机器学习实战：支持向量机

支持向量机（Support Vector Machine, SVM）是一类按监督学习（supervised learning）方式对数据进行二元分类（binary classification）的广义线性分类器（generalized linear classifier），其决策边界是对学习样本求解的最大边距超平面（maximum-margin hyperplane）。

SVM使用铰链损失函数（hinge loss）计算经验风险（empirical risk）并在求解系统中加入了正则化项以优化结构风险（structural risk），是一个具有稀疏性和稳健性的分类器。SVM可以通过核方法（kernel method）进行非线性分类，是常见的核学习（kernel learning）方法之一。

SVM被提出于1964年，在二十世纪90年代后得到快速发展并衍生出一系列改进和扩展算法，在人像识别（face recognition）、文本分类（text categorization）等模式识别（pattern recognition）问题中有得到应用。

机器学习实战源码：

'''
Created on Nov 4, 2010
Chapter 5 source file for Machine Learing in Action
@author: Peter
'''
from numpy import *
from time import sleepdef loadDataSet(fileName):dataMat = []; labelMat = []fr = open(fileName)for line in fr.readlines():lineArr = line.strip().split('\t')dataMat.append([float(lineArr[0]), float(lineArr[1])])labelMat.append(float(lineArr[2]))return dataMat,labelMatdef selectJrand(i,m):j=i #we want to select any J not equal to iwhile (j==i):j = int(random.uniform(0,m))return jdef clipAlpha(aj,H,L):if aj > H:aj = Hif L > aj:aj = Lreturn ajdef smoSimple(dataMatIn, classLabels, C, toler, maxIter):dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()b = 0; m,n = shape(dataMatrix)alphas = mat(zeros((m,1)))iter = 0while (iter < maxIter):alphaPairsChanged = 0for i in range(m):fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + bEi = fXi - float(labelMat[i])#if checks if an example violates KKT conditionsif ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):j = selectJrand(i,m)fXj = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + bEj = fXj - float(labelMat[j])alphaIold = alphas[i].copy(); alphaJold = alphas[j].copy();if (labelMat[i] != labelMat[j]):L = max(0, alphas[j] - alphas[i])H = min(C, C + alphas[j] - alphas[i])else:L = max(0, alphas[j] + alphas[i] - C)H = min(C, alphas[j] + alphas[i])if L==H: print("L==H"); continueeta = 2.0 * dataMatrix[i,:]*dataMatrix[j,:].T - dataMatrix[i,:]*dataMatrix[i,:].T - dataMatrix[j,:]*dataMatrix[j,:].Tif eta >= 0: print("eta>=0"); continuealphas[j] -= labelMat[j]*(Ei - Ej)/etaalphas[j] = clipAlpha(alphas[j],H,L)if (abs(alphas[j] - alphaJold) < 0.00001): print("j not moving enough"); continuealphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])#update i by the same amount as j#the update is in the oppostie directionb1 = b - Ei- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[i,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[i,:]*dataMatrix[j,:].Tb2 = b - Ej- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[j,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[j,:]*dataMatrix[j,:].Tif (0 < alphas[i]) and (C > alphas[i]): b = b1elif (0 < alphas[j]) and (C > alphas[j]): b = b2else: b = (b1 + b2)/2.0alphaPairsChanged += 1print("iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))if (alphaPairsChanged == 0): iter += 1else: iter = 0print("iteration number: %d" % iter)return b,alphasdef kernelTrans(X, A, kTup): #calc the kernel or transform data to a higher dimensional spacem,n = shape(X)K = mat(zeros((m,1)))if kTup[0]=='lin': K = X * A.T   #linear kernelelif kTup[0]=='rbf':for j in range(m):deltaRow = X[j,:] - AK[j] = deltaRow*deltaRow.TK = exp(K/(-1*kTup[1]**2)) #divide in NumPy is element-wise not matrix like Matlabelse: raise NameError('Houston We Have a Problem -- \That Kernel is not recognized')return Kclass optStruct:def __init__(self,dataMatIn, classLabels, C, toler, kTup):  # Initialize the structure with the parametersself.X = dataMatInself.labelMat = classLabelsself.C = Cself.tol = tolerself.m = shape(dataMatIn)[0]self.alphas = mat(zeros((self.m,1)))self.b = 0self.eCache = mat(zeros((self.m,2))) #first column is valid flagself.K = mat(zeros((self.m,self.m)))for i in range(self.m):self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup)def calcEk(oS, k):fXk = float(multiply(oS.alphas,oS.labelMat).T*oS.K[:,k] + oS.b)Ek = fXk - float(oS.labelMat[k])return Ekdef selectJ(i, oS, Ei):         #this is the second choice -heurstic, and calcs EjmaxK = -1; maxDeltaE = 0; Ej = 0oS.eCache[i] = [1,Ei]  #set valid #choose the alpha that gives the maximum delta EvalidEcacheList = nonzero(oS.eCache[:,0].A)[0]if (len(validEcacheList)) > 1:for k in validEcacheList:   #loop through valid Ecache values and find the one that maximizes delta Eif k == i: continue #don't calc for i, waste of timeEk = calcEk(oS, k)deltaE = abs(Ei - Ek)if (deltaE > maxDeltaE):maxK = k; maxDeltaE = deltaE; Ej = Ekreturn maxK, Ejelse:   #in this case (first time around) we don't have any valid eCache valuesj = selectJrand(i, oS.m)Ej = calcEk(oS, j)return j, Ejdef updateEk(oS, k):#after any alpha has changed update the new value in the cacheEk = calcEk(oS, k)oS.eCache[k] = [1,Ek]def innerL(i, oS):Ei = 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 = selectJ(i, oS, Ei) #this has been changed from selectJrandalphaIold = 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 0eta = 2.0 * oS.K[i,j] - oS.K[i,i] - oS.K[j,j] #changed for kernelif eta >= 0: print("eta>=0"); return 0oS.alphas[j] -= oS.labelMat[j]*(Ei - Ej)/etaoS.alphas[j] = clipAlpha(oS.alphas[j],H,L)updateEk(oS, j) #added this for the Ecacheif (abs(oS.alphas[j] - alphaJold) < 0.00001): print("j not moving enough"); return 0oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])#update i by the same amount as jupdateEk(oS, i) #added this for the Ecache                    #the update is in the oppostie directionb1 = 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 = b1elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]): oS.b = b2else: oS.b = (b1 + b2)/2.0return 1else: return 0def smoP(dataMatIn, classLabels, C, toler, maxIter,kTup=('lin', 0)):    #full Platt SMOoS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler, kTup)iter = 0entireSet = True; alphaPairsChanged = 0while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):alphaPairsChanged = 0if entireSet:   #go over allfor i in range(oS.m):alphaPairsChanged += innerL(i,oS)print("fullSet, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))iter += 1else:#go over non-bound (railed) alphasnonBoundIs = 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 += 1if entireSet: entireSet = False #toggle entire set loopelif (alphaPairsChanged == 0): entireSet = Trueprint("iteration number: %d" % iter)return oS.b,oS.alphasdef calcWs(alphas,dataArr,classLabels):X = mat(dataArr); labelMat = mat(classLabels).transpose()m,n = shape(X)w = zeros((n,1))for i in range(m):w += multiply(alphas[i]*labelMat[i],X[i,:].T)return wdef testRbf(k1=1.3):dataArr,labelArr = loadDataSet('testSetRBF.txt')b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) #C=200 importantdatMat=mat(dataArr); labelMat = mat(labelArr).transpose()svInd=nonzero(alphas.A>0)[0]sVs=datMat[svInd] #get matrix of only support vectorslabelSV = labelMat[svInd];print("there are %d Support Vectors" % shape(sVs)[0])m,n = shape(datMat)errorCount = 0for i in range(m):kernelEval = kernelTrans(sVs,datMat[i,:],('rbf', k1))predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + bif sign(predict)!