這篇文章是《機器學習實戰》（Machine Learning in Action）第六章 支援向量機演算法的Python實現程式碼。

1 參考連結

（1）支援向量機通俗導論(理解SVM的三層境界)
（2）支援向量機—SMO論文詳解（序列最小最優化演算法）

2 實現程式碼

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, labelMat

def selectJrand(i,m):
    j=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
 
 ((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) < 0.0001):
                    print "j not moving enough"
                    continue
                alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])
                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):
    m,n = shape(X)
    K = mat(zeros((m,1)))
    if kTup[0]=='lin': K=X*A.T
    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))
    else: raise NameError('Houston We Have a Problem -- That Kernal is not recognized.')
    return K

#class optStruct:
#    def __init__(self,dataMatIn, classLabels, C, toler, kTup):
#        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)))
#        self.K = mat(zeros((self.m, self.m)))
#        for i in range(self.m):
#            self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup)

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):
    maxK = -1; maxDeltaE = 0; Ej = 0
    oS.eCache[i] = [1, Ei]
    validEcacheList = nonzero(oS.eCache[:,0].A)[0]
    if (len(validEcacheList)) > 1:
        for k in validEcacheList:
            if k ==i: continue
            Ek = calcEk(oS, k)
            deltaE = abs(Ei - Ek)
            if (deltaE > maxDeltaE):
                maxK = k; maxDeltaE = deltaE; Ej = Ek
        return maxK, Ej
    else:
        j = selectJrand(i, oS.m)
        Ej = calcEk(oS, j)
    return j,Ej

def updateEk(oS, k):
    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)
           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]
           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)
           if (abs(oS.alphas[j]-alphaJold) < 0.0001):
               print "j not moving enough"; return 0
           oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])
           updateEk(oS,i)
           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)):
    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:
            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:
            nonBoundsIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
            for i in nonBoundsIs:
                alphaPairsChanged += innerL(i, oS)
                print "non-bound, iter: %d i: %d, pairs changed %d" % (iter, i, alphaPairsChanged)
            iter += 1
        if entireSet: entireSet = False
        elif (alphaPairsChanged == 0): entireSet = True
        print "iteration number: %d" % iter
    return oS.b, oS.alphas

def 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 w

def plot(dataArr, labelArr, sVs):
    import matplotlib.pyplot as plt
    m = shape(dataArr)[0]
    xcord1 = []; ycord1 = []
    xcord2 = []; ycord2 = []
    for i in range(m):
        if int(labelArr[i]) == 1:
            xcord1.append(dataArr[i,0]); ycord1.append(dataArr[i,1]); 
        else:
            xcord2.append(dataArr[i,0]); ycord2.append(dataArr[i,1]); 
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.scatter(xcord1, ycord1, s=50, c='red', marker='s')
    ax.scatter(xcord2, ycord2, s=50, c='green')
    ax.scatter(sVs[:,0], sVs[:,1], s=100, c='blue', marker='+')
    plt.xlabel('X1'); plt.ylabel('X2')
    plt.show()

def testRbf(k1=1.3):
    # training
    dataArr, labelArr = loadDataSet('testSetRBF.txt')
    b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1))
    dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
    svInd = nonzero(alphas.A>0)[0]
    sVs = dataMat[svInd]
    labelSV = labelMat[svInd]
    print "there are %d Support Vectors" % shape(sVs)[0]
    # test self
    m,n = shape(dataMat)
    errorCount = 0
    for i in range(m):
        kernelEval = kernelTrans(sVs, dataMat[i,:],('rbf',k1))
        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)
    # test other
    dataArr, labelArr = loadDataSet('testSetRBF2.txt')
    errorCount = 0
    dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
    m,n = shape(dataMat)
    for i in range(m):
        kernelEval = kernelTrans(sVs, dataMat[i,:],('rbf',k1))
        predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
        if sign(predict) != sign(labelArr[i]): errorCount += 1
    print errorCount, m
    print "the training error rate is: %f" % (float(errorCount)/m)
    # plot the figure
    dataArr=array(dataArr); labelArr=array(labelArr)
    plot(dataArr,labelArr, sVs)

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 returnVect

def loadImages(dirName):
    from os import listdir
    hwLabels = []
    trainingFileList = listdir(dirName)
    m = len(trainingFileList)
    trainingMat = zeros((m, 1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]
        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('trainingDigits')
    b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTup)
    dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
    svInd = nonzero(alphas.A>0)[0]
    sVs = dataMat[svInd]
    labelSV = labelMat[svInd]
    print "there are %d Support Vectors" % shape(sVs)[0]
    m,n = shape(dataMat)
    errorCount = 0
    for i in range(m):
        kernelEval = kernelTrans(sVs, dataMat[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('testDigits')
    errorCount = 0
    dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
    m,n = shape(dataMat)

    for i in range(m):
        kernelEval = kernelTrans(sVs, dataMat[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)

# TEST
testRbf()

3 執行結果