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本节讲解如何预测患者需要佩戴的隐形眼镜类型。

1、使用决策树预测隐形眼镜类型的一般流程

(1)收集数据：提供的文本文件(数据来源于UCI数据库)

(2)准备数据：解析tab键分隔的数据行

(3)分析数据：快速检查数据，确保正确地解析数据内容，使用createPlot()函数绘制最终的树形图

(4)训练算法：createTree()函数

(5)测试算法：编写测试函数验证决策树可以正确分类给定的数据实例

(6)使用算法：存储数的数据结构，以使下次使用时无需重新构造树

trees.py如下：

#!/usr/bin/python

# -*- coding: utf-8 -*-

from math import log

#计算给定数据集的香农熵

def calcShannonEnt(dataSet):

numEntries=len(dataSet)

labelCounts={}

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

#按照给定特征划分数据集

def splitDataSet(dataSet,axis,value):

retDataSet=[]

for featVec in dataSet:

if featVec[axis]==value:

reducedFeatVec=featVec[:axis]

reducedFeatVec.extend(featVec[axis+1:])

retDataSet.append(reducedFeatVec)

return retDataSet

#选择最好的数据集划分方式

def chooseBestFeatureToSplit(dataSet):

numFeatures=len(dataSet[0])-1

baseEntropy=calcShannonEnt(dataSet) #计算整个数据集的原始香农熵

bestInfoGain=0.0;bestFeature=-1

for i in range(numFeatures): #循环遍历数据集中的所有特征

featList=[example[i] for example in dataSet]

uniqueVals=set(featList)

newEntropy=0.0

for value in uniqueVals:

subDataSet=splitDataSet(dataSet,i,value)

prob=len(subDataSet)/float(len(dataSet))

newEntropy+=prob*calcShannonEnt(subDataSet)

infoGain=baseEntropy-newEntropy

if(infoGain>bestInfoGain):

bestInfoGain=infoGain

bestFeature=i

return bestFeature

def majorityCnt(classList):

classCount={}

for vote in classList:

if vote not in classCount.keys():classCount[vote]=0

classCount[vote]+=1

sortedClassCount=sorted(classCount.iteritems(),key=operator.itemgetter(1),reverse=True)

return sortedClassCount[0][0]

#创建树的函数代码

def createTree(dataSet,labels):

classList=[example[-1] for example in dataSet]

if classList.count(classList[0])==len(classList): #类别完全相同规则停止继续划分

return classList[0]

if len(dataSet[0])==1: return majorityCnt(classList)

bestFeat=chooseBestFeatureToSplit(dataSet)

bestFeatLabel=labels[bestFeat]

myTree={bestFeatLabel:{}}

del(labels[bestFeat]) #得到列表包含的所有属性

featValues=[example[bestFeat] for example in dataSet]

uniqueVals=set(featValues)

for value in uniqueVals:

subLabels=labels[:]

myTree[bestFeatLabel][value]=createTree(splitDataSet(dataSet,bestFeat,value),subLabels)

return myTree

#测试算法：使用决策树执行分类

def classify(inputTree,featLabels,testVec):

firstStr=inputTree.keys()[0]

secondDict=inputTree[firstStr]

featIndex=featLabels.index(firstStr)

for key in secondDict.keys():

if testVec[featIndex]==key:

if type(secondDict[key]).__name__==‘dict‘:

classLabel=classify(secondDict[key],featLabels,testVec)

else:classLabel=secondDict[key]

return classLabel

#使用算法：决策树的存储

def storeTree(inputTree,filename):

import pickle

fw=open(filename,‘w‘)

pickle.dump(inputTree,fw)

fw.close()

def grabTree(filename):

import pickle

fr=open(filename)

return pickle.load(fr)

treePlotter.py如下：

#!/usr/bin/python

# -*- coding: utf-8 -*-

import matplotlib.pyplot as plt

from numpy import *

import operator

#定义文本框和箭头格式

decisionNode=dict(boxstyle="sawtooth",fc="0.8")

leafNode=dict(boxstyle="round4",fc="0.8")

arrow_args=dict(arrowstyle="

#绘制箭头的注解

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 createPlot():

fig=plt.figure(1,facecolor=‘white‘)

fig.clf()

createPlot.ax1=plt.subplot(111,frameon=False)

plotNode(U‘决策节点‘,(0.5,0.1),(0.1,0.5),decisionNode)

plotNode(U‘叶节点‘,(0.8,0.1),(0.3,0.8),leafNode)

plt.show()

#获取叶节点的数目和树的层数

def getNumLeafs(myTree):

numLeafs=0

firstStr=myTree.keys()[0]

secondDict=myTree[firstStr]

for key in secondDict.keys():

if type(secondDict[key]).__name__==‘dict‘:

numLeafs += getNumLeafs(secondDict[key])

else: numLeafs +=1

return numLeafs

def getTreeDepth(myTree):

maxDepth=0

firstStr=myTree.keys()[0]

secondDict=myTree[firstStr]

for key in secondDict.keys():

if type(secondDict[key]).__name__==‘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]

#在父节点间填充文本信息

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)

#计算宽和高

def plotTree(myTree,parentPt,nodeTxt):

numLeafs=getNumLeafs(myTree)

depth=getTreeDepth(myTree)

firstStr=myTree.keys()[0]

cntrPt=(plotTree.xOff+(1.0+float(numLeafs))/2.0/plotTree.totalW,plotTree.yOff)

plotMidText(cntrPt,parentPt,nodeTxt) #计算父节点和子节点的中间位置

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()

lenses.txt如下：

运行如下：

1 >>> importtrees2 >>> importtreePlotter3 >>> fr=open(‘lenses.txt‘)4 >>> lenses=[inst.strip().split(‘\t‘) for inst infr.readlines()]5 >>> lensesLabels=[‘age‘,‘prescript‘,‘astigmatic‘,‘tearRate‘]6 >>> lensesTree=trees.createTree(lenses,lensesLabels)7 >>>lensesTree8 {‘tearRate‘: {‘reduced‘: ‘no lenses‘, ‘normal‘: {‘astigmatic‘: {‘yes‘: {‘prescript‘: {‘hyper‘: {‘age‘: {‘pre‘: ‘no lenses‘, ‘presbyopic‘: ‘no lenses‘, ‘young‘: ‘hard‘}}, ‘myope‘: ‘hard‘}}, ‘no‘: {‘age‘: {‘pre‘: ‘soft‘, ‘presbyopic‘: {‘prescript‘: {‘hyper‘: ‘soft‘, ‘myope‘: ‘no lenses‘}}, ‘young‘: ‘soft‘}}}}}}9 >>> treePlotter.createPlot(lensesTree)

由图看出决策树非常好地匹配了实验数据，然而这些匹配选项可能太多。我们将这种问题称之为过度匹配(overfitting)。为了减少过度匹配问题，我们可以裁剪决策树，去掉一些不必要的叶子节点。如果叶子节点只能增加少许信息，则可以删除该节点，将它并入到其他叶子节点中。

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