决策树之系列二—C4.5原理与代码实现
本文系作者原创，转载请注明出处:https://www.cnblogs.com/further-further-further/p/9435712.html
ID3算法缺点
它一般会优先选择有较多属性值的Feature，因为属性值多的特征会有相对较大的信息增益，信息增益反映的是，在给定一个条件以后，不确定性减少的程度，
这必然是分得越细的数据集确定性更高，也就是条件熵越小，信息增益越大。为了解决这个问题，C4.5就应运而生，它采用信息增益率来作为选择分支的准则。
C4.5算法原理
信息增益率定义为：
其中，分子为信息增益（信息增益计算可参考上一节ID3的算法原理），分母为属性X的熵。
需要注意的是，增益率准则对可取值数目较少的属性有所偏好。
所以一般这样选取划分属性：选择增益率最高的特征列作为划分属性的依据。
代码实现
与ID3代码实现不同的是：只改变计算香农熵的函数calcShannonEnt，以及选择最优特征索引函数chooseBestFeatureToSplit，具体代码如下：
# -*- coding: utf-8 -*-
"""
Created on Thu Aug 2 17:09:34 2018
决策树ID3,C4.5的实现
@author: weixw
"""
from math import log
import operator
#原始数据
def createDataSet():
dataSet = [[1, 1, 'yes'],
[1, 1, 'yes'],
[1, 0, 'no'],
[0, 1, 'no'],
[0, 1, 'no']]
labels = ['no surfacing','flippers']
return dataSet, labels #多数表决器
#列中相同值数量最多为结果
def majorityCnt(classList):
classCounts = {}
for value in classList:
if(value not in classCounts.keys()):
classCounts[value] = 0
classCounts[value] +=1
sortedClassCount = sorted(classCounts.iteritems(),key = operator.itemgetter(1),reverse =True)
return sortedClassCount[0][0] #划分数据集
#dataSet:原始数据集
#axis:进行分割的指定列索引
#value:指定列中的值
def splitDataSet(dataSet,axis,value):
retDataSet= []
for featDataVal in dataSet:
if featDataVal[axis] == value:
#下面两行去除某一项指定列的值，很巧妙有没有
reducedFeatVal = featDataVal[:axis]
reducedFeatVal.extend(featDataVal[axis+1:])
retDataSet.append(reducedFeatVal)
return retDataSet #计算香农熵
#columnIndex = -1表示获取数据集每一项的最后一列的标签值
#其他表示获取特征列
def calcShannonEnt(columnIndex, dataSet):
#数据集总项数
numEntries = len(dataSet)
#标签计数对象初始化
labelCounts = {}
for featDataVal in dataSet:
#获取数据集每一项的最后一列的标签值
currentLabel = featDataVal[columnIndex]
#如果当前标签不在标签存储对象里，则初始化，然后计数
if currentLabel not in labelCounts.keys():
labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
#熵初始化
shannonEnt = 0.0
#遍历标签对象，求概率，计算熵
for key in labelCounts.keys():
prop = labelCounts[key]/float(numEntries)
shannonEnt -= prop*log(prop,2)
return shannonEnt #通过信息增益，选出最优特征列索引(ID3)
def chooseBestFeatureToSplit(dataSet):
#计算特征个数，dataSet最后一列是标签属性，不是特征量
numFeatures = len(dataSet[0])-1
#计算初始数据香农熵
baseEntropy = calcShannonEnt(-1, dataSet)
#初始化信息增益，最优划分特征列索引
bestInfoGain = 0.0
bestFeatureIndex = -1
for i in range(numFeatures):
#获取每一列数据
featList = [example[i] for example in dataSet]
#将每一列数据去重
uniqueVals = set(featList)
newEntropy = 0.0
for value in uniqueVals:
subDataSet = splitDataSet(dataSet,i,value)
#计算条件概率
prob = len(subDataSet)/float(len(dataSet))
#计算条件熵
newEntropy +=prob*calcShannonEnt(-1, subDataSet)
#计算信息增益
infoGain = baseEntropy - newEntropy
if(infoGain > bestInfoGain):
bestInfoGain = infoGain
bestFeatureIndex = i
return bestFeatureIndex #通过信息增益率，选出最优特征列索引(C4.5)
def chooseBestFeatureToSplitOfFurther(dataSet):
#计算特征个数，dataSet最后一列是标签属性，不是特征量
numFeatures = len(dataSet[0])-1
#计算初始数据香农熵H(Y)
baseEntropy = calcShannonEnt(-1, dataSet)
#初始化信息增益，最优划分特征列索引
bestInfoGainRatio = 0.0
bestFeatureIndex = -1
for i in range(numFeatures):
#获取每一特征列香农熵H(X)
featEntropy = calcShannonEnt(i, dataSet)
#获取每一列数据
featList = [example[i] for example in dataSet]
#将每一列数据去重
uniqueVals = set(featList)
newEntropy = 0.0
for value in uniqueVals:
subDataSet = splitDataSet(dataSet,i,value)
#计算条件概率
prob = len(subDataSet)/float(len(dataSet))
#计算条件熵
newEntropy +=prob*calcShannonEnt(-1, subDataSet)
#计算信息增益
infoGain = baseEntropy - newEntropy
#计算信息增益率
