SVM作为机器学习里面的经典算法在实际中一直被广泛采用，而且其准确性也是非常之高，特别是在引入了核函数之后对识别性能变得非常高。

说明：本文不打算就SVM原理就深入分析，虽然对其原理略懂一二，但是对于SMO算法的理解确实比较浅，所以也不打算班门弄斧，略微介绍，本文重点在于SVM的应用，也就是对垃圾邮件的文本分类

关于支持向量机的原理性分析在CSDN上有July大神的博客 ：http://blog.csdn.net/v_july_v/article/details/7624837，我就之略微介绍一下原理

一，SVM原理象征性简述：

SVM主要应用是分类操作，以二元线性分类为例，主要思想是根据特征向量的超空间创建一条超平面分隔线，当然在加入核函数后，可以把非线性分类映射到高维空间使之成为线性分类，而在求参数的过程中会使用SMO算法选取参数，会有不错的性能

二，SVM对垃圾邮件的分类：

这篇文章中的SVM的python实现代码参考自《Machine Learning in Action》一书，其训练数据来自该书的朴素贝叶斯分类一章，朴素贝叶斯也是一种比较简单而实用的分类方法，这里是使用了那一章的邮件数据

步骤说明：

1，提取训练邮件数据的特征向量

由于邮件的内容很多，因此找出其主要的分类关键词尤为关键，在找出关键词后就可以用这些关键词对邮件进行特征标记，也就是如果关键词在这篇文章中标记为1不出现则标记为0

其中每一个邮件类别中的关键词的选取方法有很多，我决定采用 TF-IDF方法选取关键词，在计算IDF的时候，考虑到我们是对整个类邮件进行分类，因此就没有采用IDF的传统计算方法，而是计算这词语在整个类邮件中的邮件占比，也就是出现该词语的文档数量除以文档总数量

关于 TF-IDF的介绍见百度百科

http://baike.baidu.com/link?url=oYpXqrTb6yQB1KaNUl8LS-01gUsy09s0w9JGpPq4QH8s_AzFI796tvWXnXtoGtpW-WAvLrKYwhsHp1l3i3JGpK

在得出所有的词语的TF-IDF数后，我选取数最大的前100个词作为这一类邮件的关键词（每个类不重复的词语数量大概在300多个）

得到关键词后我们就可以对每个邮件进行特征向量标记了，每个邮件由100个特征值标记，也就是对每个上文提出的关键词，如果这个邮件存在这个词语就标记为1，如果不存在，那么这个词语就标记为0，

这样就可以得出了每个邮件的特征向量值了

2，将步骤1得到的特征值使用SVM训练，本文的SVM代码实现基本是基于李航的《统计学习方法》一书，因为本文不是来叙述原理的，所以也略过不表，在这个例子中使用了rbf作为核函数

3，得到训练模型后就可以使用交叉验证方法验证数据的正确性了，具体的说，就是使用50个训练数据中的40个邮件的特征向量训练数据，使用剩下的10个邮件的特征向量作为测试向量

还是那句话，代码是硬道理，下面直接上代码

SVM主要代码：

# -*- coding: utf-8 -*-
from numpy import *
from time import sleep
import matplotlib.pyplot as pltdef 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" % iterreturn 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 parameters self.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 = True  print "iteration number: %d" % iterreturn oS.b,oS.alphas

提取特征以及使用SVM训练测试代码

# -*- coding: cp936 -*-
"""
基于支持向量机的邮件分类系统
使用0,1标记词的出现与否
author :luchi
data :1025/11/29
"""
import re
from math import *
from SVMKernel import *
#切割文本,统计词频
def splitText(bigString):wordlist={}rtnList=[]wordFreqList={}#分词listofTokens=re.split(r'\W*',bigString)length=len(listofTokens)for token in listofTokens:if  not wordlist.has_key(token):wordlist[token]=1rtnList.append(token)else:wordlist[token]+=1wordFreqList[token]=float(wordlist[token])/lengthreturn rtnList,wordFreqList#统计单词反文档频率
def docFre(word):fre=0for i in range(1,26):if word in re.split(r'\W*',open('spam/%d.txt' % i).read()):fre+=1return float(fre)/25#特征词提取，这里面使用TF-IDF方法def extractFeature(textType):docList=[];classList=[];fullText=[]wordTFIDF={}#每个类测试邮件一共有25封for i in range(1,26):wordlist,wordFreqList=splitText(open(textType+'/%d.txt' % i).read())fullText.append(wordlist)for word in wordFreqList:wordIDF=docFre(word)wordTFIDFValue=wordIDF*wordFreqList[word]if not  wordTFIDF.has_key(word):wordTFIDF[word]=wordTFIDFValueelse :wordTFIDF[word]+=wordTFIDFValuesortedWordTFIDF=sorted(wordTFIDF.iteritems(),key=lambda asd:asd[1],reverse=True)#选取前100个词为分类词keywords=[word[0] for word in sortedWordTFIDF[:100]]return keywords#对一个邮件词集构建特征向量（使用0,1表示存在与否）
def extaxtDocFeatureVec(text,keyword):vec=[]for i,word in enumerate(keyword):if word in text:vec.append(1)else :vec.append(0)return vec#抽取所有邮件的特征向量
def extactFeatureVec():hamWordsVec=extractFeature('ham')spamWordsVec=extractFeature('spam')wordVecs=[]classList=[]for i in range(1,26):wordlistHam,wordFreqList=splitText(open('ham/%d.txt' % i).read())wordlistSpam,wordFreqList=splitText(open('spam/%d.txt' % i).read())vecHam=extaxtDocFeatureVec(wordlistHam,hamWordsVec)vecSpam=extaxtDocFeatureVec(wordlistSpam,spamWordsVec)wordVecs.append(vecHam)classList.append(1)wordVecs.append(vecSpam)classList.append(-1)
##    print wordVecs
##    print classListreturn wordVecs,classList#使用SVM训练数据并使用交叉测试测试正确率
def textSpam(k1=1.3):dataArr,labelArr=extactFeatureVec()trainDataArr=dataArr[:40]trainLabelArr=labelArr[:40]b,alphas = smoP(trainDataArr, trainLabelArr, 200, 0.0001, 10000, ('rbf', k1)) #C=200 importantdatMat=mat(trainDataArr); labelMat = mat(trainLabelArr).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]testDataMat=mat(dataArr[39:-1])testLabel=labelArr[39:-1]
##    testLabel[2]=testLabel[2]*-1m,n = shape(testDataMat)errorCount = 0for i in range(m):kernelEval = kernelTrans(sVs,testDataMat[i,:],('rbf', k1))predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + bif sign(predict)!=sign(testLabel[i]): errorCount += 1print "the training error rate is: %f" % (float(errorCount)/m)if __name__=='__main__':textSpam()

测试结果如下：

iteration number: 8
there are 38 Support Vectors
the training error rate is: 0.000000

可以看出，SVM对于分类是具有很好的性能，这也是SVM强大之处，本例中使用了100维向量，但是SVM对更高维的数据也有很好的作用，然后我选取了15个数据作为训练数据，检测的失败率是22%，所以说SVM方法还是需要训练数据支持的

代码和测试数据都在附件

参考文献：

http://blog.csdn.net/v_july_v/article/details/7624837

李航 《统计学习方法》

Peter Harrington 《Machine Learning in Action》