机器学习——决策树

1.决策树的构造

优点:计算复杂度不高,输出结果易于理解,对中间值的缺失不敏感,可以处理不相关特征数据

缺点:可能会产生过度匹配问题

适用数据类型:数值型和标称型

 

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# coding:utf-8
# !/usr/bin/env python
 
'''
Created on Oct 12, 2010
Decision Tree Source Code for Machine Learning in Action Ch. 3
@author: Peter Harrington
'''
from math import log
import operator
 
#通过是否浮出水面和是否有脚蹼,来划分鱼类和非鱼类
def createDataSet():
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing','flippers']
    #change to discrete values
    return dataSet, labels
 
def calcShannonEnt(dataSet):    #计算给定数据集的香农熵
    numEntries = len(dataSet)   #数据集中的实例总数
    labelCounts = {}
    #为所有可能的分类创建字典,键是可能的特征属性,值是含有这个特征属性的总数
    for featVec in dataSet:
        currentLabel = featVec[-1]
        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
        labelCounts[currentLabel] += 1
    #计算香农熵
    shannonEnt = 0.0
    #为所有的分类计算香农熵
    for key in labelCounts:
        prob = float(labelCounts[key])/numEntries
        shannonEnt -= prob * log(prob,2)    #以2为底求对数
    #香农熵Ent的值越小,纯度越高,即通过这个特征属性来分类,属于同一类别的结点会比较多
    return shannonEnt
     
def splitDataSet(dataSet, axis, value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet
     
def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0; bestFeature = -1
    for i in range(numFeatures):        #iterate over all the features
        featList = [example[i] for example in dataSet]#create a list of all the examples of this feature
        uniqueVals = set(featList)       #get a set of unique values
        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     #calculate the info gain; ie reduction in entropy
        if (infoGain > bestInfoGain):       #compare this to the best gain so far
            bestInfoGain = infoGain         #if better than current best, set to best
            bestFeature = i
    return bestFeature                      #returns an integer
 
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]
 
def createTree(dataSet,labels):
    classList = [example[-1] for example in dataSet]
    if classList.count(classList[0]) == len(classList):
        return classList[0]#stop splitting when all of the classes are equal
    if len(dataSet[0]) == 1: #stop splitting when there are no more features in dataSet
        return majorityCnt(classList)
    bestFeat = chooseBestFeatureToSplit(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[:]       #copy all of labels, so trees don't mess up existing labels
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
    return myTree                           
     
def classify(inputTree,featLabels,testVec):
    firstStr = inputTree.keys()[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)
    key = testVec[featIndex]
    valueOfFeat = secondDict[key]
    if isinstance(valueOfFeat, dict):
        classLabel = classify(valueOfFeat, featLabels, testVec)
    else: classLabel = valueOfFeat
    return classLabel
 
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)
     
     
if __name__ == '__main__':
    myDat,labels = createDataSet()
    print myDat
    print calcShannonEnt(myDat)
    

 

 

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#通过是否浮出水面和是否有脚蹼,来划分鱼类和非鱼类
def createDataSet():
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing','flippers']
    #change to discrete values
    return dataSet, labels
 
def calcShannonEnt(dataSet):    #计算给定数据集的香农熵
    numEntries = len(dataSet)   #数据集中的实例总数
    labelCounts = {}
    #为所有可能的分类创建字典,键是可能的特征属性,值是含有这个特征属性的总数
    for featVec in dataSet:
        currentLabel = featVec[-1]
        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
        labelCounts[currentLabel] += 1
    #计算香农熵
    shannonEnt = 0.0
    #为所有的分类计算香农熵
    for key in labelCounts:
        prob = float(labelCounts[key])/numEntries
        shannonEnt -= prob * log(prob,2)    #以2为底求对数
    #香农熵Ent的值越小,纯度越高,即通过这个特征属性来分类,属于同一类别的结点会比较多
    return shannonEnt

 

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myDat,labels = createDataSet()
print myDat
print calcShannonEnt(myDat)

 

 

2.划分数据集

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def splitDataSet(dataSet, axis, value):     #按照给定特征划分数据集,axis表示根据第几个特征,value表示特征的值
    retDataSet = []             #创建新的list对象
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]     #切片
            reducedFeatVec.extend(featVec[axis+1:]) #把序列添加到列表reducedFeatVec中
            #print reducedFeatVec
            retDataSet.append(reducedFeatVec)       #把对象reducedFeatVec(是一个list)添加到列表retDataSet中
    return retDataSet

 

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def chooseBestFeatureToSplit(dataSet):      #选择最好的数据集划分方式
    numFeatures = len(dataSet[0]) - 1       #特征的数量,最后一列是标签,所以减去1
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0; bestFeature = -1    #信息增益和最好的特征下标
    for i in range(numFeatures):            #递归所有特征
        featList = [example[i] for example in dataSet]  #创建一个列表,包含第i个特征的所有值
        uniqueVals = set(featList)          #创建一个集合set,由不同的元素组成
        newEntropy = 0.0
        for value in uniqueVals:
            subDataSet = splitDataSet(dataSet, i, value)    #按照所有特征的可能划分数据集
            prob = len(subDataSet)/float(len(dataSet))      #计算所有特征的可能性
            newEntropy += prob * calcShannonEnt(subDataSet)    
        infoGain = baseEntropy - newEntropy     #计算信息增益
        if (infoGain > bestInfoGain):        #比较不同特征之间信息增益的大小
            bestInfoGain = infoGain             #选取信息增益大的特征
            bestFeature = i
    return bestFeature                          #返回特征的下标

 

3.递归构建决策树

 

