svm实现
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from numpy import *
#文件操作
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
#随机选择另一个α优化
def selectJrand(i,m):
j=i
while (j==i):
j = int(random.uniform(0,m))
return j
#控制范围在L和H之间
def clipAlpha(aj,H,L):
if aj > H:
aj = H
if L > aj:
aj = L
return aj
#简单版本的smo算法，随机选择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) < 0.00001): 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
#记录alphas值的数据结构，便于选取aj
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)
#计算错误的中间函数
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
#选取最佳的j
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):
maxDeltaE = deltaE
maxK = k
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]
#迭代内循环
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]
# 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] = 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.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]
# 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
return 1
else: return 0
#完整版smo算法
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:
nonBoundIs= nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
for i in nonBoundIs:
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
#计算权值
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
#根据核函数做出变换
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 Kernel is not recognized')
return K
#测试样例，并且比较效果
def testRbf(k1 = 1.5):
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]
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)
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 'the test error rate is: %f' % (float(errorCount) / m)
# xcord0 = []
# ycord0 = []
# xcord1 = []
# ycord1 = []
# fr = open('testSetRBF.txt')
# for line in fr.readlines():
# lineSplit = line.strip().split('\t')
# xPt = float(lineSplit[0])
# yPt = float(lineSplit[1])
# label = float(lineSplit[2])
# if (label < 0):
# xcord0.append(xPt)
# ycord0.append(yPt)
# else:
# xcord1.append(xPt)
# ycord1.append(yPt)
# fr.close()
# fig = plt.figure()
# ax = fig.add_subplot(111)
# ax.scatter(xcord0,ycord0, marker='s', s=90)
# ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
# plt.title('Support Vectors Circled')
# sv = array(sVs)
# for li in range(shape(sv)[0]):
# circle = Circle((sv[li][0], sv[li][1]), 0.05, facecolor='none', edgecolor=(0,0.8,0.8), linewidth=3, alpha=0.5)
# ax.add_patch(circle)
# ax.axis([-1,1,-1,1])
# plt.show()
#读取图像文件（手写识别）
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) #load the training set
m = len(trainingFileList)
trainingMat = zeros((m,1024))
for i in range(m):
fileNameStr = trainingFileList[i]
fileStr = fileNameStr.split('.')[0] #take off .txt
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
#测试核函数为高斯核的效果
def testDigits(kTup=('rbf', 10)):
dataArr,labelArr = loadImages('trainingDigits')
b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTup)
datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
svInd=nonzero(alphas.A>0)[0]
sVs=datMat[svInd]
labelSV = labelMat[svInd];
print "there are %d Support Vectors" % shape(sVs)[0]
m,n = shape(datMat)
errorCount = 0
for i in range(m):
kernelEval = kernelTrans(sVs,datMat[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
datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
m,n = shape(datMat)
for i in range(m):
kernelEval = kernelTrans(sVs,datMat[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)
testDigits(('rbf', 10))
#测试代码
# dataArr, labelArr = loadDataSet('testSet.txt');
# b, alphas = smoP(dataArr, labelArr, 0.6, 0.01, 40)
# ws = calcWs(alphas, dataArr, labelArr)
# print(ws)
# print(alphas)
# print(b)
# t1 = 0.0
# t2 = 0.0
# for i in range(len(alphas)):
# if alphas[i] > 0.0:
# print dataArr[i]
# t1 += alphas[i] * dataArr[i][0] * labelArr[i]
# t2 += alphas[i] * dataArr[i][1] * labelArr[i]
# print(t1)
# print(t2)
svm数据可视化
非线性可分的数据
from numpy import *
import matplotlib
import matplotlib.pyplot as plt
xcord0 = []; ycord0 = []; xcord1 = []; ycord1 = []
markers =[]
