SVM

ch05-SVM/Kernel.py

+# -*- coding: utf-8 -*-
+"""
+Created on Tue Jul 10 12:59:45 2018
+
+@author: Administrator
+"""
+
+from numpy import *
+from load_data import *
+import SMO_platt
+import numpy
+
+def kernelTrans( X, A, kTup):
+    '''
+    RBF kernel function
+    '''
+    m ,n = shape(X)
+    K = mat(zeros((m,1)))
+    if kTup[0] == 'lin': K = X * A.T
+    elif kTup[0] == 'rbf':
+        for j in range(m):
+            deltaRow = X[j,:] - A
+            K[j] = deltaRow * deltaRow.T
+        K = numpy.exp(K / (-1 * kTup[1] ** 2))
+    
+    else:   raise NameError('huston ---')
+    return K
+
+def testRbf(k1=1.3):
+    dataArr,labelArr = loadDataSet('testSetRBF.txt')
+    b,alphas = SMO_platt.smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) #C=200 important
+    datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
+    svInd=nonzero(alphas.A>0)[0]
+    sVs=datMat[svInd] #get matrix of only support vectors
+    labelSV = labelMat[svInd];
+    print("there are %d Support Vectors" % shape(sVs)[0])
+    m,n = shape(datMat)
+    errorCount = 0
+    for i in range(m):
+        kernelEval = kernelTrans(sVs,datMat[i,:],('rbf', k1))
+        predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + b
+        if sign(predict)!=sign(labelArr[i]): errorCount += 1
+    print("the training error rate is: %f" % (float(errorCount)/m))
+    dataArr,labelArr = loadDataSet('testSetRBF2.txt')
+    errorCount = 0
+    datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
+    m,n = shape(datMat)
+    for i in range(m):
+        kernelEval = kernelTrans(sVs,datMat[i,:],('rbf', k1))
+        predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + b
+        if sign(predict)!=sign(labelArr[i]): errorCount += 1    
+    print("the test error rate is: %f" % (float(errorCount)/m))    
\ No newline at end of file

ch05-SVM/Opt_smo.py

+# -*- coding: utf-8 -*-
+"""
+Created on Tue Jul 10 12:26:21 2018
+
+@author: Administrator
+"""
+
+from numpy import *
+from Kernel import *
+
+#启发式SMO算法的支持函数
+#新建一个类的收据结构，保存当前重要的值
+class optStruct:
+    def __init__(self,dataMatIn,classLabels,C,toler, kTup):
+        self.X=dataMatIn
+        self.labelMat=classLabels
+        self.C=C
+        self.tol=toler
+        self.m=shape(dataMatIn)[0]
+        self.alphas=mat(zeros((self.m,1)))
+        self.b=0
+        self.Cache=mat(zeros((self.m,2)))
+        self.K = mat(zeros((self.m,self.m)))
+        for i in range(self.m):
+            self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup)
+#格式化计算误差的函数，方便多次调用
+
+
+def calcEk(oS, k):
+    '''计算预测误差'''
+    fXk = float(multiply(oS.alphas,oS.labelMat).T*oS.K[:,k] + oS.b)
+    Ek = fXk - float(oS.labelMat[k])
+    return Ek
+#修改选择第二个变量alphaj的方法
+def selectJ(i,oS,Ei):
+    maxK=-1;maxDeltaE= 0 ;Ej=0
+    #将误差矩阵每一行第一列置1，以此确定出误差不为0
+    #的样本
+    oS.Cache[i]=[1,Ei]
+    #获取缓存中Ei不为0的样本对应的alpha列表
+    validEcacheList=nonzero(oS.Cache[:,0].A)[0]
+    #在误差不为0的列表中找出使abs(Ei-Ej)最大的alphaj
+    if(len(validEcacheList)>0):
+        for k in validEcacheList:
+            if k ==i:continue
+            Ek=calcEk(oS,k)
+            deltaE=abs(Ei-Ek)
+            if(deltaE>maxDeltaE):
+                maxK=k;maxDeltaE=deltaE;Ej=Ek
+        return maxK,Ej
+    else:
+    #否则，就从样本集中随机选取alphaj
+        j=selectJrand(i,oS.m)
+        Ej=calcEk(oS,j)
+    return j,Ej
+#更新误差矩阵
+def updateEk(oS,k):
+    Ek=calcEk(oS,k)
+    oS.Cache[k]=[1,Ek]
\ No newline at end of file

