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 innerL(i, os):
Ei = optStruct.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 = optStruct.selectJ(i, os, Ei)
alphaIold = os.alphas[i].copy()
alphaJold = os.alphas[j].copy()
if(os.labelMat[i] != os.alphas[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.C + os.alphas[j] + os.alphas[i])
if L == H:print('L == H');reutrn (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] -= svmMLiA.clipAlpha(os.alphas[j], H, L)
optStruct.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 - Ej - os.labelMat[i] * (os.alphas[i] - alphaIold) * os.X[i, :] * os.X[i, :].T -os.labelMat[j] * (os.alphas[j] - alphaJold) * os.X[i, :]*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(o < os.alphas[j]) and (os.C > os.alphas[j]): os.b = b2
else:os.b =(b1 + b2)/2
return 1
else:
return 0
def innerLK(i, oS):
# 计算误差
Ei = calcEkK(oS, i)
# 违背kkt条件
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 = selectJK(i, oS, Ei) #this has been changed from selectJrand
alphaIold = oS.alphas[i].copy()
alphaJold = oS.alphas[j].copy()
# 计算上下界
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
# 计算两个alpha值
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] = svmMLiA.clipAlpha(oS.alphas[j], H, L)
updateEkK(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
updateEkK(
oS, i
) #added this for the Ecache #the update is in the oppostie direction
#
# 在这两个alpha值情况下，计算对应的b值
# 注，非线性可分情况，将所有内积项替换为核函数K[i,j]
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[i, :] * 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
# 如果有alpha对更新
return 1
# 否则返回0
else:
return 0
def innerLL(i, oS):
Ei = calcEkK(oS, i)
# 如果标签与误差相乘之后在容错范围之外，且超过各自对应的常数值，则进行优化
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)):
# 启发式选择第二个alpha值
j, Ej = selectJJ(i, oS, Ei)
# 利用copy存储刚才的计算值，便于后期比较
alphaIold = oS.alphas[i].copy()
alphaJold = oS.alphas[j].copy()
# 保证alpha在0和C之间
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
# 对新的alphas[j]进行阈值处理
oS.alphas[j] = svm.clipAlpha(oS.alphas[j], H, L)
# 更新误差缓存
updateEkK(oS, j)
# 如果新旧值差很小，则不做处理跳出本次循环
if (abs(oS.alphas[j] - alphaJold) < 0.00001):
# print('j not moving enough')
return 0
# 对i进行修改，修改量相同，但是方向相反
oS.alphas[i] += oS.labelMat[j] * oS.labelMat[i] * (alphaJold - oS.alphas[j])
updateEkK(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]
# 谁在0到C之间，就听谁的，否则就取平均值
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 innerLoop(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] = svmMLiA.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[i, :] * 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] < oS.C:
oS.b = b1
elif 0 < oS.alphas[j] < oS.C:
oS.b = b2
else:
oS.b = (b1 + b2) / 2.0
return 1
else:
return 0
def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
import numpy as np
dataMatrix = np.mat(dataMatIn)
labelMat = np.mat(classLabels).transpose()
#print(labelMat.shape,'显示维度')
b = 0
m, n = np.shape(dataMatrix)
alphas = np.mat(np.zeros((m, 1))) #初始化alpha的值
iter = 0
while (iter < maxIter):
alphaPairsChanged = 0 #更新成功标志
for i in range(m):
fXi=float(np.multiply(alphas,labelMat).T*\
(dataMatrix*dataMatrix[i,:].T))+b
Ei = fXi - float(labelMat[i]) #计算第一个变量的误差
if ((labelMat[i]*Ei<-toler) and (alphas[i]<C)) or \
((labelMat[i]*Ei>toler) and \
(alphas[i]>0)):
j = selectJrand(i, m) #随机选择第二个变量
fXj=float(np.multiply(alphas,labelMat).T*\
(dataMatrix*dataMatrix[j,:].T))+b#计算第二个变量的误差
Ej = fXj - float(labelMat[j])
alphaIold = alphas[i].copy() #保存旧的alpha值
alphaJold = alphas[j].copy() #保存旧的alpha值
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#计算2k12-k11-k22
