机器学习实战（6）：SVM-SMO-核函数 手写识别

SVM判断模型只与支持向量有关：

# coding=utf-8#Created on Nov 4, 2010#Chapter 5 source file for Machine Learing in Action#@author: Peter##########简单的SMO程序#########################################################################from numpy import *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,labelMatdef 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 jdef clipAlpha(aj,H,L):    if aj > H:         aj = H    if L > aj:        aj = L    return ajdef smoSimple(dataMatIn, classLabels, C, toler, maxIter): #toler:容错率-KKT条件判定精度    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#dataArr,labelArr=loadDataSet(r'C:\Users\li\Downloads\machinelearninginaction\Ch06\testSet.txt')#b,alphas=smoSimple(dataArr, labelArr, 0.6, 0.001, 40)#print(b)#print(alphas[alphas>0])#print(shape(alphas[alphas>0]))#for i in range(100):#    if alphas[i]>0.0: print(dataArr[i],labelArr[i])    #################################################################################################完整的 Platt SMO程序 增加误差缓存、寻值优化，采用核函数##外循环，对alpha1,采用两种方式交替进行，1、对所有数据集上进行单遍扫描；2、在非边界alpha（0和C之间）中实现单遍扫描，##先建立非边界alpha值的列表，再遍历，并跳过那些已知的不会改变的alpha值。##内循环，对alpha2，建立全局缓存用于保存误差值，并从中选择使得步长或者说E1-E2最大的alpha值###############################################################################################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':             #radial basis function        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  ??why not -2    else: 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 = 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, Ejdef 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 0def 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##################################################SVM SMO求解手写识别问题##############################################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 listdir    hwLabels = []    trainingFileList = listdir(dirName)           #load the training set    m = len(trainingFileList)    trainingMat = zeros((m,1024))    for i in range(m):        fileNameStr = trainingFileList[i]        fileStr = fileNameStr.split('.')[0]     #take off .txt        classNumStr = int(fileStr.split('_')[0])        if classNumStr == 9: hwLabels.append(-1)        else: hwLabels.append(1)        trainingMat[i,:] = img2vector('%s/%s' % (dirName, fileNameStr))    return trainingMat, hwLabels    def testDigits(kTup=('rbf', 10)):    dataArr,labelArr = loadImages(r'C:\Users\li\Downloads\machinelearninginaction\Ch06\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 = 0    for i in range(m):        kernelEval = kernelTrans(sVs,datMat[i,:],kTup)        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 = loadImages(r'C:\Users\li\Downloads\machinelearninginaction\Ch06\testDigits')    errorCount = 0    datMat=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]) + b        if sign(predict)!=sign(labelArr[i]): errorCount += 1        print ("the test error rate is: %f" % (float(errorCount)/m))    testDigits(('lin',20))