python編寫分類決策樹的代碼

決策樹通常在機器學習中用于分類。

優(yōu)點：計算復雜度不高，輸出結果易于理解，對中間值缺失不敏感，可以處理不相關特征數據。
缺點：可能會產生過度匹配問題。
適用數據類型：數值型和標稱型。

1.信息增益

劃分數據集的目的是：將無序的數據變得更加有序。組織雜亂無章數據的一種方法就是使用信息論度量信息。通常采用信息增益，信息增益是指數據劃分前后信息熵的減少值。信息越無序信息熵越大，獲得信息增益最高的特征就是最好的選擇。
熵定義為信息的期望，符號xi的信息定義為：

其中p(xi)為該分類的概率。
熵，即信息的期望值為：

計算信息熵的代碼如下：

def calcShannonEnt(dataSet):
  numEntries = len(dataSet)
  labelCounts = {}
  for featVec in dataSet:
    currentLabel = featVec[-1]
    if currentLabel not in labelCounts:
      labelCounts[currentLabel] = 0
    labelCounts[currentLabel] += 1
  shannonEnt = 0
  for key in labelCounts:
    shannonEnt = shannonEnt - (labelCounts[key]/numEntries)*math.log2(labelCounts[key]/numEntries)
  return shannonEnt

可以根據信息熵，按照獲取最大信息增益的方法劃分數據集。

2.劃分數據集

劃分數據集就是將所有符合要求的元素抽出來。    
def splitDataSet(dataSet,axis,value):
  retDataset = []
  for featVec in dataSet:
    if featVec[axis] == value:
      newVec = featVec[:axis]
      newVec.extend(featVec[axis+1:])
      retDataset.append(newVec)
  return retDataset

3.選擇最好的數據集劃分方式

信息增益是熵的減少或者是信息無序度的減少。    
def chooseBestFeatureToSplit(dataSet):
  numFeatures = len(dataSet[0]) - 1
  bestInfoGain = 0
  bestFeature = -1
  baseEntropy = calcShannonEnt(dataSet)
  for i in range(numFeatures):
    allValue = [example[i] for example in dataSet]#列表推倒，創(chuàng)建新的列表
    allValue = set(allValue)#最快得到列表中唯一元素值的方法
    newEntropy = 0
    for value in allValue:
      splitset = splitDataSet(dataSet,i,value)
      newEntropy = newEntropy + len(splitset)/len(dataSet)*calcShannonEnt(splitset)
    infoGain = baseEntropy - newEntropy
    if infoGain > bestInfoGain:
      bestInfoGain = infoGain
      bestFeature = i
  return bestFeature

4.遞歸創(chuàng)建決策樹

結束條件為：程序遍歷完所有劃分數據集的屬性，或每個分支下的所有實例都具有相同的分類。
當數據集已經處理了所有屬性，但是類標簽還不唯一時，采用多數表決的方式決定葉子節(jié)點的類型。    
def majorityCnt(classList):
 classCount = {}
 for value in classList:
  if value not in classCount: classCount[value] = 0
  classCount[value] += 1
 classCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)
 return classCount[0][0]

生成決策樹：    
def createTree(dataSet,labels):
 classList = [example[-1] for example in dataSet]
 labelsCopy = labels[:]
 if classList.count(classList[0]) == len(classList):
  return classList[0]
 if len(dataSet[0]) == 1:
  return majorityCnt(classList)
 bestFeature = chooseBestFeatureToSplit(dataSet)
 bestLabel = labelsCopy[bestFeature]
 myTree = {bestLabel:{}}
 featureValues = [example[bestFeature] for example in dataSet]
 featureValues = set(featureValues)
 del(labelsCopy[bestFeature])
 for value in featureValues:
  subLabels = labelsCopy[:]
  myTree[bestLabel][value] = createTree(splitDataSet(dataSet,bestFeature,value),subLabels)
 return myTree

