{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from numpy import *\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 训练算法 使用梯度上升找到最佳参数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 使用 Logistic 回归在简单数据集上的分类\n",
    "\n",
    "# 解析数据\n",
    "def loadDataSet(file_name):\n",
    "    '''\n",
    "    Desc: \n",
    "        加载并解析数据\n",
    "    Args:\n",
    "        file_name -- 文件名称，要解析的文件所在磁盘位置\n",
    "    Returns:\n",
    "        dataMat -- 原始数据的特征\n",
    "        labelMat -- 原始数据的标签，也就是每条样本对应的类别\n",
    "    '''\n",
    "    # dataMat为原始数据， labelMat为原始数据的标签\n",
    "    dataMat = []; labelMat = []\n",
    "    fr = open(file_name)\n",
    "    for line in fr.readlines():\n",
    "        lineArr = line.strip().split()\n",
    "        # 为了方便计算，我们将 X0 的值设为 1.0 ，也就是在每一行的开头添加一个 1.0 作为 X0\n",
    "        dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])\n",
    "        labelMat.append(int(lineArr[2]))\n",
    "    return dataMat,labelMat"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# sigmoid跳跃函数\n",
    "def sigmoid(inX):\n",
    "    return 1.0/(1+exp(-inX))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 正常的处理方案\n",
    "# 两个参数：第一个参数==> dataMatIn 是一个2维NumPy数组，每列分别代表每个不同的特征，每行则代表每个训练样本。\n",
    "# 第二个参数==> classLabels 是类别标签，它是一个 1*100 的行向量。为了便于矩阵计算，需要将该行向量转换为列向量，做法是将原向量转置，再将它赋值给labelMat。\n",
    "def gradAscent(dataMatIn, classLabels):\n",
    "    '''\n",
    "    Desc:\n",
    "        正常的梯度上升法\n",
    "    Args:\n",
    "        dataMatIn -- 输入的 数据的特征 List\n",
    "        classLabels -- 输入的数据的类别标签\n",
    "    Returns:\n",
    "        array(weights) -- 得到的最佳回归系数\n",
    "    '''\n",
    "\n",
    "    # 转化为矩阵[[1,1,2],[1,1,2]....]\n",
    "    dataMatrix = mat(dataMatIn)             # 转换为 NumPy 矩阵\n",
    "    # 转化为矩阵[[0,1,0,1,0,1.....]]，并转制[[0],[1],[0].....]\n",
    "    # transpose() 行列转置函数\n",
    "    # 将行向量转化为列向量   =>  矩阵的转置\n",
    "    labelMat = mat(classLabels).transpose() # 首先将数组转换为 NumPy 矩阵，然后再将行向量转置为列向量\n",
    "    # m->数据量，样本数 n->特征数\n",
    "    m,n = shape(dataMatrix)\n",
    "    # print m, n, '__'*10, shape(dataMatrix.transpose()), '__'*100\n",
    "    # alpha代表向目标移动的步长\n",
    "    alpha = 0.001\n",
    "    # 迭代次数\n",
    "    maxCycles = 500\n",
    "    # 生成一个长度和特征数相同的矩阵，此处n为3 -> [[1],[1],[1]]\n",
    "    # weights 代表回归系数， 此处的 ones((n,1)) 创建一个长度和特征数相同的矩阵，其中的数全部都是 1\n",
    "    weights = ones((n,1))\n",
    "    for k in range(maxCycles):              #heavy on matrix operations\n",
    "        # m*3 的矩阵 * 3*1 的单位矩阵 ＝ m*1的矩阵\n",
    "        # 那么乘上单位矩阵的意义，就代表：通过公式得到的理论值\n",
    "        # 参考地址： 矩阵乘法的本质是什么？ https://www.zhihu.com/question/21351965/answer/31050145\n",
