Support Vector Machines.ipynb

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   "cells": [
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     "cell_type": "code",
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     "input": [
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "class SVC():\n",
      "    \"\"\"\n",
      "    support vector machines for classification\n",
      "    \"\"\"\n",
      "    def __init__(self,C=1.0,kernel='linear',gamma=0.0,max_iter=40,tol=0.001):\n",
      "        self.C=C\n",
      "        self.kernel=kernel\n",
      "        self.gamma=gamma\n",
      "        self.max_iter=max_iter\n",
      "        self.tol=tol\n",
      "        self.alphas=None\n",
      "        self.b=0\n",
      "        self.w=None\n",
      "        self.errorCache=None\n",
      "        self.y_uniques=None\n",
      "        return None\n",
      "    def calcError(self,X,y,i):\n",
      "        \"\"\"\n",
      "        calculate the term Ei\n",
      "        \"\"\"\n",
      "        #print self.alphas*y,'\\n'\n",
      "        #print np.dot(X,X[i,:]),'\\n'\n",
      "        ui=(self.alphas*y).dot(np.dot(X,X[i,:]))+self.b\n",
      "        #print ui\n",
      "        Ei=ui-y[i]\n",
      "        return Ei\n",
      "    def selectj(self,X,y,i,Ei):\n",
      "        \"\"\"\n",
      "        given the first ai,find the second aj,making the absolute value of ei-ej bigggest\n",
      "        \"\"\"\n",
      "        maxj=-1\n",
      "        maxDeltaE=0\n",
      "        Ej=0\n",
      "        self.errorCache[i]=[i,Ei]\n",
      "        validation_indices=nonzero(self.errorCache[:,0])[0]\n",
      "        if len(validation_indices)>1:\n",
      "            for k in validation_indices:\n",
      "                if k==i:continue\n",
      "                Ek=self.calcError(X,y,k)\n",
      "                deltaE=abs(Ek-Ei)\n",
      "                if(deltaE>maxDeltaE):\n",
      "                    maxDeltaE=deltaE\n",
      "                    maxj=k\n",
      "                    Ej=Ek\n",
      "        else:\n",
      "            j=i\n",
      "            while j==i:\n",
      "                j=int(random.uniform(0,len(X)))\n",
      "            Ej=self.calcError(X,y,j)\n",
      "        return maxj,Ej\n",
      "    def updateEk(self,X,y,k):\n",
      "        \"\"\"\n",
      "        store the error\n",
      "        \"\"\"\n",
      "        Ek=self.calcError(X,y,k)\n",
      "        self.errorCache[k]=[1,Ek]\n",
      "        return None\n",
      "    def solveLagrangeMultipliers(self,X,y,i):\n",
      "        \"\"\"\n",
      "        calculate the ai and aj, and b\n",
      "        \"\"\"\n",
      "        Ei=self.calcError(X,y,i)\n",
      "        \n",
      "        if ((y[i]*Ei<-self.tol) and (self.alphas[i]<self.C)) or ((y[i]*Ei)>self.tol and (self.alphas[i]>0)):\n",
      "            j,Ej=self.selectj(X,y,i,Ei)\n",
      "            alphaI_old=self.alphas[i]\n",
      "            alphaJ_old=self.alphas[j]\n",
      "            \n",
      "            if(y[i]!=y[j]):\n",
      "                L=max(0,self.alphas[j]-self.alphas[i])\n",
      "                H=min(self.C,self.C+self.alphas[j]-self.alphas[i])\n",
      "            else:\n",
      "                L=max(0,self.alphas[j]+self.alphas[i]-self.C)\n",
      "                H=min(self.C,self.alphas[j]+self.alphas[i])\n",
      "            if L==H:\n",
      "                print \"L==H\"\n",
      "                return 0\n",
      "            eta=X[i,:].dot(X[i,:])+X[j,:].dot(X[j,:])-2.0*X[i,:].dot(X[j,:])\n",
      "            if eta>0:\n",
      "                self.alphas[j]+=y[j]*(Ei-Ej)/eta*1.0\n",
      "                if self.alphas[j]<L:\n",
      "                    self.alphas[j]=L\n",
      "                elif self.alphas[j]>H:\n",
      "                    self.alphas[j]=H\n",
      "            else:#in practice can be handled by calcaludate the objective function value lobj and hobj\n",