=sign(labelArr[i]): errorCount += 1print("the training error rate is: %f" % (float(errorCount)/m))dataArr,labelArr = loadDataSet('testSetRBF2.txt')errorCount = 0datMat=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]) + bif sign(predict)!=sign(labelArr[i]): errorCount += 1print("the test error rate is: %f" % (float(errorCount)/m))def img2vector(filename):returnVect = zeros((1,1024))fr = open(filename)for i in range(32):lineStr = fr.readline()for j in range(32):returnVect[0,32*i+j] = int(lineStr[j])return returnVectdef loadImages(dirName):from os import listdirhwLabels = []trainingFileList = listdir(dirName)           #load the training setm = len(trainingFileList)trainingMat = zeros((m,1024))for i in range(m):fileNameStr = trainingFileList[i]fileStr = fileNameStr.split('.')[0]     #take off .txtclassNumStr = int(fileStr.split('_')[0])if classNumStr == 9: hwLabels.append(-1)else: hwLabels.append(1)trainingMat[i,:] = img2vector('%s/%s' % (dirName, fileNameStr))return trainingMat, hwLabelsdef testDigits(kTup=('rbf', 10)):dataArr,labelArr = loadImages('trainingDigits')b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTup)datMat=mat(dataArr); labelMat = mat(labelArr).transpose()svInd=nonzero(alphas.A>0)[0]sVs=datMat[svInd]labelSV = labelMat[svInd];print("there are %d Support Vectors" % shape(sVs)[0])m,n = shape(datMat)errorCount = 0for i in range(m):kernelEval = kernelTrans(sVs,datMat[i,:],kTup)predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + bif sign(predict)!=sign(labelArr[i]): errorCount += 1print("the training error rate is: %f" % (float(errorCount)/m))dataArr,labelArr = loadImages('testDigits')errorCount = 0datMat=mat(dataArr); labelMat = mat(labelArr).transpose()m,n = shape(datMat)for i in range(m):kernelEval = kernelTrans(sVs,datMat[i,:],kTup)predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + bif sign(predict)!=sign(labelArr[i]): errorCount += 1print("the test error rate is: %f" % (float(errorCount)/m))'''#######********************************
Non-Kernel VErsions below
'''#######********************************class optStructK:def __init__(self,dataMatIn, classLabels, C, toler):  # Initialize the structure with the parametersself.X = dataMatInself.labelMat = classLabelsself.C = Cself.tol = tolerself.m = shape(dataMatIn)[0]self.alphas = mat(zeros((self.m,1)))self.b = 0self.eCache = mat(zeros((self.m,2))) #first column is valid flagdef calcEkK(oS, k):fXk = float(multiply(oS.alphas,oS.labelMat).T*(oS.X*oS.X[k,:].T)) + oS.bEk = fXk - float(oS.labelMat[k])return Ekdef selectJK(i, oS, Ei):         #this is the second choice -heurstic, and calcs EjmaxK = -1; maxDeltaE = 0; Ej = 0oS.eCache[i] = [1,Ei]  #set valid #choose the alpha that gives the maximum delta EvalidEcacheList = nonzero(oS.eCache[:,0].A)[0]if (len(validEcacheList)) > 1:for k in validEcacheList:   #loop through valid Ecache values and find the one that maximizes delta Eif k == i: continue #don't calc for i, waste of timeEk = calcEk(oS, k)deltaE = abs(Ei - Ek)if (deltaE > maxDeltaE):maxK = k; maxDeltaE = deltaE; Ej = Ekreturn maxK, Ejelse:   #in this case (first time around) we don't have any valid eCache valuesj = selectJrand(i, oS.m)Ej = calcEk(oS, j)return j, Ejdef updateEkK(oS, k):#after any alpha has changed update the new value in the cacheEk = calcEk(oS, k)oS.eCache[k] = [1,Ek]def innerLK(i, oS):Ei = 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 = selectJ(i, oS, Ei) #this has been changed from selectJrandalphaIold = 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 0eta = 2.0 * oS.X[i,:]*oS.X[j,:].T - oS.X[i,:]*oS.X[i,:].T - oS.X[j,:]*oS.X[j,:].Tif eta >= 0: print("eta>=0"); return 0oS.alphas[j] -= oS.labelMat[j]*(Ei - Ej)/etaoS.alphas[j] = clipAlpha(oS.alphas[j],H,L)updateEk(oS, j) #added this for the Ecacheif (abs(oS.alphas[j] - alphaJold) < 0.00001): print("j not moving enough"); return 0oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j]) #update i by the same amount as jupdateEk(oS, i) #added this for the Ecache                    #the update is in the oppostie directionb1 = oS.b - Ei- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.X[i,:]*oS.X[i,:].T - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.X[i,:]*oS.X[j,:].Tb2 = oS.b - Ej- oS.labelMat[i]*(oS.alphas[i]-alphaIold)*oS.X[i,:]*oS.X[j,:].T - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.X[j,:]*oS.X[j,:].Tif (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]): oS.b = b1elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]): oS.b = b2else: oS.b = (b1 + b2)/2.0return 1else: return 0def smoPK(dataMatIn, classLabels, C, toler, maxIter):    #full Platt SMOoS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler)iter = 0entireSet = True; alphaPairsChanged = 0while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):alphaPairsChanged = 0if entireSet:   #go over allfor i in range(oS.m):alphaPairsChanged += innerL(i,oS)print("fullSet, iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged))iter += 1else:#go over non-bound (railed) alphasnonBoundIs = 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 += 1if entireSet: entireSet = False #toggle entire set loopelif (alphaPairsChanged == 0): entireSet = Trueprint("iteration number: %d" % iter)return oS.b,oS.alphasif __name__ == '__main__':testRbf()

运行结果：

"C:\Program Files\Python\Python37\python.exe" "D:/Pycharm Projects/MLDemo/MLDemo.py"
L==H
fullSet, iter: 0 i:0, pairs changed 0
fullSet, iter: 0 i:1, pairs changed 1
fullSet, iter: 0 i:2, pairs changed 2
fullSet, iter: 0 i:3, pairs changed 3
fullSet, iter: 0 i:4, pairs changed 3
fullSet, iter: 0 i:5, pairs changed 4
fullSet, iter: 0 i:6, pairs changed 5
fullSet, iter: 0 i:7, pairs changed 5
fullSet, iter: 0 i:8, pairs changed 6
fullSet, iter: 0 i:9, pairs changed 6
fullSet, iter: 0 i:10, pairs changed 7
fullSet, iter: 0 i:11, pairs changed 8
j not moving enough
fullSet, iter: 0 i:12, pairs changed 8
fullSet, iter: 0 i:13, pairs changed 9
fullSet, iter: 0 i:14, pairs changed 10
fullSet, iter: 0 i:15, pairs changed 11
fullSet, iter: 0 i:16, pairs changed 12
fullSet, iter: 0 i:17, pairs changed 12
fullSet, iter: 0 i:18, pairs changed 13
fullSet, iter: 0 i:19, pairs changed 14
fullSet, iter: 0 i:20, pairs changed 14
fullSet, iter: 0 i:21, pairs changed 15
fullSet, iter: 0 i:22, pairs changed 15
fullSet, iter: 0 i:23, pairs changed 15
fullSet, iter: 0 i:24, pairs changed 16
j not moving enough
fullSet, iter: 0 i:25, pairs changed 16
