Python机器学习（十九）决策树之系列二—C4.5原理与代码实现
作者：互联网
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：
1 # -*- coding: utf-8 -*-
2 """
3 Created on Thu Aug 2 17:09:34 2018
4 决策树ID3,C4.5的实现
5 @author: weixw
6 """
7 from math import log
8 import operator
9 #原始数据
10 def createDataSet():
11 dataSet = [[1, 1, 'yes'],
12 [1, 1, 'yes'],
13 [1, 0, 'no'],
14 [0, 1, 'no'],
15 [0, 1, 'no']]
16 labels = ['no surfacing','flippers']
17 return dataSet, labels
18
19 #多数表决器
20 #列中相同值数量最多为结果
21 def majorityCnt(classList):
22 classCounts = {}
23 for value in classList:
24 if(value not in classCounts.keys()):
25 classCounts[value] = 0
26 classCounts[value] +=1
27 sortedClassCount = sorted(classCounts.iteritems(),key = operator.itemgetter(1),reverse =True)
28 return sortedClassCount[0][0]
29
30
31 #划分数据集
32 #dataSet:原始数据集
33 #axis:进行分割的指定列索引
34 #value:指定列中的值
35 def splitDataSet(dataSet,axis,value):
36 retDataSet= []
37 for featDataVal in dataSet:
38 if featDataVal[axis] == value:
39 #下面两行去除某一项指定列的值，很巧妙有没有
40 reducedFeatVal = featDataVal[:axis]
41 reducedFeatVal.extend(featDataVal[axis+1:])
42 retDataSet.append(reducedFeatVal)
43 return retDataSet
44
45 #计算香农熵
46 #columnIndex = -1表示获取数据集每一项的最后一列的标签值
47 #其他表示获取特征列
48 def calcShannonEnt(columnIndex, dataSet):
49 #数据集总项数
50 numEntries = len(dataSet)
51 #标签计数对象初始化
52 labelCounts = {}
53 for featDataVal in dataSet:
54 #获取数据集每一项的最后一列的标签值
55 currentLabel = featDataVal[columnIndex]
56 #如果当前标签不在标签存储对象里，则初始化，然后计数
57 if currentLabel not in labelCounts.keys():
58 labelCounts[currentLabel] = 0
59 labelCounts[currentLabel] += 1
60 #熵初始化
61 shannonEnt = 0.0
62 #遍历标签对象，求概率，计算熵
63 for key in labelCounts.keys():
64 prop = labelCounts[key]/float(numEntries)
65 shannonEnt -= prop*log(prop,2)
66 return shannonEnt
67
68
69 #通过信息增益，选出最优特征列索引(ID3)
70 def chooseBestFeatureToSplit(dataSet):
71 #计算特征个数，dataSet最后一列是标签属性，不是特征量
72 numFeatures = len(dataSet[0])-1
73 #计算初始数据香农熵
74 baseEntropy = calcShannonEnt(-1, dataSet)
75 #初始化信息增益，最优划分特征列索引
76 bestInfoGain = 0.0
77 bestFeatureIndex = -1
78 for i in range(numFeatures):
79 #获取每一列数据
80 featList = [example[i] for example in dataSet]
81 #将每一列数据去重
82 uniqueVals = set(featList)
83 newEntropy = 0.0
84 for value in uniqueVals:
85 subDataSet = splitDataSet(dataSet,i,value)
86 #计算条件概率
87 prob = len(subDataSet)/float(len(dataSet))
88 #计算条件熵
89 newEntropy +=prob*calcShannonEnt(-1, subDataSet)
90 #计算信息增益
91 infoGain = baseEntropy - newEntropy
92 if(infoGain > bestInfoGain):
93 bestInfoGain = infoGain
94 bestFeatureIndex = i
95 return bestFeatureIndex
96
97 #通过信息增益率，选出最优特征列索引(C4.5)
98 def chooseBestFeatureToSplitOfFurther(dataSet):
99 #计算特征个数，dataSet最后一列是标签属性，不是特征量
100 numFeatures = len(dataSet[0])-1
101 #计算初始数据香农熵H(Y)
102 baseEntropy = calcShannonEnt(-1, dataSet)
103 #初始化信息增益，最优划分特征列索引
104 bestInfoGainRatio = 0.0
105 bestFeatureIndex = -1
106 for i in range(numFeatures):
107 #获取每一特征列香农熵H(X)
108 featEntropy = calcShannonEnt(i, dataSet)
109 #获取每一列数据
110 featList = [example[i] for example in dataSet]
111 #将每一列数据去重
112 uniqueVals = set(featList)
113 newEntropy = 0.0
114 for value in uniqueVals:
115 subDataSet = splitDataSet(dataSet,i,value)
116 #计算条件概率
117 prob = len(subDataSet)/float(len(dataSet))
118 #计算条件熵
119 newEntropy +=prob*calcShannonEnt(-1, subDataSet)
120 #计算信息增益
121 infoGain = baseEntropy - newEntropy
122 #计算信息增益率
123 infoGainRatio = infoGain/float(featEntropy)
124 if(infoGainRatio > bestInfoGainRatio):
125 bestInfoGainRatio = infoGainRatio
126 bestFeatureIndex = i
127 return bestFeatureIndex
128
129 #决策树创建
130 def createTree(dataSet,labels):
131 #获取标签属性，dataSet最后一列，区别于labels标签名称
132 classList = [example[-1] for example in dataSet]
