SVM支持向量机总结（不包括高维核函数等）
2013-12-02 17:18
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SVM支持向量机总结
本文将会讲到：
1.从原问题到最终结果主要公式展示
2.个人编写的python代码及结果演示
------------------------------------------------------------------------------------
1.从原问题到最终结果主要公式展示
2.个人编写的python代码及结果演示
(1)训练集
trainDataSet.txt
3.542485
1.977398
-1
3.018896 2.556416
-1
7.551510 -1.580030
1
2.114999 -0.004466
-1
8.127113 1.274372
1
7.108772 -0.986906
1
8.610639 2.046708
1
2.326297 0.265213
-1
3.634009 1.730537
-1
0.341367 -0.894998
-1
3.125951 0.293251
-1
2.123252 -0.783563
-1
0.887835 -2.797792
-1
7.139979 -2.329896
1
1.696414 -1.212496
-1
8.117032 0.623493
1
8.497162 -0.266649
1
4.658191 3.507396
-1
8.197181 1.545132
1
1.208047 0.213100
-1
1.928486 -0.321870
-1
2.175808 -0.014527
-1
7.886608 0.461755
1
3.223038 -0.552392
-1
3.628502 2.190585
-1
7.407860 -0.121961
1
7.286357 0.251077
1
2.301095 -0.533988
-1
-0.232542 -0.547690
-1
3.457096 -0.082216
-1
3.023938 -0.057392
-1
8.015003 0.885325
1
8.991748 0.923154
1
7.916831 -1.781735
1
7.616862 -0.217958
1
2.450939 0.744967
-1
7.270337 -2.507834
1
1.749721 -0.961902
-1
1.803111 -0.176349
-1
8.804461 3.044301
1
1.231257 -0.568573
-1
2.074915 1.410550
-1
-0.743036 -1.736103
-1
3.536555 3.964960
-1
8.410143 0.025606
1
7.382988 -0.478764
1
6.960661 -0.245353
1
8.234460 0.701868
1
8.168618 -0.903835
1
1.534187 -0.622492
-1
9.229518 2.066088
1
7.886242 0.191813
1
2.893743 -1.643468
-1
1.870457 -1.040420
-1
5.286862 -2.358286
1
6.080573 0.418886
1
2.544314 1.714165
-1
6.016004 -3.753712
1
0.926310 -0.564359
-1
0.870296 -0.109952
-1
2.369345 1.375695
-1
1.363782 -0.254082
-1
7.279460 -0.189572
1
1.896005 0.515080
-1
8.102154 -0.603875
1
2.529893 0.662657
-1
1.963874 -0.365233
-1
8.132048 0.785914
1
8.245938 0.372366
1
6.543888 0.433164
1
-0.236713 -5.766721
-1
8.112593 0.295839
1
9.803425 1.495167
1
1.497407 -0.552916
-1
1.336267 -1.632889
-1
9.205805 -0.586480
1
1.966279 -1.840439
-1
8.398012 1.584918
1
7.239953 -1.764292
1
7.556201 0.241185
1
9.015509 0.345019
1
8.266085 -0.230977
1
8.545620 2.788799
1
9.295969 1.346332
1
2.404234 0.570278
-1
2.037772 0.021919
-1
1.727631 -0.453143
-1
1.979395 -0.050773
-1
8.092288 -1.372433
1
1.667645 0.239204
-1
9.854303 1.365116
1
7.921057 -1.327587
1
8.500757 1.492372
1
1.339746 -0.291183
-1
3.107511 0.758367
-1
2.609525 .902979
-1
3.263585 1.367898
-1
2.912122 -0.202359
-1
1.731786 0.589096
-1
2.387003 1.573131
-1
-------------------------------------------------
（2）python代码
import math,random,numpy
import matplotlib.pyplot as plt
from numpy import *
'''
read training data set
'''
def loadTrainDataSet(fileName):
data = []
label = []
fileread = open(fileName)
for line in fileread.readlines():
words = line.strip().split('\t')
data.append([float(words[0]),float(words[1])])
label.append(float(words[2]))
fileread.close()
return data,label
'''
update alphaj2
'''
def clipAlpha(alpha,H,L):
if alpha > H:
alpha = H
if alpha < L:
alpha = L
return alpha
'''
select some index of alphaj who is different from alphai
'''
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 selectJ(i,m):
j = 0
if i < m-1:
j = i+1
else:
j = 0
return j
'''
SMO Algorithm
'''
def simpleSMO_heuristicSearch(dataX,labelY,C,limit,maxIter):
X = dataX
Y = labelY
b = 0
m = len(Y)
alphas = [0.0] * m
itercnt = 0
W = 0.0
while(itercnt < maxIter):