fullSet, iter: 0 i:26, pairs changed 16
j not moving enough
fullSet, iter: 0 i:27, pairs changed 16
fullSet, iter: 0 i:28, pairs changed 16
fullSet, iter: 0 i:29, pairs changed 16
j not moving enough
fullSet, iter: 0 i:30, pairs changed 16
fullSet, iter: 0 i:31, pairs changed 17
fullSet, iter: 0 i:32, pairs changed 17
fullSet, iter: 0 i:33, pairs changed 18
j not moving enough
fullSet, iter: 0 i:34, pairs changed 18
fullSet, iter: 0 i:35, pairs changed 18
fullSet, iter: 0 i:36, pairs changed 19
fullSet, iter: 0 i:37, pairs changed 19
fullSet, iter: 0 i:38, pairs changed 19
j not moving enough
fullSet, iter: 0 i:39, pairs changed 19
fullSet, iter: 0 i:40, pairs changed 20
fullSet, iter: 0 i:41, pairs changed 21
L==H
fullSet, iter: 0 i:42, pairs changed 21
fullSet, iter: 0 i:43, pairs changed 21
j not moving enough
fullSet, iter: 0 i:44, pairs changed 21
fullSet, iter: 0 i:45, pairs changed 22
fullSet, iter: 0 i:46, pairs changed 22
fullSet, iter: 0 i:47, pairs changed 22
fullSet, iter: 0 i:48, pairs changed 23
fullSet, iter: 0 i:49, pairs changed 23
fullSet, iter: 0 i:50, pairs changed 24
j not moving enough
fullSet, iter: 0 i:51, pairs changed 24
fullSet, iter: 0 i:52, pairs changed 25
fullSet, iter: 0 i:53, pairs changed 25
fullSet, iter: 0 i:54, pairs changed 26
fullSet, iter: 0 i:55, pairs changed 26
fullSet, iter: 0 i:56, pairs changed 27
L==H
fullSet, iter: 0 i:57, pairs changed 27
fullSet, iter: 0 i:58, pairs changed 27
fullSet, iter: 0 i:59, pairs changed 27
j not moving enough
fullSet, iter: 0 i:60, pairs changed 27
fullSet, iter: 0 i:61, pairs changed 28
fullSet, iter: 0 i:62, pairs changed 29
fullSet, iter: 0 i:63, pairs changed 29
fullSet, iter: 0 i:64, pairs changed 29
fullSet, iter: 0 i:65, pairs changed 29
fullSet, iter: 0 i:66, pairs changed 29
fullSet, iter: 0 i:67, pairs changed 29
fullSet, iter: 0 i:68, pairs changed 29
fullSet, iter: 0 i:69, pairs changed 29
fullSet, iter: 0 i:70, pairs changed 29
fullSet, iter: 0 i:71, pairs changed 29
fullSet, iter: 0 i:72, pairs changed 29
fullSet, iter: 0 i:73, pairs changed 29
fullSet, iter: 0 i:74, pairs changed 30
j not moving enough
fullSet, iter: 0 i:75, pairs changed 30
fullSet, iter: 0 i:76, pairs changed 30
fullSet, iter: 0 i:77, pairs changed 30
fullSet, iter: 0 i:78, pairs changed 30
fullSet, iter: 0 i:79, pairs changed 30
j not moving enough
fullSet, iter: 0 i:80, pairs changed 30
fullSet, iter: 0 i:81, pairs changed 30
L==H
fullSet, iter: 0 i:82, pairs changed 30
fullSet, iter: 0 i:83, pairs changed 30
fullSet, iter: 0 i:84, pairs changed 30
fullSet, iter: 0 i:85, pairs changed 30
fullSet, iter: 0 i:86, pairs changed 30
fullSet, iter: 0 i:87, pairs changed 30
fullSet, iter: 0 i:88, pairs changed 30
fullSet, iter: 0 i:89, pairs changed 30
fullSet, iter: 0 i:90, pairs changed 30
fullSet, iter: 0 i:91, pairs changed 30
fullSet, iter: 0 i:92, pairs changed 30
fullSet, iter: 0 i:93, pairs changed 30
fullSet, iter: 0 i:94, pairs changed 30
fullSet, iter: 0 i:95, pairs changed 30
L==H
fullSet, iter: 0 i:96, pairs changed 30
fullSet, iter: 0 i:97, pairs changed 30
fullSet, iter: 0 i:98, pairs changed 30
L==H
fullSet, iter: 0 i:99, pairs changed 30
iteration number: 1
non-bound, iter: 1 i:0, pairs changed 1
j not moving enough
non-bound, iter: 1 i:1, pairs changed 1
non-bound, iter: 1 i:2, pairs changed 2
j not moving enough
non-bound, iter: 1 i:3, pairs changed 2
