linear_multiple.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(47L, 3L)\n[[  2104      3 399900]\n [  1600      3 329900]\n [  2400      3 369000]\n [  1416      2 232000]\n [  3000      4 539900]]\n(47L, 2L)\n(47L, 1L)\n[[2104    3]\n [1600    3]\n [2400    3]\n [1416    2]\n [3000    4]]\n[[399900]\n [329900]\n [369000]\n [232000]\n [539900]]\n"
     ]
    }
   ],
   "source": [
    "#本文是多元线性回归模型\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#load data from file\n",
    "#导入数据，并且观察一下\n",
    "def load_data(filename):\n",
    "    data = []\n",
    "    file = open(filename)\n",
    "    for line in file.readlines():\n",
    "        lineArr = line.strip().split(',')\n",
    "        col_num = len(lineArr)\n",
    "        temp = []\n",
    "        for i in xrange(col_num):\n",
    "            temp.append(int(lineArr[i]))\n",
    "        data.append(temp)\n",
    "    return np.array(data)\n",
    "\n",
    "    \n",
    "data = load_data('ex1data2.txt')\n",
    "print data.shape\n",
    "print data[:5]\n",
    "\n",
    "X = data[:,:-1]\n",
    "y = data[:,-1:]\n",
    "print X.shape\n",
    "print y.shape\n",
    "print X[:5]\n",
    "print y[:5]\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#feature normalize,Scale features and set them to zero mean\n",
    "#定义一下特征缩放函数，因为每个特征的取值范围不同，且差异很大\n",
    "def featureNormalize(X):\n",
    "    X_norm = X\n",
    "    mu = np.zeros((1,X.shape[1]))\n",
    "    sigma = np.zeros((1,X.shape[1]))\n",
    "    \n",
    "    mu = np.mean(X,axis=0) #mean value of every feature\n",
    "    sigma = np.std(X,axis=0)#std of every feature\n",
    "    X_norm = (X - mu) / sigma\n",
    "    \n",
    "    return X_norm,mu,sigma \n",
    "    \n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "run gradient descent\nTheta computed from gradient descent:  [[ 340227.89154751]\n [ 107315.97282379]\n [  -4447.3463406 ]]\n"
     ]
    }
   ],
   "source": [
    "X_norm,mu,sigma = featureNormalize(data[:,:-1])\n",
    "num_train = X.shape[0]\n",
    "one = np.ones((num_train,1))\n",
    "X = np.hstack((one,X_norm))#add one\n",
    "W = np.zeros((X.shape[1],1)) #初始化全0，that is ok\n",
    "#计算cost\n",
    "def compute_cost(X_test,y_test,theta):\n",
    "    num_X = X_test.shape[0]\n",
    "    cost = 0.5 * np.sum(np.square(X_test.dot(theta) - y_test)) / num_X\n",
    "    return cost\n",
    "#计算梯度下降\n",
    "def gradient_descent(X_test,y_test,theta,alpha = 0.005,iters = 1500):\n",
    "    J_history = []\n",
    "    num_X = X_test.shape[0]\n",
    "    for i in xrange(iters):\n",
    "        theta = theta - alpha * X_test.T.dot(X_test.dot(theta) - y_test) / num_X\n",
    "        cost = compute_cost(X_test,y_test,theta)\n",
    "        J_history.append(cost)\n",
    "    return theta,J_history\n",
    "#测试一下结果\n",
    "print 'run gradient descent'\n",
    "theta,J_history = gradient_descent(X,y,W)\n",
    "print 'Theta computed from gradient descent: ',theta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GK/B7PNUZEasiYiawGbCLpO277D8zItoioq21tXWQyll7s2enu18ta4priM3M3qnXwJd0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\nn1HsJFbHAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ab36d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot the j_cost,绘制训练的cost曲线,可以调节学习率\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(J_history,color = 'b')\n",
    "plt.xlabel('iters')\n",
    "plt.ylabel('j_cost')\n",
    "plt.title('cost variety')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted price of a 1650 sq-ft, 3 br house (using gradient descent)\n[[ 293365.7762653]]\n"
     ]
    }
   ],
   "source": [
    "#predict (Note :normalize the feature with the train sets)\n",
    "#预测一下，记得使用训练集的均值和方差去进行特征缩放\n",
    "X_t = ([[1650,3]] - mu) / sigma\n",
    "X_test = np.hstack((np.ones((1,1)),X_t))\n",
    "predict = X_test.dot(theta)\n",
    "print 'Predicted price of a 1650 sq-ft, 3 br house (using gradient descent)'\n",
    "print predict\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(47L, 3L)\n(47L, 1L)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Theta computed from the normal equations:\n[[ 89597.90954435]\n [   139.21067402]\n [ -8738.01911278]]\n"
     ]
    }
   ],
   "source": [
    "#compute the gradient by using Normal Equations  \n",
    "#without feature scaling and gradient descent\n",
    "#直接使用公式求解最佳theta,不用梯度下降法\n",
    "XX = data[:,:-1]\n",
    "yy = data[:,-1:]\n",
    "m = XX.shape[0]\n",
    "\n",
    "one = np.ones((m,1))\n",
    "XX = np.hstack((one,data[:,:-1]))\n",
    "print XX.shape\n",
    "print yy.shape\n",
    "\n",
    "def normalEquation(X_train,y_train):\n",
    "    w = np.zeros((X_train.shape[0],1))\n",
    "    w = ((np.linalg.pinv(X_train.T.dot(X_train))).dot(X_train.T)).dot(y_train)\n",
    "    return w\n",
    "w = normalEquation(XX,yy)\n",
    "print 'Theta computed from the normal equations:'\n",
    "print w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted price of a 1650 sq-ft, 3 br house (using normal equations)\n[[ 293081.46433506]]\n"
     ]
    }
   ],
   "source": [
    "#predict price\n",
    "price = np.dot(np.array([[1,1650,3]]),w)\n",
    "print 'Predicted price of a 1650 sq-ft, 3 br house (using normal equations)'\n",
    "print price\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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