#print 'iter count:',itercnt,'\n'
for i in range(m):
alphaPairsChanged = 0
sumi = [0.0,0.0]
FXi = 0
for k in range(m):
sumi += numpy.dot(dot(Y[k],alphas[k]),X[k])
#FXi is the represention of WTXi+b
FXi = numpy.dot(sumi,X[i]) + b
Ei = FXi - float(Y[i])
# check out the example who violates the KKT condition
if ((alphas[i]>0 and alphas[i]<C and Y[i]*Ei !=0) or (alphas[i] ==C and Y[i]*Ei >0) or (alphas[i]==0 and Y[i]*Ei<0 )):
j = selectJrand(i,m)
sumj = [0.0,0.0]
FXj = 0
for k in range(m):
sumj += numpy.dot(dot(Y[k],alphas[k]),X[k])
FXj = numpy.dot(sumj,X[j]) + b
Ej = FXj - float(Y[j])
alphaIold = numpy.copy(alphas[i])
alphaJold = numpy.copy(alphas[j])
if(Y[i]!=Y[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
n = float(numpy.dot(X[i],X[i])+numpy.dot(X[j],X[j])-2*numpy.dot(X[i],X[j]))
if (n <= 0):
#print 'when n<=0 no min value!'
continue
alphas[j] += Y[j]*(Ei - Ej)/n
alphas[j] = clipAlpha(alphas[j],H,L)
if (abs(alphas[j]- alphaJold) < limit):
#print 'alphaj update convergence!'
continue
#update alphai by some alphaj
alphas[i] += Y[i]*Y[j]*(alphaJold - alphas[j])
#------------------------- update b --------------------#
b1 = b - Ei - Y[i]*(alphas[i]-alphaIold)*dot(X[i],X[i]) - Y[j]*(alphas[j]-alphaJold)*dot(X[i],X[j])
b2 = b - Ej - Y[i]*(alphas[i]-alphaIold)*dot(X[i],X[j]) - Y[j]*(alphas[j]-alphaJold)*dot(X[j],X[j])
if((alphas[i] > 0) and (alphas[i] < C)):
b = b1
elif((alphas[j] > 0) and (alphas[j] < C)):
b = b2
else:
b = (b1+b2)/2.0
alphaPairsChanged += 1
#print 'changed:alpha',i,'\t','update success:',alphaPairsChanged,'\n'
alphaPairsChanged = 0
#----------- W(Alpha) ----------#
sumW = 0.0
for p in range(m):
#for q in range(m):
sumW += Y[p]*Y[p]*alphas[p]*alphas[p]*dot(X[p],X[p])
print '---------------- max W(alphas)-------------'
print 'W(alphas)=',0.5*sumW - sum(alphas),'\n'
itercnt += 1
#print 'b=',b,'\n'
#print 'alphas = ',alphas,'\n'
return b,alphas
if __name__ == '__main__':
dataX = []
labelY = []
[dataX,labelY] = loadTrainDataSet("trainDataSet.txt")
Xlen =len(dataX)
Ylen = len(labelY)
#------------ simpleSMO_heuristic search -----------#
bias = 0
alphass = [0.0]* Ylen
[bias,alphass] = simpleSMO_heuristicSearch(dataX,labelY,0.1,0.0001,100)
#----------------- line show -----------------------#
W = [0.0,0.0]
for i in range(Ylen):
W += dot(labelY[i]*alphass[i],dataX[i])
xx =[-2,1,5,10]
xy =[0.0]*4
for j in range(4):
xy[j] = (-W[0]*xx[j]-bias)/W[1]
plt.plot(xx,xy)
for i in range(Ylen):
if labelY[i] == 1.0 and alphass[i]==0:
plt.plot(dataX[i][0],dataX[i][1],'o')
if labelY[i] == -1.0 and alphass[i]==0:
plt.plot(dataX[i][0],dataX[i][1],'or')
if alphass[i]!=0:
plt.plot(dataX[i][0],dataX[i][1],'*')
plt.xlabel('X1')
plt.ylabel('X2')
plt.title('trainDataSet')
print 'the line function is : F(x)=',-W[0]/W[1],'X ',- bias/W[1],'\n'
plt.show()
（3）实验结果，给大家看看当C的值不同时的不同情况（C越大，容忍越小）
C = 1.0 时，图像：
C = 1000.0时
C = 0.001时
C =0.1
当 C=1. 0 时，max W（alphas）变化情况，及最后函数
---------------- max W(alphas)-------------
W(alphas)= 0.145449910692
---------------- max W(alphas)-------------
W(alphas)= 0.109034120556
---------------- max W(alphas)-------------
W(alphas)= 0.117310017424
---------------- max W(alphas)-------------
W(alphas)= 0.117310017424
---------------- max W(alphas)-------------
W(alphas)= 0.208741283826
---------------- max W(alphas)-------------