      "                print 'eta<0'\n",
      "                return 0\n",
      "            self.updateEk(X,y,j)\n",
      "            if(abs(self.alphas[j]-alphaJ_old)<0.00001):\n",
      "                print 'j the second a not moving enough'\n",
      "                return 0\n",
      "            self.alphas[i]+=y[i]*y[j]*(alphaJ_old-self.alphas[j])\n",
      "            self.updateEk(X,y,i)\n",
      "            \n",
      "            b1=self.b-Ei-y[i]*(self.alphas[i]-alphaI_old)*X[i,:].dot(X[i,:])-y[j]*(self.alphas[j]-alphaJ_old)*X[i,:].dot(X[j,:])\n",
      "            b2=self.b-Ej-y[i]*(self.alphas[i]-alphaI_old)*X[i,:].dot(X[j,:])-y[j]*(self.alphas[j]-alphaJ_old)*X[j,:].dot(X[j,:])\n",
      "            \n",
      "            if((self.alphas[i]>0) and (self.alphas[i]<self.C)):\n",
      "                self.b=b1\n",
      "            elif ((self.alphas[j]>0) and (self.alphas[j]<self.C)):\n",
      "                self.b=b2\n",
      "            else:\n",
      "                self.b=(b1+b2)/2.0\n",
      "        return 1\n",
      "    def smoP(self,X,y):\n",
      "        \"\"\"\n",
      "        the outer loop of the smo\n",
      "        \"\"\"\n",
      "        iteration_num=0\n",
      "        entireSet=True\n",
      "        alphaPairChanged=0\n",
      "        while (iteration_num<self.max_iter) and ((alphaPairChanged>0) or entireSet):\n",
      "            alphaPairChanged=0\n",
      "            if entireSet:\n",
      "                for i in range(len(X)):\n",
      "                    alphaPairChanged+=self.solveLagrangeMultipliers(X,y,i)\n",
      "                    #print 'fullset ,iter:%d i:%d, pairs changed %d' %(iteration_num,i,alphaPairChanged)\n",
      "                iteration_num+=1\n",
      "            else:\n",
      "                nonBoundIndices=nonzero((self.alphas>0)*(self.alphas<self.C))[0]\n",
      "                for i in nonBoundIndices:\n",
      "                    alphaPairChanged+=self.solveLagrangeMultipliers(X,y,i)\n",
      "                    #print 'fullset ,iter:%d i:%d, pairs changed %d' %(iteration_num,i,alphaPairChanged)\n",
      "                iteration_num+=1\n",
      "            if entireSet:entireSet=False\n",
      "            elif alphaPairChanged==0:entireSet=True\n",
      "            #print 'iteration number :%d ' % iteration_num\n",
      "        return self.alphas,self.b\n",
      "    def fit(self,X,y):\n",
      "        \"\"\"\n",
      "        fit the data\n",
      "        \"\"\"\n",
      "        self.alphas=np.zeros(len(X))\n",
      "        self.errorCache=np.zeros((len(X),2))\n",
      "        self.w=np.zeros(X.shape[1])\n",
      "        if len(np.unique(y))!=2:\n",
      "            print 'there more than 2 class label'\n",
      "            return\n",
      "        self.y_uniques=sorted(np.unique(y))\n",
      "        y[y==self.y_uniques[0]]=-1\n",
      "        y[y==self.y_uniques[1]]=1\n",
      "        \n",
      "        self.smoP(X,y)\n",
      "        for i in range(len(X)):\n",
      "            self.w+=self.alphas[i]*y[i]*X[i,:]\n",
      "        #print y,self.y_uniques,'\\n'\n",
      "        return self\n",
      "    def predict(self,test_X):\n",
      "        \"\"\"\n",
      "        predict the test sample,classification\n",
      "        \"\"\"\n",
      "        predictions=[]\n",
      "        for test_vec in test_X:\n",
      "            if np.dot(self.w,test_vec)+self.b>0:\n",
      "                predictions.append(self.y_uniques[1])\n",
      "            else:\n",
      "                predictions.append(self.y_uniques[0])\n",
      "        return np.array(predictions)\n",
      "    "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 49
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(__doc__)\n",
      "import pdb\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "\n",
