3047037   4.55709797 -3.40250192]\n",
      "第55次: theta = [-0.30475013  4.55743467 -3.40280037]\n",
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      "第4944次: theta = [-0.45445919  5.79845206 -4.49894808]\n",
      "第4945次: theta = [-0.45448036  5.79864923 -4.49912141]\n",
      "第4946次: theta = [-0.45450153  5.79884639 -4.49929472]\n",
      "第4947次: theta = [-0.4545227   5.79904353 -4.49946802]\n",
      "第4948次: theta = [-0.45454386  5.79924065 -4.4996413 ]\n",
      "第4949次: theta = [-0.45456503  5.79943776 -4.49981457]\n",
      "第4950次: theta = [-0.45458618  5.79963485 -4.49998782]\n",
      "第4951次: theta = [-0.45460734  5.79983192 -4.50016106]\n",
      "第4952次: theta = [-0.4546285   5.80002898 -4.50033429]\n",
      "第4953次: theta = [-0.45464965  5.80022602 -4.5005075 ]\n",
      "第4954次: theta = [-0.4546708   5.80042305 -4.50068069]\n",
      "第4955次: theta = [-0.45469195  5.80062006 -4.50085387]\n",
      "第4956次: theta = [-0.45471309  5.80081705 -4.50102704]\n",
      "第4957次: theta = [-0.45473423  5.80101403 -4.50120019]\n",
      "第4958次: theta = [-0.45475537  5.80121099 -4.50137333]\n",
      "第4959次: theta = [-0.45477651  5.80140794 -4.50154645]\n",
      "第4960次: theta = [-0.45479765  5.80160486 -4.50171956]\n",
      "第4961次: theta = [-0.45481878  5.80180178 -4.50189265]\n",
      "第4962次: theta = [-0.45483991  5.80199867 -4.50206573]\n",
      "第4963次: theta = [-0.45486104  5.80219555 -4.50223879]\n",
      "第4964次: theta = [-0.45488217  5.80239242 -4.50241184]\n",
      "第4965次: theta = [-0.45490329  5.80258926 -4.50258488]\n",
      "第4966次: theta = [-0.45492441  5.80278609 -4.5027579 ]\n",
      "第4967次: theta = [-0.45494553  5.80298291 -4.5029309 ]\n",
      "第4968次: theta = [-0.45496665  5.80317971 -4.5031039 ]\n",
      "第4969次: theta = [-0.45498777  5.80337649 -4.50327687]\n",
      "第4970次: theta = [-0.45500888  5.80357326 -4.50344983]\n",
      "第4971次: theta = [-0.45502999  5.80377001 -4.50362278]\n",
      "第4972次: theta = [-0.4550511   5.80396674 -4.50379572]\n",
      "第4973次: theta = [-0.4550722   5.80416346 -4.50396863]\n",
      "第4974次: theta = [-0.4550933   5.80436016 -4.50414154]\n",
      "第4975次: theta = [-0.4551144   5.80455685 -4.50431443]\n",
      "第4976次: theta = [-0.4551355   5.80475352 -4.5044873 ]\n",
      "第4977次: theta = [-0.4551566   5.80495017 -4.50466016]\n",
      "第4978次: theta = [-0.45517769  5.80514681 -4.50483301]\n",
      "第4979次: theta = [-0.45519878  5.80534343 -4.50500584]\n",
      "第4980次: theta = [-0.45521987  5.80554003 -4.50517866]\n",
      "第4981次: theta = [-0.45524096  5.80573662 -4.50535146]\n",
      "第4982次: theta = [-0.45526204  5.80593319 -4.50552425]\n",
      "第4983次: theta = [-0.45528313  5.80612975 -4.50569702]\n",
      "第4984次: theta = [-0.45530421  5.80632629 -4.50586978]\n",
      "第4985次: theta = [-0.45532528  5.80652281 -4.50604252]\n",
      "第4986次: theta = [-0.45534636  5.80671932 -4.50621525]\n",
      "第4987次: theta = [-0.45536743  5.80691581 -4.50638797]\n",
      "第4988次: theta = [-0.4553885   5.80711229 -4.50656067]\n",
      "第4989次: theta = [-0.45540957  5.80730875 -4.50673336]\n",
      "第4990次: theta = [-0.45543064  5.80750519 -4.50690603]\n",
      "第4991次: theta = [-0.4554517   5.80770162 -4.50707868]\n",
      "第4992次: theta = [-0.45547276  5.80789803 -4.50725133]\n",
      "第4993次: theta = [-0.45549382  5.80809443 -4.50742396]\n",
      "第4994次: theta = [-0.45551488  5.80829081 -4.50759657]\n",
      "第4995次: theta = [-0.45553593  5.80848717 -4.50776917]\n",
      "第4996次: theta = [-0.45555698  5.80868352 -4.50794175]\n",
      "第4997次: theta = [-0.45557803  5.80887985 -4.50811432]\n",
      "第4998次: theta = [-0.45559908  5.80907616 -4.50828688]\n",
      "第4999次: theta = [-0.45562012  5.80927246 -4.50845942]\n",
      "第5000次: theta = [-0.45564117  5.80946874 -4.50863195]\n"
     ]
    }
   ],
   "source": [
    "# 学习率\n",
    "ETA = 1e-3\n",
    "\n",
    "# 重复次数\n",
    "epoch = 5000\n",
    "\n",
    "# 更新次数\n",
    "count = 0\n",
    "\n",
    "# 重复学习\n",
    "for _ in range(epoch):\n",
    "    theta = theta - ETA * np.dot(f(X) - train_y, X)\n",
    "    \n",
    "    # 日志输出\n",
    "    count += 1\n",
    "    print('第{}次: theta = {}'.format(count, theta))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-4-4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "x0 = np.linspace(-2, 2, 100)\n",
    "plt.plot(train_z[train_y == 1, 0], train_z[train_y == 1, 1], 'o')\n",
    "plt.plot(train_z[train_y == 0, 0], train_z[train_y == 0, 1], 'x')\n",
    "plt.plot(x0, -(theta[0] + theta[1] * x0) / theta[2], linestyle='dashed')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-4-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.91659356, 0.02986157])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(to_matrix(standardize([\n",
    "    [200,100], # 200×100的横向图片\n",
    "    [100,200] # 100×200的纵向图片\n",
    "])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 示例代码5-4-6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def classify(x):\n",
    "    return (f(x) >= 0.5).astype(np.int)\n",
    "\n",
    "classify(to_matrix(standardize([\n",
    "    [200,100], # 200×100的横向图片\n",
    "    [100,200] # 100×200的纵向图片\n",
    "])))"
   ]
  },
  {
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}