logic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(100L, 3L)\n[[ 34.62365962  78.02469282   0.        ]\n [ 30.28671077  43.89499752   0.        ]\n [ 35.84740877  72.90219803   0.        ]\n [ 60.18259939  86.3085521    1.        ]\n [ 79.03273605  75.34437644   1.        ]]\n(100L, 2L)\n(100L, 1L)\n[[ 34.62365962  78.02469282]\n [ 30.28671077  43.89499752]\n [ 35.84740877  72.90219803]\n [ 60.18259939  86.3085521 ]\n [ 79.03273605  75.34437644]]\n[[ 0.]\n [ 0.]\n [ 0.]\n [ 1.]\n [ 1.]]\n"
     ]
    }
   ],
   "source": [
    "#本文是逻辑回归算法实现\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "#load data from file导入txt数据\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(float(lineArr[i]))\n",
    "        data.append(temp)\n",
    "    return np.array(data)\n",
    "\n",
    "    \n",
    "data = load_data('ex2data1.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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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iLZYO3Jj6xBnFhIgcCBwADAmOqeoP6njdbwBL/BFM/43XAT4A+LGInA6sB06o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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x80e5e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#可视化一下数据集\n",
    "import matplotlib.pyplot as plt\n",
    "label0 = np.where(y.ravel() == 0)\n",
    "plt.scatter(X[label0,0],X[label0,1],marker='x',color = 'r',label = 'Not admitted')\n",
    "label1 = np.where(y.ravel() == 1)\n",
    "plt.scatter(X[label1,0],X[label1,1],marker='o',color = 'b',label = 'Admitted')\n",
    "plt.xlabel('Exam 1 score')\n",
    "plt.ylabel('Exam 2 score')\n",
    "plt.legend(loc = 'upper left')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "compute with w=[0,0,0]\nExpected cost (approx):0.693...\n0.69314718056\nExpected gradients (approx):[-0.1,-12,-11]\n[ -0.1        -12.00921659 -11.26284221]\ncompute with w=[-24,0.2,0.2]\nExpected cost (approx):0.218....\n0.218330193827\nExpected gradients (approx): [0.04,2.566,0.646]\n[ 0.04290299  2.56623412  2.64679737]\n"
     ]
    }
   ],
   "source": [
    "#compute the cost计算cost以及梯度gradient\n",
    "def sigmoid(x):\n",
    "    return 1 / (1+np.exp(-x))\n",
    "def out(x,w):\n",
    "    return sigmoid(np.dot(x,w))\n",
    "def compute_cost(X_train,y_train,theta):\n",
    "    m = X_train.shape[0]\n",
    "    J = 0\n",
    "    theta = theta.reshape(-1,1)\n",
    "    grad = np.zeros((X_train.shape[1],1))\n",
    "    h = out(X_train,theta)\n",
    "    J = -1*np.sum(y_train*np.log(h) + (1-y_train)*np.log((1-h))) / m\n",
    "    grad = X_train.T.dot((h-y_train)) / m\n",
    "    grad = grad.ravel()\n",
    "    \n",
    "    return J,grad\n",
    "\n",
    "#test the grad，用简单的数值测试一下，编写的代码是否计算正确\n",
    "m = X.shape[0]\n",
    "one = np.ones((m,1))\n",
    "X = np.hstack((one,data[:,:-1]))\n",
    "W = np.zeros((X.shape[1],1))\n",
    "\n",
    "cost,grad = compute_cost(X,y,W)\n",
    "print 'compute with w=[0,0,0]'\n",
    "print 'Expected cost (approx):0.693...'\n",
    "print cost\n",
    "print 'Expected gradients (approx):[-0.1,-12,-11]'\n",
    "print grad\n",
    "\n",
    "cost1,grad1 = compute_cost(X,y,np.array([[-24],[0.2],[0.2]]))\n",
    "print 'compute with w=[-24,0.2,0.2]'\n",
    "print 'Expected cost (approx):0.218....'\n",
    "print cost1\n",
    "print 'Expected gradients (approx): [0.04,2.566,0.646]'\n",
    "print grad1\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Warning: Desired error not necessarily achieved due to precision loss.\n         Current function value: 0.203530\n         Iterations: 38\n         Function evaluations: 96\n         Gradient evaluations: 84\n[-25.56159061   0.20990211   0.20440384]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda2\\lib\\site-packages\\ipykernel_launcher.py:12: RuntimeWarning: divide by zero encountered in log\n  if sys.path[0] == '':\nE:\\Anaconda2\\lib\\site-packages\\ipykernel_launcher.py:12: RuntimeWarning: invalid value encountered in multiply\n  if sys.path[0] == '':\n"
