MLiA笔记_svm

#-*-coding:utf-8-*-
from numpy import *

#6.1 helper funtions for the SMO algorithm

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


#6.2 the simplified SMO algorithm
def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
    dataMatrix = mat(dataMatIn)
    labelMat = mat(classLabels).transpose()
    m,n = shape(dataMatrix)
    #初始化b和alphas的值
    b = 0
    alphas = mat(zeros((m,1)))
    #alpha没有改变的情况下遍历数据的次数
    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)):
                #如果满足优化条件，随机选取非i的一个点，进行优化比较
                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()
                #!= 表示异側，异側相减，同侧相加
                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是alphas[j]的最优修改量，如果eta==0，需要退出for循环的当前迭代过程
                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
                #计算出一个新的alphas[j]值
                alphas[j] -= labelMat[j]*(Ei - Ej)/eta
                #并使用辅助函数、L、H对其进行调整
                alphas[j] = clipAlpha(alphas[j],H,L)
                #检查alphas[j]是否只是轻微的改变，如果是的话，就退出for循环
                if  (abs(alphas[j] - alphaJold) < 0.00001):
                    print "j not moving"
                    continue
                #alphas[i], alphas[j]同样进行改变， 大小一样，方向相反
                alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])
                #优化之后设置一个常数b
                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)
        #在for循环外，检查alpha值是否做了更新，如果更新则将iter设为0后继续运行程序
        #知道更新完毕后，iter次循环无变化，才推出循环
        if (alphaPairsChanged == 0):
            iter += 1
        else:
            iter = 0
        print "iteration number : %d" %iter
    return b, alphas


#6.3 support functions for full Platt SMO
class optStruct:
    def __init__(self, dataMatIn, classLabels, C, toler):
        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)))

def calcEk(oS,K):
    fXk = float(multiply(oS.alphas,oS.labelMat).T * (oS.X*oS.X[K,:].T) + 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]

#6.4 full platt SMO optimization routine
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.X[i,:]*oS.X[j,:].T - oS.X[i,:]*oS.X[i,:].T - oS.X[j,:]*oS.X[j,:].T
        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) < 0.00001):
            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.X[i,:]*oS.X[i,:].T - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.X[j,:]*oS.X[j,:].T
        b2 = oS.b - Ej - oS.labelMat[i]*(oS.alphas[i] - alphaIold)*oS.X[i,:]*oS.X[j,:].T - oS.labelMat[j]*(oS.alphas[j]-alphaJold)*oS.X[j,:]*oS.X[j,:].T
        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 0
    else: return 0



#6.6 kenel transformation function
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
        #径向基函数的高斯版本
        K = exp(K/(-1*kTup[1]**2))
    else:
        raise NameError("houton We have a problem -- that kernel 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)

def calcEK(oS,k):
    fXk = float(multiply(oS.alphas, oS.labelMat).T * oS.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] - oS.alphas[i]) < 0.00001):
            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

#6.5 full platt SMO loop
def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin',0)):
    #创建一个optStruct对象
    oS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler,kTup)
    iter = 0
    entireSet = True
    alphaPairsChanged = 0

    #遍历循环：循环maxIter次，且（alphaPairsChanged存在可以改变) or (所有行遍历一遍)
    while (iter < maxIter) and ((alphaPairsChanged > 0)or (entireSet)):
        alphaPairsChanged = 0
        #当entirSet=Ture or 非边界alpha对没有了，就开始寻找alpha对，然后决定是否要进行else
        if entireSet:
            for i in range(oS.m):
                #是否存在alpha对，存在就加一
                alphaPairsChanged += innerL(i,oS)
            #对已存在alpha对， 选出非边界的alpha值，进行优化
        else:
            # 遍历所有的非边界alpha值，也就是不在边界0或C上
            nonBoundIs = nonzero((oS.alphas.A > 0)*(oS.alphas.A < C))[0]
            for i in nonBoundIs:
                alphaPairsChanged += innerL(i, oS)
        #如果找到alpha对，就优化非边界alpha值，否则，就重新进行寻找，如果遍历所有行还是没有找到，就退出循环
        if entireSet:
            entireSet = False
        elif (alphaPairsChanged == 0):
            entireSet = True
        print("iteration number: %d" %iter)
    return oS.b,oS.alphas

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

# 6.8 利用核函数进行分类的径向基测试函数
def testRbf(k1=1.3):
    dataArr, labelArr = loadDataSet('testSetRBF.txt')
    b, alphas = smoP(dataArr, labelArr, 200, 0.00001, 10000,('rbf',k1))
    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,:],('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))
    dataArr, labelArr = loadDataSet('testSetRBF2.txt')
    errorCount = 0
    datMat = mat(dataArr)
    labelMat = mat(labelArr).transpose()
    m,n = shape(datMat)
    for i in range(m):
        kernelEval  =kernelTrans(sVs, datMat[i,:],('rbf',k1))
        predict = kernelEval.T * multiply(labelSV,alphas[svInd]) + b
        if sign(predict) != sign(labelArr[i]):
            errorCount += 1
            if sign(predict) != sign(labelArr[i]):
                errorCount += 1
    print "the test error rate is : %f " %(float(errorCount)/m)

#6.9 基于SVM的手写数字识别
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 loadImage(dirName):
    from os import listdir
    hwLables = []
    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:
            hwLables.append(-1)
        else: hwLables.append(1)
        trainingMat[i,:] = img2vector('%s%s' %(dirName,fileNameStr))
    return trainingMat, hwLables

def testDigits(kTup=('rbf',10)):
    #导入训练数据集
    dataArr, labelArr = loadImages('trainingDigits')
    b, alphas = smoP(dataArr, labelArr, 200, 0.00001,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))
    #导入测试数据集
    dataArr, labelArr = loadImage('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))