决策树算法

谷歌笔记本（可选）

from google.colab import drive
drive.mount("/content/drive")
output

Mounted at /content/drive

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：可能产生过度匹配的问题
• 适用数据类型：数值型和标称型

（1）收集数据

（2）准备数据

（3）分析数据

（4）训练算法

（5）测试算法

（6）使用算法

信息增益

# 计算给定数据集的香农熵
from math import log
def calcShannonEnt(dataSet):
numEntries = len(dataSet)
labelCounts = {}
for featVec in dataSet:
currentLabel = featVec[-1]
if currentLabel not in labelCounts.keys():
labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
shannonEnt = 0
for key in labelCounts:
prob = float(labelCounts[key]) / numEntries
shannonEnt -= prob * log(prob, 2)
return shannonEnt
def createDataSet():
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 = createDataSet()
myDat, labels
output

([[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']],
['no surfacing', 'flippers'])
calcShannonEnt(myDat)
output
0.9709505944546686
myDat[0][-1] = 'maybe'
myDat

划分数据集

# 按照给定特征划分数据集
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
myDat, labels = createDataSet()
splitDataSet(myDat, 0, 1)

output

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

myDat, labels = createDataSet()
calcShannonEnt(myDat)

output

0.9709505944546686

# 选择最好的数据集划分方式
def chooseBestFeatureToSplit(dataSet):
numFeatures = len(dataSet[0]) - 1   # 2
baseEntropy = calcShannonEnt(dataSet)  # 0.9709505944546686
bestInfoGain = 0
bestFeature = -1
for i in range(numFeatures):
featList = [example[i] for example in dataSet]
uniqueVals = set(featList)
newEntropy = 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
chooseBestFeatureToSplit(myDat)

output

0

递归构建决策树

import operator

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=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]
# 创建树的代码
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
myDat, labels = createDataSet()
myTree = createTree(myDat, labels)
myTree

output

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

使用Matplotlib注解绘制树形图

Matplotlib注解

# 使用文本注解绘制树节点
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings("ignore")
decisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
arrow_args = dict(arrowstyle="<-")
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 createPlot():
fig = plt.figure(1, facecolor='white')
fig.clf()
createPlot.ax1 = plt.subplot(111, frameon=False)
plotNode('leaf01', (0.5, 0.1), (0.1, 0.5), decisionNode)
plotNode('leaf02', (0.8, 0.1), (0.3, 0.8), leafNode)
plt.show()
createPlot()

output

构造注解树

# 获取叶节点的数目
def getNumLeafs(myTree):
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 numLeafs
# 获取树的层数
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
if thisDepth > maxDepth:
maxDepth = thisDepth
return maxDepth
def retrieveTree(i):
listOfTrees = [{'no surfacing': {0:'no', 1:{'flippers':{0:'no',1:'yes'}}}},
return listOfTrees[i]
retrieveTree(1)

output

{'no surfacing': {0: 'no',

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

myTree = retrieveTree(0)
getNumLeafs(myTree)

output

3

getTreeDepth(myTree)

output

2

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)
firstStr = list(myTree.keys())[0]
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)
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()
myTree = retrieveTree(0)
createPlot(myTree)

output

myTree['no surfacing'][2] = 'maybe'
myTree

output

{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}, 2: 'maybe'}}

createPlot(myTree)

output

测试和存储分类器

测试算法：使用决策树执行分类

# 使用决策树的分类函数
def classify(inputTree, featLabels, testVec):
firstStr = list(inputTree.keys())[0]
secondDict = inputTree[firstStr]
featIndex = featLabels.index(firstStr)
for key in secondDict.keys():
if testVec[featIndex] == key:
if type(secondDict[key]).__name__ == 'dict':
classLabel = classify(secondDict[key], featLabels, testVec)
else:
classLabel = secondDict[key]
return classLabel
myDat, labels = createDataSet()
myTree = retrieveTree(0)
classify(myTree, labels, [1,0])

output

'no'

classify(myTree, labels, [1,1])

output

'yes'

使用算法：决策树的存储

# 使用pickle模块存储决策树
def storeTree(inputTree,filename):
import pickle
fw = open(filename,'wb')
pickle.dump(inputTree,fw)
fw.close()

def grabTree(filename):
import pickle
fr = open(filename, 'rb')
return pickle.load(fr)
myTree

output

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

storeTree(myTree, 'classifierStorage.txt')

grabTree('classifierStorage.txt')

output

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

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