infoGainRatio = infoGain/float(featEntropy)
if(infoGainRatio > bestInfoGainRatio):
bestInfoGainRatio = infoGainRatio
bestFeatureIndex = i
return bestFeatureIndex #决策树创建
def createTree(dataSet,labels):
#获取标签属性，dataSet最后一列，区别于labels标签名称
classList = [example[-1] for example in dataSet]
#树极端终止条件判断
#标签属性值全部相同，返回标签属性第一项值
if classList.count(classList[0]) == len(classList):
return classList[0]
#没有特征，只有标签列（1列）
if len(dataSet[0]) == 1:
#返回实例数最大的类
return majorityCnt(classList)
# #获取最优特征列索引ID3
# bestFeatureIndex = chooseBestFeatureToSplit(dataSet)
#获取最优特征列索引C4.5
bestFeatureIndex = chooseBestFeatureToSplitOfFurther(dataSet)
#获取最优索引对应的标签名称
bestFeatureLabel = labels[bestFeatureIndex]
#创建根节点
myTree = {bestFeatureLabel:{}}
#去除最优索引对应的标签名，使labels标签能正确遍历
del(labels[bestFeatureIndex])
#获取最优列
bestFeature = [example[bestFeatureIndex] for example in dataSet]
uniquesVals = set(bestFeature)
for value in uniquesVals:
#子标签名称集合
subLabels = labels[:]
#递归
myTree[bestFeatureLabel][value] = createTree(splitDataSet(dataSet,bestFeatureIndex,value),subLabels)
return myTree #获取分类结果
#inputTree:决策树字典
#featLabels:标签列表
#testVec:测试向量 例如：简单实例下某一路径 [1,1] => yes（树干值组合，从根结点到叶子节点）
def classify(inputTree,featLabels,testVec):
#获取根结点名称，将dict转化为list
firstSide = list(inputTree.keys())
#根结点名称String类型
firstStr = firstSide[0]
#获取根结点对应的子节点
secondDict = inputTree[firstStr]
#获取根结点名称在标签列表中对应的索引
featIndex = featLabels.index(firstStr)
#由索引获取向量表中的对应值
key = testVec[featIndex]
#获取树干向量后的对象
valueOfFeat = secondDict[key]
#判断是子结点还是叶子节点：子结点就回调分类函数，叶子结点就是分类结果
#if type(valueOfFeat).__name__=='dict': 等价 if isinstance(valueOfFeat, dict):
if isinstance(valueOfFeat, dict):
classLabel = classify(valueOfFeat,featLabels,testVec)
else:
classLabel = valueOfFeat
return classLabel #将决策树分类器存储在磁盘中，filename一般保存为txt格式
def storeTree(inputTree,filename):
import pickle
fw = open(filename,'wb+')
pickle.dump(inputTree,fw)
fw.close()
#将瓷盘中的对象加载出来，这里的filename就是上面函数中的txt文件
def grabTree(filename):
import pickle
fr = open(filename,'rb')
return pickle.load(fr)
决策树算法
'''
Created on Oct 14, 2010 @author: Peter Harrington
'''
import matplotlib.pyplot as plt decisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
arrow_args = dict(arrowstyle="<-") #获取树的叶子节点
def getNumLeafs(myTree):
numLeafs = 0
#dict转化为list
firstSides = list(myTree.keys())
firstStr = firstSides[0]
secondDict = myTree[firstStr]
for key in secondDict.keys():
#判断是否是叶子节点（通过类型判断，子类不存在，则类型为str；子类存在，则为dict）
if type(secondDict[key]).__name__=='dict':#test to see if the nodes are dictonaires, if not they are leaf nodes
numLeafs += getNumLeafs(secondDict[key])
else: numLeafs +=1
return numLeafs #获取树的层数
def getTreeDepth(myTree):
maxDepth = 0
#dict转化为list
firstSides = list(myTree.keys())
firstStr = firstSides[0]
secondDict = myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]).__name__=='dict':#test to see if the nodes are dictonaires, if not they are leaf nodes
thisDepth = 1 + getTreeDepth(secondDict[key])
else: thisDepth = 1
if thisDepth > maxDepth: maxDepth = thisDepth
return maxDepth def plotNode(nodeTxt, centerPt, parentPt, nodeType):
createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction',
xytext=centerPt, textcoords='axes fraction',
va="center", ha="center", bbox=nodeType, arrowprops=arrow_args ) def plotMidText(cntrPt, parentPt, txtString):
