运行环境：Anaconda——Jupyter Notebook

Python版本为：3.6.6

数据集:lense.txt

提取码：9wsp

1.决策树

决策树也是最经常使用的数据挖掘算法，长方形代表判断模块（decision block），椭圆形代表终止模块（terminating block），表示已经得出结论，可以终止运行。从判断模块引出的左右箭头称作分支（branch），它可以到达另一个判断模块或者终止模块。

k-近邻算法最大的缺点就是无法给出数据的内在含义，决策树的主要优势就在于数据形式非常容易理解。

决策树算法能够读取数据集合，决策树的一个重要任务是为了数据中所蕴含的知识信息，因此决策树可以使用不熟悉的数据集合，并从中提取出一系列规则，在这些机器根据数据集创建规则时，就是机器学习的过程。

1.1 决策树的构造

决策树

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。

首先我们讨论数学上如何使用信息论划分数据集，然后编写代码将理论应用到具体的数据集上，最后编写代码构建决策树。

创建分支的伪代码函数createBranch()如下所示：

检测数据集中的每个子项是否属于同一分类：

If so return 类标签；

Else寻找划分数据集的最好特征划分数据集创建分支节点for 每个划分的子集调用函数createBranch并增加返回结果到分支节点中return 分支节点

决策树的一般流程

(1) 收集数据：可以使用任何方法。

(2) 准备数据：树构造算法只适用于标称型数据，因此数值型数据必须离散化。

(3) 分析数据：可以使用任何方法，构造树完成之后，我们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：此步骤可以适用于任何监督学习算法，而使用决策树可以更好地理解数据的内在含义。

本文使用ID3算法划分数据集，该算法处理如何划分数据集，何时停止划分数据集，每次划分数据集时我们只选取一个特征属性。现在我们想要决定依据第一个特征还是第二个特征划分数据。在回答这个问题之前，我们必须采用量化的方法判断如何划分数据。在日常生活中，极少发生 的事件一旦发生是容易引起人们关注的（新闻说发生空难了，那必然会引起人们很大的关注，但事实是发生空难的概率很小很小），而 司空见惯的事不会引起注意 ，也就是说，极少见的事件所带来的信息量多。如果用统计学的术语来描述，就是出现概率小的事件信息量多。因此，事件出现得概率越小，信息量愈大。即信息量的多少是与事件发生频繁（即概率大小）成反比 。

2.1.1 信息增益

划分数据集的大原则是：将无序的数据变得更加有序。

我们可以在划分数据之前或之后使用信息论量化度量信息的内容。

在划分数据集之前之后信息发生的变化称为信息增益。

获得信息增益最高的特征就是最好的选择。

在可以评测哪种数据划分方式是最好的数据划分之前，我们必须学习如何计算信息增益。集合信息的度量方式称为香农熵或者简称为熵。

我们日常生活中会接收到无数的消息，但是只有那些你关心在意（或对你有用）的才叫做信息。

熵定义为信息的期望值，如果待分类的事务可能划分在多个分类之中，则符号xi的信息定义为：

其中p(xi)是选择该分类的概率。

为了计算熵，我们需要计算所有类别所有可能值包含的信息期望值:

def dataSet():dataSet = [[1,1,'yes'],[1,1,'yes'],[1,0,'no'],[0,1,'no'],[0,1,'no']]labels = ['no surfacing','flippers']return dataSet,labels

myDat,labels = dataSet()

myDat

[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]

labels

['no surfacing', 'flippers']

# 计算给定数据集的香农熵from math import logdef caclShannonEnt(dataSet):#计算实例总数numEntries = len(dataSet)labelCounts = {}# 1.为所有可能分类创建字典for featVec in dataSet:currentLabel = featVec[-1]# 为所有可能的分类创建字典，如果当前的键值不存在，则扩展字典并将当前键值加入字典。每个键值都记录了当前类别出现的次数。if currentLabel not in labelCounts.keys():labelCounts[currentLabel] = 0labelCounts[currentLabel] += 1shannonEnv = 0.0for key in labelCounts:prob = float(labelCounts[key])/numEntries# 2.以2为底求对数shannonEnv -= prob*log(prob,2)return shannonEnv

caclShannonEnt(myDat)

0.9709505944546686

熵越高，则混合的数据也越多，在数据集中添加更多的分类，观察熵是如何变化的。

得到熵之后，我们就可以按照获取最大信息增益的方法划分数据集

myDat[0][-1] = 'maybe'myDat

[[1, 1, 'maybe'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]

caclShannonEnt(myDat)

