《机器学习实战》（七）—— AdaBoost（提升树）

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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] = -1.0else:retArray[dataMat[:,dimen] > threshVal] = -1.0return retArray#  构建决策树桩
def buildStump(dataArr,classLabels,D):dataMat = mat(dataArr);labelMat = mat(classLabels).Tm,n = shape(dataMat)numSteps = 10.0;bestStump = {};bestClassEst = mat(zeros((m,1)))minError = inffor 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 * stepSizepredictedVals = stumpClassify(dataMat,i,threshVal,inequal)errArr = mat(ones((m,1)))errArr[predictedVals == labelMat] = 0weightedError = D.T * errArrif weightedError < minError:minError = weightedErrorbestClassEst = predictedVals.copy()bestStump['dim'] = ibestStump['thresh'] = threshValbestStump['ineq'] = inequalreturn 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/mD = mat(ones((m,1))/m)aggClassEst = mat(zeros((m,1)))for i in range(numIt):bestStump,error,ClassEst = buildStump(dataArr,classLabels,D)# 见式 8.2alpha = float(0.5*log((1-error)/max(error,1e-16)))bestStump['alpha'] = alphaweakClassArr.append(bestStump)# 见式 8.4expon = multiply(-1*alpha*mat(classLabels).T,ClassEst)D = multiply(D,exp(expon))D = D/D.sum()# 见式 8.6aggClassEst += alpha*ClassEstaggErrors = multiply(sign(aggClassEst) != mat(classLabels).T,ones((m,1)))errorRate = aggErrors.sum()/mprint ("error rate : ",errorRate)if errorRate == 0:breakreturn 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 8.7aggClassEst += classifierArr[i]['alpha']*classEstprint aggClassEstreturn 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.]]

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