DIY/SVM.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#==================== Part 0: Basic Function ====================\n",
    "import numpy as np\n",
    "#用吴恩达课程的数据老是跑不对，theta相差很大，也找不出问题，换了一个sk自带的数据，又可以了。。。不知道问题出在哪\n",
    "with open('F:\\data\\svmdata.txt', 'r') as f:  \n",
    "    data = f.readlines()  #txt中所有字符串读入data  \n",
    "datamat = []\n",
    "for line in data:  \n",
    "    odom = line.strip().split('   ')        #将单个数据分隔开存好 \n",
    "    numbers_float = list(map(float, odom)) #转化为浮点数  \n",
    "    datamat.append(numbers_float)\n",
    "datanp = np.array(datamat)\n",
    "m=datanp.shape[0]\n",
    "#print(m)\n",
    "x = datanp[:,(0,1)].reshape((m,2))  \n",
    "y = datanp[:,2].reshape((m,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FpQRJXKln3omocF10+QLCHu7+NIC730KQpXyDmX0G0G8zilq/qo5a+rqWurik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\nAUFERAD4/7EXfbIdz/PAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x272e476a898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% ==================== Part 1: Plotting ====================\n",
    "#We start the exercise by first plotting the data to understand the the problem we are working with.\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def plotData(x,y):\n",
    "    fig = plt.figure()  \n",
    "    ax= fig.add_subplot(111) #使画在一个图上\n",
    "    \n",
    "    pos = np.where(y[:,0]==1) #y为类似矩阵形式，所以要再取第一列\n",
    "    neg = np.where(y[:,0]==-1)\n",
    "    ax1 = plt.scatter(x[pos,0], x[pos,1], marker = 'x', color = 'm')  \n",
    "    ax2 = plt.scatter(x[neg,0], x[neg,1], marker = 'o', color = 'r')  \n",
    "    plt.xlabel('exam1 score') \n",
    "    plt.ylabel('exam2 score')\n",
    "    \n",
    "    plt.legend([ax1, ax2], ['Admitted', 'Not admitted'])\n",
    "    plt.show()\n",
    "\n",
    "plotData(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      ".........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................[ 8.1595834 -1.3511488] [-4246.83984074]\n",
      "[-42.46839841] -39.0921663657\n"
     ]
    }
   ],
   "source": [
    "#============ Part 2: Compute ============\n",
    "\n",
    "class SVM(object):\n",
    "    def __init__(self):\n",
    "        self.x = 0\n",
    "        self.y = 0\n",
    "        self.w = 0\n",
    "        self.b = 0\n",
    "        self.b2 = 0\n",
    "        \n",
    "    def fit(self,x,y):\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        alpha = self.SMO(x,y)\n",
    "        self.w = np.sum(alpha*y*x,axis=0) #1*n\n",
    "        b_tmp = y - np.dot(x,self.w.T) #原始公式w就包含了α了，所以这里实际就是对满足条件的b求均值\n",
    "        self.b2=np.mean(b_tmp)\n",
    "        return\n",
    "    \n",
    "    def Kernel(self,x1,x2,kernel='GS'):\n",
    "        if kernel == 'GS':\n",
    "            return x1.dot(x2.T)\n",
    "        \n",
    "    def clipAlpha(self,z,C,yi,yj,ai,aj):\n",
    "        if yi!=yj:\n",
    "            L=max(0,aj-ai)\n",
    "            H=min(C,C+aj-ai)\n",
    "        else:\n",
    "            L=max(0,aj+ai-C)\n",
    "            H=min(C,aj+ai)\n",
    "        if z<L:\n",
    "            z = L\n",
    "        if z>H:\n",
    "            z= H\n",
    "        return z\n",
    "    \n",
    "    def g_func(self,alpha,i):\n",
    "        g = float(np.sum(alpha*self.y*self.Kernel(self.x,self.x[i])))+self.b\n",
    "        return g\n",
    "    \n",
    "    def error_y(self,alpha,i):\n",
    "        error = self.g_func(alpha,i) - self.y[i][0]\n",
    "        return error\n",
    "    \n",
    "    def selectJ(self,m,i):\n",
    "        #测试简化版，随机选择J\n",
    "        j = i\n",
    "        while (j==i):\n",
    "            j=int(np.random.uniform(0,m))\n",
    "        return j\n",
    "        '''\n",
    "        final_j = 0\n",
    "        maxE=0\n",
    "        for j in range(m):\n",
    "            E[j] = self.error_y(alpha,j)\n",
    "\n",
    "            if i!=j and np.abs(E[i]-E[j])>maxE:\n",
    "                final_j = j\n",
    "                maxE = np.abs(E[i]-E[j])\n",
