机器学习——adaboost元算法

from numpy import *

def loadSimpData():
    datMat = matrix([[ 1. ,  2.1],
        [ 1.5,  1.6],
        [ 1.3,  1. ],
        [ 1. ,  1. ],
        [ 2. ,  1. ]])
    classLabels = [1.0, 1.0, -1.0, -1.0, 1.0]
    return datMat,classLabels

def plotBestFit(weakClassArr):		#画出数据集和所有的基学习器
	#import matplotlib.pyplot as plt
	dataMat,labelMat=loadSimpData()	#数据矩阵和标签向量
	dataArr = array(dataMat)		#转换成数组
	n = shape(dataArr)[0] 
	xcord1 = []; ycord1 = []		#声明两个不同颜色的点的坐标
	xcord2 = []; ycord2 = []
	for i in range(n):
		if int(labelMat[i])== 1:
			xcord1.append(dataArr[i,0]); ycord1.append(dataArr[i,1])
		else:
			xcord2.append(dataArr[i,0]); ycord2.append(dataArr[i,1])
	fig = plt.figure()
	ax = fig.add_subplot(111)
	ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
	ax.scatter(xcord2, ycord2, s=30, c='green')
	print "weakClassArr[0]['thresh']",weakClassArr[0]['dim']
	for j in range(len(weakClassArr)):
		if(weakClassArr[j]['dim'] == 1):
			x = arange(-0.0, 2.5, 0.1)
			y = x*0+weakClassArr[j]['thresh']
			ax.plot(x, y)
		else:
			y = array(arange(-0.0, 2.5, 0.1))
			x = y*0+weakClassArr[j]['thresh']
			ax.plot(x, y)
	plt.xlabel('X1'); plt.ylabel('X2');
	plt.show()

def stumpClassify(dataMatrix,dimen,threshVal,threshIneq):	#通过阈值比较对数据进行分类
    retArray = ones((shape(dataMatrix)[0],1))				#首先将返回的数组的全部元素设置为1
    if threshIneq == 'lt':
        retArray[dataMatrix[:,dimen] <= threshVal] = -1.0	#将满足<=不等式的元素设为-1
    else:
        retArray[dataMatrix[:,dimen] > threshVal] = -1.0	#将满足>不等式的元素设为-1
    return retArray
    

def buildStump(dataArr,classLabels,D):		#遍历stumpClassify()函数所有的可能输入值，并找到数据集上最佳的单层决策树
    dataMatrix = mat(dataArr); labelMat = mat(classLabels).T
    m,n = shape(dataMatrix)					#m=5,n=2
    numSteps = 10.0; bestStump = {}; bestClasEst = mat(zeros((m,1)))
    minError = inf 							#初始误差总和，为无穷大
    for i in range(n):						#循环X和Y两个维度
        rangeMin = dataMatrix[:,i].min(); rangeMax = dataMatrix[:,i].max();		#取得X和Y两个维度的最大值和最小值特征
        stepSize = (rangeMax-rangeMin)/numSteps									#步进长度
        for j in range(-1,int(numSteps)+1):				#从-1到10步进
            for inequal in ['lt', 'gt']: 				#"lt"为满足<=不等式，"gt"为满足>不等式
                threshVal = (rangeMin + float(j) * stepSize)					#当前阈值
                predictedVals = stumpClassify(dataMatrix,i,threshVal,inequal)	#根据阈值和不等式，计算预测的分类
                errArr = mat(ones((m,1)))
                errArr[predictedVals == labelMat] = 0	#样本估计错误的标记为1
                weightedError = D.T*errArr  			#通过权重和错误标记，计算泛化误差
                #print "split: dim %d, thresh %.2f, thresh ineqal: %s, the weighted error is %.3f" % (i, threshVal, inequal, weightedError)
                if weightedError < minError:			#如果泛化误差是最小的
                    minError = weightedError
                    bestClasEst = predictedVals.copy()	#保存最佳预测结果
                    bestStump['dim'] = i				#保存维度、阈值、不等式符号
                    bestStump['thresh'] = threshVal
                    bestStump['ineq'] = inequal
    return bestStump,minError,bestClasEst


def adaBoostTrainDS(dataArr,classLabels,numIt=40):	#基于单层决策树的AdaBoost训练
    weakClassArr = []
    m = shape(dataArr)[0]							#需要分类的数据量，m=5
    D = mat(ones((m,1))/m)   						#D为权重向量，初始D1...D5的和等于1
    aggClassEst = mat(zeros((m,1)))					#基分类器的线性组合
    for i in range(numIt):
	    #建立单层决策树，bestStump包括维度，不等式，阈值，error泛化误差，classEst是每个基分类器
        bestStump,error,classEst = buildStump(dataArr,classLabels,D)	
        print "最佳决策树=",bestStump,"泛化误差=",error,"更新前的分类器预测结果=",classEst.T 
        #print "D:",D.T
        alpha = float(0.5*log((1.0-error)/max(error,1e-16)))	#根据泛化误差，计算基分类器的权重α值
        bestStump['alpha'] = alpha  							#把权重α值添加到最佳决策树的列表中
        print "最佳决策树=",bestStump
        weakClassArr.append(bestStump)                  		#保存单层最佳决策树参数到数组中
        print "预测分类: ",classEst.T
        expon = multiply(-1*alpha*mat(classLabels).T,classEst) 	#权重α×真实分类×预测分类，multiply为对应元素相乘，不是矩阵相乘
        D = multiply(D,exp(expon))                              #Calc New D for next iteration
        D = D/D.sum()											#更新D,D.sum()为规范化因子
        #calc training error of all classifiers, if this is 0 quit for loop early (use break)
        aggClassEst += alpha*classEst
        print "更新后的分类器预测结果: ",aggClassEst.T
        aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T,ones((m,1)))	#boolean值和1相乘
        errorRate = aggErrors.sum()/m												#计算错误率
        print "total error: ",errorRate
        if errorRate == 0.0: break
    return weakClassArr,aggClassEst

def adaClassify(datToClass,classifierArr):			#AdaBoost分类函数
    dataMatrix = mat(datToClass)					#输入[0,0]转换成[[0,0]]矩阵
    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'])				#维度、阈值、不等式符号
        aggClassEst += classifierArr[i]['alpha']*classEst				#计算在每一个基分类器上的预测值的累加和
        print "aggClassEst=",aggClassEst
    return sign(aggClassEst)

# coding:utf-8
# !/usr/bin/env python

import adaboost

if __name__ == '__main__':
	datMat,classLabels = adaboost.loadSimpData()
	weakClassArr,aggClassEst = adaboost.adaBoostTrainDS(datMat,classLabels)
	print "弱分类器组合:",weakClassArr
	print adaboost.adaClassify([[0,0],[5,5]],weakClassArr)
	adaboost.plotBestFit(weakClassArr)