解决策树如何预测患者需要佩戴的隐形眼镜类型。使用小数据
集，我们就可以利用决策树学到很多知识：眼科医生是如何判断患者需要佩戴的镜片类型；一旦
理解了决策树的工作原理，我们甚至也可以帮助人们判断需要佩戴的镜片类型。

隐 形 眼 镜 数 据 集 是 非 常 著 名 的 数 据 集 ，它 包 含 很 多 患 者 眼 部 状 况 的 观 察 条 件 以 及 医 生 推 荐 的
隐 形 眼 镜 类 型 。隐 形 眼 镜 类 型 包 括 硬 材 质 、软 材 质 以 及 不 适 合 佩 戴 隐 形 眼 镜 。数 据 来 源 于UCI 数 据
库。

import numpy as np
import operator as op
from math import log

def calcShannonEnt(dataSet):
labelCounts = {}
for featVec in dataSet:
currentLabel = featVec[-1]
if(currentLabel not in labelCounts.keys()):
labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
shannonEnt = 0.0
rowNum = len(dataSet)
for key in labelCounts:
prob = float(labelCounts[key])/rowNum
shannonEnt -= prob * log(prob,2)
return shannonEnt

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

def chooseBestFeatureToSplit(dataSet):
numFeatures = np.shape(dataSet)[1]-1
baseEntropy = calcShannonEnt(dataSet)
bestInfoGain = 0.0
bestFeature = -1
for i in range(numFeatures):
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.items(), key=op.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)
bestFeatLabel = labels[bestFeat]
myTree = {bestFeatLabel:{}}
del(labels[bestFeat])
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

def classify(inputTree,featLabels,testVec):
for i in inputTree.keys():
firstStr = i
break
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

data = open("F:\\machinelearninginaction\\Ch03\\lenses.txt")
dataSet = [inst.strip().split("\t") for inst in data.readlines()]
print(dataSet)
print(np.shape(dataSet))
labels = ["age","prescript","astigmatic","tearRate"]
tree = createTree(dataSet,labels)
print(tree)

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):
numLeafs = 0
for i in myTree.keys():
firstStr = i
break
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
for i in myTree.keys():
firstStr = i
break
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 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 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):
numLeafs = getNumLeafs(myTree)
depth = getTreeDepth(myTree)
for i in myTree.keys():
firstStr = i
break
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':
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)
#createPlot.ax1 = plt.subplot(111, frameon=False) #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()

createPlot(tree)

可 以 发 现 ，医 生 最 多 需 要 问 四 个 问 题 就 能 确 定 患 者 需 要 佩 戴 哪 种 类 型 的 隐 形 眼 镜 。

小结：