    "        # print 'dataMatrix====', dataMatrix \n",
    "        # print 'weights====', weights\n",
    "        # n*3   *  3*1  = n*1\n",
    "        h = sigmoid(dataMatrix*weights)     # 矩阵乘法\n",
    "        # print 'hhhhhhh====', h\n",
    "        # labelMat是实际值\n",
    "        error = (labelMat - h)              # 向量相减\n",
    "        # 0.001* (3*m)*(m*1) 表示在每一个列上的一个误差情况，最后得出 x1,x2,xn的系数的偏移量\n",
    "        weights = weights + alpha * dataMatrix.transpose() * error # 矩阵乘法，最后得到回归系数\n",
    "    return array(weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 4.12414349],\n",
       "       [ 0.48007329],\n",
       "       [-0.6168482 ]])"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataArr, labelMat = loadDataSet(\"testSet.txt\")\n",
    "dataArr = mat(dataArr)\n",
    "#labelMat = mat(labelMat)\n",
    "\n",
    "\n",
    "gradAscent(dataArr, labelMat)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分析数据：画出决策边界"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 可视化展示\n",
    "def plotBestFit(weights):\n",
    "    '''\n",
    "        Desc:\n",
    "            将我们得到的数据可视化展示出来\n",
    "        Args:\n",
    "            dataArr:样本数据的特征\n",
    "            labelMat:样本数据的类别标签，即目标变量\n",
    "            weights:回归系数\n",
    "        Returns:\n",
    "            None\n",
    "    '''\n",
    "    \n",
    "    n = shape(dataArr)[0]\n",
    "    xcord1 = []; ycord1 = []\n",
    "    xcord2 = []; ycord2 = []\n",
    "    for i in range(n):\n",
    "        if int(labelMat[i])== 1:\n",
    "            xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2])\n",
    "        else:\n",
    "            xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2])\n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)\n",
    "    ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')\n",
    "    ax.scatter(xcord2, ycord2, s=30, c='green')\n",
    "    x = arange(-3.0, 3.0, 0.1)\n",
    "    \"\"\"\n",
    "    y的由来，卧槽，是不是没看懂？\n",
    "    首先理论上是这个样子的。\n",
    "    dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])\n",
    "    w0*x0+w1*x1+w2*x2=f(x)\n",
    "    x0最开始就设置为1叻， x2就是我们画图的y值，而f(x)被我们磨合误差给算到w0,w1,w2身上去了\n",
    "    所以： w0+w1*x+w2*y=0 => y = (-w0-w1*x)/w2   \n",
    "    \"\"\"\n",
    "    y = (-weights[0]-weights[1]*x)/weights[2]\n",
    "    ax.plot(x, y)\n",
    "    plt.xlabel('X'); plt.ylabel('Y')\n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1152134e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "weights = gradAscent(dataArr, labelMat)\n",