     ]
    }
   ],
   "source": [
    "#这里使用了最优算法，不是选择梯度下降法，例如你可以选择BFGS等\n",
    "from scipy import optimize\n",
    "params = np.zeros((X.shape[1],1)).ravel()\n",
    "args = (X,y)\n",
    "\n",
    "def f(params,*args):\n",
    "    X_train,y_train = args\n",
    "    m,n = X_train.shape\n",
    "    J = 0\n",
    "    theta = params.reshape((n,1))\n",
    "    h = out(X_train,theta)\n",
    "    J = -1*np.sum(y_train*np.log(h) + (1-y_train)*np.log((1-h))) / m\n",
    "    \n",
    "    return J\n",
    "\n",
    "def gradf(params,*args):\n",
    "    X_train,y_train = args\n",
    "    m,n = X_train.shape\n",
    "    theta = params.reshape(-1,1)\n",
    "    h = out(X_train,theta)\n",
    "    grad = np.zeros((X_train.shape[1],1))\n",
    "    grad = X_train.T.dot((h-y_train)) / m\n",
    "    g = grad.ravel()\n",
    "    return g\n",
    "\n",
    "#res = optimize.minimize(f,x0=init_theta,args=args,method='BFGS',jac=gradf,\\\n",
    "#                        options={'gtol': 1e-6, 'disp': True})\n",
    "res = optimize.fmin_cg(f,x0=params,fprime=gradf,args=args,maxiter=500)\n",
    "print res\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4sNOhFc3a74eP4pKpg0nWEoQJilAbcrx79+5kZmby0EMPMXHiRJo1a8aiRYuc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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x80b7860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#可视化一下线性的决策边界\n",
    "label = np.array(y)\n",
    "index_0 = np.where(label.ravel()==0)\n",
    "plt.scatter(X[index_0,1],X[index_0,2],marker='x'\\\n",
    "            ,color = 'b',label = 'Not admitted',s = 15)\n",
    "index_1 =np.where(label.ravel()==1)\n",
    "plt.scatter(X[index_1,1],X[index_1,2],marker='o',\\\n",
    "            color = 'r',label = 'Admitted',s = 15)\n",
    "\n",
    "#show the decision boundary\n",
    "x1 = np.arange(20,100,0.5)\n",
    "x2 = (- res[0] - res[1]*x1) / res[2]\n",
    "plt.plot(x1,x2,color = 'black')\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('X2')\n",
    "plt.legend(loc = 'upper left')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "For a student with scores 45 and 85, we predict an admission \nExpected value: 0.775 +/- 0.002\n[ 0.77873864]\nExpected accuracy (approx): 89.0\n0.89\n"
     ]
    }
   ],
   "source": [
    "#预测函数\n",
    "def predict(X,theta):\n",
    "    h = out(X,theta)\n",
    "    y_pred = np.where(h>=0.5,1.0,0)\n",
    "    \n",
    "    return y_pred \n",
    "\n",
    "#test\n",
    "prob = out(np.array([[1,45,85]]),res)\n",
    "print \"For a student with scores 45 and \\\n",
    "85, we predict an admission \"\n",
    "print \"Expected value: 0.775 +/- 0.002\"\n",
    "\n",
    "print prob\n",
    "\n",
    "p = predict(X,res)\n",
    "print \"Expected accuracy (approx): 89.0\"\n",
    "print np.mean(p==y.ravel())\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "#下面是自己整理的逻辑回归类，所以，如果想写的规范，也可以自己整理成class\n",
    "import numpy as np\n",
    "\n",
    "class logistic(object):\n",
    "    def __init__(self):\n",
    "        self.W = None\n",
    "    def train(self,X,y,learn_rate = 0.01,num_iters = 2000):\n",
    "        num_train,num_feature = X.shape\n",
    "        #init the weight\n",
    "        self.W = 0.001*np.random.randn(num_feature,1).reshape((-1,1))\n",
    "        loss = []\n",
    "        \n",
    "        for i in range(num_iters):\n",
    "            error,dW = self.compute_loss(X,y)\n",
    "            self.W += -learn_rate*dW\n",
    "            \n",
    "            loss.append(error)\n",
    "            if i%200==0:\n",
    "                print 'i=%d,error=%f' %(i,error)\n",
    "        return loss\n",
    "    \n",
    "    def compute_loss(self,X,y):\n",
    "        num_train = X.shape[0]\n",
    "        h = self.output(X)\n",