j not moving enough
non-bound, iter: 1 i:6, pairs changed 2
j not moving enough
non-bound, iter: 1 i:8, pairs changed 2
j not moving enough
non-bound, iter: 1 i:10, pairs changed 2
j not moving enough
non-bound, iter: 1 i:11, pairs changed 2
j not moving enough
non-bound, iter: 1 i:13, pairs changed 2
j not moving enough
non-bound, iter: 1 i:14, pairs changed 2
non-bound, iter: 1 i:15, pairs changed 3
j not moving enough
non-bound, iter: 1 i:16, pairs changed 3
j not moving enough
non-bound, iter: 1 i:18, pairs changed 3
j not moving enough
non-bound, iter: 1 i:19, pairs changed 3
j not moving enough
non-bound, iter: 1 i:21, pairs changed 3
j not moving enough
non-bound, iter: 1 i:27, pairs changed 3
j not moving enough
non-bound, iter: 1 i:30, pairs changed 3
j not moving enough
non-bound, iter: 1 i:31, pairs changed 3
j not moving enough
non-bound, iter: 1 i:33, pairs changed 3
j not moving enough
non-bound, iter: 1 i:36, pairs changed 3
j not moving enough
non-bound, iter: 1 i:40, pairs changed 3
non-bound, iter: 1 i:41, pairs changed 3
j not moving enough
non-bound, iter: 1 i:42, pairs changed 3
j not moving enough
non-bound, iter: 1 i:45, pairs changed 3
j not moving enough
non-bound, iter: 1 i:48, pairs changed 3
j not moving enough
non-bound, iter: 1 i:50, pairs changed 3
j not moving enough
non-bound, iter: 1 i:52, pairs changed 3
j not moving enough
non-bound, iter: 1 i:54, pairs changed 3
non-bound, iter: 1 i:56, pairs changed 4
j not moving enough
non-bound, iter: 1 i:61, pairs changed 4
non-bound, iter: 1 i:62, pairs changed 5
j not moving enough
non-bound, iter: 1 i:74, pairs changed 5
iteration number: 2
j not moving enough
non-bound, iter: 2 i:1, pairs changed 0
j not moving enough
non-bound, iter: 2 i:2, pairs changed 0
j not moving enough
non-bound, iter: 2 i:3, pairs changed 0
j not moving enough
non-bound, iter: 2 i:6, pairs changed 0
non-bound, iter: 2 i:8, pairs changed 1
j not moving enough
non-bound, iter: 2 i:10, pairs changed 1
non-bound, iter: 2 i:11, pairs changed 2
j not moving enough
non-bound, iter: 2 i:13, pairs changed 2
j not moving enough
non-bound, iter: 2 i:14, pairs changed 2
j not moving enough
non-bound, iter: 2 i:16, pairs changed 2
j not moving enough
non-bound, iter: 2 i:18, pairs changed 2
j not moving enough
non-bound, iter: 2 i:19, pairs changed 2
j not moving enough
non-bound, iter: 2 i:21, pairs changed 2
j not moving enough
non-bound, iter: 2 i:27, pairs changed 2
j not moving enough
non-bound, iter: 2 i:30, pairs changed 2
j not moving enough
non-bound, iter: 2 i:31, pairs changed 2
j not moving enough
non-bound, iter: 2 i:33, pairs changed 2
j not moving enough
non-bound, iter: 2 i:36, pairs changed 2
j not moving enough
non-bound, iter: 2 i:40, pairs changed 2
j not moving enough
non-bound, iter: 2 i:41, pairs changed 2
j not moving enough
non-bound, iter: 2 i:42, pairs changed 2
j not moving enough
non-bound, iter: 2 i:45, pairs changed 2
j not moving enough
non-bound, iter: 2 i:48, pairs changed 2
j not moving enough
non-bound, iter: 2 i:50, pairs changed 2
j not moving enough
non-bound, iter: 2 i:52, pairs changed 2
j not moving enough
non-bound, iter: 2 i:54, pairs changed 2
j not moving enough
non-bound, iter: 2 i:56, pairs changed 2
j not moving enough
non-bound, iter: 2 i:61, pairs changed 2
j not moving enough
non-bound, iter: 2 i:62, pairs changed 2
