#-*-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))
MLiA笔记_svm
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