smoSimple.py

def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
    """
    简化版SMO算法
    :param dataMatIn:       X
    :param classLabels:     Y
    :param C:               惩罚参数
    :param toler:           容错率
    :param maxIter:         最大循环次数
    :return:
    """
    dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()
    b = 0; m,n = shape(dataMatrix)  # m:=训练实例的个数；n:=每个实例的维度
    alphas = mat(zeros((m,1)))
    iter = 0
    while (iter < maxIter):
        alphaPairsChanged = 0   #alpha是否已经进行了优化
        for i in range(m):
            #   w = alpha * y * x;  f(x_i) = w^T * x_i + b
            fXi = float(multiply(alphas,labelMat).T*dataMatrix*dataMatrix[i,:].T) + b     # 预测的类别
            Ei = fXi - float(labelMat[i])   #得到误差，如果误差太大，检查是否可能被优化
            if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)): #必须满足约束
                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()                # 教材中的α_1^old和α_2^old
                if (labelMat[i] != labelMat[j]):                                          # 两者所在的对角线段端点的界
                    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 * K12 - K11 - K22)，且Eta非负，此处eta = -Eta则非正
                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)
                #如果内层循环通过以上方法选择的α_2不能使目标函数有足够的下降，那么放弃α_1
                if (abs(alphas[j] - alphaJold) < 0.00001): print "j not moving enough"; 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