决策树算法

简介: 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

决策树的一般流程

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