《机器学习实战》AdaBoost算法（手稿+代码）

Adaboost：多个弱分类器组成一个强分类器，按照每个弱分类器的作用大小给予不同的权重

一.Adaboost理论部分

　　1.1 adaboost运行过程

　　　　注释：算法是利用指数函数降低误差，运行过程通过迭代进行。其中函数的算法怎么来的，你不用知道！当然你也可以尝试使用其它的函数代替指数函数，看看效果如何。

　　1.2 举例说明算法流程

　　　　略，花几分钟就可以看懂的例子。见：《统计学习方法》李航大大

　　　　博客都是借鉴（copy）李航博士的：http://blog.csdn.net/v_july_v/article/details/40718799 ，July算总结（copy）最好的吧！

　　1.3 算法误差界的证明

　　　　注释：误差的上界限由Z_m约束，然而Zm又是由G_m(x_i)约束，所以选择适当的G_m(x_i)可以加快误差的减小。

二.代码实现

　　注释：这里参考大神博客http://blog.csdn.net/guyuealian/article/details/70995333，举例子很详细。

　　2.1程序流程图

　　2.2基本程序实现

　　　　注释：真是倒霉玩意，本来代码全部注释好了，突然Ubuntu奔溃了，全部程序就GG了。。。下面的代码就是官网的代码，部分补上注释。现在使用Deepin桌面版了，其它方面都比Ubuntu好，但是有点点卡。

 from numpy import *

 def loadDataSet(fileName):      #general function to parse tab -delimited floats
     numFeat = len(open(fileName).readline().split('\t')) #get number of fields
     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

 def stumpClassify(dataMatrix,dimen,threshVal,threshIneq):#just classify the data
     retArray = ones((shape(dataMatrix)[0],1))
     if threshIneq == 'lt':
         retArray[dataMatrix[:,dimen] <= threshVal] = -1.0
     else:
         retArray[dataMatrix[:,dimen] > threshVal] = -1.0
     return retArray

 def buildStump(dataArr,classLabels,D):
     dataMatrix = mat(dataArr); labelMat = mat(classLabels).T
     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):#loop over all dimensions
         rangeMin = dataMatrix[:,i].min(); rangeMax = dataMatrix[:,i].max();
         stepSize = (rangeMax-rangeMin)/numSteps
         for j in range(-1,int(numSteps)+1):#loop over all range in current dimension
             for inequal in ['lt', 'gt']: #go over less than and greater than
                 threshVal = (rangeMin + float(j) * stepSize)
                 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  #calc total error multiplied by D
                 #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

 def adaBoostTrainDS(dataArr,classLabels,numIt=40):
     weakClassArr = []
     m = shape(dataArr)[0]
     D = mat(ones((m,1))/m)   #init D to all equal
     aggClassEst = mat(zeros((m,1)))
     for i in range(numIt):
         bestStump,error,classEst = buildStump(dataArr,classLabels,D)#build Stump
         #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)                  #store Stump Params in Array
         #print "classEst: ",classEst.T
         expon = multiply(-1*alpha*mat(classLabels).T,classEst) #exponent for D calc, getting messy
         D = multiply(D,exp(expon))                              #Calc New D for next iteration
         D = D/D.sum()
         #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,aggClassEst

 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)

 def plotROC(predStrengths, classLabels):
     import matplotlib.pyplot as plt
     cur = (1.0,1.0) #cursor
     ySum = 0.0 #variable to calculate AUC
     numPosClas = sum(array(classLabels)==1.0)#标签等于1的和（也等于个数）
     yStep = 1/float(numPosClas); xStep = 1/float(len(classLabels)-numPosClas)
     sortedIndicies = predStrengths.argsort()#get sorted index, it's reverse
     sortData = sorted(predStrengths.tolist()[0])

     fig = plt.figure()
     fig.clf()
     ax = plt.subplot(111)
     #loop through all the values, drawing a line segment at each point
     for index in sortedIndicies.tolist()[0]:
         if classLabels[index] == 1.0:
             delX = 0; delY = yStep;
         else:
             delX = xStep; delY = 0;
             ySum += cur[1]
         #draw line from cur to (cur[0]-delX,cur[1]-delY)
         ax.plot([cur[0],cur[0]-delX],[cur[1],cur[1]-delY], c='b')
         cur = (cur[0]-delX,cur[1]-delY)
     ax.plot([0,1],[0,1],'b--')
     plt.xlabel('False positive rate'); plt.ylabel('True positive rate')
     plt.title('ROC curve for AdaBoost horse colic detection system')
     ax.axis([0,1,0,1])
     plt.show()
     print ("the Area Under the Curve is: ",ySum*xStep)

注释：重点说明一下非均衡分类的图像绘制问题，想了很久才想明白！

　　　都是相对而言的，其中本文说的曲线在左上方就为好，也是相对而言的，看你怎么定义个理解！

参考文献：

　　　　《统计学习方法》李航

　　　　　　http://blog.csdn.net/v_july_v/article/details/40718799没有书的就看这个大神的博客，基本是上面那本数的原版