colors =[]
fr = open('testSet.txt')#this file was generated by 2normalGen.py
for line in fr.readlines():
lineSplit = line.strip().split('\t')
xPt = float(lineSplit[0])
yPt = float(lineSplit[1])
label = int(lineSplit[2])
if (label == 0):
xcord0.append(xPt)
ycord0.append(yPt)
else:
xcord1.append(xPt)
ycord1.append(yPt)
fr.close()
fig = plt.figure()
ax = fig.add_subplot(221)
xcord0 = []; ycord0 = []; xcord1 = []; ycord1 = []
for i in range(300):
[x,y] = random.uniform(0,1,2)
if ((x > 0.5) and (y < 0.5)) or ((x < 0.5) and (y > 0.5)):
xcord0.append(x); ycord0.append(y)
else:
xcord1.append(x); ycord1.append(y)
ax.scatter(xcord0,ycord0, marker='s', s=90)
ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
plt.title('A')
ax = fig.add_subplot(222)
xcord0 = random.standard_normal(150); ycord0 = random.standard_normal(150)
xcord1 = random.standard_normal(150)+2.0; ycord1 = random.standard_normal(150)+2.0
ax.scatter(xcord0,ycord0, marker='s', s=90)
ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
plt.title('B')
ax = fig.add_subplot(223)
xcord0 = []; ycord0 = []; xcord1 = []; ycord1 = []
for i in range(300):
[x,y] = random.uniform(0,1,2)
if (x > 0.5):
xcord0.append(x*cos(2.0*pi*y)); ycord0.append(x*sin(2.0*pi*y))
else:
xcord1.append(x*cos(2.0*pi*y)); ycord1.append(x*sin(2.0*pi*y))
ax.scatter(xcord0,ycord0, marker='s', s=90)
ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
plt.title('C')
ax = fig.add_subplot(224)
xcord1 = zeros(150); ycord1 = zeros(150)
xcord0 = random.uniform(-3,3,350); ycord0 = random.uniform(-3,3,350);
xcord1[0:50] = 0.3*random.standard_normal(50)+2.0; ycord1[0:50] = 0.3*random.standard_normal(50)+2.0
xcord1[50:100] = 0.3*random.standard_normal(50)-2.0; ycord1[50:100] = 0.3*random.standard_normal(50)-3.0
xcord1[100:150] = 0.3*random.standard_normal(50)+1.0; ycord1[100:150] = 0.3*random.standard_normal(50)
ax.scatter(xcord0,ycord0, marker='s', s=90)
ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
plt.title('D')
plt.show()
支持向量可视化
#其中参数是有svm算法得出的结果
from numpy import *
import matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Circle
xcord0 = []
ycord0 = []
xcord1 = []
ycord1 = []
markers =[]
colors =[]
fr = open('testSet.txt')#this file was generated by 2normalGen.py
for line in fr.readlines():
lineSplit = line.strip().split('\t')
xPt = float(lineSplit[0])
yPt = float(lineSplit[1])
label = int(lineSplit[2])
if (label == -1):
xcord0.append(xPt)
ycord0.append(yPt)
else:
xcord1.append(xPt)
ycord1.append(yPt)
fr.close()
fig = plt.figure()
ax = fig.add_subplot(111)
ax.scatter(xcord0,ycord0, marker='s', s=90)
ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
plt.title('Support Vectors Circled')
circle = Circle((4.6581910000000004, 3.507396), 0.5, facecolor='none', edgecolor=(0,0.8,0.8), linewidth=3, alpha=0.5)
ax.add_patch(circle)
circle = Circle((3.4570959999999999, -0.082215999999999997), 0.5, facecolor='none', edgecolor=(0,0.8,0.8), linewidth=3, alpha=0.5)
ax.add_patch(circle)
circle = Circle((6.0805730000000002, 0.41888599999999998), 0.5, facecolor='none', edgecolor=(0,0.8,0.8), linewidth=3, alpha=0.5)
ax.add_patch(circle)
#plt.plot([2.3,8.5], [-6,6]) #seperating hyperplane
b = -3.75567; w0=0.8065; w1=-0.2761
x = arange(-2.0, 12.0, 0.1)
y = (-w0*x - b)/w1
ax.plot(x,y)
ax.axis([-2,12,-8,6])
plt.show()
随机生成非线性可分的数据
from numpy import *
import matplotlib
import matplotlib.pyplot as plt
xcord0 = []; ycord0 = []; xcord1 = []; ycord1 = []
fw = open('testSetRBF2.txt', 'w')#generate data
fig = plt.figure()
ax = fig.add_subplot(111)
xcord0 = []; ycord0 = []; xcord1 = []; ycord1 = []
for i in range(100):
[x,y] = random.uniform(0,1,2)
xpt=x*cos(2.0*pi*y); ypt = x*sin(2.0*pi*y)
if (x > 0.5):
xcord0.append(xpt); ycord0.append(ypt)
label = -1.0
else:
xcord1.append(xpt); ycord1.append(ypt)
label = 1.0
fw.write('%f\t%f\t%f\n' % (xpt, ypt, label))
ax.scatter(xcord0,ycord0, marker='s', s=90)
ax.scatter(xcord1,ycord1, marker='o', s=50, c='red')
plt.title('Non-linearly Separable Data for Kernel Method')
plt.show()
fw.close()