if eta >= 0:
print('eta>=0')
continue
alphas[j] -= labelMat[j] * (Ei - Ej) / eta #计算alpha1^new,unc
alphas[j] = clipAlpha(alphas[j], H, L) #计算alpha1^new
if (abs(alphas[j] - alphaJold) < 0.00001): print\
('j not moving enough')
continue #设置终止条件
alphas[i]+=labelMat[j]*labelMat[i]*\
(alphaJold-alphas[j])#计算alpha2^new
b1=b-Ei-labelMat[i]*(alphas[i]-alphaJold)*\
dataMatrix[i,:]*dataMatrix[i,:].T-\
labelMat[j]*(alphas[j]-alphaJold)*\
dataMatrix[i,:]*dataMatrix[j,:].T#计算b1^new
b2=b-Ej-labelMat[i]*(alphas[i]-alphaIold)*\
dataMatrix[i,:]*dataMatrix[j,:].T-\
labelMat[j]*(alphas[j]-alphaJold)*\
dataMatrix[j,:]*dataMatrix[j,:].T#计算b2^new
if (0 < alphas[i]) and (C > alphas[i]): b = b1
elif (0 < alphas[i]) and (C > alphas[i]): b = b2
else: b = (b1 + b2) / 2.0 #确定最终的b
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 innerL(i, oS):
"""
优化的SMO算法
Parameters：
i - 标号为i的数据的索引值
oS - 数据结构
Returns:
1 - 有任意一对alpha值发生变化
0 - 没有任意一对alpha值发生变化或变化太小
"""
#步骤1：计算误差Ei
Ei = calcEk(oS, i)
#优化alpha,设定一定的容错率。
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)):
#使用内循环启发方式2选择alpha_j,并计算Ej
j, Ej = selectJ(i, oS, Ei)
#保存更新前的aplpha值，使用深拷贝
alphaIold = oS.alphas[i].copy()
alphaJold = oS.alphas[j].copy()
#步骤2：计算上下界L和H
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
#步骤3：计算eta
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
#步骤4：更新alpha_j
oS.alphas[j] -= oS.labelMat[j] * (Ei - Ej) / eta
#步骤5：修剪alpha_j
oS.alphas[j] = sm.clipAlpha(oS.alphas[j], H, L)
#更新Ej至误差缓存
updateEk(oS, j)
if (abs(oS.alphas[j] - alphaJold) < 0.00001):
print("alpha_j变化太小")
return 0
#步骤6：更新alpha_i
oS.alphas[i] += oS.labelMat[j] * oS.labelMat[i] * (alphaJold -
oS.alphas[j])
#更新Ei至误差缓存
updateEk(oS, i)
#步骤7：更新b_1和b_2
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[i, :] * 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
#步骤8：根据b_1和b_2更新b
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 smoSimple(dataMatIn, classLabels, C, toler, maxIter):
#转换为numpy的mat存储
dataMatrix = np.mat(dataMatIn)
labelMat = np.mat(classLabels).transpose()
#初始化b参数，统计dataMatrix的维度
b = 0
m, n = np.shape(dataMatrix)
#初始化alpha参数，设为0
alphas = np.mat(np.zeros((m, 1)))
#初始化迭代次数
iter_num = 0
#最多迭代matIter次
while (iter_num < maxIter):
alphaPairsChanged = 0
for i in range(m):
#步骤1：计算误差Ei
fXi = float(
np.multiply(alphas, labelMat).T *
(dataMatrix * dataMatrix[i, :].T)) + b
Ei = fXi - float(labelMat[i])
#优化alpha，更设定一定的容错率。
if ((labelMat[i] * Ei < -toler) and
(alphas[i] < C)) or ((labelMat[i] * Ei > toler) and
(alphas[i] > 0)):
#随机选择另一个与alpha_i成对优化的alpha_j
j = sm.selectJrand(i, m)
#步骤1：计算误差Ej
fXj = float(
np.multiply(alphas, labelMat).T *
(dataMatrix * dataMatrix[j, :].T)) + b
Ej = fXj - float(labelMat[j])
#保存更新前的aplpha值，使用深拷贝
alphaIold = alphas[i].copy()
alphaJold = alphas[j].copy()
#步骤2：计算上下界L和H
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
#步骤3：计算eta
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
#步骤4：更新alpha_j
alphas[j] -= labelMat[j] * (Ei - Ej) / eta
#步骤5：修剪alpha_j
alphas[j] = sm.clipAlpha(alphas[j], H, L)
if (abs(alphas[j] - alphaJold) < 0.00001):
print("alpha_j变化太小")
continue
#步骤6：更新alpha_i
alphas[i] += labelMat[j] * labelMat[i] * (alphaJold -
alphas[j])
#步骤7：更新b_1和b_2
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
#步骤8：根据b_1和b_2更新b
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
#统计优化次数
alphaPairsChanged += 1
#打印统计信息
print("第%d次迭代 样本:%d, alpha优化次数:%d" %
(iter_num, i, alphaPairsChanged))
#更新迭代次数
if (alphaPairsChanged == 0): iter_num += 1
else: iter_num = 0
print("迭代次数: %d" % iter_num)
return b, alphas
