数学建模——支持向量机模型详解Python代码
2021/7/25 11:45:03
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数学建模——支持向量机模型详解Python代码
from numpy import *
import random
import matplotlib.pyplot as plt
import numpy
def kernelTrans(X,A,kTup): # 核函数(此例未使用)
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 # ||w||^2 = w^T * w
K =exp(K/(-1*kTup[1]**2)) # K = e^(||x-y||^2 / (-2*sigma^2))
else:
raise NameError("Houston we Have a problem --")
return K
class optStruct:
def __init__(self,dataMain,classLabel,C,toler,kTup):
self.X = dataMain # 样本矩阵
self.labelMat = classLabel
self.C = C # 惩罚因子
self.tol = toler # 容错率
self.m = shape(dataMain)[0] # 样本点个数
self.alphas = mat(zeros((self.m,1))) # 产生m个拉格郎日乘子，组成一个m×1的矩阵
self.b =0 # 决策面的截距
self.eCache = mat(zeros((self.m,2))) # 产生m个误差 E=f(x)-y ,设置成m×2的矩阵，矩阵第一列是标志位，标志为1就是E计算好了，第二列是误差E
# self.K = mat(zeros((self.m,self.m)))
# for i in range(self.m): # K[,]保存的是任意样本之间的相似度(用高斯核函数表示的相似度)
# self.K[:,i]=kernelTrans(self.X,self.X[i,:],kTup)
def loadDataSet(filename): # 加载数据
dataMat = []
labelMat = []
fr = open(filename)
for line in fr.readlines():
lineArr = line.split()
dataMat.append([float(lineArr[0]),float(lineArr[1])])
labelMat.append(float(lineArr[2])) # 一维列表
return dataMat, labelMat
def selectJrand(i, m): # 随机选择一个不等于i的下标
j =i
while(j==i):
j = int(random.uniform(0,m))
return j
def clipAlpha(aj, H,L):
if aj>H: # 如果a^new 大于上限值，那么就把上限赋给它
aj = H
if L>aj: # 如果a^new 小于下限值，那么就把下限赋给它
aj = L
return aj
def calcEk(oS, k): # 计算误差E, k代表第k个样本点，它是下标，oS是optStruct类的实例
# fXk = float(multiply(oS.alphas,oS.labelMat).T * oS.K[:,k] + oS.b) # 公式f(x)=sum(ai*yi*xi^T*x)+b
fXk = float(multiply(oS.alphas,oS.labelMat).T * (oS.X*oS.X[k,:].T)) +oS.b
Ek = fXk - float(oS.labelMat[k]) # 计算误差 E=f(x)-y
return Ek
def selectJ(i, oS, Ei): # 选择两个拉格郎日乘子,在所有样本点的误差计算完毕之后，寻找误差变化最大的那个样本点及其误差
maxK = -1 # 最大步长的因子的下标
maxDeltaE = 0 # 最大步长
Ej = 0 # 最大步长的因子的误差
oS.eCache[i] = [1,Ei]
valiEcacheList = nonzero(oS.eCache[:,0].A)[0] # nonzero结果是两个array数组，第一个数组是不为0的元素的x坐标，第二个数组是该位置的y坐标
# 此处寻找误差矩阵第一列不为0的数的下标
print("valiEcacheList is {}".format(valiEcacheList))
if (len(valiEcacheList))>1:
for k in valiEcacheList: # 遍历所有计算好的Ei的下标，valiEcacheLIst保存了所有样本点的E，计算好的有效位置是1,没计算好的是0
if k == i:
continue
Ek = calcEk(oS,k)
deltaE = abs(Ei-Ek) # 距离第一个拉格朗日乘子a1绝对值最远的作为第二个朗格朗日乘子a2
if deltaE>maxDeltaE:
maxK = k # 记录选中的这个乘子a2的下标
maxDeltaE = deltaE # 记录他俩的绝对值
Ej = Ek # 记录a2此时的误差
return maxK, Ej
else: # 如果是第一次循环，随机选择一个alphas
j = selectJrand(i, oS.m)
# j = 72
Ej = calcEk(oS, j)
return j,Ej
def updateEk(oS, k):
Ek = calcEk(oS, k)
oS.eCache[k] = [1,Ek] # 把第k个样本点的误差计算出来，并存入误差矩阵，有效位置设为1
def innerL(i, oS):
Ei = calcEk(oS, i) # KKT条件， 若yi*(w^T * x +b)-1<0 则 ai=C 若yi*(w^T * x +b)-1>0 则 ai=0
print("i is {0},Ei is {1}".format(i,Ei))
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)
print("第二个因子的坐标{}".format(j))