1.3709505944546687

1.1.2 划分数据集

分类算法除了需要测量信息熵，还需要划分数据集，度量划分数据集的熵，以便判断当前是否正确地划分了数据集。我们将对每个特征划分数据集的结果计算一次信息熵，然后判断按照哪个特征划分数据集是最好的划分方式。

# 程序清单 按照给定特征划分数据集def splitDataSet(dataSet,axis,value):# 1.创建新的list对象retDataSet = []for featVec in dataSet:if (featVec[axis] == value):# 2.抽取reducedFeatVec = featVec[:axis]reducedFeatVec.extend(featVec[axis+1:])retDataSet.append(reducedFeatVec)return retDataSet

splitDataSet(myDat,0,1)

[[1, 'maybe'], [1, 'yes'], [0, 'no']]

splitDataSet(myDat,0,0)

[[1, 'no'], [1, 'no']]

遍历整个数据集，循环计算香农熵和splitDataSet()函数，找到最好的特征划分方式

def chooseBestFeatureToSplit(dataSet):numFeatures = len(dataSet[0])-1baseEntropy = caclShannonEnt(dataSet)bestInfoGain = 0.0bestFeature = -1for i in range(numFeatures):# print('i:',i)featList = [example[i] for example in dataSet]# print(featList)uniqueVals = set(featList)# print(uniqueVals)newEntropy = 0.0for value in uniqueVals:subDataSet = splitDataSet(dataSet,i,value)prob = len(subDataSet)/float(len(dataSet))newEntropy += prob*log(prob,2)# print(value,prob,subDataSet)if (baseEntropy - newEntropy > bestInfoGain):bestInfoGain = baseEntropy - newEntropybestFeature = ireturn bestFeature

chooseBestFeatureToSplit(myDat)

0

1.1.3 递归构建决策树

# 多数表决import operatordef majorityCnt(classList):classCount = {}for vote in classCount:if vote not in classCount.keys():classCount[vote] = 0classCount[vote] += 1sortedClassCount = sorted(classCount.items(),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]if len(dataSet[0])==1:return majorityCnt(classList)bestFeat = chooseBestFeatureToSplit(dataSet)print('bestFeat:',bestFeat)bestFeatLabel = labels[bestFeat]print('bestFeatLabel:',bestFeatLabel)myTree = {bestFeatLabel:{}}del(labels[bestFeat])featValues = [example[bestFeat] for example in dataSet]print('featValues:',featValues)uniqueVals = set(featValues)print('uniqueVals:',uniqueVals)for value in uniqueVals:subLabels = labels[:]print(splitDataSet(dataSet,bestFeat,value))myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet,bestFeat,value),subLabels)print('myTree:',myTree)return myTree

myTree = createTree(myDat,labels)

bestFeat: 0bestFeatLabel: no surfacingfeatValues: [1, 1, 1, 0, 0]uniqueVals: {0, 1}[[1, 'no'], [1, 'no']]myTree: {'no surfacing': {0: 'no'}}[[1, 'maybe'], [1, 'yes'], [0, 'no']]bestFeat: 0bestFeatLabel: flippersfeatValues: [1, 1, 0]uniqueVals: {0, 1}[['no']]myTree: {'flippers': {0: 'no'}}[['maybe'], ['yes']]myTree: {'flippers': {0: 'no', 1: None}}myTree: {'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: None}}}}

1.22 在Python中使用Matplotlib注解绘制树形图

import matplotlib.pyplot as pltdecisionNode = dict(boxstyle='sawtooth',fc='0.8')leafNode = dict(boxstyle='round4',fc='0.8')arrow_args = dict(arrowstyle='<-')def plotNode(nodeText,centerPt,parentPt,nodeType):# nodeTxt为要显示的文本，centerPt为文本的中心点，parentPt为指向文本的点 createPlot.ax1.annotate(nodeText,xytext=centerPt,textcoords="axes fraction",\xy=parentPt,xycoords="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"叶子节点",(0.8,0.1),(0.3,0.8),leafNode)plt.show()

# 求叶子节点数def getNumLeafs(myTree):numNode = 0firstStr = list(myTree.keys())[0]secondDict = myTree[firstStr]for key in secondDict.keys():if type(secondDict[key]).__name__ == 'dict':numNode += getNumLeafs(secondDict[key])else:numNode += 1return numNode

getNumLeafs(myTree)

