PYTHON机器学习实战——SVM支持向量机
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支持向量机不是很好被理解,主要是因为里面涉及到了许多数学知识,需要慢慢地理解。理论知识参考:
http://www.cnblogs.com/steven-yang/p/5658362.html
一下附上源码:
#-*- coding:utf-8 -*-#!/usr/bin/python'''支持向量积 用的话,建议使用libsvm'''#测试程序 import svmMLiA as svm svm.testRbf() svm.testDigits()from numpy import *from time import sleep# 载入数据def loadDataSet(fileName): dataMat = []; labelMat = []# 数据 和 标签 fr = open(fileName) for line in fr.readlines(): lineArr = line.strip().split('\t') dataMat.append([float(lineArr[0]), float(lineArr[1])])# 前两个为 数据 labelMat.append(float(lineArr[2])) # 后一个为 标签 return dataMat,labelMat# m 是 pha 的数量 i 是一个 pha 的下标 ,j 为另外一个 不同pha 的下标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# 调整 pha在 上下限 范围内def clipAlpha(aj,H,L): if aj > H: aj = H if L > aj: aj = L return aj# 简化版 smo 优化算法 解 svm分类def smoSimple(dataMatIn, classLabels, C, toler, maxIter): dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()# 数据 和 标签 b = 0; m,n = shape(dataMatrix)# m为样本数量 alphas = mat(zeros((m,1))) # 每个样本对应一个alphas 初始化为0 iter = 0 while (iter < maxIter): alphaPairsChanged = 0 # 记录 alpha 是否已被优化 for i in range(m): # 每个样本 fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b # 每个样本 预测的类别 Ei = fXi - float(labelMat[i]) #误差 if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):#误差过大 需要优化 alpha j = selectJrand(i,m)# 另一个 alpha下标 fXj = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + b # 计算该样本的 预测的类别 Ej = fXj - float(labelMat[j])#误差 alphaIold = alphas[i].copy(); alphaJold = alphas[j].copy(); # 两个alpha if (labelMat[i] != labelMat[j]):#两标签不一样 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# 最优修改量 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])#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]) 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# 核方法 低维 到 高维 可以 用超平面分割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# 完整版 platt SMO 算法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, Ejdef 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] < oS.C)) or ((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) < 0.00001): print "j not moving enough"; return 0 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]) 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 0def 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 < maxIter) and ((alphaPairsChanged > 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 < 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 #toggle entire set loop elif (alphaPairsChanged == 0): entireSet = True print "iteration number: %d" % iter return oS.b,oS.alphasdef 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 wdef 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 "支持向量机个数: %d" % 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 "训练错误率: %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 "测试错误率: %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 returnVectdef 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 #手写字体识别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 "支持向量机个数: %d" % 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 "训练错误率: %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 "测试错误率: %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, Ejdef 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] < oS.C)) or ((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) < 0.00001): print "j not moving enough"; return 0 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]) 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 0def 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 < maxIter) and ((alphaPairsChanged > 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 < 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 #toggle entire set loop elif (alphaPairsChanged == 0): entireSet = True print "iteration number: %d" % iter return oS.b,oS.alphas
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