决策树

决策树的一般流程:

1. 收集数据:anymethd
2. 准备数据:树构造算法只适用于标称型数据，因此数值型必须离散化
3. 分析数据:可以使用任何方法，树构造完成后应该检查图形是否符合预期
4. 训练算法:构造树的数据结构
5. 测试算法:使用经验树计算错误率
6. 使用算法:适用于任何监督学习算法，而使用决策树可更好的理解数据的内在含义

计算给定数据集的香农熵（集合信息的度量方式，度量数据集的无序程度）

         熵定义为信息的期望值，熵越高，混合的数据也越多。

def calcShannonEnt(dataSet):    numEntries=len(dataSet)    labelCounts={}    for featVec in dataSet:#统计所有类标签发生的次数        currentLabel=featVec[-1]        if currentLabel not in labelCounts.keys():            labelCounts[currentLabel]=0        labelCounts[currentLabel]+=1    shannoEnt=0.0    for key in labelCounts:        prob=float(labelCounts[key])/numEntries        shannoEnt-=prob*log(prob,2)    return shannoEntdef createDataSet():#创建简单数据集    dataSet=[[1,1,'yes'],             [1,1,'yes'],             [1,0,'no'],             [0,1,'no'],             [0,1,'no']]    labels=['no surfacing','flippers']    return dataSet,labels

划分数据集（度量划分数据集的熵，判断当前是否正确划分了数据集）

       对每个特征划分数据集的结果计算一次信息熵，然后判断哪个特征是划分数据集的最好划分方式。

#splitDataSet(待划分的数据集、划分数据集的特征、特征的返回值)def splitDataSet(dataset,axis,value):    retDataSet=[]    for featVec in dataset:        if featVec[axis]==value:        #判断特征值为axis的列，其值是否等于value,        #splitDataSet(dataset,0,0)---即判断featVec[0]是否等于0            reducedFeatVec=featVec[:axis]            print(reducedFeatVec)            reducedFeatVec.extend(featVec[axis+1:])            print(reducedFeatVec)            retDataSet.append(reducedFeatVec)            print(retDataSet)    return retDataSetm,l=createDataSet()calcShannonEnt(m)splitDataSet(m,0,0)[][1, 'no'][[1, 'no']][][1, 'no'][[1, 'no'], [1, 'no']]#-----------------------------------------------------------------------------------------------#遍历整个数据集，循环计算熵和splitDataSet(),找到最好的特征划分方式。def chooseBestFeatureToSplit(dataSet):    numFeatures=len(dataSet[0])-1#计算特征值数    baseEntropy=calcShannonEnt(dataSet)    bestInfoGain=0.0    bestFeature=-1#最好的特征值    for i in range(numFeatures):        featList=[example[i] for example in dataSet]#列表推导 i遍历dataSet,并且将每行的第i列存放到example        uniqueVals=set(featList)#Build an unordered collection of unique elements.        newEntropy=0.0        for value in uniqueVals:            subDataSet=splitDataSet(dataSet,i,value)            prob=len(subDataSet)/float(len(dataSet))#选择该分类的概率            newEntropy+=prob*calcShannonEnt(subDataSet)#新的熵值        infoGain=baseEntropy-newEntropy        if(infoGain>bestInfoGain):            bestInfoGain=infoGain            bestFeature=i    return bestFeature#返回最好的特征值

递归构建决策树

        工作原理:得到原始数据集，然后基于最好的属性值划分数据集，由于特征值可能多于两个，因此可能存在大于2个分支的数据集划分。

        采用递归处理:结束条件为（遍历完所有划分数据集的属性 or 每个分支下的所有实例都具有相同的分类）

def majorityCnt(classList):#返回次数最多的分类名称    classCount={}    for vote in classList:        if vote not in classCount.keys():            classCount[vote]=0        classCount+=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):#所有的类标签完全相同，则直接返回该类标签        return classList[0]    if len(dataSet[0]) == 1:#遍历完所有特征仍然不能把数据集划分成仅包含唯一类别的分组，则返回出现次数最多的返回        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，不改变原始列表的内容        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)    return myTree 