    "        if final_j == 0:\n",
    "            continue\n",
    "        '''\n",
    "        \n",
    "    def SMO(self,x,y,C=0.1):\n",
    "        m,n=x.shape\n",
    "        alpha = np.zeros((m,1))\n",
    "        E = np.zeros((m,1)) \n",
    "        iter = 0\n",
    "        while True:\n",
    "            alphaChanged = 0\n",
    "            for i in range(m):\n",
    "                if (alpha[i]==0 and y[i]*self.g_func(alpha,i)>=1) or (alpha[i]>0 and alpha[i]<C and y[i]*self.g_func(alpha,i)==1)\\\n",
    "                    or (alpha[i]==C and y[i]*self.g_func(alpha,i)<=1):\n",
    "                    continue\n",
    "                print('.',end = '')\n",
    "                E[i] = self.error_y(alpha,i)\n",
    "                \n",
    "                j = self.selectJ(m,i)   \n",
    "                E[j] = self.error_y(alpha,j)\n",
    "                eta = (self.Kernel(x[i],x[i])+self.Kernel(x[j],x[j])-2*self.Kernel(x[i],x[j]))\n",
    "                if eta<=0:\n",
    "                    print('eta<=0')\n",
    "                    continue\n",
    "                alpha_j_unclip=alpha[j]+y[j]*(E[i]-E[j])/eta\n",
    "                alphaj_old = alpha[j]\n",
    "                alpha[j] = self.clipAlpha(alpha_j_unclip,C,y[i],y[j],alpha[i],alpha[j])\n",
    "                alphai_old = alpha[i]\n",
    "                alpha[i] = alpha[i]+y[i]*y[j]*(alphaj_old-alpha[j])\n",
    "                \n",
    "                b1 = self.b-E[i]-y[i]*self.Kernel(x[i],x[i])*(alpha[i]-alphai_old) - y[j]*self.Kernel(x[j],x[i])*(alpha[j]-alphaj_old)\n",
    "                b2 = self.b-E[j]-y[i]*self.Kernel(x[i],x[j])*(alpha[i]-alphai_old) - y[j]*self.Kernel(x[j],x[j])*(alpha[j]-alphaj_old)\n",
    "                if 0<alpha[i] and alpha[i]<C:\n",
    "                    b=b1\n",
    "                elif 0<alpha[j] and alpha[j]<C:\n",
    "                    b=b2\n",
    "                else:\n",
    "                    b = (b1+b2)/2.0\n",
    "                \n",
    "                self.b=b\n",
    "                alphaChanged+=1\n",
    "\n",
    "            if alphaChanged==0:#没有α改变时最多遍历maxIter次数据集\n",
    "                break\n",
    "\n",
    "        return alpha\n",
    "\n",
    "model = SVM()\n",
    "model.fit(x,y)\n",
    "\n",
    "print(model.w,model.b)\n",
    "print(model.b/m,model.b2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
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CCAQNLzWgaFoRCqcVonllM5pXNqNoetFpNRL//Ye/MByqnuTQvLIZAAKPF2H/ZIQtZovI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\nSDNmeD79J7I+BJD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      "text/plain": [
       "<matplotlib.figure.Figure at 0x272e57f0208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#%% ============= Part 3: Visualizing J(theta_0, theta_1) =============\n",
    "def plotPerc(pre_theta,pre_b,X,y):\n",
    "    fig = plt.figure()  \n",
    "    ax= fig.add_subplot(111) #使画在一个图上\n",
    "    \n",
    "    pos = np.where(y[:,0]==1) #y为类似矩阵形式，所以要再取第一列\n",
    "    neg = np.where(y[:,0]==-1)\n",
    "    \n",
    "    ax1 = plt.scatter(x[pos,0], x[pos,1], marker = 'x', color = 'm')  \n",
    "    ax2 = plt.scatter(x[neg,0], x[neg,1], marker = 'o', color = 'r')  \n",
    "    \n",
    "    plt.xlabel('x1') \n",
    "    plt.ylabel('x2')\n",
    "    \n",
    "    plotX = np.arange(3,8,1)\n",
    "    plotY = (-pre_b-pre_theta[0]*plotX)/pre_theta[1]\n",
    "    plt.plot(plotX,plotY)\n",
    "    \n",
    "    plt.show()\n",
    "\n",
    "plotPerc(model.w,model.b2,x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "很奇怪...b总是要除以m后画出的图像才是对的...检查了好几遍公式和代码..不知道问题在哪里...\n",
    "\n",
    "#### update：\n",
    "\n",
    "换了求b的公式，结果就对了....\n",
    "\n",
    "研究了下，原因应该是这样：在SMO中求的b是用来更新E的，虽然也是一样代入wx+b公式来算，但是实际并不是原函数的b，SMO算法最终只是求出一个α。\n",
    "\n",
    "求出α之后，再拿回去求出w和b。\n",
    "\n",
    "可以随便选择一个支持向量的分量来计算b，但由于对原始的b是一个范围，所以实际中选取了所有满足条件点的的均值。"
   ]
  },
  {
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