j not moving enough
non-bound, iter: 2 i:74, pairs changed 2
iteration number: 3
j not moving enough
non-bound, iter: 3 i:1, pairs changed 0
j not moving enough
non-bound, iter: 3 i:2, pairs changed 0
j not moving enough
non-bound, iter: 3 i:3, pairs changed 0
j not moving enough
non-bound, iter: 3 i:6, pairs changed 0
j not moving enough
non-bound, iter: 3 i:8, pairs changed 0
j not moving enough
non-bound, iter: 3 i:10, pairs changed 0
non-bound, iter: 3 i:11, pairs changed 0
j not moving enough
non-bound, iter: 3 i:13, pairs changed 0
j not moving enough
non-bound, iter: 3 i:14, pairs changed 0
j not moving enough
non-bound, iter: 3 i:16, pairs changed 0
j not moving enough
non-bound, iter: 3 i:18, pairs changed 0
j not moving enough
non-bound, iter: 3 i:19, pairs changed 0
j not moving enough
non-bound, iter: 3 i:21, pairs changed 0
j not moving enough
non-bound, iter: 3 i:27, pairs changed 0
j not moving enough
non-bound, iter: 3 i:30, pairs changed 0
j not moving enough
non-bound, iter: 3 i:31, pairs changed 0
j not moving enough
non-bound, iter: 3 i:33, pairs changed 0
j not moving enough
non-bound, iter: 3 i:36, pairs changed 0
j not moving enough
non-bound, iter: 3 i:40, pairs changed 0
j not moving enough
non-bound, iter: 3 i:41, pairs changed 0
j not moving enough
non-bound, iter: 3 i:42, pairs changed 0
j not moving enough
non-bound, iter: 3 i:45, pairs changed 0
j not moving enough
non-bound, iter: 3 i:48, pairs changed 0
j not moving enough
non-bound, iter: 3 i:50, pairs changed 0
j not moving enough
non-bound, iter: 3 i:52, pairs changed 0
j not moving enough
non-bound, iter: 3 i:54, pairs changed 0
j not moving enough
non-bound, iter: 3 i:56, pairs changed 0
j not moving enough
non-bound, iter: 3 i:61, pairs changed 0
j not moving enough
non-bound, iter: 3 i:62, pairs changed 0
j not moving enough
non-bound, iter: 3 i:74, pairs changed 0
iteration number: 4
j not moving enough
fullSet, iter: 4 i:0, pairs changed 0
j not moving enough
fullSet, iter: 4 i:1, pairs changed 0
j not moving enough
fullSet, iter: 4 i:2, pairs changed 0
j not moving enough
fullSet, iter: 4 i:3, pairs changed 0
fullSet, iter: 4 i:4, pairs changed 0
fullSet, iter: 4 i:5, pairs changed 0
j not moving enough
fullSet, iter: 4 i:6, pairs changed 0
fullSet, iter: 4 i:7, pairs changed 0
j not moving enough
fullSet, iter: 4 i:8, pairs changed 0
fullSet, iter: 4 i:9, pairs changed 0
j not moving enough
fullSet, iter: 4 i:10, pairs changed 0
fullSet, iter: 4 i:11, pairs changed 0
fullSet, iter: 4 i:12, pairs changed 0
j not moving enough
fullSet, iter: 4 i:13, pairs changed 0
j not moving enough
fullSet, iter: 4 i:14, pairs changed 0
fullSet, iter: 4 i:15, pairs changed 0
j not moving enough
fullSet, iter: 4 i:16, pairs changed 0
L==H
fullSet, iter: 4 i:17, pairs changed 0
j not moving enough
fullSet, iter: 4 i:18, pairs changed 0
j not moving enough
fullSet, iter: 4 i:19, pairs changed 0
fullSet, iter: 4 i:20, pairs changed 0
j not moving enough
fullSet, iter: 4 i:21, pairs changed 0
fullSet, iter: 4 i:22, pairs changed 0
fullSet, iter: 4 i:23, pairs changed 0
j not moving enough
fullSet, iter: 4 i:24, pairs changed 0
L==H
fullSet, iter: 4 i:25, pairs changed 0
fullSet, iter: 4 i:26, pairs changed 0
j not moving enough
fullSet, iter: 4 i:27, pairs changed 0
fullSet, iter: 4 i:28, pairs changed 0
fullSet, iter: 4 i:29, pairs changed 0