    "plotBestFit(weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 训练算法：随机梯度上升"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 随机梯度上升\n",
    "# 梯度上升优化算法在每次更新数据集时都需要遍历整个数据集，计算复杂都较高\n",
    "# 随机梯度上升一次只用一个样本点来更新回归系数\n",
    "def stocGradAscent0(dataMatrix, classLabels):\n",
    "    '''\n",
    "    Desc:\n",
    "        随机梯度上升，只使用一个样本点来更新回归系数\n",
    "    Args:\n",
    "        dataMatrix -- 输入数据的数据特征（除去最后一列）\n",
    "        classLabels -- 输入数据的类别标签（最后一列数据）\n",
    "    Returns:\n",
    "        weights -- 得到的最佳回归系数\n",
    "    '''\n",
    "    m,n = shape(dataMatrix)\n",
    "    alpha = 0.01\n",
    "    # n*1的矩阵\n",
    "    # 函数ones创建一个全1的数组\n",
    "    weights = ones(n)   # 初始化长度为n的数组，元素全部为 1\n",
    "    for i in range(m):\n",
    "        # sum(dataMatrix[i]*weights)为了求 f(x)的值， f(x)=a1*x1+b2*x2+..+nn*xn,此处求出的 h 是一个具体的数值，而不是一个矩阵\n",
    "        h = sigmoid(sum(dataMatrix[i]*weights))\n",
    "        # print 'dataMatrix[i]===', dataMatrix[i]\n",
    "        # 计算真实类别与预测类别之间的差值，然后按照该差值调整回归系数\n",
    "        error = classLabels[i] - h\n",
    "        # 0.01*(1*1)*(1*n)\n",
    "     #   print (weights, \"*\"*10 , dataMatrix[i], \"*\"*10 , error)\n",
    "        weights = weights + alpha * error * dataMatrix[i]\n",
    "    return weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Vz9x4Nj8+qxsx4d5Iqb5P9jY81dTByVFVS4A6/7eo6rPAs+GJyJjQWb/7CI/m\n5PLRhn10Tojn/105gOvPSSEu3JP3Tqrvk72br3iM4xwvjhsTyXYcLObx+bn8c/UuEuJj+dW4ftx6\nfhotmzs0ec+YILDEYSKPCwqs+4pO8OzHebyxbAexzYQ7R/bmrgt7k9gqLizPb0woWeIwkcfBAuuR\nE2XM/HQLLy/ZSll5BTdkpXDvxel0btsi5M/tqGAla6uteIIlDmOC4ERZOa8t3cbzCzdzuLiMywd1\n55ej+5KW1Nrp0MIjWMnaaiueYInDmCbwlVfw15U7eWrBJvYcOcFFGZ14aEwGA5ITnQ6tbvbJ3jSB\nJQ5j6lJLF0xFQls+XLKBx+blsuXAMYaktuPJGwZzbq+ODgTZCPbJ3jSBJQ5j6lItaSiwOO1spo38\nGWvf+Iq+Xdrw4s8yufTMzj/cSMmYCGaJw0SeEHXDfN2tL9kX/pylZwyix+E9PHbtIK48O5lm4Z68\nZ4zDLHGYyBPkbphNHVN4dMQt5GScT8djh/nP+dO5cfVc4qeXBfV5GswFw41rfG6rmUQNSxzG1KLg\n8HGeHH8ffx9wMa3KSvjl4te5fcU/aVN63NnA3Liek9VMooolDmOqOXi0hOcXbuYvS7dD/wu5fcX7\n/OsXf6XDcWscjQFLHMaccrTEx0uLt/DS4q0Ul/q4dmgK9917Od1317AvhnXBmChmicNEvRJfObO/\n2MGzn+Rx6Fgp4wd05cExfenTOQGu2eZ0eJHFjfUZEzBLHMYbQtDglFco//hqJ08u2ETB4eMM79OR\nh8f2Y3BKuyYG2wDR2oC6sT5jAmaJw3hDEBscVWXet3t5NCeXTfuOMrBHIo/8dCAXpCc1McgANOX3\nsRFMxmGWOExUWbr5II/M3cCq/MP0SmrN8xOHMH5AV29N3ovkKxLjCZY4zA9FaBfKNwWFZOfksmjj\nfrq2bcEjPz2Lnw7pQaxTGykZ42GOJg4RGQc8BTQDXlLVP1W7X/z3TwCKgVtV9auwBxpNIqwPeuuB\nYzw2L5cP1uymXas4fjvhTG457wxaxHlwI6UITerGexxLHCLSDHgOGA3sBJaLyPuq+m2V08YD6f6v\nYcAL/n+NV4Wp8dtTeIKnPtrEOyvyad4shikX9+GOkb1o28LDGylFQlK3+kxEcPKKIwvIU9UtACLy\nFnAFUDVxXAG8pqoKfCEi7USkm6ruDn+4Jiga2/g1sME5XFzKC59uZtZn26hQZeKwVKZcnE6nhPhG\nBhwi0dpUbFy+AAANXElEQVSA2pVRRHAycSQD+VVu7+T0q