3

#获取决策树的深度def getTreeDepth(myTree):maxDepth = 0firstStr = 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 = 1return thisDepth

getTreeDepth(myTree)

2

接着，函数retrieveTree输出预先存储的树信息，避免每次测试代码时都要从数据中创建树的函数。

#预定义的树，用来测试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]

myTree = retrieveTree(0)

myTree

{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}

print('getNumLeaf: %d,getNumDepth: %d' %(getNumLeafs(myTree),getTreeDepth(myTree)))

getNumLeaf: 3,getNumDepth: 2

labels = ['no surfacing', 'flippers']

#绘制中间文本（在父子节点间填充文本信息）def plotMidText(cntrPt,parentPt,txtString):#求中间点的横坐标xMid = (parentPt[0]- cntrPt[0])/2.0 + cntrPt[0]#求中间点的纵坐标yMid = (parentPt[1] - cntrPt[1])/2.0 + cntrPt[1]#绘制树节点createPlot.ax1.text(xMid,yMid,txtString,va='center',ha='center',rotation=30)#绘制决策树def plotTree(myTree,parentPt,nodeTxt):#获得决策树的叶子节点数与深度numLeafs = getNumLeafs(myTree)depth = getTreeDepth(myTree)#firstStr = myTree.keys()[0]firstSides = list(myTree.keys())firstStr = firstSides[0]cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalw,plotTree.yOff)print('c:',cntrPt)plotMidText(cntrPt,parentPt,nodeTxt)plotNode(firstStr,cntrPt,parentPt,decisionNode)secondDict = myTree[firstStr]plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalDprint('d:',plotTree.yOff)for key in secondDict.keys():#如果secondDict[key]是一颗子决策树，即字典if type(secondDict[key]) is dict:#递归地绘制决策树plotTree(secondDict[key],cntrPt,str(key))else:plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalwprint('e:',plotTree.xOff)plotNode(secondDict[key],(plotTree.xOff,plotTree.yOff),cntrPt,leafNode)plotMidText((plotTree.xOff,plotTree.yOff),cntrPt,str(key))plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalDprint('f:',plotTree.yOff)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.totalwplotTree.yOff = 1.0plotTree(inTree,(0.5,1.0),'')plt.show()

axprops = dict(xticks=[],yticks=[])

xticks是一个列表，其中的元素就是x轴上将显示的坐标，yticks是y轴上显示的坐标，这里空列表则不显示坐标。

createPlot(retrieveTree(0))

c: (0.5, 1.0)d: 0.5e: 0.16666666666666666c: (0.6666666666666666, 0.5)d: 0.0e: 0.5e: 0.8333333333333333f: 0.5f: 1.0

#参数：inputTree--决策树模型 #featLabels--Feature标签对应的名称# testVec--测试输入的数据#返回结果 classLabel分类的结果值(需要映射label才能知道名称)def classify(inTree,featLabels,testVec):firstStr = list(inTree.keys())[0]secondDict = inTree[firstStr]featIndex = featLabels.index(firstStr)key = testVec[featIndex]valueOfFeat = secondDict[key]if isinstance(valueOfFeat,dict):classLabel = classify(valueOfFeat,featLabels,testVec)else:classLabel = valueOfFeatreturn classLabel

classify(myTree,labels,(1,0))

'no'

myTree = retrieveTree(1)

#使用pickle模块存储决策树def storeTree(inputTree,filename):import pickle#创建一个可以'写'的文本文件#这里，如果按树中写的'w',将会报错write() argument must be str,not bytes#所以这里改为二进制写入'wb'with open(filename,'wb') as fw:pickle.dump(inputTree,fw) #将inputTree保存到fw中fw.close()def grabTree(filename):import pickle#对应于二进制方式写入数据，'rb'采用二进制形式读出数据fr = open(filename,'rb')return pickle.load(fr) #读取

storeTree(myTree,'classifierStorage.txt')

grabTree('classifierStorage.txt')

