SVM实战之垃圾邮件过滤

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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

伦理片 http://www.dotdy.com/

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

影音先锋电影 http://www.iskdy.com/

 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