使用Matplotlib注解绘制树形图

1.Matplotlib注解

import matplotlib.pyplot as pltdecisionNode = dict(boxstyle="sawtooth", fc="0.8")leafNode = dict(boxstyle="round4", fc="0.8")arrow_args = dict(arrowstyle="<-")def plotNode(nodeTxt, centerPt, parentPt, nodeType):    #import matplotlib.pyplot as plt    #plt.annotate()文本注释    createPlot.ax1.annotate(nodeTxt, xy=parentPt,  xycoords='axes fraction',             xytext=centerPt, textcoords='axes fraction',             va="center", ha="center", bbox=nodeType, arrowprops=arrow_args )# =============================================================================#subplot(row,col,plotNum)#     将绘图区域分为row*col列子域,并且按照从左往右，上到下对每个#     子区域编号，若row,col,plotNum都小于10，可用3位数字之间代替#     在plotNum的区域中创建轴对象。#plot(*args, **kwargs)#    plot(x, y)        # plot x and y using default line style and color#    plot(x, y, 'bo')  # plot x and y using blue circle markers#figure(num=None, figsize=None, dpi=None, facecolor=None,#    edgecolor=None, frameon=True, FigureClass=<class 'matplotlib.figure.Figure'>, #    **kwargs)    #Creates a new figure#clf()#    Clear the current figure.#createPlot.ax1#    import dis#    def func():#    func().ax1=123#    dis.dis(func)#    一切皆对象，对函数也可以添加属性# =============================================================================def createPlot():    fig = plt.figure(1, facecolor='white')    fig.clf()    createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses     plotNode('a decision node', (0.5, 0.1), (0.1, 0.5), decisionNode)    plotNode('a leaf node', (0.8, 0.1), (0.3, 0.8), leafNode)    plt.show()

2.构造注解树

def getNumLeafs(myTree):#获取叶节点    numLeafs=0    firstStr=list(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 numLeafsdef getTreeDepth(myTree):#获取树的层数    maxDepth=0#    python 2.x  D.keys()->list#    python 3.x  D.keys(...)-> a set-like object providing a view on D's keys    firstStr=list(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 maxDepthdef retrieveTree(i):#输出预先存储的树信息，主要用于测试    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]myTree=retrieveTree(0)getNumLeafs(myTree)# 3getNumTreeDepth(myTree)# 2

------------------------以下将前面所学组合一起，绘制一颗完整树-----------------------------

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):#if the first key tells you what feat was split on    numLeafs = getNumLeafs(myTree)  #this determines the x width of this tree    depth = getTreeDepth(myTree)    firstStr = list(myTree.keys())[0]     #the text label for this node should be this    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':#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.totalDdef createPlot(inTree):         fig = plt.figure(1, facecolor='white')        fig.clf()        axprops=dict(xticks=[],yticks=[])        createPlot.ax1 = plt.subplot(111, frameon=False,**axprops) #ticks for demo puropses         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()def createPlot(inTree):     fig = plt.figure(1, facecolor='white')    fig.clf()    axprops=dict(xticks=[],yticks=[])    createPlot.ax1 = plt.subplot(111, frameon=False,**axprops) #ticks for demo puropses     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() 

测试和存储分类器

#1.测试算法：创建使用决策树的分类器def classify(inputTree,featLabels,testVec):#使用决策树的分类函数    firstStr=list(inputTree.keys())[0]    secondDict=inputTree[firstStr]    featIndex=featLabels.index(firstStr)#将标签字符串转换为索引    for key in secondDict.keys():        if testVec[featIndex]==key:#比较testVec变量中的值与树节点的值            if type(secondDict[key]).__name__=='dict':                classLabel=classify(secondDict[key],featLabels,testVec)            else:                classLabel=secondDict[key]    return classLabel# =============================================================================# In[]: m,l=trees.createDataSet()# Out[]: ['no surfacing', 'flippers']# # In[]: myTree=treePlotter.retrieveTree(0)# # In[]: myTree# Out[]: {'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}# In[]: trees.classify(myTree,l,[1,0])# Out[]: 'no'# =============================================================================#2.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)

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