133 #树极端终止条件判断
134 #标签属性值全部相同，返回标签属性第一项值
135 if classList.count(classList[0]) == len(classList):
136 return classList[0]
137 #没有特征，只有标签列（1列）
138 if len(dataSet[0]) == 1:
139 #返回实例数最大的类
140 return majorityCnt(classList)
141 # #获取最优特征列索引ID3
142 # bestFeatureIndex = chooseBestFeatureToSplit(dataSet)
143 #获取最优特征列索引C4.5
144 bestFeatureIndex = chooseBestFeatureToSplitOfFurther(dataSet)
145 #获取最优索引对应的标签名称
146 bestFeatureLabel = labels[bestFeatureIndex]
147 #创建根节点
148 myTree = {bestFeatureLabel:{}}
149 #去除最优索引对应的标签名，使labels标签能正确遍历
150 del(labels[bestFeatureIndex])
151 #获取最优列
152 bestFeature = [example[bestFeatureIndex] for example in dataSet]
153 uniquesVals = set(bestFeature)
154 for value in uniquesVals:
155 #子标签名称集合
156 subLabels = labels[:]
157 #递归
158 myTree[bestFeatureLabel][value] = createTree(splitDataSet(dataSet,bestFeatureIndex,value),subLabels)
159 return myTree
160
161 #获取分类结果
162 #inputTree:决策树字典
163 #featLabels:标签列表
164 #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）
165 def classify(inputTree,featLabels,testVec):
166 #获取根结点名称，将dict转化为list
167 firstSide = list(inputTree.keys())
168 #根结点名称String类型
169 firstStr = firstSide[0]
170 #获取根结点对应的子节点
171 secondDict = inputTree[firstStr]
172 #获取根结点名称在标签列表中对应的索引
173 featIndex = featLabels.index(firstStr)
174 #由索引获取向量表中的对应值
175 key = testVec[featIndex]
176 #获取树干向量后的对象
177 valueOfFeat = secondDict[key]
178 #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
179 #if type(valueOfFeat).__name__=='dict': 等价 if isinstance(valueOfFeat, dict):
180 if isinstance(valueOfFeat, dict):
181 classLabel = classify(valueOfFeat,featLabels,testVec)
182 else:
183 classLabel = valueOfFeat
184 return classLabel
185
186
187 #将决策树分类器存储在磁盘中，filename一般保存为txt格式
188 def storeTree(inputTree,filename):
189 import pickle
190 fw = open(filename,'wb+')
191 pickle.dump(inputTree,fw)
192 fw.close()
193 #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
194 def grabTree(filename):
195 import pickle
196 fr = open(filename,'rb')
197 return pickle.load(fr)
198
199
200
决策树算法
1 '''
2 Created on Oct 14, 2010
3
4 @author: Peter Harrington
5 '''
6 import matplotlib.pyplot as plt
7
8 decisionNode = dict(boxstyle="sawtooth", fc="0.8")
9 leafNode = dict(boxstyle="round4", fc="0.8")
10 arrow_args = dict(arrowstyle="<-")
11
12 #获取树的叶子节点
13 def getNumLeafs(myTree):
14 numLeafs = 0
15 #dict转化为list
16 firstSides = list(myTree.keys())
17 firstStr = firstSides[0]
18 secondDict = myTree[firstStr]
19 for key in secondDict.keys():
20 #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）
21 if type(secondDict[key]).__name__=='dict':#test to see if the nodes are dictonaires, if not they are leaf nodes
22 numLeafs += getNumLeafs(secondDict[key])
23 else: numLeafs +=1
24 return numLeafs
25
26 #获取树的层数
27 def getTreeDepth(myTree):
28 maxDepth = 0
29 #dict转化为list
30 firstSides = list(myTree.keys())
31 firstStr = firstSides[0]
32 secondDict = myTree[firstStr]
33 for key in secondDict.keys():
34 if type(secondDict[key]).__name__=='dict':#test to see if the nodes are dictonaires, if not they are leaf nodes
35 thisDepth = 1 + getTreeDepth(secondDict[key])
36 else: thisDepth = 1
37 if thisDepth > maxDepth: maxDepth = thisDepth
38 return maxDepth
39
40 def plotNode(nodeTxt, centerPt, parentPt, nodeType):
41 createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction',
42 xytext=centerPt, textcoords='axes fraction',
43 va="center", ha="center", bbox=nodeType, arrowprops=arrow_args )
44
45 def plotMidText(cntrPt, parentPt, txtString):
46 xMid = (parentPt[0]-cntrPt[0])/2.0 + cntrPt[0]
47 yMid = (parentPt[1]-cntrPt[1])/2.0 + cntrPt[1]