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def createTree(dataSet,labels):     #创建决策树的函数,采用字典的表示形式
    classList = [example[-1] for example in dataSet]
    if classList.count(classList[0]) == len(classList):     #如果类别完全相同则停止继续划分
        return classList[0]
    if len(dataSet[0]) == 1:                    #遍历完所有特征时返回出现次数最多的
        return majorityCnt(classList)
    bestFeat = chooseBestFeatureToSplit(dataSet)        #选择信息增益最大的特征下标
    bestFeatLabel = labels[bestFeat]                #选择信息增益最大的特征
    myTree = {bestFeatLabel:{}}
    del(labels[bestFeat])                   #从标签中删除已经划分好的特征
    featValues = [example[bestFeat] for example in dataSet] #取得该特征的所有可能取值
    uniqueVals = set(featValues)                #建立一个集合
    for value in uniqueVals:
        subLabels = labels[:]      
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels) #递归createTree
    return myTree 

 

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myDat,labels = createDataSet()
myTree = createTree(myDat,labels)
print myTree
 
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}

 

 

4.在Python中使用Matplotlib注解绘制树形图

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myDat,labels = createDataSet()
print myDat
import treePlotter
treePlotter.createPlot(myTree)  #绘制树形图

 

 

5.构造注解树

 获取叶节点的数目和树的层数

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import matplotlib.pyplot as plt
 
decisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
arrow_args = dict(arrowstyle="<-")
 
def getNumLeafs(myTree):        #获取叶子节点的数目
    numLeafs = 0
    firstStr = myTree.keys()[0]
    secondDict = myTree[firstStr]
    for key in secondDict.keys():
        if type(secondDict[key]).__name__=='dict'#测试节点的数据类型是否为字典
            numLeafs += getNumLeafs(secondDict[key])    #递归
        else:   numLeafs +=1                #如果不是字典,则说明是叶子节点
    return numLeafs
 
def getTreeDepth(myTree):       #获取树的层数
    maxDepth = 0
    firstStr = myTree.keys()[0]
    secondDict = myTree[firstStr]
    for key in secondDict.keys():
        if type(secondDict[key]).__name__=='dict'#测试节点的数据类型是否为字典,如果不是字典,则说明是叶子节点
            thisDepth = 1 + getTreeDepth(secondDict[key])   #递归
        else:   thisDepth = 1              
        if thisDepth > maxDepth: maxDepth = thisDepth
    return maxDepth

 绘制树形图

 

 

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def plotNode(nodeTxt, centerPt, parentPt, nodeType):    #绘制带箭头的注解
    #annotate参数:nodeTxt:标注文本,xy:所要标注的位置坐标,xytext:标注文本所在位置,arrowprops:标注箭头属性信息
    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):       #在父子节点间填充文本信息
    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)              #计算宽与高
    depth = getTreeDepth(myTree)
    firstStr = myTree.keys()[0]                 #the text label for this node should be this
    print plotTree.xOff
    cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)
    print parentPt
    print cntrPt
    plotMidText(cntrPt, parentPt, nodeTxt)      #标记子节点属性值
    plotNode(firstStr, cntrPt, parentPt, decisionNode)
    secondDict = myTree[firstStr]
    plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD #减少y偏移
    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
 
def createPlot(inTree):         #绘制树形图,调用了plotTree()
    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))    #存储树的宽度
    plotTree.totalD = float(getTreeDepth(inTree))   #存储树的深度
    plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0;
    plotTree(inTree, (0.5,1.0), '')
    plt.show()

 

 

测试和存储分类器

1.测试算法:使用决策树执行分类

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def classify(inputTree,featLabels,testVec): #使用决策树的分类函数
    firstStr = inputTree.keys()[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)  #将标签字符串转换为索引
    key = testVec[featIndex]
    valueOfFeat = secondDict[key]
    if isinstance(valueOfFeat, dict):
        classLabel = classify(valueOfFeat, featLabels, testVec)
    else: classLabel = valueOfFeat
    return classLabel

 

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myDat,labels = createDataSet()
Labels = labels
print "myDat="
print myDat
print "labels="
print labels
 
import treePlotter
myTree = treePlotter.retrieveTree(0)    #绘制树形图
print myTree
print classify(myTree,Labels,[0,1])

 

 2.使用算法:决策树的存储

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def storeTree(inputTree,filename):  #使用pickle模块存储决策树
    import pickle
    fw = open(filename,'w')
    pickle.dump(inputTree,fw)
    fw.close()
     
def grabTree(filename):         #查看决策树
    import pickle
    fr = open(filename)
    return pickle.load(fr)

 

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myDat,labels = createDataSet()
Labels = labels
print "myDat="
print myDat
print "labels="
print labels
import treePlotter
myTree = treePlotter.retrieveTree(0)    #绘制树形图
print myTree
storeTree(myTree,'classifierStorage.txt')
print grabTree('classifierStorage.txt')

 

示例:使用决策树预测隐形眼镜类型

 

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import treePlotter
import simplejson
import ch
ch.set_ch()
from matplotlib import pyplot as plt
fr = open('lenses.txt')
lenses = [inst.strip().split('\t') for inst in fr.readlines()]  #读取一行数据,以tab键分割并去掉空格
lensesLabels = [u'年龄',u'近远视',u'散光',u'眼泪等级']         #使用unicode,不然编码会报错
lensesTree = createTree(lenses,lensesLabels)
print simplejson.dumps(lensesTree, encoding="UTF-8", ensure_ascii=False)    #使用simplejson模块输出对象中的中文
treePlotter.createPlot(lensesTree)

 

posted @   tonglin0325  阅读(2298)  评论(0编辑  收藏  举报
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