《机器学习实战》第3章学习小结

第三章，决策树。因为初学机器学习和Python，想先过一遍书，所以并没有看得精细（比如如何用MatPlotlib画出树结构就暂时跳过了）。

如何构造树：首先寻找用来划分数据集的特征，书中通过求解信息增益的方法找到当前最好的特征，并用它划分数据集，创建分支，函数采用递归的思想。

1. 信息增益

def calcShannonEnt(dataSet):
numEntries = len(dataSet)
labelCounts = {}    #保存每类键值的个数
for featVec in dataSet:    #the the number of unique elements and their occurance
currentLabel = featVec[-1]   #获得样本的键值
if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0   #创建
labelCounts[currentLabel] += 1
shannonEnt = 0.0
for key in labelCounts:
prob = float(labelCounts[key])/numEntries
shannonEnt -= prob * log(prob,2)   #log base 2
return shannonEnt

2. 划分数据集

def splitDataSet(dataSet, axis, value):     #划分数据集
retDataSet = []
for featVec in dataSet:
if featVec[axis] == value:    #指定特征的值与给定的value一致，保留其余特征值和键值，并添加到retDataSet
reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
reducedFeatVec.extend(featVec[axis+1:])
retDataSet.append(reducedFeatVec)
return retDataSet

def chooseBestFeatureToSplit(dataSet):    #选择最好的特征划分数据集
numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
baseEntropy = calcShannonEnt(dataSet)   #计算初始的熵
bestInfoGain = 0.0; bestFeature = -1
for i in range(numFeatures):         #iterate over all the features 遍历所有特征
featList = [example[i] for example in dataSet]#create a list of all the examples of this feature
uniqueVals = set(featList)       #get a set of unique values
newEntropy = 0.0
for value in uniqueVals:
subDataSet = splitDataSet(dataSet, i, value)   #用第i个特征划分数组
prob = len(subDataSet)/float(len(dataSet))
newEntropy += prob * calcShannonEnt(subDataSet)    #计算熵
infoGain = baseEntropy - newEntropy     #calculate the info gain; ie reduction in entropy
if (infoGain > bestInfoGain):       #compare this to the best gain so far
bestInfoGain = infoGain         #if better than current best, set to best
bestFeature = i
return bestFeature                      #returns an integer

3. 构造树

def createTree(dataSet,labels):
classList = [example[-1] for example in dataSet]     #获得所有键值
if classList.count(classList[0]) == len(classList):
return classList[0]      #stop splitting when all of the classes are equal
if len(dataSet[0]) == 1:     #stop splitting when there are no more features in dataSet，只剩键值
return majorityCnt(classList)
bestFeat = chooseBestFeatureToSplit(dataSet)   #选择最好的特征并划分数据集
bestFeatLabel = labels[bestFeat]
myTree = {bestFeatLabel:{}}   #创建新的分支
del(labels[bestFeat])   #将当前最好特征从labels数组中剔除
featValues = [example[bestFeat] for example in dataSet]  #当前最好特征在数据集中所有出现的情况
uniqueVals = set(featValues)   #获得当前最好特征在数据集中出现的所有类别
for value in uniqueVals:
subLabels = labels[:]       #copy all of labels, so trees don't mess up existing labels
myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels) #递归
return myTree