4mazkkGLHFEm3oanOOl5fz5861MX7iZ\nohIfVw1O5oHRfUnp0CpMAQbIGlDjYRFTHBeRScAkgNTUVIejMeFSVl7BW8vzefqjTewvKuHSMzvz\n0NgM+nVt63RoxkQsJxNHAZBS5XYP/7FAzwFAVWcCMwEyMzM1eGFGGY90oVRUKP+7ZhePz9/I9oPF\nnJPWnhcmDiEzrYPToRkT8ZxMHMuBdBHpSWUyuAG4qdo57wP3+Osfw4BCq2+EmMu7UFSVhbn7yc7J\nZf3uI/TrmsCfbz2HizI6eWsuRmN4JKmbyOdY4lBVn4jcA+RQORz3FVVdJyKT/fdPB+ZQORQ3j8rh\nuLc5Fa9potpGU53UgMZvxbZDZM/N5ctth0jt0IqnbhjMTwZ2JyZaNlJyeVI30UMqByxFlszMTF2x\nYoXTYZiq6roaqOc9uGHPER7NyWXB+n10Sojn3kvSuT4zheaxUTZ5z+ZxmBASkZWqmtmQcyOmOG4i\nz46DxTyxYCPvrSqgTXwsD4/N4LbhabRqHqVv20iYx2EiQpT+DzRutr+ohGc/3sQbX+4gRoQ7R/Zm\n8oW9aNequdOhGWOwxGFc5MiJMl5ctIWXl2ylxFfBdZkp3HdJOl0TWzgdmjGmCkscxnEnysp5bek2\nnl+4mcPFZVw2sBsPjsmgZ1Jrp0MzxtTAEocJjxqGkvokhr+dcxlPTlvIniMnGNm3E1PHZjAgOdGh\nII0xDWGJw4RHlVE/qsqH3+zh0Xm5bNl/jLPbteCJ6wdzXu+ODgboATaPw7iEJQ4TVks2HeCRuRtY\nW1BIeuc2zLxlKKP7d4n8yXvBYENujUtY4jBhsTr/MNk5G/gs7yDJ7Vry6LWDuOrsZJq5ZfKezZEw\npsEscZiQyttXxKM5G5m7bg8dWzfn95f1Z+K5qcTHumwjJZsjYUyDWeIA+7QZAgWHj/PUgo38beVO\nWsY144FL+/KLET1pEx9lbzl7b5kIFGX/i2thnzaD5tCxUp7/JI/XvtgOCree35O7R/WmYxuXbaRU\nVdsQLsFu7y0TgSxxmKA4VuLj5SVbmbloC8WlPn46pAf3j+5LcruWTodWP2vEjQmIJQ7TJCW+ct5c\ntoNnPs7j4LFSxv6oCw+PzaBPZxsiakykssRhGqW8Qnnv6wIen7+RgsPHObdXB14a14+zU9s7HVpw\n2RwJY05jicMERFVZsH4f03I2sHHvUQYkt+V/rj6LEelJkTsXo6bfy4rbJopZ4gCbkdtAy7Yc5JG5\nG/hqx2F6JrXmuZuGMH5A18jeSKmpxW17b5kIZIkD7JNjPdbtKmRaTi4Lc/fTpW08/3P1WVwztAdx\nzSJkI6W6GvemFs7tvWUikCOJQ0SmAT8BSoHNwG2qeriG87YBRUA54Gvo7lQmOLYdOMZj8zfyv6t3\nkdgyjt+M78fPz0+jRZwDk/dCOR+irsdHavebMU3g1BXHfOA3/n3HHwF+A/yqlnNHqeqB8IVm9h45\nwdMfbeLt5fnENYvhnlF9uGNkLxJbxjkXlM2HMMY1HEkcqjqvys0vgGuciMP8UGFxGdMXbebPn23F\nV67cNCyVey7uQ+cE20jJGPM9N9Q4bgferuU+BRaISDkwQ1Vnhi+s6HG8tJxZn2/jhYV5FJX4uGJQ\nd345OoPUjq2cDs15Vtw25jQhSxwisgDoWsNdv1XVf/rP+S3gA2bX8mMuUNUCEekMzBeRDaq6qJbn\nmwRMAkhNTW1y/NGgrLyCt5fn8/RHm9hXVMIl/Trz0NgMzuwWwiU4vMaK28acJmSJQ1Uvret+EbkV\nuAy4RFW1lp9R4P93n4i8C2QBNSYO/9XITIDMzMwaf56pVFGhfLB2N4/Py2XbwWIyz2jPcxOHcE5a\nB6dDM8Z4gFOjqsYBU4ELVbW4lnNaAzGqWuT/fgzwhzCGGXFUlU837id7bi7f7j5Cv64JvHJrJqMy\nOrt/8p51GRnjGk7VOJ4F4qnsfgL4QlUni0h34CVVnQB0Ad713x8LvKGqcx2K1/NWbj/EI3Nz+XLr\nIVI6tOTJ6wdz+aDu3pm8Z11GxriGU6Oq+tRyfBcwwf/9FmBQOOOKRLl7ipiWk8uC9XtJahPPH674\nETeck0rz2AiZvFcb2wfDmJBxw6gqEwL5h4p5YsFG3v26gDbNY3l4bAa3DU+jVfMoeclt3ocxIRMl\nrUj02F9UwnOf5DF72XZiRLhjRC/uurA37Vs3dzo0Y0yEsMQRIYpOlPHioi28tGQrJb4Krsvswb2X\npNMt0QMbKRljPMUSh8edKCvn9S+289wneXxXXMaEs7ry4JgMendq43RoxpgIZYnDo3zlFfzjqwKe\nXLCRXYUnGJGexMNjMxjYo53ToRljIpwlDo9RVXLW7WFaTi6b9x9jUEo7Hr12EOf3SXI6NHexeR/G\nhIwlDg/5PO8Aj+Tksjr/MH06t2H6zUMY+6Ou7p+85wQbcmtMyFji8IA1Ow8zLSeXxZsO0D2xBdnX\nDOTqs5OJjZSNlIwxnmKJw8U27z/KY/NymbN2D+1bxfHvPz6Tm889w5mNlIwxxs8ShwvtLjzOUws2\n8deVO2kRG8N9l6TzLyN6ktDCwY2UjDHGzxKHi3x3rJTnF+bx6tLtoPCz887g7lF9SGoT73Roxhhz\niiUOFzhW4uOVJVuZuWgLx0p9XD2kB/dfmk6P9raRkjHGfSxxOOzzvAPc+9bXHDhaypj+XXhobAZ9\nu9iQUWOMe1nicFjPTq3p3z2R+y9NZ0hqe6fDMcaYelnicFi3xJa8dnuW02EYY0yD2UQAY4wxAbHE\nYYwxJiCOJA4R+U8RKRCRVf6vCbWcN05EckUkT0R+He44jTHGnM7JGscTqvpobXeKSDPgOWA0sBNY\nLiLvq+q34QrQGGPM6dzcVZUF5KnqFlUtBd4CrnA4JmOMiXpOJo4pIrJGRF4RkZrGoSYD+VVu7/Qf\nq5GITBKRFSKyYv/+/cGO1RhjjF/IEoeILBCRb2r4ugJ4AegFDAZ2A4819flUdaaqZqpqZqdOnZr6\n44wxxtQiZDUOVb20IeeJyIvABzXcVQCkVLndw3/MGGOMgxwpjotIN1Xd7b95FfBNDactB9JFpCeV\nCeMG4KaG/PyVK1ceEJHtQQk2PJKAA04H0QgWd/h4MWawuMOpqTGf0dATnRpVlS0igwEFtgF3AohI\nd+AlVZ2gqj4RuQfIAZoBr6jquob8cFX1VF+ViKxQ1Uyn4wiUxR0+XowZLO5wCmfMjiQOVb2lluO7\ngAlVbs8B5oQrLmOMMfVz83BcY4wxLmSJwx1mOh1AI1nc4ePFmMHiDqewxSyqGq7nMsYYEwHsisMY\nY0xALHG4hIj8t38m/SoRmecfYeZ6IjJNRDb4Y39XRNo5HVN9RORaEVknIhUi4vqRM15c7NO/IsQ+\nEalpqL0riUiKiHwiIt/63x/3OR1TQ4hICxH5UkRW++P+r5A/p3VVuYOItFXVI/7v7wX6q+pkh8Oq\nl4iMAT72D59+BEBVf+VwWHUSkTOBCmAG8JCqrnA4pFr5F/vcSJXFPoEb3b7Yp4iMBI4Cr6nqAKfj\naQgR6QZ0U9WvRCQBWAlc6YG/tQCtVfWoiMQBS4D7VPWLUD2nXXG4xMmk4deayjkurqeq81TV57/5\nBZUz/F1NVderaq7TcTSQJxf7VNVFwCGn4wiEqu5W1a/83xcB66ljfTy30EpH/Tfj/F8hbT8scbiI\niPxRRPKBicDvnY6nEW4HPnQ6iAgT0GKfJjhEJA04G1jmbCQNIyLNRGQVsA+Yr6ohjdsSRxjVs/Aj\nqvpbVU0BZgP3OBvt9+qL23/ObwEflbE7riExG1MTEWkD/B24v1pPgGuparmqDqbyij9LRELaPejk\nRk5Rp6ELP1LZ+M4B/iOE4TRYfXGLyK3AZcAl6pKiWQB/a7ezxT7DyF8j+DswW1X/4XQ8gVLVwyLy\nCTCOmtcADAq74nAJEUmvcvMKYINTsQRCRMYBU4HLVbXY6Xgi0KnFPkWkOZWLfb7vcEwRyV9kfhlY\nr6qPOx1PQ4lIp5OjGUWkJZUDKULaftioKpcQkb8DGVSO9tkOTFZV13+yFJE8IB446D/0hdtHg4nI\nVcAzQCfgMLBKVcc6G1XtRGQC8CTfL/b5R4dDqpeIvAlcROWKrXuB/1DVlx0Nqh4icgGwGFhL5f9D\ngH/zr5nnWiIyEHiVyvdHDPCOqv4hpM9picMYY0wgrKvKGGNMQCxxGGOMCYglDmOMMQGxxGGMMSYg\nljiMMcYExBKHMSHmX3V1q4h08N9u77+d5mxkxjSOJQ5jQkxV84EXgD/5D/0JmKmq2xwLypgmsHkc\nxoSBfymLlcArwB3AYFUtczYqYxrH1qoyJgxUtUxEHgbmAmMsaRgvs64qY8JnPLAb8MTGRsbUxhKH\nMWEgIoOpXHzuXOAB/25zxniSJQ5jQsy/6uoLVO7vsAOYBjzqbFTGNJ4lDmNC7w5gh6rO999+HjhT\nRC50MCZjGs1GVRljjAmIXXEYY4wJiCUOY4wxAbHEYYwxJiCWOIwxxgTEEocxxpiAWOIwxhgTEEsc\nxhhjAmKJwxhjTED+P84RRaFak8JQAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114ffbc18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "weights = stocGradAscent0(array(dataArr), labelMat)\n",
    "plotBestFit(weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 随机梯度上升算法（随机化）\n",
    "def stocGradAscent1(dataMatrix, classLabels, numIter=150):\n",
    "    '''\n",
    "    Desc:\n",
    "        改进版的随机梯度上升，使用随机的一个样本来更新回归系数\n",
    "    Args:\n",
    "        dataMatrix -- 输入数据的数据特征（除去最后一列数据）\n",
    "        classLabels -- 输入数据的类别标签（最后一列数据）\n",
    "        numIter=150 --  迭代次数\n",
    "    Returns:\n",
    "        weights -- 得到的最佳回归系数\n",