alphaIold = oS.alphas[i].copy() # 用了浅拷贝， alphaIold 就是old a1,对应公式
alphaJold = oS.alphas[j].copy()
if oS.labelMat[i] != oS.labelMat[j]: # 也是根据公式来的，y1 不等于 y2时
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: # 如果这个j让L=H,i和j这两个样本是同一类别，且ai=aj=0或ai=aj=C，或者不同类别，aj=C且ai=0
# 当同类别时 ai+aj = 常数 ai是不满足KKT的，假设ai=0,需增大它，那么就得减少aj，aj已经是0了，不能最小了，所以此情况不允许发生
# 当不同类别时 ai-aj=常数，ai是不满足KKT的，ai=0,aj=C,ai需增大，它则aj也会变大，但是aj已经是C的不能再大了，故此情况不允许
print("L=H")
return 0
# eta = 2.0*oS.K[i,j]-oS.K[i,i]-oS.K[j,j] # eta=K11+K22-2*K12
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: # 这里跟公式正好差了一个负号，所以对应公式里的 K11+K22-2*K12 <=0，即开口向下，或为0成一条直线的情况不考虑
print("eta>=0")
return 0
oS.alphas[j]-=oS.labelMat[j]*(Ei-Ej)/eta # a2^new = a2^old+y2(E1-E2)/eta
print("a2 归约之前是{}".format(oS.alphas[j]))
oS.alphas[j]=clipAlpha(oS.alphas[j],H,L) # 根据公式，看看得到的a2^new是否在上下限之内
print("a2 归约之后is {}".format(oS.alphas[j]))
# updateEk(oS,j) # 把更新后的a2^new的E更新一下
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]) # 根据公式a1^new = a1^old+y1*y2*(a2^old-a2^new)
print("a1更新之后是{}".format(oS.alphas[i]))
# updateEk(oS,i)
# b1^new = b1^old+(a1^old-a1^new)y1*K11+(a2^old-a2^new)y2*K12-E1
# 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]
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.K[i,j]-oS.labelMat[j]* \
# (oS.alphas[j]-alphaJold)*oS.K[j,j]
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
updateEk(oS,j) # 个人认为更新误差应在更新b之后，因为公式算出的b的公式使用的是以前的Ei
updateEk(oS,i)
# b2^new=b2^old+(a1^old-a1^new)y1*K12+(a2^old-a2^new)y2*K22-E2
if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]):
oS.b = b1.A[0][0]
elif (0<oS.alphas[j]) and (oS.C > oS.alphas[j]):
oS.b = b2.A[0][0]
else:
oS.b = (b1+b2)/2.0
print("b is {}".format(oS.b))
return 1
else:
return 0
def smoP(dataMatIn, classLabels, C,toler,maxIter,kTup=('lin',)):
oS = optStruct(mat(dataMatIn), mat(classLabels).transpose(),C,toler,kTup)
iter = 0
entireSet = True # 两种遍历方式交替
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
print("第一种遍历alphaRairChanged is {}".format(alphaPairsChanged))
print("-----------eCache is {}".format(oS.eCache))
print("***********alphas is {}".format(oS.alphas))
print("---------------------------------------")
else:
nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0] # 这时数组相乘，里面其实是True 和False的数组，得出来的是
# 大于0并且小于C的alpha的下标
for i in nonBoundIs:
alphaPairsChanged += innerL(i,oS)
print("non-bound, iter: %d i:%d, pairs changed %d"%(iter,i,alphaPairsChanged))
print("第二种遍历alphaPairChanged is {}".format(alphaPairsChanged))
iter+=1
if entireSet:
entireSet = False # 当第二种遍历方式alpha不再变化，那么继续第一种方式扫描，第一种方式不再变化，此时alphachanged为0且entireSet为false，退出循环
elif (alphaPairsChanged==0):
entireSet=True
print("iteration number: %d"%iter)
return oS.b,oS.alphas
def calcWs(alphas,dataArr,classLabels): # 通过alpha来计算w
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) # w = sum(ai*yi*xi)
return w
