版权声明：本文为博主原创文章，未经博主允许不得转载。 https://blog.csdn.net/zhuxiaoyang2000/article/details/54314778
这篇文章是《机器学习实战》（Machine Learning in Action）第六章 支持向量机算法的Python实现代码。
1 参考链接
（1）支持向量机通俗导论(理解SVM的三层境界)
（2）支持向量机—SMO论文详解（序列最小最优化算法）
2 实现代码
from numpy import *
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
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 ((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) < 0.0001):
print "j not moving enough"
continue
alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])
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 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
K = exp(K/(-1*kTup[1]**2))
else: raise NameError('Houston We Have a Problem -- That Kernal 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)
class optStruct:
def __init__(self,dataMatIn, classLabels, C, toler, kTup): # Initialize the structure with the parameters
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))) #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)
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
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]-alphaJold) < 0.0001):
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
def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin',0)):
oS = optStruct(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 += innerL(i, oS)
print "fullSet, iter: %d i: %d, pairs changed %d" %(iter,i, alphaPairsChanged)
iter += 1
else:
nonBoundsIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
for i in nonBoundsIs:
alphaPairsChanged += innerL(i, oS)
print "non-bound, iter: %d i: %d, pairs changed %d" % (iter, i, alphaPairsChanged)
iter += 1
if entireSet: entireSet = False
elif (alphaPairsChanged == 0): entireSet = True
print "iteration number: %d" % iter
return oS.b, oS.alphas
def calcWs(alphas, dataArr, classLabels):
X = mat(dataArr); labelMat = mat(classLabels).transpose()
m,n = shape(X)
w = zeros((n,1))
for i in range(m):
w += multiply(alphas[i]*labelMat[i],X[i,:].T)
return w
def plot(dataArr, labelArr, sVs):
import matplotlib.pyplot as plt
m = shape(dataArr)[0]
xcord1 = []; ycord1 = []
xcord2 = []; ycord2 = []
for i in range(m):
if int(labelArr[i]) == 1:
xcord1.append(dataArr[i,0]); ycord1.append(dataArr[i,1]);
else:
xcord2.append(dataArr[i,0]); ycord2.append(dataArr[i,1]);
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(xcord1, ycord1, s=50, c='red', marker='s')
ax.scatter(xcord2, ycord2, s=50, c='green')
ax.scatter(sVs[:,0], sVs[:,1], s=100, c='blue', marker='+')
plt.xlabel('X1'); plt.ylabel('X2')
plt.show()
def testRbf(k1=1.3):
# training
dataArr, labelArr = loadDataSet('testSetRBF.txt')
b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1))
dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
svInd = nonzero(alphas.A>0)[0]
sVs = dataMat[svInd]
labelSV = labelMat[svInd]
print "there are %d Support Vectors" % shape(sVs)[0]
# test self
m,n = shape(dataMat)
errorCount = 0
for i in range(m):
kernelEval = kernelTrans(sVs, dataMat[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)
# test other
dataArr, labelArr = loadDataSet('testSetRBF2.txt')
errorCount = 0
dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
m,n = shape(dataMat)
for i in range(m):
kernelEval = kernelTrans(sVs, dataMat[i,:],('rbf',k1))
predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
if sign(predict) != sign(labelArr[i]): errorCount += 1
print errorCount, m
print "the training error rate is: %f" % (float(errorCount)/m)
# plot the figure
dataArr=array(dataArr); labelArr=array(labelArr)
plot(dataArr,labelArr, sVs)
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 loadImages(dirName):
from os import listdir
hwLabels = []
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: hwLabels.append(-1)
else: hwLabels.append(1)
trainingMat[i,:] = img2vector('%s/%s' % (dirName, fileNameStr))
return trainingMat, hwLabels
def testDigits(kTup=('rbf', 10)):
dataArr, labelArr = loadImages('trainingDigits')
b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTup)
dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
svInd = nonzero(alphas.A>0)[0]
sVs = dataMat[svInd]
labelSV = labelMat[svInd]
print "there are %d Support Vectors" % shape(sVs)[0]
m,n = shape(dataMat)
errorCount = 0
for i in range(m):
kernelEval = kernelTrans(sVs, dataMat[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)
dataArr, labelArr = loadImages('testDigits')
errorCount = 0
dataMat = mat(dataArr); labelMat = mat(labelArr).transpose()
m,n = shape(dataMat)
for i in range(m):
kernelEval = kernelTrans(sVs, dataMat[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)
# TEST
testRbf()
