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DecisionTree_getInfoGain.py
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#!/usr/bin/python
# coding: utf8
from math import log
def calcShannonEnt(dataSet):
"""calcShannonEnt(calculate Shannon entropy 计算label分类标签的香农熵)
Args:
dataSet 数据集
Returns:
返回香农熵的计算值
Raises:
"""
# 求list的长度，表示计算参与训练的数据量
numEntries = len(dataSet)
# print(type(dataSet), 'numEntries: ', numEntries)
# 计算分类标签label出现的次数
labelCounts = {}
# the the number of unique elements and their occurance
for featVec in dataSet:
currentLabel = featVec[-1]
if currentLabel not in labelCounts.keys():
labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
# print('-----', featVec, labelCounts)
# 对于label标签的占比，求出label标签的香农熵
shannonEnt = 0.0
for key in labelCounts:
prob = float(labelCounts[key])/numEntries
# log base 2
shannonEnt -= prob * log(prob, 2)
# print('---', prob, prob * log(prob, 2), shannonEnt)
return shannonEnt
def splitDataSet(dataSet, axis, value):
"""splitDataSet(通过遍历dataSet数据集，求出axis对应的colnum列的值为value的行)
Args:
dataSet 数据集
axis 表示每一行的axis列
value 表示axis列对应的value值
Returns:
axis列为value的数据集【该数据集需要排除axis列】
Raises:
"""
retDataSet = []
for featVec in dataSet:
# axis列为value的数据集【该数据集需要排除axis列】
if featVec[axis] == value:
# chop out axis used for splitting
reducedFeatVec = featVec[:axis]
'''
请百度查询一下： extend和append的区别
'''
reducedFeatVec.extend(featVec[axis+1:])
# 收集结果值 axis列为value的行【该行需要排除axis列】
retDataSet.append(reducedFeatVec)
return retDataSet
def getFeatureShannonEnt(dataSet, labels):
"""chooseBestFeatureToSplit(选择最好的特征)
Args:
dataSet 数据集
Returns:
bestFeature 最优的特征列
Raises:
"""
# 求第一行有多少列的 Feature
numFeatures = len(dataSet[0]) - 1
# label的信息熵
baseEntropy = calcShannonEnt(dataSet)
# 最优的信息增益值, 和最优的Featurn编号
bestInfoGain, bestFeature, endEntropy = 0.0, -1, 0.0
# iterate over all the features
for i in range(numFeatures):
# create a list of all the examples of this feature
# 获取每一个feature的list集合
featList = [example[i] for example in dataSet]
# get a set of unique values
# 获取剔重后的集合
uniqueVals = set(featList)
# 创建一个临时的信息熵
newEntropy = 0.0
# 遍历某一列的value集合，计算该列的信息熵
for value in uniqueVals:
subDataSet = splitDataSet(dataSet, i, value)
prob = len(subDataSet)/float(len(dataSet))
newEntropy += prob * calcShannonEnt(subDataSet)
# gain[信息增益] 值越大，意味着该分类提供的信息量越大，该特征对分类的不确定程度越小
# gain[信息增益]=0, 表示与类别相同，无需其他的分类
# gain[信息增益]=baseEntropy, 表示分类和没分类没有区别
infoGain = baseEntropy - newEntropy
# print(infoGain)
if (infoGain > bestInfoGain):
endEntropy = newEntropy
bestInfoGain = infoGain
bestFeature = i
else:
if numFeatures < 0:
labels[bestFeature] = 'null'
return labels[bestFeature], baseEntropy, endEntropy, bestInfoGain
if __name__ == '__main__':
labels = ['no surfacing', 'flippers']
dataSet1 = [['yes'], ['yes'], ['no'], ['no'], ['no']]
dataSet2 = [['a', 1, 'yes'], ['a', 2, 'yes'], ['b', 3, 'no'], ['c', 4, 'no'], ['c', 5, 'no']]
dataSet3 = [[1, 'yes'], [1, 'yes'], [1, 'no'], [3, 'no'], [3, 'no']]
infoGain1 = getFeatureShannonEnt(dataSet1, labels)
infoGain2 = getFeatureShannonEnt(dataSet2, labels)
infoGain3 = getFeatureShannonEnt(dataSet3, labels)
print('信息增益: \n\t%s, \n\t%s, \n\t%s' % (infoGain1, infoGain2, infoGain3))