{'no surfacing': {0: 'no',1: {'flippers': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}}

fr = open('lenses.txt')lenses = [inst.strip().split('\t') for inst in fr.readlines()]lenseLabels = ['age','prescript','astigmatic','tearRate']lenseTree = createTree(lenses,lenseLabels)lenseTree

bestFeat: 0bestFeatLabel: agefeatValues: ['young', 'young', 'young', 'young', 'young', 'young', 'young', 'young', 'pre', 'pre', 'pre', 'pre', 'pre', 'pre', 'pre', 'pre', 'presbyopic', 'presbyopic', 'presbyopic', 'presbyopic', 'presbyopic', 'presbyopic', 'presbyopic', 'presbyopic']uniqueVals: {'pre', 'presbyopic', 'young'}[['myope', 'no', 'reduced', 'no lenses'], ['myope', 'no', 'normal', 'soft'], ['myope', 'yes', 'reduced', 'no lenses'], ['myope', 'yes', 'normal', 'hard'], ['hyper', 'no', 'reduced', 'no lenses'], ['hyper', 'no', 'normal', 'soft'], ['hyper', 'yes', 'reduced', 'no lenses'], ['hyper', 'yes', 'normal', 'no lenses']]bestFeat: 0bestFeatLabel: prescriptfeatValues: ['myope', 'myope', 'myope', 'myope', 'hyper', 'hyper', 'hyper', 'hyper']uniqueVals: {'hyper', 'myope'}[['no', 'reduced', 'no lenses'], ['no', 'normal', 'soft'], ['yes', 'reduced', 'no lenses'], ['yes', 'normal', 'no lenses']]bestFeat: 0bestFeatLabel: astigmaticfeatValues: ['no', 'no', 'yes', 'yes']uniqueVals: {'yes', 'no'}[['reduced', 'no lenses'], ['normal', 'no lenses']]myTree: {'astigmatic': {'yes': 'no lenses'}}[['reduced', 'no lenses'], ['normal', 'soft']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['soft']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}myTree: {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}myTree: {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}[['no', 'reduced', 'no lenses'], ['no', 'normal', 'soft'], ['yes', 'reduced', 'no lenses'], ['yes', 'normal', 'hard']]bestFeat: 0bestFeatLabel: astigmaticfeatValues: ['no', 'no', 'yes', 'yes']uniqueVals: {'yes', 'no'}[['reduced', 'no lenses'], ['normal', 'hard']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['hard']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}}}[['reduced', 'no lenses'], ['normal', 'soft']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['soft']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}myTree: {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}myTree: {'age': {'pre': {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}}}[['myope', 'no', 'reduced', 'no lenses'], ['myope', 'no', 'normal', 'no lenses'], ['myope', 'yes', 'reduced', 'no lenses'], ['myope', 'yes', 'normal', 'hard'], ['hyper', 'no', 'reduced', 'no lenses'], ['hyper', 'no', 'normal', 'soft'], ['hyper', 'yes', 'reduced', 'no lenses'], ['hyper', 'yes', 'normal', 'no lenses']]bestFeat: 0bestFeatLabel: prescriptfeatValues: ['myope', 'myope', 'myope', 'myope', 'hyper', 'hyper', 'hyper', 'hyper']uniqueVals: {'hyper', 'myope'}[['no', 'reduced', 'no lenses'], ['no', 'normal', 'soft'], ['yes', 'reduced', 'no lenses'], ['yes', 'normal', 'no lenses']]bestFeat: 0bestFeatLabel: astigmaticfeatValues: ['no', 'no', 'yes', 'yes']uniqueVals: {'yes', 'no'}[['reduced', 'no lenses'], ['normal', 'no lenses']]myTree: {'astigmatic': {'yes': 'no lenses'}}[['reduced', 'no lenses'], ['normal', 'soft']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['soft']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}myTree: {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}myTree: {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}[['no', 'reduced', 'no lenses'], ['no', 'normal', 'no lenses'], ['yes', 'reduced', 'no lenses'], ['yes', 'normal', 'hard']]bestFeat: 0bestFeatLabel: astigmaticfeatValues: ['no', 'no', 'yes', 'yes']uniqueVals: {'yes', 'no'}[['reduced', 'no lenses'], ['normal', 'hard']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['hard']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}}}[['reduced', 'no lenses'], ['normal', 'no lenses']]myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': 'no lenses'}}myTree: {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': 'no lenses'}}}}myTree: {'age': {'pre': {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}, 'presbyopic': {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': 'no lenses'}}}}}}[['myope', 'no', 'reduced', 'no lenses'], ['myope', 'no', 'normal', 'soft'], ['myope', 'yes', 'reduced', 'no lenses'], ['myope', 'yes', 'normal', 'hard'], ['hyper', 'no', 'reduced', 'no lenses'], ['hyper', 'no', 'normal', 'soft'], ['hyper', 'yes', 'reduced', 'no lenses'], ['hyper', 'yes', 'normal', 'hard']]bestFeat: 0bestFeatLabel: prescriptfeatValues: ['myope', 'myope', 'myope', 'myope', 'hyper', 'hyper', 'hyper', 'hyper']uniqueVals: {'hyper', 'myope'}[['no', 'reduced', 'no lenses'], ['no', 'normal', 'soft'], ['yes', 'reduced', 'no lenses'], ['yes', 'normal', 'hard']]bestFeat: 0bestFeatLabel: astigmaticfeatValues: ['no', 'no', 'yes', 'yes']uniqueVals: {'yes', 'no'}[['reduced', 'no lenses'], ['normal', 'hard']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['hard']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}}}[['reduced', 'no lenses'], ['normal', 'soft']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['soft']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}myTree: {'prescript': {'hyper': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}[['no', 'reduced', 'no lenses'], ['no', 'normal', 'soft'], ['yes', 'reduced', 'no lenses'], ['yes', 'normal', 'hard']]bestFeat: 0bestFeatLabel: astigmaticfeatValues: ['no', 'no', 'yes', 'yes']uniqueVals: {'yes', 'no'}[['reduced', 'no lenses'], ['normal', 'hard']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['hard']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}}}[['reduced', 'no lenses'], ['normal', 'soft']]bestFeat: 0bestFeatLabel: tearRatefeatValues: ['reduced', 'normal']uniqueVals: {'reduced', 'normal'}[['no lenses']]myTree: {'tearRate': {'reduced': 'no lenses'}}[['soft']]myTree: {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}myTree: {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}myTree: {'prescript': {'hyper': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}myTree: {'age': {'pre': {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}, 'presbyopic': {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses', 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': 'no lenses'}}}}, 'young': {'prescript': {'hyper': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}, 'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses', 'normal': 'hard'}}, 'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}}}

