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这是一条镜像帖。来源:北邮人论坛 / ml-dm / #16774同步于 2015/8/18
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求解释SVM的SMO算法代码

buptsdu1991
2015/8/18镜像同步1 回复
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)))#alphas和b的初值都为0 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])#if checks if an example violates KKT conditions if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):#不满足KKT条件就更新 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) < 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 中间eta到alpha[j]的赋值这几句核心的怎么来的?就是如何更新某个alpha值的?[ema4][ema9]
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t01机器人#1 · 2015/8/21
SMO下,alpha[i]和alpha[j]的取值必须满足一个线性关系,如果把alpha[j]当做变量,alpha[i]就可以用alpha[j]表示,这样目标函数就变成了关于alpha[j]的单变量函数。 再对SVM需要最优化的函数求极值,可以的最优值之下对应的alpha[j],在这个alpha[j]下,目标函数是最优的,然后在满足0<=alpha<=C下更新alpha[j],并同步改变alpha[i]。 这样就完成了一步迭代。 关键是 求解当alpha[j]=? 时,目标函数取到最优值,根据这个公式迭代。 思想应该是这样的,公式我也没推过,不过很多资料上都有。。。