python 使用Id3算法实现决策树

依然是学习《统计学习方法》一书所做的简单实验，写代码的过程参考了大量其他的博客，本人在此深表感谢。代码实现的依然是书上的例子：

import numpy as np
import math
import operator

def CreateDataSet():
dataset = [ [1, 0,0,0,'no'],
[1, 0,0,1,'no'],
[1, 1,0,1,'yes'],
[1, 1,1,0,'yes'],
[1, 0,0,0,'no'],

[2, 0,0,0,'no'],
[2, 0,0,1,'no'],
[2, 1,1,1,'yes'],
[2, 0,1,2,'yes'],
[2, 0,1,2,'yes'],

[3, 0,1,2,'yes'],
[3, 0,1,1,'yes'],
[3, 1,0,1,'yes'],
[3, 1,0,2,'yes'],
[3, 0,0,0,'no'] ]
labels = ['age', 'job','building','credit']
return dataset, labels

#计算香农熵
def calcShannonEnt(dataSet):
Ent = 0.0
numEntries = len(dataSet)
labelCounts = {}
for feaVec in dataSet:
currentLabel = feaVec[-1]
if currentLabel not in labelCounts:
labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
for key in labelCounts:
prob = float(labelCounts[key])/numEntries
Ent -= prob * math.log(prob, 2)
return Ent

def majorityCnt(classList):
classCount = {}
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 splitDataSet(dataSet,axis,value):
retDataSet=[]
for featVec in dataSet:
if featVec[axis]==value :
reduceFeatVec=featVec[:axis]
reduceFeatVec.extend(featVec[axis+1:])
retDataSet.append(reduceFeatVec)
return retDataSet #返回不含划分特征的子集

def choiceBestFea(dataSet):
baseEntropy = calcShannonEnt(dataSet)
numberFeatures = len(dataSet[0]) - 1
bestFeatureId = -1;
bestInfoGain = 0.0
for i in range(numberFeatures):
featList = [example[i] for example in dataSet]
uniqueVals = set(featList)
newEntropy = 0.0
for value in uniqueVals:
subFea = splitDataSet(dataSet,i,value)
prob = len(subFea) / float(len(dataSet))
newEntropy += prob * calcShannonEnt(subFea)
infoGain = baseEntropy - newEntropy
if (infoGain > bestInfoGain):
bestInfoGain = infoGain
bestFeatureId = i
return bestFeatureId

def createDTree(dataSet,labels):
#第一步，判断数据是不是都是同一类的，如果是同一类的，则只有一个节点即根节点
classList = [example[-1] for example in dataSet]
if classList.count(classList[0]) == len(classList):
return classList[0]

# 第二步，判断特征的个数，特征集为空，则只有一个节点即根节点,此时，需要通过投票的方式决定根节点的属性
if len(dataSet[0]) == 1:
return majorityCnt(classList)

# 第三步，通过计算信息增益，选择出最优的特征，也就是信息增益最大的特征
bestFeaId = choiceBestFea(dataSet)
#第四步，选择出信息增益最大的特征，并使用该特征切分数据
bestFeatLabel = labels[bestFeaId]
del (labels[bestFeaId])
featValues = [example[bestFeaId] for example in dataSet]
uniqueVals = set(featValues)

myTree = {bestFeatLabel: {}}
#第五步，递归调用createDTree
for value in uniqueVals:
subLabels = labels[:]
myTree[bestFeatLabel][value] = createDTree(splitDataSet(dataSet, bestFeaId, value), subLabels)
return myTree

#输入两个变量（决策树，测试的数据）
def classify(inputTree,testVec):
print(inputTree)
firstStr=list(inputTree.keys())[0] #获取树的第一个特征属性
secondDict=inputTree[firstStr] #树的分支，子集合Dict
i=0
classLabel = ""
for key in secondDict.keys():
if testVec[i]==key:
if type(secondDict[key]).__name__=='dict':
classLabel=classify(secondDict[key],testVec)
else:
#表明已经是叶子节点了
classLabel=secondDict[key]
break
i += 1

return classLabel

def storeTree(inputTree,filename):
import pickle
fw=open(filename,'wb') #pickle默认方式是二进制，需要制定'wb'
pickle.dump(inputTree,fw)
fw.close()

def reStoreTree(filename):
import pickle
fr=open(filename,'rb')#需要制定'rb'，以byte形式读取
return pickle.load(fr)

def test():
dataSet,labels = CreateDataSet1()
tree = createDTree(dataSet,labels);
print(tree)

return None

def train():
myDat, labels = CreateDataSet()
tree = createDTree(myDat, labels)
storeTree(tree,"dtree.txt")
return None

def test():
tree = reStoreTree("dtree.txt")
result = classify(tree,[0,0])
return result

result = test()
print(result)
#train()

train（）方法用来生成决策树，生成的决策树会被保存在dtree.txt文件中

test（）方法用来测试决策树。

从生成的决策树来看，总共只有两个节点。第一个节点是有没有房，第二个节点是有没有工作。所以，测试的时候只需输入【0，0】或者【1，0】这样的长度为2的向量即可。