ch05-SVM/SMO_platt.py

+# -*- coding: utf-8 -*-
+"""
+Created on Tue Jul 10 12:32:40 2018
+
+@author: Administrator
+"""
+
+from smo_simp import *
+
+from Opt_smo import *
+import Opt_smo
+
+#内循环寻找alphaj
+def innerL(i, oS):
+    Ei = Opt_smo.calcEk(oS, i)
+    if ((oS.labelMat[i]*Ei < -oS.tol) and (oS.alphas[i] < oS.C)) or ((oS.labelMat[i]*Ei > oS.tol) and (oS.alphas[i] > 0)):
+        j,Ej = Opt_smo.selectJ(i, oS, Ei) #this has been changed from selectJrand
+        alphaIold = oS.alphas[i].copy(); alphaJold = oS.alphas[j].copy();
+        if (oS.labelMat[i] != oS.labelMat[j]):
+            L = max(0, oS.alphas[j] - oS.alphas[i])
+            H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i])
+        else:
+            L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C)
+            H = min(oS.C, oS.alphas[j] + oS.alphas[i])
+        if L==H: print("L==H"); return 0
+        eta = 2.0 * oS.K[i,j] - oS.K[i,i] - oS.K[j,j] #changed for kernel
+        if eta >= 0: print("eta>=0"); return 0
+        oS.alphas[j] -= oS.labelMat[j]*(Ei - Ej)/eta
+        oS.alphas[j] = clipAlpha(oS.alphas[j],H,L)
+        Opt_smo.updateEk(oS, j) #added this for the Ecache
+        if (abs(oS.alphas[j] - alphaJold) < 0.00001): print("j not moving enough"); return 0
+        oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])#update i by the same amount as j
+        Opt_smo.updateEk(oS, i) #added this for the Ecache                    #the update is in the oppostie direction
+        b1 = oS.b - Ei- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.K[i,i] - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.K[i,j]
+        b2 = oS.b - Ej- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.K[i,j]- oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.K[j,j]
+        if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]): oS.b = b1
+        elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]): oS.b = b2
+        else: oS.b = (b1 + b2)/2.0
+        return 1
+    else: return 0
+
+def smoP(dataMatIn, classLabels, C, toler, maxIter,kTup=('lin', 0)):    #full Platt SMO
+    oS = Opt_smo.optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler, kTup)
+    iter = 0
+    entireSet = True; alphaPairsChanged = 0
+    while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
+        alphaPairsChanged = 0
+        if entireSet:   #go over all
+            for i in range(oS.m):        
+                alphaPairsChanged += innerL(i,oS)
+                print("fullSet, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))
+            iter += 1
+        else:#go over non-bound (railed) alphas
+            nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
+            for i in nonBoundIs:
+                alphaPairsChanged += innerL(i,oS)
+                print("non-bound, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))
+            iter += 1
+        if entireSet: entireSet = False #toggle entire set loop
+        elif (alphaPairsChanged == 0): entireSet = True  
+        print("iteration number: %d" % iter)
+    return oS.b,oS.alphas
\ No newline at end of file

ch05-SVM/__init__.py

+#
\ No newline at end of file

ch05-SVM/__main__.py

+# -*- coding: utf-8 -*-
+"""
+Created on Tue Jul 10 11:54:15 2018
+
+@author: Administrator
+"""
+
+from numpy import *
+from load_data import *
+from smo_simp import *
+from Opt_smo import *
+from SMO_platt import *
+from Kernel import *
+from image_recog import *
+
+if __name__ == '__main__':
+    data, label = loadDataSet('testSet.txt')
+    #b, alpha = smoP(data, label, 0.6, 0.001, 40)
+    testRbf()
+    testDigits()
\ No newline at end of file

ch05-SVM/digits/testDigits/0_0.txt

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ch05-SVM/digits/testDigits/0_1.txt

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ch05-SVM/digits/testDigits/0_10.txt

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ch05-SVM/digits/testDigits/0_12.txt

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ch05-SVM/digits/testDigits/0_16.txt

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ch05-SVM/digits/testDigits/0_17.txt

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ch05-SVM/digits/testDigits/0_18.txt

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ch05-SVM/digits/testDigits/0_19.txt

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ch05-SVM/digits/testDigits/0_2.txt

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ch05-SVM/digits/testDigits/0_20.txt

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ch05-SVM/digits/testDigits/0_21.txt

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ch05-SVM/digits/testDigits/0_22.txt

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ch05-SVM/digits/testDigits/0_23.txt

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ch05-SVM/digits/testDigits/0_24.txt

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ch05-SVM/digits/testDigits/0_25.txt

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ch05-SVM/digits/testDigits/0_26.txt

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ch05-SVM/digits/testDigits/0_27.txt

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ch05-SVM/digits/testDigits/0_28.txt

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ch05-SVM/digits/testDigits/0_29.txt