    "        loss = -np.sum((y*np.log(h) + (1-y)*np.log((1-h))))\n",
    "        loss = loss / num_train\n",
    "        \n",
    "        dW = X.T.dot((h-y)) / num_train\n",
    "    \n",
    "        return loss,dW\n",
    "    \n",
    "    def output(self,X):\n",
    "        g = np.dot(X,self.W)\n",
    "        return self.sigmod(g)\n",
    "    def sigmod(self,X):\n",
    "        return 1/(1+np.exp(-X))\n",
    "    \n",
    "    def predict(self,X_test):\n",
    "        h = self.output(X_test)\n",
    "        y_pred = np.where(h>=0.5,1,0)\n",
    "        return y_pred\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5.1  1.4]\n [ 4.9  1.4]\n [ 4.7  1.3]\n [ 4.6  1.5]\n [ 5.   1.4]]\n[1 1 1 1 1]\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEKCAYAAAARnO4WAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkR54oDV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      "text/plain": [
       "<matplotlib.figure.Figure at 0x8e86630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#用iris数据集去测试\n",
    "from sklearn.datasets import load_iris\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "iris = load_iris()\n",
    "data = iris.data\n",
    "target = iris.target\n",
    "#print data[:10]\n",
    "#print target[10:]\n",
    "X = data[0:100,[0,2]]\n",
    "y = target[0:100]\n",
    "print X[:5]\n",
    "print y[-5:]\n",
    "label = np.array(y)\n",
    "index_0 = np.where(label.ravel()==0)\n",
    "plt.scatter(X[index_0,0],X[index_0,1],marker='x',color = 'b',label = '0',s = 15)\n",
    "index_1 =np.where(label.ravel()==1)\n",
    "plt.scatter(X[index_1,0],X[index_1,1],marker='o',color = 'r',label = '1',s = 15)\n",
    "\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('X2')\n",
    "plt.legend(loc = 'upper left')\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "i=0,error=0.691406\ni=200,error=0.363361\ni=400,error=0.237585\ni=600,error=0.174747\ni=800,error=0.137928\ni=1000,error=0.113953\ni=1200,error=0.097163\ni=1400,error=0.084771\ni=1600,error=0.075254\ni=1800,error=0.067719\n[[-0.46036069]\n [-1.19601995]\n [ 2.53615251]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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sciLj5bmU52XqaCiJWTxDYRdQFTU+LZg2Yu5+K3ArRPoUTrw0kfEhMy3SQT1v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\noP8PEtRJRkvXacUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x80c1f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#观察并且可视化一下训练过程\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "y = y.reshape((-1,1)) #有时候经常需要reshape,我建议多用，避免不必要的bug\n",
    "#add the x0=1\n",
    "one = np.ones((X.shape[0],1))\n",
    "X_train = np.hstack((one,X))\n",
    "classify = logistic()\n",
    "loss = classify.train(X_train,y)\n",
    "print classify.W\n",
    "\n",
    "plt.plot(loss)\n",
    "plt.xlabel('Iteration number')\n",
    "plt.ylabel('Loss value')\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BWAUAM2bMyLgDFGCsqukqVcV7772X8uTM22+/nVIS+O67706O3oNcEphGZqiAXw7g7wA0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\nIhjwiYgiggGfiCgi/h83HbXPklwX9wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8fad278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#可视化一下决策边界\n",
    "label = np.array(y)\n",
    "index_0 = np.where(label.ravel()==0)\n",
    "plt.scatter(X[index_0,0],X[index_0,1],marker='x',color = 'b',label = '0',s = 15)\n",
    "index_1 =np.where(label.ravel()==1)\n",
    "plt.scatter(X[index_1,0],X[index_1,1],marker='o',color = 'r',label = '1',s = 15)\n",
    "\n",
    "#show the decision boundary\n",
    "x1 = np.arange(4,7.5,0.5)\n",
    "x2 = (- classify.W[0] - classify.W[1]*x1) / classify.W[2]\n",
    "plt.plot(x1,x2,color = 'black')\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('X2')\n",
    "plt.legend(loc = 'upper left')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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