xMid = (parentPt[0]-cntrPt[0])/2.0 + cntrPt[0]
yMid = (parentPt[1]-cntrPt[1])/2.0 + cntrPt[1]
createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30) def plotTree(myTree, parentPt, nodeTxt):#if the first key tells you what feat was split on
numLeafs = getNumLeafs(myTree) #this determines the x width of this tree
depth = getTreeDepth(myTree)
firstSides = list(myTree.keys())
firstStr = firstSides[0] #the text label for this node should be this
cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)
plotMidText(cntrPt, parentPt, nodeTxt)
plotNode(firstStr, cntrPt, parentPt, decisionNode)
secondDict = myTree[firstStr]
plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD
for key in secondDict.keys():
if type(secondDict[key]).__name__=='dict':#test to see if the nodes are dictonaires, if not they are leaf nodes
plotTree(secondDict[key],cntrPt,str(key)) #recursion
else: #it's a leaf node print the leaf node
plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW
plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode)
plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key))
plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalD
#if you do get a dictonary you know it's a tree, and the first element will be another dict
#绘制决策树
def createPlot(inTree):
fig = plt.figure(1, facecolor='white')
fig.clf()
axprops = dict(xticks=[], yticks=[])
createPlot.ax1 = plt.subplot(111, frameon=False, **axprops) #no ticks
#createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses
plotTree.totalW = float(getNumLeafs(inTree))
plotTree.totalD = float(getTreeDepth(inTree))
plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0;
plotTree(inTree, (0.5,1.0), '')
plt.show() #绘制树的根节点和叶子节点（根节点形状：长方形，叶子节点：椭圆形）
#def createPlot():
# fig = plt.figure(1, facecolor='white')
# fig.clf()
# createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses
# plotNode('a decision node', (0.5, 0.1), (0.1, 0.5), decisionNode)
# plotNode('a leaf node', (0.8, 0.1), (0.3, 0.8), leafNode)
# plt.show() def retrieveTree(i):
listOfTrees =[{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}},
{'no surfacing': {0: 'no', 1: {'flippers': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}}
]
return listOfTrees[i] #thisTree = retrieveTree(0)
#createPlot(thisTree)
#createPlot()
#myTree = retrieveTree(0)
#numLeafs =getNumLeafs(myTree)
#treeDepth =getTreeDepth(myTree)
#print(u"叶子节点数目：%d"% numLeafs)
#print(u"树深度：%d"%treeDepth)
绘制决策树
# -*- coding: utf-8 -*-
"""
Created on Fri Aug 3 19:52:10 2018 @author: weixw
"""
import myTrees as mt
import treePlotter as tp
#测试
dataSet, labels = mt.createDataSet()
#copy函数：新开辟一块内存，然后将list的所有值复制到新开辟的内存中
labels1 = labels.copy()
#createTree函数中将labels1的值改变了，所以在分类测试时不能用labels1
myTree = mt.createTree(dataSet,labels1)
#保存树到本地
mt.storeTree(myTree,'myTree.txt')
#在本地磁盘获取树
myTree = mt.grabTree('myTree.txt')
print(u"采用C4.5算法的决策树结果")
print (u"决策树结构：%s"%myTree)
#绘制决策树
print(u"绘制决策树：")
tp.createPlot(myTree)
numLeafs =tp.getNumLeafs(myTree)
treeDepth =tp.getTreeDepth(myTree)
print(u"叶子节点数目：%d"% numLeafs)
print(u"树深度：%d"%treeDepth)
#测试分类 简单样本数据3列
labelResult =mt.classify(myTree,labels,[1,1])
print(u"[1,1] 测试结果为：%s"%labelResult)
labelResult =mt.classify(myTree,labels,[1,0])
print(u"[1,0] 测试结果为：%s"%labelResult)
测试
运行结果
不要让懒惰占据你的大脑，不要让妥协拖垮你的人生。青春就是一张票，能不能赶上时代的快车，你的步伐掌握在你的脚下。