W(alphas)= 0.145774558452
---------------- max W(alphas)-------------
W(alphas)= 0.214635282019
---------------- max W(alphas)-------------
W(alphas)= 0.214406342912
---------------- max W(alphas)-------------
W(alphas)= 0.215661425503
---------------- max W(alphas)-------------
W(alphas)= 0.262514693433
---------------- max W(alphas)-------------
W(alphas)= 0.262514693433
---------------- max W(alphas)-------------
W(alphas)= 0.298964958248
---------------- max W(alphas)-------------
W(alphas)= 0.298931357619
---------------- max W(alphas)-------------
W(alphas)= 0.285197304204
---------------- max W(alphas)-------------
W(alphas)= 0.152757945319
---------------- max W(alphas)-------------
W(alphas)= 0.710549717934
---------------- max W(alphas)-------------
W(alphas)= 0.710549717934
---------------- max W(alphas)-------------
W(alphas)= 0.710770567073
---------------- max W(alphas)-------------
W(alphas)= 0.916464185695
---------------- max W(alphas)-------------
W(alphas)= 0.916464185695
---------------- max W(alphas)-------------
W(alphas)= 0.916065417441
---------------- max W(alphas)-------------
W(alphas)= 0.897747262982
---------------- max W(alphas)-------------
W(alphas)= 0.897747262982
---------------- max W(alphas)-------------
W(alphas)= 0.887148444406
---------------- max W(alphas)-------------
W(alphas)= 0.894184257071
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.97437607653
---------------- max W(alphas)-------------
W(alphas)= 0.97437607653
---------------- max W(alphas)-------------
W(alphas)= 0.975068782717
---------------- max W(alphas)-------------
W(alphas)= 0.975068782717
---------------- max W(alphas)-------------
W(alphas)= 1.05602850898
---------------- max W(alphas)-------------
W(alphas)= 1.05602850898
---------------- max W(alphas)-------------
W(alphas)= 1.05602850898
---------------- max W(alphas)-------------
W(alphas)= 1.09935581252
---------------- max W(alphas)-------------
W(alphas)= 1.1000959207
---------------- max W(alphas)-------------
W(alphas)= 1.1020184241
---------------- max W(alphas)-------------
W(alphas)= 1.37252176298
---------------- max W(alphas)-------------
W(alphas)= 1.37318113788
---------------- max W(alphas)-------------
W(alphas)= 1.30420424719
---------------- max W(alphas)-------------
W(alphas)= 1.27448105315
---------------- max W(alphas)-------------
W(alphas)= 1.27448105315
---------------- max W(alphas)-------------
W(alphas)= 1.29659804543
---------------- max W(alphas)-------------
W(alphas)= 1.29659804543
---------------- max W(alphas)-------------
W(alphas)= 1.45357178013
---------------- max W(alphas)-------------
W(alphas)= 1.44283554071
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.44174164661
---------------- max W(alphas)-------------
W(alphas)= 1.44174164661
---------------- max W(alphas)-------------
W(alphas)= 1.44174164661
---------------- max W(alphas)-------------
W(alphas)= 1.5255097852
---------------- max W(alphas)-------------
W(alphas)= 1.52799651754
---------------- max W(alphas)-------------
W(alphas)= 1.52799651754
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.713308663
the line function is : F(x) = 2.93694985569 X - 13.7908490406
本文将会讲到：
1.从原问题到最终结果主要公式展示
2.个人编写的python代码及结果演示
------------------------------------------------------------------------------------