{'age': {'pre': {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses','no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}},'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses','normal': 'hard'}},'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}},'presbyopic': {'prescript': {'hyper': {'astigmatic': {'yes': 'no lenses','no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}},'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses','normal': 'hard'}},'no': 'no lenses'}}}},'young': {'prescript': {'hyper': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses','normal': 'hard'}},'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}},'myope': {'astigmatic': {'yes': {'tearRate': {'reduced': 'no lenses','normal': 'hard'}},'no': {'tearRate': {'reduced': 'no lenses', 'normal': 'soft'}}}}}}}}

createPlot(lenseTree)

c: (0.5, 1.0)d: 0.75c: (0.16666666666666666, 0.75)d: 0.5c: (0.07142857142857142, 0.5)d: 0.25e: 0.023809523809523808c: (0.09523809523809523, 0.25)d: 0.0e: 0.07142857142857142e: 0.11904761904761904f: 0.25f: 0.5c: (0.23809523809523808, 0.5)d: 0.25c: (0.19047619047619047, 0.25)d: 0.0e: 0.16666666666666666e: 0.21428571428571427f: 0.25c: (0.2857142857142857, 0.25)d: 0.0e: 0.26190476190476186e: 0.3095238095238095f: 0.25f: 0.5f: 0.75c: (0.47619047619047616, 0.75)d: 0.5c: (0.4047619047619047, 0.5)d: 0.25e: 0.3571428571428571c: (0.4285714285714285, 0.25)d: 0.0e: 0.4047619047619047e: 0.45238095238095233f: 0.25f: 0.5c: (0.5476190476190476, 0.5)d: 0.25c: (0.5238095238095237, 0.25)d: 0.0e: 0.49999999999999994e: 0.5476190476190476f: 0.25e: 0.5952380952380951f: 0.5f: 0.75c: (0.8095238095238094, 0.75)d: 0.5c: (0.7142857142857142, 0.5)d: 0.25c: (0.6666666666666665, 0.25)d: 0.0e: 0.6428571428571428e: 0.6904761904761905f: 0.25c: (0.7619047619047619, 0.25)d: 0.0e: 0.7380952380952381e: 0.7857142857142858f: 0.25f: 0.5c: (0.9047619047619049, 0.5)d: 0.25c: (0.8571428571428572, 0.25)d: 0.0e: 0.8333333333333335e: 0.8809523809523812f: 0.25c: (0.9523809523809526, 0.25)d: 0.0e: 0.9285714285714288e: 0.9761904761904765f: 0.25f: 0.5f: 0.75f: 1.0