48 createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30)
49
50 def plotTree(myTree, parentPt, nodeTxt):#if the first key tells you what feat was split on
51 numLeafs = getNumLeafs(myTree) #this determines the x width of this tree
52 depth = getTreeDepth(myTree)
53 firstSides = list(myTree.keys())
54 firstStr = firstSides[0] #the text label for this node should be this
55 cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)
56 plotMidText(cntrPt, parentPt, nodeTxt)
57 plotNode(firstStr, cntrPt, parentPt, decisionNode)
58 secondDict = myTree[firstStr]
59 plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD
60 for key in secondDict.keys():
61 if type(secondDict[key]).__name__=='dict':#test to see if the nodes are dictonaires, if not they are leaf nodes
62 plotTree(secondDict[key],cntrPt,str(key)) #recursion
63 else: #it's a leaf node print the leaf node
64 plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW
65 plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode)
66 plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key))
67 plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalD
68 #if you do get a dictonary you know it's a tree, and the first element will be another dict
69 #绘制决策树
70 def createPlot(inTree):
71 fig = plt.figure(1, facecolor='white')
72 fig.clf()
73 axprops = dict(xticks=[], yticks=[])
74 createPlot.ax1 = plt.subplot(111, frameon=False, **axprops) #no ticks
75 #createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses
76 plotTree.totalW = float(getNumLeafs(inTree))
77 plotTree.totalD = float(getTreeDepth(inTree))
78 plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0;
79 plotTree(inTree, (0.5,1.0), '')
80 plt.show()
81
82 #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）
83 #def createPlot():
84 # fig = plt.figure(1, facecolor='white')
85 # fig.clf()
86 # createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses
87 # plotNode('a decision node', (0.5, 0.1), (0.1, 0.5), decisionNode)
88 # plotNode('a leaf node', (0.8, 0.1), (0.3, 0.8), leafNode)
89 # plt.show()
90
91 def retrieveTree(i):
92 listOfTrees =[{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}},
93 {'no surfacing': {0: 'no', 1: {'flippers': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}}
94 ]
95 return listOfTrees[i]
96
97 #thisTree = retrieveTree(0)
98 #createPlot(thisTree)
99 #createPlot()
100 #myTree = retrieveTree(0)
101 #numLeafs =getNumLeafs(myTree)
102 #treeDepth =getTreeDepth(myTree)
103 #print(u"叶子节点数目：%d"% numLeafs)
104 #print(u"树深度：%d"%treeDepth)
绘制决策树
1 # -*- coding: utf-8 -*-
2 """
3 Created on Fri Aug 3 19:52:10 2018
4
5 @author: weixw
6 """
7 import myTrees as mt
8 import treePlotter as tp
9 #测试
10 dataSet, labels = mt.createDataSet()
11 #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
12 labels1 = labels.copy()
13 #createTree函数中将labels1的值改变了，所以在分类测试时不能用labels1
14 myTree = mt.createTree(dataSet,labels1)
15 #保存树到本地
16 mt.storeTree(myTree,'myTree.txt')
17 #在本地磁盘获取树
18 myTree = mt.grabTree('myTree.txt')
19 print(u"采用C4.5算法的决策树结果")
20 print (u"决策树结构：%s"%myTree)
21 #绘制决策树
22 print(u"绘制决策树：")
23 tp.createPlot(myTree)
24 numLeafs =tp.getNumLeafs(myTree)
25 treeDepth =tp.getTreeDepth(myTree)
26 print(u"叶子节点数目：%d"% numLeafs)
27 print(u"树深度：%d"%treeDepth)
28 #测试分类 简单样本数据3列
29 labelResult =mt.classify(myTree,labels,[1,1])
30 print(u"[1,1] 测试结果为：%s"%labelResult)
31 labelResult =mt.classify(myTree,labels,[1,0])
32 print(u"[1,0] 测试结果为：%s"%labelResult)
测试
运行结果
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标签：myTree,Python,plotTree,value,dataSet,标签,C4.5,def,决策树 来源： https://www.cnblogs.com/huanghanyu/p/13154159.html