机器学习-决策树-C4.5决策树
针对ID3算法存在的一些问题,1993年,Quinlan将ID3算法改进为C4.5算法。该算法成功地解决了ID3算法遇到的诸多问题,发展成为机器学习的十大算法之一。
C4.5并没有改变ID3的算法逻辑,基本的程序结构仍与ID3相同,但在节点的划分标准上做了改进。C4.5使用信息增益率(GainRatio)来替代信息增益(Gain)进行特征的选择,克服了信息增益选择特征时偏向于特征值个数较多的不足。
信息增益率:
GainRatio(S,A) = Gain(S,A) / SplitInfo(S,A)
其中Gain(S,A)就是ID3算法中的信息增益,而划分信息SplitInfo(S,A)代表了按照特征A划分样本集S的广度和均匀性。
![](https://img.laitimes.com/img/_0nNw4CM6IyYiwiM6ICdiwiI0gTMx81dsQWZ4lmZf1GLlpXazVmcvwFciV2dsQXYtJ3bm9CX9s2RkBnVHFmb1clWvB3MaVnRtp1XlBXe0xCMy81dvRWYoNHLwEzX5xCMx8FesU2cfdGLwMzX0xiRGZkRGZ0Xy9GbvNGLpZTY1EmMZVDUSFTU4VFRR9Fd4VGdsYTMfVmepNHLrJXYtJXZ0F2dvwVZnFWbp1zczV2YvJHctM3cv1Ce-cmbw5yMygjMxQmNlBDZlRmZlJTYyYzX2QjNxUTMwEzLcZDMyIDMy8CXn9Gbi9CXzV2Zh1WavwVbvNmLvR3YxUjLyM3Lc9CX6MHc0RHaiojIsJye.png)
代码
# C4.5决策树,使用信息增益率确定最优特征
from numpy import *
import math
import copy
import pickle
class C45DTree(object):
def __init__(self): # 构造方法
self.tree = {} # 生成的树
self.dataSet = [] # 数据集
self.labels = [] # 标签集
# 数据导入函数
def loadDataSet(self, path, labels):
recordlist = []
fp = open(path, "r") # 读取文件内容
content = fp.read()
fp.close()
rowlist = content.splitlines() # 按行转换为一维表
recordlist = [row.split("\t") for row in rowlist if row.strip()]
self.dataSet = recordlist
self.labels = labels
# 执行决策树函数
def train(self):
labels = copy.deepcopy(self.labels)
self.tree = self.buildTree(self.dataSet, labels)
# 创建决策树主程序
def buildTree(self, dataSet, labels):
cateList = [data[-1] for data in dataSet] # 抽取源数据集的决策标签列
# 程序终止条件1:如果classList只有一种决策标签,停止划分,返回这个决策标签
if cateList.count(cateList[0]) == len(cateList):
return cateList[0]
# 程序终止条件2:如果数据集的第一个决策标签只有一个,则返回这个决策标签
if len(dataSet[0]) == 1:
return self.maxCate(cateList)
# 算法核心:
bestFeat,featValueList = self.getBestFeat(dataSet) # 返回数据集的最优特征轴
bestFeatLabel = labels[bestFeat]
tree = {bestFeatLabel: {}}
del (labels[bestFeat])
# 抽取最优特征轴的列向量
for value in featValueList: # 决策树递归生长
subLabels = labels[:] # 将删除后的特征类别集建立子类别集
# 按最优特征列和值分隔数据集
splitDataset = self.splitDataSet(dataSet, bestFeat, value)
subTree = self.buildTree(splitDataset, subLabels) # 构建子树
tree[bestFeatLabel][value] = subTree
return tree
# 计算出现次数最多的类别标签
def maxCate(self, catelist):
items = dict([(catelist.count(i), i) for i in catelist])
return items[max(items.keys())]
# 计算信息熵
def computeEntropy(self, dataSet):
datalen = float(len(dataSet))
cateList = [data[-1] for data in dataSet] # 从数据集中得到类别标签
# 得到类别为key、出现次数value的字典
items = dict([(i, cateList.count(i)) for i in cateList])
infoEntropy = 0.0 # 初始化香农熵
for key in items: # 香农熵:
prob = float(items[key]) / datalen
infoEntropy -= prob * math.log(prob, 2)
return infoEntropy
# 划分数据集;分隔数据集;删除特征轴所在的数据列,返回剩余的数据集
# dataSet:数据集 axis:特征轴 value:特征轴的取值
def splitDataSet(self, dataSet, axis, value):
