Python之支持向量机

上图可以说是超平面的直观图示，支持向量就是离分隔超平面最近的点。

附code:

from numpy import *

from time import sleep

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

#函数selectJrand()有两个参数值，其中i是第一个alpha的下标， m是所有alpha的数目。只要函数值不等于输入值i，函数就会进行随机选择。

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

#辅助函数就是clipAlpha()，它是用于调整大于H或小于L的alpha值。

def clipAlpha(aj,H,L):

if aj > H:

aj = H

if L > aj:

aj = L

return aj

##########################################################

import pandas as pd

import os

#更改当前工作目录

os.chdir('C:\Users\E440\Desktop\PythonStudy\MLiA_SourceCode\machinelearninginaction\Ch06')

os.getcwd()

dataArr,labelArr=loadDataSet('testSet.txt')

labelArr

####################################################################

# 简化版SMO算法

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

alphaPairsChanged = 0#每次循环当中，将alphaPairsChanged先设为0，然后再对整个集合顺序遍历。变量alphaPairsChanged用于记录alpha是否已经进行优化。

for i in range(m):

fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b

Ei = fXi - float(labelMat[i])#if checks if an example violates KKT conditions

if ((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)

alphas[i] += labelMat[j]*labelMat[i]*(alphaJold - alphas[j])#update i by the same amount as j

#the update is in the oppostie direction

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]): b = b1

elif (0 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

############################################################

b,alphas=smoSimple(dataArr,labelArr,0.6,0.001,40)

b

alphas[alphas>0]

shape(alphas[alphas>0])

for i in range(100):

if alphas[i]>0.0:print dataArr[i],labelArr[i]

###############################################################

def kernelTrans(X, A, kTup): #calc the kernel or transform data to a higher dimensional space

m,n = shape(X)

K = mat(zeros((m,1)))

if kTup[0]=='lin': K = X * A.T #linear kernel

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)) #divide in NumPy is element-wise not matrix like Matlab

else: raise NameError('Houston We Have a Problem -- \

That Kernel is not recognized')

return K

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): #this is the second choice -heurstic, and calcs Ej

maxK = -1; maxDeltaE = 0; Ej = 0

oS.eCache[i] = [1,Ei] #set valid #choose the alpha that gives the maximum delta E

validEcacheList = nonzero(oS.eCache[:,0].A)[0]

if (len(validEcacheList)) > 1:

for k in validEcacheList: #loop through valid Ecache values and find the one that maximizes delta E

if k == i: continue #don't calc for i, waste of time

Ek = calcEk(oS, k)

deltaE = abs(Ei - Ek)

if (deltaE > maxDeltaE):

maxK = k; maxDeltaE = deltaE; Ej = Ek

return maxK, Ej

else: #in this case (first time around) we don't have any valid eCache values

j = selectJrand(i, oS.m)

Ej = calcEk(oS, j)

return j, Ej

def updateEk(oS, k):#after any alpha has changed update the new value in the cache

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] > 0)):

j,Ej = selectJ(i, oS, Ei) #this has been changed from selectJrand

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] #changed for kernel

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) #added this for the Ecache

if (abs(oS.alphas[j] - alphaJold)

oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])#update i by the same amount as j

updateEk(oS, i) #added this for the Ecache #the update is in the oppostie direction

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]): oS.b = b1

elif (0 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)): #full Platt SMO

oS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler, kTup)

iter = 0

entireSet = True; alphaPairsChanged = 0

while (iter 0) or (entireSet)):

alphaPairsChanged = 0

if entireSet: #go over all

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:#go over non-bound (railed) alphas

nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A

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 #toggle entire set loop

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 testRbf(k1=1.3):

dataArr,labelArr = loadDataSet('testSetRBF.txt')

b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) #C=200 important

datMat=mat(dataArr); labelMat = mat(labelArr).transpose()

svInd=nonzero(alphas.A>0)[0]

sVs=datMat[svInd] #get matrix of only support vectors

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,:],('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

datMat=mat(dataArr); labelMat = mat(labelArr).transpose()

m,n = shape(datMat)

for i in range(m):

kernelEval = kernelTrans(sVs,datMat[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)

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

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)

'''#######********************************

Non-Kernel VErsions below

'''#######********************************

class optStructK:

def __init__(self,dataMatIn, classLabels, C, toler): # 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

def calcEkK(oS, k):

fXk = float(multiply(oS.alphas,oS.labelMat).T*(oS.X*oS.X[k,:].T)) + oS.b

Ek = fXk - float(oS.labelMat[k])

return Ek

def selectJK(i, oS, Ei): #this is the second choice -heurstic, and calcs Ej

maxK = -1; maxDeltaE = 0; Ej = 0

oS.eCache[i] = [1,Ei] #set valid #choose the alpha that gives the maximum delta E

validEcacheList = nonzero(oS.eCache[:,0].A)[0]

if (len(validEcacheList)) > 1:

for k in validEcacheList: #loop through valid Ecache values and find the one that maximizes delta E

if k == i: continue #don't calc for i, waste of time

Ek = calcEk(oS, k)

deltaE = abs(Ei - Ek)

if (deltaE > maxDeltaE):

maxK = k; maxDeltaE = deltaE; Ej = Ek

return maxK, Ej

else: #in this case (first time around) we don't have any valid eCache values

j = selectJrand(i, oS.m)

Ej = calcEk(oS, j)

return j, Ej

def updateEkK(oS, k):#after any alpha has changed update the new value in the cache

Ek = calcEk(oS, k)

oS.eCache[k] = [1,Ek]

def innerLK(i, oS):

Ei = calcEk(oS, i)

if ((oS.labelMat[i]*Ei oS.tol) and (oS.alphas[i] > 0)):

j,Ej = selectJ(i, oS, Ei) #this has been changed from selectJrand

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.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) #added this for the Ecache

if (abs(oS.alphas[j] - alphaJold)

oS.alphas[i] += oS.labelMat[j]*oS.labelMat[i]*(alphaJold - oS.alphas[j])#update i by the same amount as j

updateEk(oS, i) #added this for the Ecache #the update is in the oppostie direction

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]): oS.b = b1

elif (0 oS.alphas[j]): oS.b = b2

else: oS.b = (b1 + b2)/2.0

return 1

else: return 0

def smoPK(dataMatIn, classLabels, C, toler, maxIter): #full Platt SMO

oS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler)

iter = 0

entireSet = True; alphaPairsChanged = 0

while (iter 0) or (entireSet)):

alphaPairsChanged = 0

if entireSet: #go over all

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:#go over non-bound (railed) alphas

nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A

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 #toggle entire set loop

elif (alphaPairsChanged == 0): entireSet = True

print "iteration number: %d" % iter

return oS.b,oS.alphas

一起学习的小伙伴如果有什么想法或者意见，欢迎沟通~