      "# we create 40 separable points\n",
      "np.random.seed(0)\n",
      "X = np.r_[np.random.randn(20, 2) - [2, 2], np.random.randn(20, 2) + [2, 2]]\n",
      "Y =np.array([0] * 20 + [1] * 20) \n",
      "\n",
      "# fit the model\n",
      "clf = SVC(max_iter=50)\n",
      "\n",
      "clf.fit(X, Y)\n",
      "\n",
      "# get the separating hyperplane\n",
      "\n",
      "w = clf.w\n",
      "print w,clf.alphas,clf.b\n",
      "\n",
      "a = -w[0] / w[1]\n",
      "xx = np.linspace(-5, 5)\n",
      "yy = a * xx -(clf.b) / w[1]\n",
      "\n",
      "\n",
      "# plot the line, the points, and the nearest vectors to the plane\n",
      "plt.plot(xx, yy, 'k')\n",
      "\n",
      "\n",
      "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)\n",
      "\n",
      "plt.axis('tight')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
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       "stream": "stdout",
       "text": [
        "Automatically created module for IPython interactive environment\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "L==H\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "j the second a not moving enough\n",
        "[ 0.85178605  0.35181497] [ 0.          0.41366501  0.          0.          0.          0.          0.\n",
        "  0.          0.          0.          0.          0.          0.05243618\n",
        "  0.          0.          0.          0.          0.          0.          0.\n",
        "  0.46610119  0.          0.          0.          0.          0.          0.\n",
        "  0.          0.          0.          0.          0.          0.          0.\n",
        "  0.          0.          0.          0.          0.          0.        ] -0.0144756821141\n"
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       "text": [
        "<matplotlib.figure.Figure at 0xb317c18>"
       ]
      }
     ],
     "prompt_number": 50
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(__doc__)\n",
      "\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "from sklearn import svm\n",
      "\n",
      "# we create 40 separable points\n",
      "np.random.seed(0)\n",
      "X = np.r_[np.random.randn(20, 2) - [2, 2], np.random.randn(20, 2) + [2, 2]]\n",
      "Y = [0] * 20 + [1] * 20\n",
      "\n",
      "# fit the model\n",
      "clf = svm.SVC(kernel='linear')\n",
      "clf.fit(X, Y)\n",
      "\n",
      "# get the separating hyperplane\n",
      "w = clf.coef_[0]\n",
      "print clf.coef_[0],clf.intercept_[0]\n",
      "a = -w[0] / w[1]\n",
      "xx = np.linspace(-5, 5)\n",
      "yy = a * xx - (clf.intercept_[0]) / w[1]\n",
      "\n",
      "# plot the parallels to the separating hyperplane that pass through the\n",
      "# support vectors\n",
      "b = clf.support_vectors_[0]\n",
      "yy_down = a * xx + (b[1] - a * b[0])\n",
      "b = clf.support_vectors_[-1]\n",
      "yy_up = a * xx + (b[1] - a * b[0])\n",
      "\n",
      "# plot the line, the points, and the nearest vectors to the plane\n",
      "plt.plot(xx, yy, 'k-')\n",
      "plt.plot(xx, yy_down, 'k--')\n",
      "plt.plot(xx, yy_up, 'k--')\n",
      "\n",
      "plt.scatter(clf.support_vectors_[:, 0], clf.support_vectors_[:, 1],\n",
      "            s=80, facecolors='none')\n",
      "plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)\n",
      "\n",
      "plt.axis('tight')\n",
      "plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Automatically created module for IPython interactive environment\n",
        "[ 0.90230696  0.64821811] -0.234521286091\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8/bOy0VXDnZv8FGZhcNFmcvN+f8ilS5d+dr72zZs3OHLkCHbu3ImYmBi5ZVBX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\n9u7VrmgRGWPKplq1apIXbABwdnbG+fP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       "text": [
        "<matplotlib.figure.Figure at 0xa56c0f0>"
       ]
      }
     ],
     "prompt_number": 51
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}