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 plt
def 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,labelMat
def selectJrand(i,m):
j=i #we want to select any J not equal to i
while (j==i):
j = int(random.uniform(0,m))
return j
def clipAlpha(aj,H,L):
if aj > H:
aj = H
if L > aj:
aj = L
return aj
def 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 = 0
while (iter < maxIter):
alphaPairsChanged = 0
for i in range(m):
fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
Ei = fXi - float(labelMat[i])#if checks if an example violates KKT conditions
if ((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)) + b
Ej = 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"; continue
eta = 2.0 * dataMatrix[i,:]*dataMatrix[j,:].T - dataMatrix[i,:]*dataMatrix[i,:].T - dataMatrix[j,:]*dataMatrix[j,:].T
if eta >= 0: print "eta>=0"; continue
alphas[j] -= labelMat[j]*(Ei - Ej)/eta
alphas[j] = clipAlpha(alphas[j],H,L)
if (abs(alphas[j] - alphaJold) < 0.00001): print "j not moving enough"; continue
alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])#update i by the same amount as j
#the update is in the oppostie direction
b1 = b - Ei- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[i,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[i,:]*dataMatrix[j,:].T
b2 = b - Ej- labelMat[i]*(alphas[i]-alphaIold)*dataMatrix[i,:]*dataMatrix[j,:].T - labelMat[j]*(alphas[j]-alphaJold)*dataMatrix[j,:]*dataMatrix[j,:].T
if (0 < alphas[i]) and (C > alphas[i]): b = b1
elif (0 < alphas[j]) and (C > alphas[j]): b = b2
else: b = (b1 + b2)/2.0
alphaPairsChanged += 1
print "iter: %d i:%d, pairs changed %d" % (iter,i,alphaPairsChanged)
if (alphaPairsChanged == 0): iter += 1
else: iter = 0
print "iteration number: %d" % iter
return b,alphas
def kernelTrans(X, A, kTup): #calc the kernel or transform data to a higher dimensional space
m,n = shape(X)
K = mat(zeros((m,1)))
if kTup[0]=='lin': K = X * A.T #linear kernel
elif kTup[0]=='rbf':
for j in range(m):
deltaRow = X[j,:] - A
K[j] = deltaRow*deltaRow.T
K = exp(K/(-1*kTup[1]**2)) #divide in NumPy is element-wise not matrix like Matlab
else: raise NameError('Houston We Have a Problem -- \
That Kernel is not recognized')
return K
class optStruct:
def __init__(self,dataMatIn, classLabels, C, toler, kTup): # Initialize the structure with the parameters
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.eCache = mat(zeros((self.m,2))) #first column is valid flag
self.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 Ek
def selectJ(i, oS, Ei): #this is the second choice -heurstic, and calcs Ej
maxK = -1; maxDeltaE = 0; Ej = 0
oS.eCache[i] = [1,Ei] #set valid #choose the alpha that gives the maximum delta E
validEcacheList = 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 E
if k == i: continue #don't calc for i, waste of time
Ek = calcEk(oS, k)
deltaE = abs(Ei - Ek)
if (deltaE > maxDeltaE):
maxK = k; maxDeltaE = deltaE; Ej = Ek
return maxK, Ej
else: #in this case (first time around) we don't have any valid eCache values
j = selectJrand(i, oS.m)
Ej = calcEk(oS, j)
return j, Ej
def updateEk(oS, k):#after any alpha has changed update the new value in the cache
Ek = 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 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)
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
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 = 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
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]=1
rtnList.append(token)
else:
wordlist[token]+=1
wordFreqList[token]=float(wordlist[token])/length
return rtnList,wordFreqList
#统计单词反文档频率
def docFre(word):
fre=0
for i in range(1,26):
if word in re.split(r'\W*',open('spam/%d.txt' % i).read()):
fre+=1
return 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]=wordTFIDFValue
else :
wordTFIDF[word]+=wordTFIDFValue
sortedWordTFIDF=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 classList
return 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 important
datMat=mat(trainDataArr); labelMat = mat(trainLabelArr).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]
testDataMat=mat(dataArr[39:-1])
testLabel=labelArr[39:-1]
## testLabel[2]=testLabel[2]*-1
m,n = shape(testDataMat)
errorCount = 0
for i in range(m):
kernelEval = kernelTrans(sVs,testDataMat[i,:],('rbf', k1))
predict=kernelEval.T * multiply(labelSV,alphas[svInd]) + b
if sign(predict)!=sign(testLabel[i]): errorCount += 1
print "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》