机器学习实战 决策树(附数据集)
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 log
def 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] = 0
labelCounts[currentLabel] += 1
shannonEnv = 0.0
for 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])-1
baseEntropy = caclShannonEnt(dataSet)
bestInfoGain = 0.0
bestFeature = -1
for i in range(numFeatures):
# print('i:',i)
featList = [example[i] for example in dataSet]
# print(featList)
uniqueVals = set(featList)
# print(uniqueVals)
newEntropy = 0.0
for 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 - newEntropy
bestFeature = i
return bestFeature
chooseBestFeatureToSplit(myDat)
0
1.1.3 递归构建决策树
# 多数表决
import operator
def majorityCnt(classList):
classCount = {}
for vote in classCount:
if vote not in classCount.keys():
classCount[vote] = 0
classCount[vote] += 1
sortedClassCount = 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: 0
bestFeatLabel: no surfacing
featValues: [1, 1, 1, 0, 0]
uniqueVals: {0, 1}
[[1, 'no'], [1, 'no']]
myTree: {'no surfacing': {0: 'no'}}
[[1, 'maybe'], [1, 'yes'], [0, 'no']]
bestFeat: 0
bestFeatLabel: flippers
featValues: [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 plt
decisionNode = 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 = 0
firstStr = list(myTree.keys())[0]
secondDict = myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]).__name__ == 'dict':
numNode += getNumLeafs(secondDict[key])
else:
numNode += 1
return numNode
getNumLeafs(myTree)
3
#获取决策树的深度
def getTreeDepth(myTree):
maxDepth = 0
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
return 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.totalD
print('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.totalw
print('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.totalD
print('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.totalw
plotTree.yOff = 1.0
plotTree(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: 0.5
e: 0.16666666666666666
c: (0.6666666666666666, 0.5)
d: 0.0
e: 0.5
e: 0.8333333333333333
f: 0.5
f: 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 = valueOfFeat
return 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: 0
bestFeatLabel: age
featValues: ['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: 0
bestFeatLabel: prescript
featValues: ['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: 0
bestFeatLabel: astigmatic
featValues: ['no', 'no', 'yes', 'yes']
uniqueVals: {'yes', 'no'}
[['reduced', 'no lenses'], ['normal', 'no lenses']]
myTree: {'astigmatic': {'yes': 'no lenses'}}
[['reduced', 'no lenses'], ['normal', 'soft']]
bestFeat: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: astigmatic
featValues: ['no', 'no', 'yes', 'yes']
uniqueVals: {'yes', 'no'}
[['reduced', 'no lenses'], ['normal', 'hard']]
bestFeat: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: prescript
featValues: ['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: 0
bestFeatLabel: astigmatic
featValues: ['no', 'no', 'yes', 'yes']
uniqueVals: {'yes', 'no'}
[['reduced', 'no lenses'], ['normal', 'no lenses']]
myTree: {'astigmatic': {'yes': 'no lenses'}}
[['reduced', 'no lenses'], ['normal', 'soft']]
bestFeat: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: astigmatic
featValues: ['no', 'no', 'yes', 'yes']
uniqueVals: {'yes', 'no'}
[['reduced', 'no lenses'], ['normal', 'hard']]
bestFeat: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: prescript
featValues: ['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: 0
bestFeatLabel: astigmatic
featValues: ['no', 'no', 'yes', 'yes']
uniqueVals: {'yes', 'no'}
[['reduced', 'no lenses'], ['normal', 'hard']]
bestFeat: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: astigmatic
featValues: ['no', 'no', 'yes', 'yes']
uniqueVals: {'yes', 'no'}
[['reduced', 'no lenses'], ['normal', 'hard']]
bestFeat: 0
bestFeatLabel: tearRate
featValues: ['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: 0
bestFeatLabel: tearRate
featValues: ['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: 0.75
c: (0.16666666666666666, 0.75)
d: 0.5
c: (0.07142857142857142, 0.5)
d: 0.25
e: 0.023809523809523808
c: (0.09523809523809523, 0.25)
d: 0.0
e: 0.07142857142857142
e: 0.11904761904761904
f: 0.25
f: 0.5
c: (0.23809523809523808, 0.5)
d: 0.25
c: (0.19047619047619047, 0.25)
d: 0.0
e: 0.16666666666666666
e: 0.21428571428571427
f: 0.25
c: (0.2857142857142857, 0.25)
d: 0.0
e: 0.26190476190476186
e: 0.3095238095238095
f: 0.25
f: 0.5
f: 0.75
c: (0.47619047619047616, 0.75)
d: 0.5
c: (0.4047619047619047, 0.5)
d: 0.25
e: 0.3571428571428571
c: (0.4285714285714285, 0.25)
d: 0.0
e: 0.4047619047619047
e: 0.45238095238095233
f: 0.25
f: 0.5
c: (0.5476190476190476, 0.5)
d: 0.25
c: (0.5238095238095237, 0.25)
d: 0.0
e: 0.49999999999999994
e: 0.5476190476190476
f: 0.25
e: 0.5952380952380951
f: 0.5
f: 0.75
c: (0.8095238095238094, 0.75)
d: 0.5
c: (0.7142857142857142, 0.5)
d: 0.25
c: (0.6666666666666665, 0.25)
d: 0.0
e: 0.6428571428571428
e: 0.6904761904761905
f: 0.25
c: (0.7619047619047619, 0.25)
d: 0.0
e: 0.7380952380952381
e: 0.7857142857142858
f: 0.25
f: 0.5
c: (0.9047619047619049, 0.5)
d: 0.25
c: (0.8571428571428572, 0.25)
d: 0.0
e: 0.8333333333333335
e: 0.8809523809523812
f: 0.25
c: (0.9523809523809526, 0.25)
d: 0.0
e: 0.9285714285714288
e: 0.9761904761904765
f: 0.25
f: 0.5
f: 0.75
f: 1.0