    "    '''\n",
    "    m,n = shape(dataMatrix)\n",
    "    weights = ones(n)   # 创建与列数相同的矩阵的系数矩阵，所有的元素都是1\n",
    "    # 随机梯度, 循环150,观察是否收敛\n",
    "    for j in range(numIter):\n",
    "        # [0, 1, 2 .. m-1]\n",
    "        dataIndex = list(range(m))\n",
    "        for i in range(m):\n",
    "            # i和j的不断增大，导致alpha的值不断减少，但是不为0\n",
    "            alpha = 4/(1.0+j+i)+0.0001    # alpha 会随着迭代不断减小，但永远不会减小到0，因为后边还有一个常数项0.0001\n",
    "            # 随机产生一个 0～len()之间的一个值\n",
    "            # random.uniform(x, y) 方法将随机生成下一个实数，它在[x,y]范围内,x是这个范围内的最小值，y是这个范围内的最大值。\n",
    "            randIndex = int(random.uniform(0,len(dataIndex)))\n",
    "            # sum(dataMatrix[i]*weights)为了求 f(x)的值， f(x)=a1*x1+b2*x2+..+nn*xn\n",
    "            h = sigmoid(sum(dataMatrix[randIndex]*weights))\n",
    "            error = classLabels[randIndex] - h\n",
    "            # print weights, '__h=%s' % h, '__'*20, alpha, '__'*20, error, '__'*20, dataMatrix[randIndex]\n",
    "            weights = weights + alpha * error * dataMatrix[randIndex]\n",
    "            del(dataIndex[randIndex])\n",
    "    return weights"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0XXDS9nxKpfLmVIhycHwB0JVzfzewrIRzFgD7wg1NYidtF5a0PR+pKqkZHDez\nlWa22cw2d3d3Rx2OiEhqRZk49gCtOfcXZo8FPQcAd1/v7h3u3tHS0lLWQKtKtXahiEjJokwcm4Al\nZrbYzCYDNwAP5Z3zEPChbHXVm4Gj7q5uqjCpDzq+lNQlJiIb43D3PjP7BPAToBa4191fMLPV2a+v\nAzYAK4DtQA/wkajilQmaMWP0AXBd/Mam5C0xEenMcXffQCY55B5bl3PbgVsqHZeEYLSk4V65OERk\nwlIzOC6SepoDIzGhxCGSFGmYACipoMQhIiKBKHGIiEggShxSGSolFUkN7cchlaFSUpHUUItDJCnU\napOYUItDJCnUapOYUItDBDRHQiQAJQ4R0BwJkQCUOEDvNiU8+tuSFFLiAL3brHZhXsT1tyUppMQh\noou4SCBKHCIiEogSh8hoNEdCZAQlDpHRaO6EyAhKHKAZuVLcRKui9LclKaSZ46B3ldWusbHwAHmx\n41D6gLr+tiSF1OKQZAhzPsSxY5nta/M/dNEXKSiSFoeZfQX4U+As8DvgI+5+pMB5O4DjQD/Q5+4d\nlYxTYkTzIURiI6oWxyPApe5+OfAb4LOjnPsOd1+qpCEiEg+RJA53/6m792XvPgUsjCIOEREJLg5j\nHB8FHi7yNQceNbMtZrZytAcxs5VmttnMNnd3d5c9SKlSqooSGSG0MQ4zexQ4v8CXbnP3H2TPuQ3o\nA+4v8jBvdfc9ZnYe8IiZveTujxU60d3XA+sBOjo6fMJPQAQ0QC5SQGiJw93fOdrXzezDwHuAa9y9\n4IXe3fdkP79qZg8AnUDBxCEpN1rJrIhUVCRdVWa2HFgDvNfde4qc02BmjYO3gWuB5ysXpcSKSmZF\nYiOqMY47gEYy3U9bzWwdgJnNN7MN2XPmAk+Y2bPA08CP3P3H0YQrIiKDIpnH4e6vLXJ8L7Aie/sV\n4IpKxiUpMmNG8a4ttVJEJiQOVVUi5acJgyKhUeIQEZFAlDhERCQQJQ4REQlEiUNERAJR4pB00lIh\nIqHRRk6STiq5FQmNWhwiIhKIEoeIiASixCEiIoEocYiISCBKHCIiEogV2Qoj0cysG9gZdRwBNAMH\nog5iHBR35SQxZlDclTTRmNvcvaWUE1OZOJLGzDa7e0fUcQSluCsniTGD4q6kSsasrioREQlEiUNE\nRAJR4oiH9VEHME6Ku3KSGDMo7kqqWMwa4xARkUDU4hARkUCUOGLCzL5oZs+Z2VYz+6mZzY86plKY\n2VfM7KUR/q8hAAADrUlEQVRs7A+Y2ayoYxqLmf17M3vBzAbMLPaVM2a23MxeNrPtZvaZqOMphZnd\na2avmtnzUcdSKjNrNbNfmNmvs38fn4w6plKY2VQze9rMns3G/feh/0x1VcWDmc1w92PZ2/8JuMTd\nV0cc1pjM7Frg5+7eZ2b/CODu/znisEZlZhcDA8BdwF+7++aIQyrKzGqB3wDvAnYDm4Ab3f3XkQY2\nBjN7G3AC+Ja7Xxp1PKUws3nAPHd/xswagS3A+xLwuzagwd1PmNkk4Angk+7+VFg/Uy2OmBhMGlkN\nQCIyurv/1N37snefAhZGGU8p3P1Fd3856jhK1Alsd/dX3P0s8F3g+ohjGpO7PwYcijqOINx9n7s/\nk719HHgRWBBtVGPzjBPZu5OyH6FeP5Q4YsTMvmRmXcB/AD4fdTzj8FHg4aiDSJkFQFfO/d0k4GKW\ndGbWDrwe2BhtJKUxs1oz2wq8Cjzi7qHGrcRRQWb2qJk9X+DjegB3v83dW4H7gU9EG+05Y8WdPec2\noI9M7JErJWaRQsxsOvA94FN5PQGx5e797r6UTIu/08xC7R7UDoAV5O7vLPHU+4ENwBdCDKdkY8Vt\nZh8G3gNc4zEZNAvwu467PUBrzv2F2WMSguwYwfeA+939+1HHE5S7HzGzXwDLgdAKE9TiiAkzW5Jz\n93rgpahiCcLMlgNrgPe6e0/U8aTQJmCJmS02s8nADcBDEceUStlB5nuAF939q1HHUyozaxmsZjSz\naWQKKUK9fqiqKibM7HvAhWSqfXYCq9099u8szWw7MAU4mD30VNyrwczs/cDtQAtwBNjq7n8SbVTF\nmdkK4GtALXCvu38p4pDGZGbfAa4ms2LrfuAL7n5PpEGNwczeCjwObCPzfwjwt+6+IbqoxmZmlwP3\nkfn7qAH+zd3/IdSfqcQhIiJBqKtKREQCUeIQEZFAlDhERCQQJQ4REQlEiUNERAJR4hAJWXbV1d+b\n2Zzs/dnZ++3RRiYyPkocIiFz9y7gTuDL2UNfBta7+47IghKZAM3jEKmA7FIWW4B7gZuBpe7eG21U\nIuOjtapEKsDde83sb4AfA9cqaUiSqatKpHKuA/YBidjYSKQYJQ6RCjCzpWQWn3sz8JfZ3eZEEkmJ\nQyRk2VVX7ySzv8Mu4CvAP0Ublcj4KXGIhO9mYJe7P5K9/w3gYjN7e4QxiYybqqpERCQQtThERCQQ\nJQ4REQlEiUNERAJR4hARkUCUOEREJBAlDhERCUSJQ0REAlHiEBGRQP4/tmdvk+B0quMAAAAASUVO\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1147b46a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "weights = stocGradAscent1(array(dataArr), labelMat)\n",
    "plotBestFit(weights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1151934e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "weights = stocGradAscent1(array(dataArr), labelMat, 500)\n",
    "plotBestFit(weights)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 示例 从疝气病症预测病马的死亡率"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# 分类函数，根据回归系数和特征向量来计算 Sigmoid的值\n",
    "def classifyVector(inX, weights):\n",
    "    '''\n",
    "    Desc: \n",
    "        最终的分类函数，根据回归系数和特征向量来计算 Sigmoid 的值，大于0.5函数返回1，否则返回0\n",
    "    Args:\n",
    "        inX -- 特征向量，features\n",
    "        weights -- 根据梯度下降/随机梯度下降 计算得到的回归系数\n",
    "    Returns:\n",
    "        如果 prob 计算大于 0.5 函数返回 1\n",
    "        否则返回 0\n",
    "    '''\n",
    "    prob = sigmoid(sum(inX*weights))\n",
    "    if prob > 0.5: return 1.0\n",
    "    else: return 0.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 打开测试集和训练集,并对数据进行格式化处理\n",
    "def colicTest():\n",
    "    '''\n",
    "    Desc:\n",
    "        打开测试集和训练集，并对数据进行格式化处理\n",
    "    Args:\n",
    "        None\n",
    "    Returns:\n",
    "        errorRate -- 分类错误率\n",
    "    '''\n",
    "    frTrain = open('horseColicTraining.txt')\n",
    "    frTest = open('horseColicTest.txt')\n",