1.从原问题到最终结果主要公式展示
2.个人编写的python代码及结果演示
(1)训练集
trainDataSet.txt
3.542485
1.977398
-1
3.018896 2.556416
-1
7.551510 -1.580030
1
2.114999 -0.004466
-1
8.127113 1.274372
1
7.108772 -0.986906
1
8.610639 2.046708
1
2.326297 0.265213
-1
3.634009 1.730537
-1
0.341367 -0.894998
-1
3.125951 0.293251
-1
2.123252 -0.783563
-1
0.887835 -2.797792
-1
7.139979 -2.329896
1
1.696414 -1.212496
-1
8.117032 0.623493
1
8.497162 -0.266649
1
4.658191 3.507396
-1
8.197181 1.545132
1
1.208047 0.213100
-1
1.928486 -0.321870
-1
2.175808 -0.014527
-1
7.886608 0.461755
1
3.223038 -0.552392
-1
3.628502 2.190585
-1
7.407860 -0.121961
1
7.286357 0.251077
1
2.301095 -0.533988
-1
-0.232542 -0.547690
-1
3.457096 -0.082216
-1
3.023938 -0.057392
-1
8.015003 0.885325
1
8.991748 0.923154
1
7.916831 -1.781735
1
7.616862 -0.217958
1
2.450939 0.744967
-1
7.270337 -2.507834
1
1.749721 -0.961902
-1
1.803111 -0.176349
-1
8.804461 3.044301
1
1.231257 -0.568573
-1
2.074915 1.410550
-1
-0.743036 -1.736103
-1
3.536555 3.964960
-1
8.410143 0.025606
1
7.382988 -0.478764
1
6.960661 -0.245353
1
8.234460 0.701868
1
8.168618 -0.903835
1
1.534187 -0.622492
-1
9.229518 2.066088
1
7.886242 0.191813
1
2.893743 -1.643468
-1
1.870457 -1.040420
-1
5.286862 -2.358286
1
6.080573 0.418886
1
2.544314 1.714165
-1
6.016004 -3.753712
1
0.926310 -0.564359
-1
0.870296 -0.109952
-1
2.369345 1.375695
-1
1.363782 -0.254082
-1
7.279460 -0.189572
1
1.896005 0.515080
-1
8.102154 -0.603875
1
2.529893 0.662657
-1
1.963874 -0.365233
-1
8.132048 0.785914
1
8.245938 0.372366
1
6.543888 0.433164
1
-0.236713 -5.766721
-1
8.112593 0.295839
1
9.803425 1.495167
1
1.497407 -0.552916
-1
1.336267 -1.632889
-1
9.205805 -0.586480
1
1.966279 -1.840439
-1
8.398012 1.584918
1
7.239953 -1.764292
1
7.556201 0.241185
1
9.015509 0.345019
1
8.266085 -0.230977
1
8.545620 2.788799
1
9.295969 1.346332
1
2.404234 0.570278
-1
2.037772 0.021919
-1
1.727631 -0.453143
-1
1.979395 -0.050773
-1
8.092288 -1.372433
1
1.667645 0.239204
-1
9.854303 1.365116
1
7.921057 -1.327587
1
8.500757 1.492372
1
1.339746 -0.291183
-1
3.107511 0.758367
-1
2.609525 .902979
-1
3.263585 1.367898
-1
2.912122 -0.202359
-1
1.731786 0.589096
-1
2.387003 1.573131
-1
-------------------------------------------------
（2）python代码
import math,random,numpy
import matplotlib.pyplot as plt
from numpy import *
'''
read training data set
'''
def loadTrainDataSet(fileName):
data = []
label = []
fileread = open(fileName)
for line in fileread.readlines():
words = line.strip().split('\t')
data.append([float(words[0]),float(words[1])])
label.append(float(words[2]))
fileread.close()
return data,label
'''
update alphaj2
'''
def clipAlpha(alpha,H,L):
if alpha > H:
alpha = H
if alpha < L:
alpha = L
return alpha
'''
select some index of alphaj who is different from alphai
'''
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 selectJ(i,m):
j = 0
if i < m-1:
j = i+1
else:
j = 0
return j
'''
SMO Algorithm
'''
def simpleSMO_heuristicSearch(dataX,labelY,C,limit,maxIter):
X = dataX
Y = labelY
b = 0
m = len(Y)
alphas = [0.0] * m
itercnt = 0
W = 0.0
while(itercnt < maxIter):
#print 'iter count:',itercnt,'\n'
for i in range(m):
alphaPairsChanged = 0
sumi = [0.0,0.0]
FXi = 0
for k in range(m):
sumi += numpy.dot(dot(Y[k],alphas[k]),X[k])
#FXi is the represention of WTXi+b
