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trees.py
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trees.py
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#coding:utf-8
'''
决策树的实现
决策树是一种预测模型,分类算法,可以利用决策树表示出数据内部蕴含的知识。
'''
from math import log
import operator
import matplotlib.pyplot as plt
###计算香农熵(为float类型)
def calShang(dataSet):
numEntries = len(dataSet)
labelCounts = {}##创建字典
for featVec in dataSet:
currentLabel = featVec[-1]
if currentLabel not in labelCounts.keys():
labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
shannonEnt = 0.0
for key in labelCounts:
prob = float(labelCounts[key]) / numEntries
shannonEnt -= prob * log(prob,2)
return shannonEnt
def creatDataSet():
dataSet = [[1,1,'yes'],
[1,1,'yes'],
[1,0,'no'],
[0,1,'no'],
[0,1,'no']]
labels = ['no surfacing','flippers']
return dataSet,labels
'''
#test
myData,labels = creatDataSet()
print("原数据为:",myData)
print("标签为:",labels)
shang = calShang(myData)
print("香农熵为:",shang)
'''
###划分数据集(以指定特征将数据进行划分)
def splitDataSet(dataSet,feature,value):##传入待划分的数据集、划分数据集的特征以及需要返回的特征的值
newDataSet = []
for featVec in dataSet:
if featVec[feature] == value:
reducedFeatVec = featVec[:feature]
reducedFeatVec.extend(featVec[feature + 1:])
newDataSet.append(reducedFeatVec)
return newDataSet
'''
#测试
myData,labels = creatDataSet()
print("原数据为:",myData)
print("标签为:",labels)
split = splitDataSet(myData,0,1)
print("划分后的结果为:",split)
'''
##选择最好的划分方式(选取每个特征划分数据集,从中选取信息增益最大的作为最优划分)在这里体现了信息增益的概念
def chooseBest(dataSet):
featNum = len(dataSet[0]) - 1
baseEntropy = calShang(dataSet)
bestInforGain = 0.0
bestFeat = -1##表示最好划分特征的下标
for i in range(featNum):
featList = [example[i] for example in dataSet] #列表
uniqueFeat = set(featList)##得到每个特征中所含的不同元素
newEntropy = 0.0
for value in uniqueFeat:
subDataSet = splitDataSet(dataSet,i,value)
prob = len(subDataSet) / len(dataSet)
newEntropy += prob * calShang(subDataSet)
inforGain = baseEntropy - newEntropy
if (inforGain > bestInforGain):
bestInforGain = inforGain
bestFeature = i#第i个特征是最有利于划分的特征
return bestFeature
'''
##测试
myData,labels = creatDataSet()
best = chooseBest(myData)
print(best)
'''
#返回出现次数最多的分类名称
def majorClass(classList):
classCount = {}
for vote in classList:
if vote not in classCount.keys():
classCount[vote] = 0
classCount[vote] += 1
#降序排序,可以指定reverse = true
sortedClassCount = sorted(classcount.iteritems(),key = operator.itemgetter(1),reverse = true)
return sortedClassCount[0][0]
#创建树
def creatTree(dataSet,labels):
classList = [example[-1] for example in dataSet]
if classList.count(classList[0]) == len(classList):
return classList[0]
if len(dataSet[0]) == 1:
return majorClass(classList)
bestFeat = chooseBest(dataSet)
bestFeatLabel = labels[bestFeat]
myTree = {bestFeatLabel:{}}
del(labels[bestFeat])
featValues = [example[bestFeat] for example in dataSet]
uniqueVals = set(featValues)
for value in uniqueVals:
subLabels = labels[:]
myTree[bestFeatLabel][value] = creatTree(splitDataSet(dataSet,bestFeat,value),subLabels)
return myTree
'''
#测试
myData,labels = creatDataSet()
mytree = creatTree(myData,labels)
print(mytree)
'''
##采用matplotlib绘制树形图
ecisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
arrow_args = dict(arrowstyle="<-")
#绘制树节点
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 )
##获取节点的数目和树的层数
def getNumLeafs(myTree):
numLeafs = 0
#firstStr = myTree.keys()[0]
firstSides = list(myTree.keys())
firstStr = firstSides[0]#找到输入的第一个元素
secondDict = myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]) == dict:
numLeafs += getNumLeafs(secondDict[key])
else: numLeafs += 1
return numLeafs
def getTreeDepth(myTree):
maxDepth = 1
firstSides = list(myTree.keys())
firstStr = firstSides[0]#找到输入的第一个元素
#firstStr = myTree.keys()[0]
secondDict = myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]) == dict:
thisDepth = 1 + getTreeDepth(secondDict[key])
else: thisDepth = 1
if thisDepth > maxDepth: maxDepth = thisDepth
return maxDepth
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]
#测试
mytree = retrieveTree(0)
print(getNumLeafs(mytree))
print(getTreeDepth(mytree))
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):
numLeafs = getNumLeafs(myTree)
depth = getTreeDepth(myTree)
firstSides = list(myTree.keys())
firstStr = firstSides[0]#找到输入的第一个元素
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':
plotTree(secondDict[key],cntrPt,str(key))
else:
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
def createPlot(inTree):
fig = plt.figure(1, facecolor='white')
fig.clf()
axprops = dict(xticks=[], yticks=[])
createPlot.ax1 = plt.subplot(111, frameon=False, **axprops)
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()
#测试
mytree = retrieveTree(0)
print(mytree)
createPlot(mytree)