决策树的ID3算法实现（Python版）

from math import log

def calcShannonEnt(dataSet):                                //计算你传给我的数据集的熵      输入参数: 数据集合
numEntries=len(dataSet)
labelCounts={}
for featVec in dataSet:
currentLabel=featVec[-1]
if currentLabel not in labelCounts.keys():
labelCounts[currentLabel]=0
labelCounts[currentLabel]+=1
shannonEnt=0.0
for key in labelCounts:
prob=float(labelCounts[key])/numEntries
shannonEnt-=prob*log(prob,2)
return shannonEnt

def createDataSet():                                                  //创建数据集
dataSet=[[1,1,'yes'],[1,1,'yes'],[1,0,'no'],[0,1,'no'],[0,1,'no']]
labels=['no surfacing','flippers']
return dataSet,labels

def createLabels():                                                  //创建特征属性集合
labels=['no surfacing','flippers']
return labels

def splitDataSet(dataSet,axis,value):                   //将原特征集按照第axis属性 划分成子属性集  输入参数: 数据集合 特征属性下标axis  第axis属性特征值
retDataSet=[]
for featVec in dataSet:
if featVec[axis]==value:
reducedFeatVec=featVec[:axis]
reducedFeatVec.extend(featVec[axis+1:])
retDataSet.append(reducedFeatVec)
return retDataSet

def chooseBestFeatureToSplit(dataSet):            //选择最后的特征划分子属性集,该函数需要调用 splitDataSet函数   输入参数: 数据集合
numFeatures=len(dataSet[0])-1
baseEntropy=calcShannonEnt(dataSet)
bestInfoGain=0.0;bestFeature=-1
for i in range(numFeatures):
featList=[example[i] for example in dataSet]
uniqueVals=set(featList)
newEntropy=0.0
for value in uniqueVals:
subDataSet=splitDataSet(dataSet,i,value)
prob=len(subDataSet)/float(len(dataSet))
newEntropy+=prob*calcShannonEnt(subDataSet)  
infoGain=baseEntropy-newEntropy                
if infoGain>bestInfoGain:                                                                          
bestInfoGain=infoGain                     

bestFeature=i
  

return bestFeature

分析公式：



def majorityCnt(classList):     //对于决策树构造到最后了，子数据集还包含好多类型，我们就用这个多数表决器函数，认为子数据集中类型较多的为最终的类型
classCount={}                                 输入参数: 子数据集的类型集合列表
for vote in classList:
if vote not in classCount.keys():
classCount[vote]=0
classCOunt[vote]+=1
sortedClassCount=sorted(classCount.iteritems(),key=operator.itemgetter(1),reverse=True)
return sortedClassCount[0][0]

def createTree(dataSet,labels):            //该函数构造决策树     输入参数: 数据集合 特征属性集合
classList=[example[-1] for example in dataSet]
if classList.count(classList[0])==len(classList):
return classList[0]
if len(dataSet[0])==1:
return majorityCnt(classList)
bestFeat=chooseBestFeatureToSplit(dataSet)
bestFeatLabel=labels[bestFeat]
myTree={bestFeatLabel:{}}
del(labels[bestFeat])
featValues=[example[bestFeat] for example in dataSet]
uniqueVals=set(featValues)
for value in uniqueVals:
subLabels=labels[:]
myTree[bestFeatLabel][value]=createTree(splitDataSet(dataSet,bestFeat,value),subLabels)
return myTree

def getNumLeafs(myTree):              //获得构造好的决策树叶子节点个数   输入参数:决策树
numLeafs=0
firstStr=myTree.keys()[0]
secondDict=myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]).__name__=='dict':
numLeafs+=getNumLeafs(secondDict[key])
else: numLeafs+=1
return numLeafs

def getTreeDepth(myTree):               //获得构造好的决策树深度            输入参数:决策树
maxDepth=0
firstStr=myTree.keys()[0]
secondDict=myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]).__name__=='dict':
thisDepth=1+getNumLeafs(secondDict[key])
else: thisDepth=1
if thisDepth>maxDepth: maxDepth=thisDepth
return maxDepth

def classify(inputTree,featLabels,testVec):     //使用决策树，对我们样本按照构造的对决策树进行分类 返回类型 输入参数：决策树 特征属性集合 测试样本
firstStr=inputTree.keys()[0]
secondDict=inputTree[firstStr]
featIndex=featLabels.index(firstStr)
for key in secondDict.keys():
if testVec[featIndex]==key:
if type(secondDict[key]).__name__=='dict':
classLabel=classify(secondDict[key],featLabels,testVec)
else: classLabel=secondDict[key]
return classLabel

结果：


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