python机器学习笔记（6）—— AdaBoost
0x00 什么是AdaBoost？
我们可以用多个弱分类器的实例来构建一个强分类器。AdaBoost就是基于这样一个理论来实现它的功能的。弱分类器意味着分类器的分类能力很弱，仅仅强于50%。在算法中会为每个分类器赋予一个权重，每次训练都会改动这个权重。比如对于某个第一次分错了，而第二次分对的样本，算法会减少第一次的权重，增加第二次的权重。其中错误率定义为：
然后权重alpha的计算公式是：
计算出alpha值后就能对权重向量D进行更新，使得正确分类的样本的权重升高，错误分类的样本的权重降低。D的计算方法如下：
如果某个样本被正确分类：
如果某个样本被错误分类：
然后再计算出D后，AdaBoost开始下一轮迭代，直到错误率为0或弱分类器的数目达到要求的数目。
- 优点：泛化错误率低，易编码，无参数调整。
- 缺点：对离群点敏感。
- 适用数据范围：数值型和标量型。
0x01 基于单层决策树构建弱分类器
就是一个在图中垂直分割判定最佳分割情况的算法。
上图是对测试数据的算法运行过程。（实际上不太对，少了个+1与-1位置交换的步骤，不过图片太多了，所以……(=.=)）
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
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
0x03 完整的算法
上面的是单步，然后与下面的结合就是完整的代码。
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
0x04 使用分类器
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)