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boosting是一种与bagging很类似的技术。不论是在boosting还是bagging中，所使用的多个分类器的类型都是一致的。但是在前者当中，不同的分类器是通过串行训练而获得的，每个新分类器都根据已训练出的分类器的性能来进行训练。boosting是通过集中关注被已有分类器分错的那些数据来获得新的分类器。

由于boosting分类的结果是基于所有分类器的加权求和结果，因此boosting和bagging不太一样。bagging中的分类器权重是相等的，而boosting中的分类器权重并不相等，每个权重代表的是其在上一轮迭代过程中的成功度。

boosting方法拥有多个版本，本章将只关注其中一个最流行的版本AdaBoost

最后直接上代码：

from numpy import *def loadSimpData():    #数据集    datMat = matrix([[ 1. ,  2.1],        [ 2. ,  1.1],        [ 1.3,  1. ],        [ 1. ,  1. ],        [ 2. ,  1. ]])    classLabels = [1.0, 1.0, -1.0, -1.0, 1.0]    return datMat,classLabelsdef loadDataSet(fileName):      #general function to parse tab -delimited floats    numFeat = len(open(fileName).readline().split('\t')) #得到特征的个数    dataMat = []; labelMat = []    fr = open(fileName)    for line in fr.readlines():        lineArr =[]        curLine = line.strip().split('\t')        for i in range(numFeat-1):            lineArr.append(float(curLine[i]))        dataMat.append(lineArr)        labelMat.append(float(curLine[-1]))    return dataMat,labelMat     #返回数据集#单层的决策树生成函数def stumpClassify(dataMatrix,dimen,threshVal,threshIneq):#分类数据    retArray = ones((shape(dataMatrix)[0],1))    if threshIneq == 'lt':        retArray[dataMatrix[:,dimen] <= threshVal] = -1.0    else:        retArray[dataMatrix[:,dimen] > threshVal] = -1.0    return retArray    #单层决策树的生成函数,这个函数是找到最优属性上的最优单层决策树def buildStump(dataArr,classLabels,D):    dataMatrix = mat(dataArr); labelMat = mat(classLabels).T  #矩阵转置    m,n = shape(dataMatrix)    numSteps = 10.0; bestStump = {}; bestClasEst = mat(zeros((m,1)))    minError = inf #init error sum, to +infinity    for i in range(n):#遍历所有的属性值（特征值）        rangeMin = dataMatrix[:,i].min(); rangeMax = dataMatrix[:,i].max();        stepSize = (rangeMax-rangeMin)/numSteps        for j in range(-1,int(numSteps)+1):#在当前维度上遍历所有的范围值            for inequal in ['lt', 'gt']: #计算出一个阈值后，那么小于这个阈值为负样本还是大于这个阈值为负样本，不得而知，因此需要遍历，找出错误率最小的                threshVal = (rangeMin + float(j) * stepSize)    #每一个阈值                predictedVals = stumpClassify(dataMatrix,i,threshVal,inequal) #call stump classify with i, j, lessThan                errArr = mat(ones((m,1)))                errArr[predictedVals == labelMat] = 0                weightedError = D.T*errArr  #计算错误率                #print "split: dim %d, thresh %.2f, thresh ineqal: %s, the weighted error is %.3f" % (i, threshVal, inequal, weightedError)                if weightedError < minError:                    minError = weightedError                    bestClasEst = predictedVals.copy()                    bestStump['dim'] = i                    bestStump['thresh'] = threshVal                    bestStump['ineq'] = inequal    return bestStump,minError,bestClasEst   #返回最优属性上的单层决策树#基于单层决策树的训练过程def adaBoostTrainDS(dataArr,classLabels,numIt=40):    weakClassArr = []    m = shape(dataArr)[0]    D = mat(ones((m,1))/m)   #刚开始的时候，初始化权重向量D相等    aggClassEst = mat(zeros((m,1)))    for i in range(numIt):    #迭代次数        bestStump,error,classEst = buildStump(dataArr,classLabels,D) #在当前维度上找到最优的单层决策树        #print "D:",D.T        alpha = float(0.5*log((1.0-error)/max(error,1e-16)))#calc alpha, throw in max(error,eps) to account for error=0        bestStump['alpha'] = alpha          weakClassArr.append(bestStump)                  #将最优的单层决策树加入到树数组中        #print "classEst: ",classEst.T        expon = multiply(-1*alpha*mat(classLabels).T,classEst)  #关键点 exponent for D calc, getting messy        D = multiply(D,exp(expon))                              #关键点 Calc New D for next iteration        D = D/D.sum()       #关键点        #calc training error of all classifiers, if this is 0 quit for loop early (use break)        aggClassEst += alpha*classEst        #print "aggClassEst: ",aggClassEst.T        aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T,ones((m,1)))        errorRate = aggErrors.sum()/m        print ("total error: ",errorRate)        if errorRate == 0.0: break    return weakClassArr#adaboost分类函数def adaClassify(datToClass,classifierArr):    dataMatrix = mat(datToClass)#do stuff similar to last aggClassEst in adaBoostTrainDS    m = shape(dataMatrix)[0]    aggClassEst = mat(zeros((m,1)))    for i in range(len(classifierArr)):        classEst = stumpClassify(dataMatrix, classifierArr[i]['dim'],\                                 classifierArr[i]['thresh'],\                                 classifierArr[i]['ineq'])#call stump classify        aggClassEst += classifierArr[i]['alpha']*classEst        print (aggClassEst)    return sign(aggClassEst)