rtnList = []
for featVec in dataSet:
if featVec[axis] == value:
rFeatVec = featVec[:axis] # list操作:提取0~(axis-1)的元素
rFeatVec.extend(featVec[axis + 1:]) # list操作:将特征轴(列)之后的元素加回
rtnList.append(rFeatVec)
return rtnList
# 计算划分信息(SpilitInfo)
def computeSplitInfo(self, featureVList):
numEntries = len(featureVList)
featureValueListSetList = list(set(featureVList))
valueCounts = [featureVList.count(featVec) for featVec in featureValueListSetList]
# 计算香农熵
pList = [float(item) / numEntries for item in valueCounts]
lList = [item * math.log(item, 2) for item in pList]
splitInfo = -sum(lList)
return splitInfo, featureValueListSetList
# 使用信息增益率划分最优节点
def getBestFeat(self, dataSet):
Num_feats = len(dataSet[0][:-1])
totality = len(dataSet)
BaseEntropy = self.computeEntropy(dataSet)
ConditionEntropy = [] # 初始化条件熵
splitInfo = [] # 计算信息增益率
allFeatVList = []
for f in range(Num_feats):
featList = [example[f] for example in dataSet]
[splitI, featureValueList] = self.computeSplitInfo(featList)
allFeatVList.append(featureValueList)
splitInfo.append(splitI)
resultGain = 0.0
for value in featureValueList:
subSet = self.splitDataSet(dataSet, f, value)
appearNum = float(len(subSet))
subEntropy = self.computeEntropy(subSet)
resultGain += (appearNum/totality) * subEntropy
ConditionEntropy.append(resultGain) # 总条件熵
infoGainArray = BaseEntropy * ones(Num_feats) - array(ConditionEntropy)
infoGainRatio = infoGainArray / array(splitInfo) # C4.5信息增益的计算
bestFeatureIndex = argsort(-infoGainRatio)[0]
return bestFeatureIndex, allFeatVList[bestFeatureIndex]
# 分类
def predict(self, inputTree, featLabels, testVec):
root = list(inputTree.keys())[0] # 树根节点
secondDict = inputTree[root] # value-子树结构或分类标签
featIndex = featLabels.index(root) # 根节点在分类标签集中的位置
key = testVec[featIndex] # 测试集数组取值
valueOfFeat = secondDict[key]
if isinstance(valueOfFeat, dict):
classLabel = self.predict(valueOfFeat, featLabels, testVec) # 递归分类
else:
classLabel = valueOfFeat
return classLabel
# 持久化
def storeTree(self, inputTree, filename):
fw = open(filename, 'wb')
pickle.dump(inputTree, fw)
fw.close()
# 从文件抓取树
def grabTree(self, filename):
fr = open(filename, 'rb')
return pickle.load(fr)
#训练
dtree = C45DTree()
dtree.loadDataSet("/Users/FengZhen/Desktop/accumulate/机器学习/决策树/决策树训练集.txt", ["age", "revenue", "student", "credit"])
dtree.train()
print(dtree.tree)
#持久化
dtree.storeTree(dtree.tree, "/Users/FengZhen/Desktop/accumulate/机器学习/决策树/决策树C45.tree")
mytree = dtree.grabTree("/Users/FengZhen/Desktop/accumulate/机器学习/决策树/决策树C45.tree")
print(mytree)
#测试
labels = ["age", "revenue", "student", "credit"]
vector = ['0','1','0','0']
print(dtree.predict(mytree, labels, vector))