FXi = numpy.dot(sumi,X[i]) + b
Ei = FXi - float(Y[i])
# check out the example who violates the KKT condition
if ((alphas[i]>0 and alphas[i]<C and Y[i]*Ei !=0) or (alphas[i] ==C and Y[i]*Ei >0) or (alphas[i]==0 and Y[i]*Ei<0 )):
j = selectJrand(i,m)
sumj = [0.0,0.0]
FXj = 0
for k in range(m):
sumj += numpy.dot(dot(Y[k],alphas[k]),X[k])
FXj = numpy.dot(sumj,X[j]) + b
Ej = FXj - float(Y[j])
alphaIold = numpy.copy(alphas[i])
alphaJold = numpy.copy(alphas[j])
if(Y[i]!=Y[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
n = float(numpy.dot(X[i],X[i])+numpy.dot(X[j],X[j])-2*numpy.dot(X[i],X[j]))
if (n <= 0):
#print 'when n<=0 no min value!'
continue
alphas[j] += Y[j]*(Ei - Ej)/n
alphas[j] = clipAlpha(alphas[j],H,L)
if (abs(alphas[j]- alphaJold) < limit):
#print 'alphaj update convergence!'
continue
#update alphai by some alphaj
alphas[i] += Y[i]*Y[j]*(alphaJold - alphas[j])
#------------------------- update b --------------------#
b1 = b - Ei - Y[i]*(alphas[i]-alphaIold)*dot(X[i],X[i]) - Y[j]*(alphas[j]-alphaJold)*dot(X[i],X[j])
b2 = b - Ej - Y[i]*(alphas[i]-alphaIold)*dot(X[i],X[j]) - Y[j]*(alphas[j]-alphaJold)*dot(X[j],X[j])
if((alphas[i] > 0) and (alphas[i] < C)):
b = b1
elif((alphas[j] > 0) and (alphas[j] < C)):
b = b2
else:
b = (b1+b2)/2.0
alphaPairsChanged += 1
#print 'changed:alpha',i,'\t','update success:',alphaPairsChanged,'\n'
alphaPairsChanged = 0
#----------- W(Alpha) ----------#
sumW = 0.0
for p in range(m):
#for q in range(m):
sumW += Y[p]*Y[p]*alphas[p]*alphas[p]*dot(X[p],X[p])
print '---------------- max W(alphas)-------------'
print 'W(alphas)=',0.5*sumW - sum(alphas),'\n'
itercnt += 1
#print 'b=',b,'\n'
#print 'alphas = ',alphas,'\n'
return b,alphas
if __name__ == '__main__':
dataX = []
labelY = []
[dataX,labelY] = loadTrainDataSet("trainDataSet.txt")
Xlen =len(dataX)
Ylen = len(labelY)
#------------ simpleSMO_heuristic search -----------#
bias = 0
alphass = [0.0]* Ylen
[bias,alphass] = simpleSMO_heuristicSearch(dataX,labelY,0.1,0.0001,100)
#----------------- line show -----------------------#
W = [0.0,0.0]
for i in range(Ylen):
W += dot(labelY[i]*alphass[i],dataX[i])
xx =[-2,1,5,10]
xy =[0.0]*4
for j in range(4):
xy[j] = (-W[0]*xx[j]-bias)/W[1]
plt.plot(xx,xy)
for i in range(Ylen):
if labelY[i] == 1.0 and alphass[i]==0:
plt.plot(dataX[i][0],dataX[i][1],'o')
if labelY[i] == -1.0 and alphass[i]==0:
plt.plot(dataX[i][0],dataX[i][1],'or')
if alphass[i]!=0:
plt.plot(dataX[i][0],dataX[i][1],'*')
plt.xlabel('X1')
plt.ylabel('X2')
plt.title('trainDataSet')
print 'the line function is : F(x)=',-W[0]/W[1],'X ',- bias/W[1],'\n'
plt.show()
（3）实验结果，给大家看看当C的值不同时的不同情况（C越大，容忍越小）
C = 1.0 时，图像：
C = 1000.0时
C = 0.001时
C =0.1
当 C=1. 0 时，max W（alphas）变化情况，及最后函数
---------------- max W(alphas)-------------
W(alphas)= 0.145449910692
---------------- max W(alphas)-------------
W(alphas)= 0.109034120556
---------------- max W(alphas)-------------
W(alphas)= 0.117310017424
---------------- max W(alphas)-------------
W(alphas)= 0.117310017424
---------------- max W(alphas)-------------
W(alphas)= 0.208741283826
---------------- max W(alphas)-------------
W(alphas)= 0.145774558452
---------------- max W(alphas)-------------
W(alphas)= 0.214635282019
---------------- max W(alphas)-------------
W(alphas)= 0.214406342912
---------------- max W(alphas)-------------
