svmMLiA.py

import numpy as np
#https://blog.csdn.net/on2way/article/details/47730367,看这篇博客
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

def selectJrand(i,m): #i表示alpha的下标，m表示alpha的总数
    j=i
    while(j==i):
        j=int(np.random.uniform(0,m)) #简化版SMO，alpha随机选择
    return j

def clipAlpha(aj,H,L): #辅助函数，用于调整alpha范围
    if aj>H:
        aj=H
    if L>aj:
        aj=L
    return aj
#SMO simple algorithm
def smoSimple(dataMatIn, classLabels, C, toler, maxIter):#toler表示容错率 常数C
    dataMatrix = np.mat(dataMatIn); labelMat = np.mat(classLabels).transpose()
    b = 0; m,n = np.shape(dataMatrix)
    alphas = np.mat(np.zeros((m,1)))
    iter = 0
    while (iter < maxIter):
        alphaPairsChanged = 0   #  标记alpha是否被优化
        for i in range(m):
            # fXi是预测的类别
            fXi = float(np.multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
            # Ei表示误差
            Ei = fXi - float(labelMat[i])# 预测结果和真实结果比对，计算误差
            # 对alpha进行优化，同时检查alpha的值满足两个条件：if
            if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):
                j = selectJrand(i,m)# 随机选择第二个alpha
                fXj = float(np.multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + b
                Ej = fXj - float(labelMat[j])
                alphaIold = alphas[i].copy(); alphaJold = alphas[j].copy(); # 分配内存 稍后比较误差
                if (labelMat[i] != labelMat[j]): # 计算L H用于将alpha[j]调整到0—C之间
                    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为alpha[j]的最优修改量
                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)
                # 检查alpha[j]是否有轻微改变
                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