    "    trainingSet = []\n",
    "    trainingLabels = []\n",
    "    # 解析训练数据集中的数据特征和Labels\n",
    "    # trainingSet 中存储训练数据集的特征，trainingLabels 存储训练数据集的样本对应的分类标签\n",
    "    for line in frTrain.readlines():\n",
    "        currLine = line.strip().split('\\t')\n",
    "        lineArr = []\n",
    "        for i in range(21):\n",
    "            lineArr.append(float(currLine[i]))\n",
    "        trainingSet.append(lineArr)\n",
    "        trainingLabels.append(float(currLine[21]))\n",
    "    # 使用 改进后的 随机梯度下降算法 求得在此数据集上的最佳回归系数 trainWeights\n",
    "    trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 500)\n",
    "    errorCount = 0\n",
    "    numTestVec = 0.0\n",
    "    # 读取 测试数据集 进行测试，计算分类错误的样本条数和最终的错误率\n",
    "    for line in frTest.readlines():\n",
    "        numTestVec += 1.0\n",
    "        currLine = line.strip().split('\\t')\n",
    "        lineArr = []\n",
    "        for i in range(21):\n",
    "            lineArr.append(float(currLine[i]))\n",
    "        if int(classifyVector(array(lineArr), trainWeights)) != int(currLine[21]):\n",
    "            errorCount += 1\n",
    "    errorRate = (float(errorCount) / numTestVec)\n",
    "    print (\"the error rate of this test is: %f\" % errorRate)\n",
    "    return errorRate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 调用 colicTest() 10次并求结果的平均值\n",
    "def multiTest():\n",
    "    numTests = 10\n",
    "    errorSum = 0.0\n",
    "    for k in range(numTests):\n",
    "        errorSum += colicTest()\n",
    "    print (\"after %d iterations the average error rate is: %f\" % (numTests, errorSum/float(numTests)) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/kyzhang/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:3: RuntimeWarning: overflow encountered in exp\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "the error rate of this test is: 0.313433\n",
      "the error rate of this test is: 0.298507\n",
      "the error rate of this test is: 0.417910\n",
      "the error rate of this test is: 0.373134\n",
      "the error rate of this test is: 0.268657\n",
      "the error rate of this test is: 0.283582\n",
      "the error rate of this test is: 0.328358\n",
      "the error rate of this test is: 0.343284\n",
      "the error rate of this test is: 0.402985\n",
      "the error rate of this test is: 0.373134\n",
      "after 10 iterations the average error rate is: 0.340299\n"
     ]
    }
   ],
   "source": [
    "multiTest()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.1"
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 },
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