W(alphas)= 0.215661425503
---------------- max W(alphas)-------------
W(alphas)= 0.262514693433
---------------- max W(alphas)-------------
W(alphas)= 0.262514693433
---------------- max W(alphas)-------------
W(alphas)= 0.298964958248
---------------- max W(alphas)-------------
W(alphas)= 0.298931357619
---------------- max W(alphas)-------------
W(alphas)= 0.285197304204
---------------- max W(alphas)-------------
W(alphas)= 0.152757945319
---------------- max W(alphas)-------------
W(alphas)= 0.710549717934
---------------- max W(alphas)-------------
W(alphas)= 0.710549717934
---------------- max W(alphas)-------------
W(alphas)= 0.710770567073
---------------- max W(alphas)-------------
W(alphas)= 0.916464185695
---------------- max W(alphas)-------------
W(alphas)= 0.916464185695
---------------- max W(alphas)-------------
W(alphas)= 0.916065417441
---------------- max W(alphas)-------------
W(alphas)= 0.897747262982
---------------- max W(alphas)-------------
W(alphas)= 0.897747262982
---------------- max W(alphas)-------------
W(alphas)= 0.887148444406
---------------- max W(alphas)-------------
W(alphas)= 0.894184257071
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.88167577001
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.847130393883
---------------- max W(alphas)-------------
W(alphas)= 0.97437607653
---------------- max W(alphas)-------------
W(alphas)= 0.97437607653
---------------- max W(alphas)-------------
W(alphas)= 0.975068782717
---------------- max W(alphas)-------------
W(alphas)= 0.975068782717
---------------- max W(alphas)-------------
W(alphas)= 1.05602850898
---------------- max W(alphas)-------------
W(alphas)= 1.05602850898
---------------- max W(alphas)-------------
W(alphas)= 1.05602850898
---------------- max W(alphas)-------------
W(alphas)= 1.09935581252
---------------- max W(alphas)-------------
W(alphas)= 1.1000959207
---------------- max W(alphas)-------------
W(alphas)= 1.1020184241
---------------- max W(alphas)-------------
W(alphas)= 1.37252176298
---------------- max W(alphas)-------------
W(alphas)= 1.37318113788
---------------- max W(alphas)-------------
W(alphas)= 1.30420424719
---------------- max W(alphas)-------------
W(alphas)= 1.27448105315
---------------- max W(alphas)-------------
W(alphas)= 1.27448105315
---------------- max W(alphas)-------------
W(alphas)= 1.29659804543
---------------- max W(alphas)-------------
W(alphas)= 1.29659804543
---------------- max W(alphas)-------------
W(alphas)= 1.45357178013
---------------- max W(alphas)-------------
W(alphas)= 1.44283554071
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.42846910637
---------------- max W(alphas)-------------
W(alphas)= 1.44174164661
---------------- max W(alphas)-------------
W(alphas)= 1.44174164661
---------------- max W(alphas)-------------
W(alphas)= 1.44174164661
---------------- max W(alphas)-------------
W(alphas)= 1.5255097852
---------------- max W(alphas)-------------
W(alphas)= 1.52799651754
---------------- max W(alphas)-------------
W(alphas)= 1.52799651754
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.66410118437
---------------- max W(alphas)-------------
W(alphas)= 1.713308663
the line function is : F(x) = 2.93694985569 X - 13.7908490406
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