j not moving enough
fullSet, iter: 4 i:30, pairs changed 0
j not moving enough
fullSet, iter: 4 i:31, pairs changed 0
fullSet, iter: 4 i:32, pairs changed 0
j not moving enough
fullSet, iter: 4 i:33, pairs changed 0
fullSet, iter: 4 i:34, pairs changed 0
fullSet, iter: 4 i:35, pairs changed 0
j not moving enough
fullSet, iter: 4 i:36, pairs changed 0
fullSet, iter: 4 i:37, pairs changed 0
L==H
fullSet, iter: 4 i:38, pairs changed 0
fullSet, iter: 4 i:39, pairs changed 0
j not moving enough
fullSet, iter: 4 i:40, pairs changed 0
j not moving enough
fullSet, iter: 4 i:41, pairs changed 0
j not moving enough
fullSet, iter: 4 i:42, pairs changed 0
j not moving enough
fullSet, iter: 4 i:43, pairs changed 0
fullSet, iter: 4 i:44, pairs changed 0
j not moving enough
fullSet, iter: 4 i:45, pairs changed 0
L==H
fullSet, iter: 4 i:46, pairs changed 0
fullSet, iter: 4 i:47, pairs changed 0
j not moving enough
fullSet, iter: 4 i:48, pairs changed 0
fullSet, iter: 4 i:49, pairs changed 0
j not moving enough
fullSet, iter: 4 i:50, pairs changed 0
fullSet, iter: 4 i:51, pairs changed 0
j not moving enough
fullSet, iter: 4 i:52, pairs changed 0
L==H
fullSet, iter: 4 i:53, pairs changed 0
j not moving enough
fullSet, iter: 4 i:54, pairs changed 0
fullSet, iter: 4 i:55, pairs changed 0
j not moving enough
fullSet, iter: 4 i:56, pairs changed 0
fullSet, iter: 4 i:57, pairs changed 0
L==H
fullSet, iter: 4 i:58, pairs changed 0
fullSet, iter: 4 i:59, pairs changed 0
fullSet, iter: 4 i:60, pairs changed 0
j not moving enough
fullSet, iter: 4 i:61, pairs changed 0
j not moving enough
fullSet, iter: 4 i:62, pairs changed 0
fullSet, iter: 4 i:63, pairs changed 0
fullSet, iter: 4 i:64, pairs changed 0
L==H
fullSet, iter: 4 i:65, pairs changed 0
L==H
fullSet, iter: 4 i:66, pairs changed 0
fullSet, iter: 4 i:67, pairs changed 0
fullSet, iter: 4 i:68, pairs changed 0
fullSet, iter: 4 i:69, pairs changed 0
j not moving enough
fullSet, iter: 4 i:70, pairs changed 0
fullSet, iter: 4 i:71, pairs changed 0
fullSet, iter: 4 i:72, pairs changed 0
L==H
fullSet, iter: 4 i:73, pairs changed 0
j not moving enough
fullSet, iter: 4 i:74, pairs changed 0
fullSet, iter: 4 i:75, pairs changed 0
L==H
fullSet, iter: 4 i:76, pairs changed 0
fullSet, iter: 4 i:77, pairs changed 0
L==H
fullSet, iter: 4 i:78, pairs changed 0
fullSet, iter: 4 i:79, pairs changed 0
fullSet, iter: 4 i:80, pairs changed 0
L==H
fullSet, iter: 4 i:81, pairs changed 0
L==H
fullSet, iter: 4 i:82, pairs changed 0
fullSet, iter: 4 i:83, pairs changed 0
fullSet, iter: 4 i:84, pairs changed 0
L==H
fullSet, iter: 4 i:85, pairs changed 0
fullSet, iter: 4 i:86, pairs changed 0
L==H
fullSet, iter: 4 i:87, pairs changed 0
fullSet, iter: 4 i:88, pairs changed 0
fullSet, iter: 4 i:89, pairs changed 0
L==H
fullSet, iter: 4 i:90, pairs changed 0
L==H
fullSet, iter: 4 i:91, pairs changed 0
L==H
fullSet, iter: 4 i:92, pairs changed 0
fullSet, iter: 4 i:93, pairs changed 0
fullSet, iter: 4 i:94, pairs changed 0
fullSet, iter: 4 i:95, pairs changed 0
L==H
fullSet, iter: 4 i:96, pairs changed 0
fullSet, iter: 4 i:97, pairs changed 0
fullSet, iter: 4 i:98, pairs changed 0
fullSet, iter: 4 i:99, pairs changed 0
iteration number: 5
there are 30 Support Vectors
the training error rate is: 0.130000
the test error rate is: 0.150000Process finished with exit code 0

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