5.測試算法——使用決策樹分類

同樣采用遞歸的方式得到分類結果。    
def classify(inputTree,featLabels,testVec):
 currentFeat = list(inputTree.keys())[0]
 secondTree = inputTree[currentFeat]
 try:
  featureIndex = featLabels.index(currentFeat)
 except ValueError as err:
  print('yes')
 try:
  for value in secondTree.keys():
   if value == testVec[featureIndex]:
    if type(secondTree[value]).__name__ == 'dict':
     classLabel = classify(secondTree[value],featLabels,testVec)
    else:
     classLabel = secondTree[value]
  return classLabel
 except AttributeError:
  print(secondTree)
6.完整代碼如下    
import numpy as np
import math
import operator
def createDataSet():
 dataSet = [[1,1,'yes'],
    [1,1,'yes'],
    [1,0,'no'],
    [0,1,'no'],
    [0,1,'no'],]
 label = ['no surfacing','flippers']
 return dataSet,label
 
def calcShannonEnt(dataSet):
 numEntries = len(dataSet)
 labelCounts = {}
 for featVec in dataSet:
  currentLabel = featVec[-1]
  if currentLabel not in labelCounts:
   labelCounts[currentLabel] = 0
  labelCounts[currentLabel] += 1
 shannonEnt = 0
 for key in labelCounts:
  shannonEnt = shannonEnt - (labelCounts[key]/numEntries)*math.log2(labelCounts[key]/numEntries)
 return shannonEnt
 
 
def splitDataSet(dataSet,axis,value):
 retDataset = []
 for featVec in dataSet:
  if featVec[axis] == value:
   newVec = featVec[:axis]
   newVec.extend(featVec[axis+1:])
   retDataset.append(newVec)
 return retDataset
 
def chooseBestFeatureToSplit(dataSet):
 numFeatures = len(dataSet[0]) - 1
 bestInfoGain = 0
 bestFeature = -1
 baseEntropy = calcShannonEnt(dataSet)
 for i in range(numFeatures):
  allValue = [example[i] for example in dataSet]
  allValue = set(allValue)
  newEntropy = 0
  for value in allValue:
   splitset = splitDataSet(dataSet,i,value)
   newEntropy = newEntropy + len(splitset)/len(dataSet)*calcShannonEnt(splitset)
  infoGain = baseEntropy - newEntropy
  if infoGain > bestInfoGain:
   bestInfoGain = infoGain
   bestFeature = i
 return bestFeature
 
def majorityCnt(classList):
 classCount = {}
 for value in classList:
  if value not in classCount: classCount[value] = 0
  classCount[value] += 1
 classCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)
 return classCount[0][0]   
 
def createTree(dataSet,labels):
 classList = [example[-1] for example in dataSet]
 labelsCopy = labels[:]
 if classList.count(classList[0]) == len(classList):
  return classList[0]
 if len(dataSet[0]) == 1:
  return majorityCnt(classList)
 bestFeature = chooseBestFeatureToSplit(dataSet)
 bestLabel = labelsCopy[bestFeature]
 myTree = {bestLabel:{}}
 featureValues = [example[bestFeature] for example in dataSet]
 featureValues = set(featureValues)
 del(labelsCopy[bestFeature])
 for value in featureValues:
  subLabels = labelsCopy[:]
  myTree[bestLabel][value] = createTree(splitDataSet(dataSet,bestFeature,value),subLabels)
 return myTree
 
 
def classify(inputTree,featLabels,testVec):
 currentFeat = list(inputTree.keys())[0]
 secondTree = inputTree[currentFeat]
 try:
  featureIndex = featLabels.index(currentFeat)
 except ValueError as err:
  print('yes')
 try:
  for value in secondTree.keys():
   if value == testVec[featureIndex]:
    if type(secondTree[value]).__name__ == 'dict':
     classLabel = classify(secondTree[value],featLabels,testVec)
    else:
     classLabel = secondTree[value]
  return classLabel
 except AttributeError:
  print(secondTree)
 
if __name__ == "__main__":
 dataset,label = createDataSet()
 myTree = createTree(dataset,label)
 a = [1,1]
 print(classify(myTree,label,a))

7.編程技巧

extend與append的區(qū)別    
newVec.extend(featVec[axis+1:])
retDataset.append(newVec)

extend([])，是將列表中的每個元素依次加入新列表中
append()是將括號中的內容當做一項加入到新列表中

列表推到

創(chuàng)建新列表的方式    
allValue = [example[i] for example in dataSet]

提取列表中唯一的元素    
allValue = set(allValue)

列表/元組排序,sorted()函數    
classCount = sorted(classCount.items(),key=operator.itemgetter(1),reverse=True)

列表的復制    
labelsCopy = labels[:]
以上就是本文的全部內容，希望對大家的學習有所幫助.