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svm-smo演算法.py
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svm-smo演算法.py
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from numpy import *
import numpy as np
#----------------------------------
# 載入資料
#----------------------------------
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
#----------------------------------
# 從0~m中找一個非i的亂數
#----------------------------------
def selectJrand(i, m):
j=i
while(j==i):
j=int(random.uniform(0, m))
return j
#-------------------------------------
# 將超過H的值改為H; 小於L的值改為L
#-------------------------------------
def clipAlpha(aj, H, L):
if aj>H:
aj=H
if L>aj:
aj=L
return aj
#==============================================================================
# SMO算法
# 1. 随机数初始化向量权重alphaa, 并计算偏移 b
# 2 初始化误差项Ei
# 3. 选取两个向量作为需要调整的点,
# 4. 令a2<new> = a2<old> + y2(E1-E2)/K
# 5. if a2<new> > V, let a2<new>=V
# 6. if a2<new> < U, let a2<new>=U
# 7. Let a1<new> = a1<old> + y1*y2*(a2<old> - a2<new>)
# 8. 以新的a1<new>及a2<new>修改Ei及b
# 9. 如達終止條件則停止, 否則再開始進行步驟3~8
#
# 實現SVM的smo演算法
# smo: Sequential Minimal Optimization(1998)
#
# C:懲罰因數
# toler:容許誤差
# maxInter:最多遞迴次數
#
# 回傳值:
# alphas:向量權重
# b:偏移量
#------------------------------------------------------------------------------
def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
dataMatrix=mat(dataMatIn)
labelMat=mat(classLabels).transpose()
b = 0 #偏移量
m, n = shape(dataMatrix)
alphas = mat(zeros((m,1))) #向量權重
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]) #誤差項
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]) #誤差項
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 engoth")
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
#==============================================================================
#載入測試檔
dataArr, labelArr=loadDataSet('testSet.txt')
dataND=np.array(dataArr)
labelND=np.array(labelArr)
#smo分類模型建立
b, alphas=smoSimple(dataArr, labelArr, 0.05, 0.001, 40)
alphasND=np.array(alphas)
alphasND=alphasND.transpose()
#==========================================
# 繪圖
#==========================================
import matplotlib.pyplot as plt
# 設定字型及大小
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['font.size'] = 14
# 設定圖標題
plt.title('圖標題')
# 設定x軸及y軸標題
plt.xlabel('x軸')
plt.ylabel('y軸')
# 資料表內的grid
plt.grid(True)
# 設定x軸及y軸的尺規範圍
plt.axis([-1, 10, -5, 5])
# 繪製資料
plt.plot(dataND[labelND==1,0], dataND[labelND==1,1], 'ys', dataND[labelND==-1,0], dataND[labelND==-1,1], 'co')
plt.plot(dataND[(alphasND!=0)[0],0], dataND[(alphasND!=0)[0],1], 'r+')
#=======================================================
# hyperplane 分隔超平面(在此是一條線)
# 方程式=(-b-m0x)/m1
#-------------------------------------------------------
w=mat([0,0])
for i in range(len(alphas)):
w=w+mat(dataArr[i])*labelArr[i]*float(alphas[i])
w=array(w)
m0=float(w[0][0])
m1=float(w[0][1])
b=float(b)
k1=[0, 10]
k2=[(-1*b-m0*k1[0])/m1, (-1*b-m0*k1[1])/m1]
print(k2)
plt.rc('lines', linewidth=2)
plt.plot(k1, k2, '-m')
#=======================================================
# 顯示圖表
plt.show()