from math import log
import operator
"""
使用ID3算法划分数据集，ID3算法可以用于划分标称型数据集
决策树分类器就像带有终止块的流程图，终止块表示分类结果。
开始处理数据集时，首先需要测量集合中数据的不一致，
然后寻找最优方案划分数据集，直到数据集中的所有数据属于同一分类
"""
def createDataSet():
""" 不浮出水面是否可以生存 是否有脚蹼 属于鱼类 """
dataSet = [[1, 1, 'yes'],
[1, 1, 'yes'],
[1, 0, 'no'],
[0, 1, 'no'],
[0, 1, 'no']]
labels = ['no surfacing', 'flippers']
#change to discrete values
return dataSet, labels
def calcShannonEnt(dataSet):
"""计算信息熵（香农熵）
H(x) = -∑P(xi)log(2,P(xi)) (i=1,2,..n)
H 表示信息熵
P 表示某种语言文字的字符出现的概率
LOG2是以二为底的对数，用的是二进制，信息熵的单位是比特（BIT，即二进制的0和1）
熵也可以作为一个系统的混乱程度的标准
另一种：基尼不纯度 也可以作为衡量系统混乱程度的标准
基尼 = 1 − ∑P(xi)^2 (i=1,2,..n)
主要的区别就是基尼中把logP(xi)换成了P(xi)，相比于熵，基尼反而有计算量小的优势
"""
numEntries = len(dataSet) # 计算数据集中实例的总数
labelCounts = {} # 类别次数字典
for featVec in dataSet: # the the number of unique elements and their occurance
currentLabel = featVec[-1]
if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
shannonEnt = 0.0 # 信息熵
for key in labelCounts:
prob = float(labelCounts[key])/numEntries # 类别出现的频率
shannonEnt -= prob * log(prob, 2) # log base 2
return shannonEnt
def splitDataSet(dataSet, axis, value):
"""
按照给定特征划分数据集 第axis个特征是value的数据集
:param dataSet: 待划分的数据集
:param axis: 划分数据集的特征索引
:param value: 需要返回的特征的值
:return: 符合的数据集
"""
retDataSet = []
for featVec in dataSet:
if featVec[axis] == value:
reducedFeatVec = featVec[:axis] #chop out axis used for splitting
reducedFeatVec.extend(featVec[axis+1:]) # [,,,]
retDataSet.append(reducedFeatVec) # [,,[]]
return retDataSet
def chooseBestFeatureToSplit(dataSet):
"""
选择最好的数据集划分方式
选择熵最小的，也就是数据最纯的
:param dataSet:
:return: 最好特征划分的索引值
"""
numFeatures = len(dataSet[0]) - 1 # 特征数，最后一个为标签 #the last column is used for the labels
baseEntropy = calcShannonEnt(dataSet)
bestInfoGain = 0.0; bestFeature = -1
for i in range(numFeatures): #iterate over all the features
featList = [example[i] for example in dataSet]#create a list of all the examples of this feature
uniqueVals = set(featList) # 当前特征中所有的唯一属性值集合 #get a set of unique values
newEntropy = 0.0
for value in uniqueVals: # 遍历当前特征中所有的唯一属性值，对每个特征划分一次数据集
subDataSet = splitDataSet(dataSet, i, value)
prob = len(subDataSet)/float(len(dataSet))
newEntropy += prob * calcShannonEnt(subDataSet)
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
def majorityCnt(classList):
"""出现次数最多的分类名称"""
classCount={}
for vote in classList:
if vote not in classCount.keys(): classCount[vote] = 0
classCount[vote] += 1
sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]
def createTree(dataSet, labels):
"""
构建决策数
:param dataSet: 数据集
:param labels: 标签列表
:return: 树
"""
print(dataSet)
classList = [example[-1] for example in dataSet] # 包含数据集的所有类标签
if classList.count(classList[0]) == len(classList): # 所有类标签完全相同，直接返回该标签
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
return majorityCnt(classList)
bestFeat = chooseBestFeatureToSplit(dataSet) # 最好特征划分的索引值
bestFeatLabel = labels[bestFeat] # 最好的特征划分标签
myTree = {bestFeatLabel:{}}
del(labels[bestFeat]) # 删除已经使用的标签
featValues = [example[bestFeat] for example in dataSet]
uniqueVals = set(featValues)
for value in uniqueVals:
subLabels = labels[:] # 拷贝标签 #copy all of labels, so trees don't mess up existing labels
myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels)
return myTree
def classify(inputTree, featLabels, testVec):
"""
决策树分类
:param inputTree: 决策树
:param featLabels: 标签
:param testVec:
:return:
"""
firstStr = list(inputTree)[0] # 相当于list(inputTree.keys())[0]
secondDict = inputTree[firstStr]
featIndex = featLabels.index(firstStr)
key = testVec[featIndex]
valueOfFeat = secondDict[key]
if isinstance(valueOfFeat, dict):
classLabel = classify(valueOfFeat, featLabels, testVec)
else: classLabel = valueOfFeat
return classLabel
"""
存储决策树
"""
def storeTree(inputTree, filename):
import pickle
fw = open(filename, 'wb')
pickle.dump(inputTree, fw)
fw.close()
def grabTree(filename):
import pickle
fr = open(filename, 'rb')
return pickle.load(fr)
if __name__ == '__main__':
# 熵越高，则混合的数据也越多
dataSet, labels = createDataSet()
# dataSet[0][-1] = 'maybe'
# print(calcShannonEnt(dataSet))
# print(splitDataSet(dataSet,1,0))
# print(splitDataSet(dataSet,0,0))
# print(chooseBestFeatureToSplit(dataSet)) # 第0个特征是最好的用于划分数据集的特征
""" 不浮出水面是否可以生存 是否有脚蹼 属于鱼类
dataSet = [[1, 1, 'yes'],
[1, 1, 'yes'],
[1, 0, 'no'],
[0, 1, 'no'],
[0, 1, 'no']]
按照第一个特征属性划分数据
特征是1的：两个鱼类，一个不是鱼类
特征是0的：都是鱼类
按照第二个特征属性划分数据
特征是1的：两个鱼类，两个不是鱼类
特征是0的：都不是鱼类
比较得出第一种分组的输出结果较好
"""
# print(createTree(dataSet, labels)) # {'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}