结合
# 核函数转换
def kernelTrans(X, A, kTup):
m, n = shape(X)
K = mat(zeros((m,1)))
if kTup[0] == 'lin':
K = X * A.T # linear kernel
elif kTup[0] == 'rbf': # radius kernel
for j in range(m):
deltaRow = X[j,:] - A
K[j] = deltaRow * deltaRow.T
K = exp(K / (-1 * kTup[1]**2)) # RBF核计算
else:
raise NameError('Houston We Have a Problem -- That Kernel is not recognized')
return K
# 优化结构类（根据第2张图）
class optStructK:
def __init__(self, dataMatIn, classLabels, C, toler, kTup=('lin',0)):
self.X = mat(dataMatIn)
self.labelMat = mat(classLabels).transpose()
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)
# 内层循环
def innerLK(i, oS): # use the kernel function
Ei = calcEk(oS, i)
# KKT条件检查
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) # 选择第二个alpha
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
# 直接调用K矩阵计算eta
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) < 0.00001:
print("j not moving enough")
return 0
oS.alphas[i] += oS.labelMat[j] * oS.labelMat[i] * (alphaJold - oS.alphas[j])
updateEk(oS, i)
# 计算b
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
# 主SMO算法
def smoPK(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
oS = optStructK(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 += innerLK(i, oS)
print("全数据集迭代: %d i:%d, 改变的alpha对: %d" % (iter,i, alphaPairsChanged))
#全数据集迭代=fullSet,iter,改变的alpha对=pairs changed
iter +=1
else:
nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
for i in nonBoundIs:
alphaPairsChanged += innerLK(i, oS)
print("非边界迭代: %d i:%d, 改变的alpha对: %d" % (iter, i,alphaPairsChanged))
#非边界迭代=non-bound,改变的alpha对=pairs changed
iter += 1
if entireSet:
entireSet = False
elif alphaPairsChanged == 0:
entireSet = True
return oS.b, oS.alphas
以及上面图片里面的程序编写并且实现带核函数的非线性SVM，并在testSetRBF.txt数据集上测试，其每行有三个数据，如-0.246873，0.833713，-1.000000。所用软件为vscode
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