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ch05-SVM/digits/testDigits/0_3.txt

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ch05-SVM/digits/testDigits/0_30.txt

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ch05-SVM/digits/testDigits/0_31.txt

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ch05-SVM/digits/testDigits/0_32.txt

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ch05-SVM/digits/testDigits/0_33.txt

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ch05-SVM/digits/testDigits/0_34.txt

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ch05-SVM/digits/testDigits/0_35.txt

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ch05-SVM/digits/testDigits/0_36.txt

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ch05-SVM/digits/testDigits/0_37.txt

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ch05-SVM/digits/testDigits/0_38.txt

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ch05-SVM/digits/testDigits/0_39.txt

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ch05-SVM/digits/testDigits/0_4.txt

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ch05-SVM/digits/testDigits/0_40.txt

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ch05-SVM/digits/testDigits/0_41.txt

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ch05-SVM/digits/testDigits/0_42.txt

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ch05-SVM/digits/testDigits/0_43.txt

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ch05-SVM/digits/testDigits/0_44.txt

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ch05-SVM/digits/testDigits/0_45.txt

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ch05-SVM/digits/testDigits/0_46.txt

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ch05-SVM/digits/testDigits/0_47.txt

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ch05-SVM/digits/testDigits/0_48.txt

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ch05-SVM/digits/testDigits/0_49.txt

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ch05-SVM/digits/testDigits/0_5.txt

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ch05-SVM/digits/testDigits/0_50.txt

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ch05-SVM/digits/testDigits/0_51.txt

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ch05-SVM/digits/testDigits/0_52.txt

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ch05-SVM/digits/testDigits/0_53.txt

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ch05-SVM/digits/testDigits/0_54.txt

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ch05-SVM/digits/testDigits/0_55.txt

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ch05-SVM/digits/testDigits/0_56.txt

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ch05-SVM/digits/testDigits/0_57.txt

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ch05-SVM/digits/testDigits/0_58.txt

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ch05-SVM/digits/testDigits/0_59.txt

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ch05-SVM/digits/testDigits/0_6.txt

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ch05-SVM/digits/testDigits/0_60.txt

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ch05-SVM/digits/testDigits/0_61.txt

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ch05-SVM/digits/testDigits/0_62.txt

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ch05-SVM/digits/testDigits/0_63.txt

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ch05-SVM/digits/testDigits/0_64.txt

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ch05-SVM/digits/testDigits/0_65.txt

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ch05-SVM/digits/testDigits/0_66.txt

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ch05-SVM/digits/testDigits/0_67.txt

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ch05-SVM/digits/testDigits/0_68.txt

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ch05-SVM/digits/testDigits/0_69.txt

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ch05-SVM/digits/testDigits/0_7.txt

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ch05-SVM/digits/testDigits/0_70.txt

+00000000000001111100000000000000
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ch05-SVM/digits/testDigits/0_71.txt

+00000000000011111100000000000000
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ch05-SVM/digits/testDigits/0_72.txt

+00000000000011111000000000000000
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ch05-SVM/digits/testDigits/0_73.txt

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ch05-SVM/digits/testDigits/0_74.txt

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ch05-SVM/digits/testDigits/0_75.txt

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ch05-SVM/digits/testDigits/0_76.txt

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ch05-SVM/digits/testDigits/0_77.txt

+00000000000111000000000000000000
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ch05-SVM/digits/testDigits/0_78.txt

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ch05-SVM/digits/testDigits/0_79.txt

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ch05-SVM/digits/testDigits/0_8.txt

+00000000000001110000000000000000
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ch05-SVM/digits/testDigits/0_80.txt

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ch05-SVM/digits/testDigits/0_81.txt

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ch05-SVM/digits/testDigits/0_82.txt

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ch05-SVM/digits/testDigits/0_83.txt

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ch05-SVM/digits/testDigits/0_84.txt

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ch05-SVM/digits/testDigits/0_85.txt

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ch05-SVM/digits/testDigits/0_86.txt

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ch05-SVM/digits/testDigits/0_9.txt

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ch05-SVM/digits/testDigits/1_0.txt

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ch05-SVM/digits/testDigits/1_1.txt

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ch05-SVM/digits/testDigits/1_10.txt

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ch05-SVM/digits/testDigits/1_11.txt

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ch05-SVM/digits/testDigits/1_12.txt

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ch05-SVM/digits/testDigits/1_13.txt

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ch05-SVM/digits/testDigits/1_14.txt

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ch05-SVM/digits/testDigits/1_15.txt

+00000000000000000000000000000000
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+00000001111111111111110000000000
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+00000001111111111000000000000000
+00000000001110000000000000000000
+00000000000000000000000000000000