AdaBoost算法

理论知识可参考：《统计学习方法》 （李航 著） 第八章

简单代码实现：

from numpy import *
import matplotlib.pyplot as plt

def loadSimpData():
    dataMat = 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 dataMat, classLabels

def stumpClassify(dataMatrix, dimen, threshVal, threshIneq):
    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
    for i in range(n):
        rangeMin = dataMatrix[:, i].min(); rangeMax = dataMatrix[:,i].max();
        stepSize = (rangeMax-rangeMin)/numSteps
        for j in range(-1, int(numSteps)+1):
            for inequal in ['lt', 'gt']:
                threshVal = (rangeMin + float(j) * stepSize)
                predictedVals = stumpClassify(dataMatrix, i, threshVal, inequal)
                errArr = mat(ones((m, 1)))
                errArr[predictedVals == labelMat] = 0
                weightedError = D.T * errArr
                #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)
    aggClassEst = mat(zeros((m, 1)))
    for i in range(numIt):
        bestStump, error, classEst = buildStump(dataArr, classLabels, D)
        print("D:", D.T)
        alpha = float(0.5*log((1.0-error)/max(error, 1e-16)))
        bestStump['alpha'] = alpha
        weakClassArr.append(bestStump)
        print("classEst:", classEst)
        expon = multiply(-1*alpha*mat(classLabels).T, classEst)
        D = multiply(D, exp(expon))
        D = D/D.sum()
        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

dataMat, classLabels = loadSimpData()
D = mat(ones((5, 1))/5)
classifierArray = adaBoostTrainDS(dataMat, classLabels, 9)
print(classifierArray)