决策树python实现小样例

  1 计算给定数据集的香农熵
  2 from math import log
  3 import operator
  4 import treePlotter
  5 
  6 
  7 def calcShannonEnt(dataSet):
  8     #计算数据集的实例总数
  9     numEntries = len(dataSet)
 10     labelCounts = {}
 11     #创建一个字典，他的键值是最后一列的数值，如果当前键值不存在，则扩展字典并将当前键值加入字典。
 12     # 每个键值都记录了当前类别出现的次数。最后，使用所有类标签的发生频率计算类别出现的概率。我们
 13     # 将用这个概率计算香农熵，统计所有类标签发生的次数。
 14     for featVec in dataSet:  # the the number of unique elements and their occurance
 15         #为所有可能分类创建字典
 16         currentLabel = featVec[-1]
 17         if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
 18         labelCounts[currentLabel] += 1
 19     shannonEnt = 0.0
 20     for key in labelCounts:
 21         prob = float(labelCounts[key]) / numEntries
 22         #以2为底求对数，香农定理
 23         shannonEnt -= prob * log(prob, 2)  # log base 2
 24     return shannonEnt
 25 def createDataSet():
 26     dataSet = [[1, 1, ‘yes‘],
 27                [1, 1, ‘yes‘],
 28                [1, 0, ‘no‘],
 29                [0, 1, ‘no‘],
 30                [0, 1, ‘no‘]]
 31     labels = [‘no surfacing‘,‘flippers‘]
 32     #change to discrete values
 33     return dataSet, labels
 34 
 35 #按照给定特征划分数据集
 36 #三个输入参数：待划分的数据集、划分数据集的特征、特征的返回值。
 37 #注：python不考虑内存分配的问题
 38 def splitDataSet(dataSet, axis, value):
 39     #创建新的list对象
 40     retDataSet = []
 41     for featVec in dataSet:
 42         if featVec[axis] == value:
 43             #抽取
 44             reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
 45             reducedFeatVec.extend(featVec[axis+1:])
 46             retDataSet.append(reducedFeatVec)
 47     return retDataSet
 48 
 49 #选择最好的数据集划分方式
 50 def chooseBestFeatureToSplit(dataSet):
 51     numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
 52     # 计算了整个数据集的香农熵
 53     baseEntropy = calcShannonEnt(dataSet)
 54     bestInfoGain = 0.0; bestFeature = -1
 55     for i in range(numFeatures):        #iterate over all the features
 56         #创建唯一的分类标签列表
 57         featList = [example[i] for example in dataSet]#create a list of all the examples of this feature
 58         uniqueVals = set(featList)       #get a set of unique values
 59         newEntropy = 0.0
 60         for value in uniqueVals:
 61             #计算每种划分方式的信息熵
 62             subDataSet = splitDataSet(dataSet, i, value)
 63             prob = len(subDataSet)/float(len(dataSet))
 64             newEntropy += prob * calcShannonEnt(subDataSet)
 65         infoGain = baseEntropy - newEntropy     #calculate the info gain; ie reduction in entropy
 66         if (infoGain > bestInfoGain):
 67             #计算最好的增益compare this to the best gain so far
 68             bestInfoGain = infoGain         #if better than current best, set to best
 69             bestFeature = i
 70     return bestFeature
 71 
 72 #这与投票代码非常类似，该函数使用分类名称的列表，然后创建键值为classList中唯一值的数据字典，字典对象
 73 # 存储了classList中每个类标签出现的频率，最后利用operator操作键值排序字典，并返回出现次数最多的分类名称。
 74 def majorityCnt(classList):
 75     classCount={}
 76     for vote in classList:
 77         if vote not in classCount.keys(): classCount[vote] = 0
 78         classCount[vote] += 1
 79     sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
 80     return sortedClassCount[0][0]
 81 
 82 #创建树的函数代码
 83 ‘‘‘
 84 两个输入参数：数据集和标签列表 
 85 ‘‘‘
 86 def createTree(dataSet,labels):
 87     classList = [example[-1] for example in dataSet]
 88     #类别完全相同则停止继续划分
 89     if classList.count(classList[0]) == len(classList):
 90         return classList[0]#stop splitting when all of the classes are equal
 91     #遍历完所有特征时，返回出现次数最多的
 92     if len(dataSet[0]) == 1: #stop splitting when there are no more features in dataSet
 93         return majorityCnt(classList)
 94     bestFeat = chooseBestFeatureToSplit(dataSet)
 95     bestFeatLabel = labels[bestFeat]
 96     myTree = {bestFeatLabel:{}}
 97     del(labels[bestFeat])
 98     #得到列表包含的所有属性值
 99     featValues = [example[bestFeat] for example in dataSet]
100     uniqueVals = set(featValues)
101     for value in uniqueVals:
102         subLabels = labels[:]       #copy all of labels, so trees don‘t mess up existing labels
103         myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
104     return myTree
105 
106 #使用决策树分类函数
107 def classify(inputTree,featLabels,testVec):
108     firstStr = list(inputTree.keys())[0]
109     secondDict = inputTree[firstStr]
110     featIndex = featLabels.index(firstStr)
111     key = testVec[featIndex]
112     valueOfFeat = secondDict[key]
113     if isinstance(valueOfFeat, dict):
114         classLabel = classify(valueOfFeat, featLabels, testVec)
115     else: classLabel = valueOfFeat
116     return classLabel
117 
118 
119 myDat,label=createDataSet()
120 
121 print(‘数据集‘+ str(myDat))
122 print(‘labels‘+ str(label))
123 # A=calcShannonEnt(myDat)
124 # print(‘香农熵‘+str(A))
125 # B=splitDataSet(myDat,0,1)
126 # print(‘按给定特征划分数据集‘+str(B))
127 # C=chooseBestFeatureToSplit(myDat)
128 # print(‘最好的增益‘+str(C))
129 ‘‘‘
130 # 结果告诉我们，第0个特征是最好的用于划分数据集的特征。
131 # 如果我们按照第一个特征属性划分数据，也就是说第一个特征是1的放在一组，
132 # 第一个特征是0的放在另一组
133 # ‘‘‘
134 mytree=treePlotter.retrieveTree(0)
135 D=classify(mytree,label,[1,0])
136 print(D)