和简单smo方法的区别是在寻找aj时会选择那些步长最大的点，从而使得变化最大，提升效率
import matplotlib.pyplot as plt
import numpy as np
import random
class optStruct: #使用类结构，方便传递参数
def __init__(self,dataMatIn,classLabels,C,toler):
self.X = dataMatIn
self.labelMat = classLabels
self.C = C
self.tol = toler
self.m = np.shape(dataMatIn)[0]
self.alphas = np.mat(np.zeros((self.m,1)))
self.b = 0
self.eCache = np.mat(np.zeros((self.m,2)))
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[-1]))
return dataMat,labelMat
def calcEk(oS,k): #计算误差
fXk = float(np.multiply(oS.alphas,oS.labelMat).T*(oS.X*oS.X[k,:].T) + oS.b)
Ek = fXk - float(oS.labelMat[k])
return Ek
def selectJrand(i,m):
j = i
while(j == i):
j = int(random.uniform(0,m))
return j
def selectJ(i,oS,Ei): #选择步长最大的aj
maxK = -1
maxDeltaE = 0
Ej = 0
oS.eCache[i] = [1,Ei]
validEcacheList = np.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): #更新Ek并存储
Ek = calcEk(oS,k)
oS.eCache[k] = [1,Ek]
def clipAlpha(aj,H,L):
if aj > H:
aj = H
if aj < L:
aj = L
return aj
def innerL(i,oS): #更新a1，a2和b
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")
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("AlphaJ变化太小")
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])and(oS.C>oS.alphas[i]):oS.b = b1
elif(oS.alphas[j]>0)and(oS.C>alphas[j]):oS.b = b2
else:oS.b = (b1+b2)/2
return 1
else:
return 0
def smoP(dataMatIn,classLabels,C,toler,maxIter): #smo改进算法主体
oS = optStruct(np.mat(dataMatIn),np.mat(classLabels).transpose(),C,toler)
iteration = 0
entireSet = True #决定ai是选择内部点还是外部点
alphaPairsChanged = 0
while(iteration<maxIter)and((alphaPairsChanged>0)or(entireSet)):
alphaPairsChanged = 0
if entireSet:
for i in range(oS.m):
alphaPairsChanged += innerL(i,oS)
print("全部遍历：第%d次迭代 样本：%d,alpha优化次数：%d"%(iteration,i,alphaPairsChanged))
iteration += 1
else:
nonBoundIs = np.nonzero((oS.alphas.A > 0) * \ #计算非边界点数量
(oS.alphas.A<C))[0]
for i in nonBoundIs :
alphaPairsChanged += innerL(i,oS)
print("非边界遍历：第%d次迭代 样本：%d，alpha优化次数：%d"%(iteration,i,alphaPairsChanged))
iteration +=1
if entireSet:
entireSet = False #若计算过边界点，则下次计算非边界点
elif(alphaPairsChanged == 0): #若上次计算非边界点但没有变化，则下次计算边界点
entireSet = True
print("迭代次数：%d"%iteration)
return oS.b,oS.alphas
def showClassifer(dataMat,classLabels,w,b,alphas): #绘图
dataPlus = []
dataMinus = []
for i in range(len(dataMat)):
if classLabels[i] > 0:
dataPlus.append(dataMat[i])
else:
dataMinus.append(dataMat[i])
dataPlusNp = np.array(dataPlus)
dataMinusNp = np.array(dataMinus)
plt.scatter(np.transpose(dataPlusNp)[0],np.transpose(dataPlusNp)[1],s=30,alpha=0.7)
plt.scatter(np.transpose(dataMinusNp)[0],np.transpose(dataMinusNp)[1],s=30,alpha=0.7)
x1 = max(dataMat)[0]
x2 = min(dataMat)[0]
a1,a2=w
b=float(b)
a1 = float(a1[0])
a2 = float(a2[0])
y1,y2 = (-b-a1*x1)/a2,(-b-a1*x2)/a2
plt.plot([x1,x2],[y1,y2])
for i,alpha in enumerate(alphas):
if abs(alpha)>0:
x,y=dataMat[i]
plt.scatter([x],[y],s=150,c='none',alpha=0.7,linewidth=1.5,edgecolor='red')
plt.show()
def calcWs(alphas,dataArr,classLabels):
X = np.mat(dataArr)
labelMat = np.mat(classLabels).transpose()
m,n = np.shape(X)
w = np.zeros((n,1))
for i in range(m):
w += np.multiply(alphas[i]*labelMat[i],X[i,:].T)
return w