def draw_points(dataArr,classlabel, w,b,alphas):
myfont = FontProperties(fname='/usr/share/fonts/simhei.ttf') # 显示中文
plt.rcParams['axes.unicode_minus'] = False # 防止坐标轴的‘-’变为方块
m = len(classlabel)
red_points_x=[]
red_points_y =[]
blue_points_x=[]
blue_points_y =[]
svc_points_x =[]
svc_points_y =[]
# print(type(alphas))
svc_point_index = nonzero((alphas.A>0) * (alphas.A <0.8))[0]
svc_points = array(dataArr)[svc_point_index]
svc_points_x = [x[0] for x in list(svc_points)]
svc_points_y = [x[1] for x in list(svc_points)]
print("svc_points_x",svc_points_x)
print("svc_points_y",svc_points_y)
for i in range(m):
if classlabel[i] ==1:
red_points_x.append(dataArr[i][0])
red_points_y.append(dataArr[i][1])
else:
blue_points_x.append(dataArr[i][0])
blue_points_y.append(dataArr[i][1])
fig = plt.figure() # 创建画布
ax = fig.add_subplot(111)
ax.set_title("SVM-Classify") # 设置图片标题
ax.set_xlabel("x") # 设置坐标名称
ax.set_ylabel("y")
ax1=ax.scatter(red_points_x, red_points_y, s=30,c='red', marker='s') #s是shape大小，c是颜色，marker是形状，'s'代表是正方形,默认'o'是圆圈
ax2=ax.scatter(blue_points_x, blue_points_y, s=40,c='green')
# ax.set_ylim([-6,5])
print("b",b)
print("w",w)
x = arange(-4.0, 4.0, 0.1) # 分界线x范围,步长为0.1
# x = arange(-2.0,10.0)
if isinstance(b,numpy.matrixlib.defmatrix.matrix):
b = b.A[0][0]
y = (-b-w[0][0]*x)/w[1][0] # 直线方程 Ax + By + C = 0
ax3,=plt.plot(x,y, 'k')
ax4=plt.scatter(svc_points_x,svc_points_y,s=50,c='orange',marker='p')
plt.legend([ax1, ax2,ax3,ax4], ["red points","blue points", "decision boundary","support vector"], loc='lower right') # 标注
plt.show()
dataArr,labelArr = loadDataSet('/home/zhangqingfeng/test/svm_test_data')
b,alphas = smoP(dataArr,labelArr,0.8,0.001,40)
w=calcWs(alphas,dataArr,labelArr)
draw_points(dataArr,labelArr,w,b,alphas)
可参考数据集
-0.397822 8.058397 -1 0.824839 13.730343 -1 1.507278 5.027866 1 0.099671 6.835839 1 -0.344008 10.717485 -1 1.785928 7.718645 1 -0.918801 11.560217 -1 -0.364009 4.747300 1 -0.841722 4.119083 1 0.490426 1.960539 1 -0.007194 9.075792 -1 0.356107 12.447863 -1 0.342578 12.281162 -1 -0.810823 -1.466018 1 2.530777 6.476801 1 1.296683 11.607559 -1 0.475487 12.040035 -1 -0.783277 11.009725 -1 0.074798 11.023650 -1 -1.337472 0.468339 1 -0.102781 13.763651 -1 -0.147324 2.874846 1 0.518389 9.887035 -1 1.015399 7.571882 -1 -1.658086 -0.027255 1 1.319944 2.171228 1 2.056216 5.019981 1 -0.851633 4.375691 1 -1.510047 6.061992 -1 -1.076637 -3.181888 1 1.821096 10.283990 -1 3.010150 8.401766 1 -1.099458 1.688274 1 -0.834872 -1.733869 1 -0.846637 3.849075 1 1.400102 12.628781 -1 1.752842 5.468166 1 0.078557 0.059736 1 0.089392 -0.715300 1 1.825662 12.693808 -1 0.197445 9.744638 -1 0.126117 0.922311 1 -0.679797 1.220530 1 0.677983 2.556666 1 0.761349 10.693862 -1 -2.168791 0.143632 1 1.388610 9.341997 -1 0.317029 14.739025 -1
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