(转载请注明出处：http://blog.csdn.net/buptgshengod)
1.背景知识
通过上一节我们通过引入拉格朗日乗子得到支持向量机变形公式。详细变法可以参考这位大神的博客——地址
参照拉格朗日公式F(x1,x2,...λ)=f(x1,x2,...)-λg(x1,x2...)。我们把上面的式子变型为：
约束条件就变成了：
下面就根据最小优化算法SMO(Sequential Minimal Optimization)。找出距离分隔面最近的点，也就是支持向量集。如下图的蓝色点所示。
2.代码
import matplotlib.pyplot as plt
from numpy import *
from time import sleep
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 #we want to select any J not equal to 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
def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()
b = 0; m,n = shape(dataMatrix)
alphas = mat(zeros((m,1)))
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 checks if an example violates KKT conditions
if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):
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();
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
if eta >= 0: print "eta>=0"; continue
alphas[j] -= labelMat[j]*(Ei - Ej)/eta
alphas[j] = clipAlpha(alphas[j],H,L)
# if (abs(alphas[j] - alphaJold) < 0.00001): print "j not moving enough"; continue
alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])#update i by the same amount as j
#the update is in the oppostie direction
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)
if (alphaPairsChanged == 0): iter += 1
else: iter = 0
# print "iteration number: %d" % iter
return b,alphas
def matplot(dataMat,lableMat):
xcord1 = []; ycord1 = []
xcord2 = []; ycord2 = []
xcord3 = []; ycord3 = []
for i in range(100):
if lableMat[i]==1:
xcord1.append(dataMat[i][0])
ycord1.append(dataMat[i][1])
else:
xcord2.append(dataMat[i][0])
ycord2.append(dataMat[i][1])
b,alphas=smoSimple(dataMat,labelMat,0.6,0.001,40)
for j in range(100):
if alphas[j]>0:
xcord3.append(dataMat[j][0])
ycord3.append(dataMat[j][1])
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(xcord1, ycord1, s=30, c=‘red‘, marker=‘s‘)
ax.scatter(xcord2, ycord2, s=30, c=‘green‘)
ax.scatter(xcord3, ycord3, s=80, c=‘blue‘)
ax.plot()
plt.xlabel(‘X1‘); plt.ylabel(‘X2‘);
plt.show()
if __name__==‘__main__‘:
dataMat,labelMat=loadDataSet(‘/Users/hakuri/Desktop/testSet.txt‘)
# b,alphas=smoSimple(dataMat,labelMat,0.6,0.001,40)
# print b,alphas[alphas>0]
matplot(dataMat,labelMat)