《机器学习实战》（七）—— AdaBoost（提升树）

http://blog.csdn.net/u011239443/article/details/77294201

AdaBoost

提升树

例子

将“身体”设为A，“业务”设为B，“潜力”设为C。对该题做大致的求解：

这里我们只计算到了f2，相信读者也知道如何继续往下计算。这里特征的取值较少，所以直接使用是否等于某个取值来作为分支条件。实际中，可以设置是否大于或者小于等于某个阈值来作为分支条件。接下来我们就来看看如何实现提升树。

实现

# -*- coding: utf-8 -*-from numpy import *# 加载数据def loadSimpData():    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,classLabels# 决策桩分类# dimen : 选取的特征# threshVal ： 特征的阈值# threshInseq ： 判别大于或者小于等于该阈值def stumpClassify(dataMat,dimen,threshVal,threshIneq):    retArray = ones((shape(dataMat)[0],1))    if threshIneq == 'lt':        retArray[dataMat[:,dimen] <= threshVal] = -1.0    else:        retArray[dataMat[:,dimen] > threshVal] = -1.0    return retArray#  构建决策树桩def buildStump(dataArr,classLabels,D):    dataMat = mat(dataArr);labelMat = mat(classLabels).T    m,n = shape(dataMat)    numSteps = 10.0;bestStump = {};bestClassEst = mat(zeros((m,1)))    minError = inf    for i in range(n):        rangeMin = dataMat[:,i].min();rangeMax = dataMat[:,i].max()        stepSize = (rangeMax - rangeMin)/numSteps        # 由于是 ‘<= threshVal’，所以要从-1开始，使得出现全都 > threshVal 的情况        for j in range(-1,int(numSteps)+1):            for inequal in ['lt','gt']:                threshVal = rangeMin + j * stepSize                predictedVals = stumpClassify(dataMat,i,threshVal,inequal)                errArr = mat(ones((m,1)))                errArr[predictedVals == labelMat] = 0                weightedError = D.T * errArr                if weightedError < minError:                    minError = weightedError                    bestClassEst = predictedVals.copy()                    bestStump['dim'] = i                    bestStump['thresh'] = threshVal                    bestStump['ineq'] = inequal    return bestStump,minError,bestClassEstdef adaBoostTrainDS(dataArr,classLabels,numIt = 40):    # 保存不同的决策树桩    weakClassArr = []    m = shape(dataArr)[0]    # 权值初始化为 1/m    D = mat(ones((m,1))/m)    aggClassEst = mat(zeros((m,1)))    for i in range(numIt):        bestStump,error,ClassEst = buildStump(dataArr,classLabels,D)        # 见式 8.2        alpha = float(0.5*log((1-error)/max(error,1e-16)))        bestStump['alpha'] = alpha        weakClassArr.append(bestStump)        # 见式 8.4        expon = multiply(-1*alpha*mat(classLabels).T,ClassEst)        D = multiply(D,exp(expon))        D = D/D.sum()        # 见式 8.6        aggClassEst += alpha*ClassEst        aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T,ones((m,1)))        errorRate = aggErrors.sum()/m        print ("error rate : ",errorRate)        if errorRate == 0:            break    return weakClassArrdef adaClassify(dataToClass,classifierArr):    dataMat = mat(dataToClass)    m = shape(dataMat)[0]    aggClassEst = mat(zeros((m,1)))    for i in range(len(classifierArr)):        classEst = stumpClassify(dataMat,classifierArr[i]['dim'],\                                 classifierArr[i]['thresh'], \                                 classifierArr[i]['ineq'])        # 见式 8.7        aggClassEst += classifierArr[i]['alpha']*classEst        print aggClassEst    return sign(aggClassEst)

测试

import myAdaboostdataMat,classLabels = myAdaboost.loadSimpData()classifierArray = myAdaboost.adaBoostTrainDS(dataMat,classLabels,30)print myAdaboost.adaClassify([0,0],classifierArray)

结果

('error rate : ', 0.20000000000000001)('error rate : ', 0.20000000000000001)('error rate : ', 0.0)[[-0.69314718]][[-1.66610226]][[-2.56198199]][[-1.]]