題目要求：根據訓練數據集，利用信息增益比（C4.5算法）生成決策樹。
信息增益比算法是id3算法的改進：
信息增益比的定義：
補充：信息增益計算方式:
代碼實現（機器學習實戰的改編，保存爲tree.py）：
from math import log
import operator
def createDataSet():
dataSet = [1,0,0,1,0],\
[1,0,0,2,0],\
[1,1,0,2,1],\
[1,1,1,1,1],\
[1,0,0,1,0],\
[2,0,0,1,0],\
[2,0,0,2,0],\
[2,1,1,2,1],\
[2,0,1,3,1],\
[2,0,1,3,1],\
[3,0,1,3,1],\
[3,0,1,2,1],\
[3,1,0,2,1],\
[3,1,0,3,1],\
[3,0,0,1,0]
labels = ['age','job','house','creadit']
return dataSet, labels
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 = 0.0
for key in labelCounts:
prob = float(labelCounts[key]) / numEntries
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 = len(dataSet[0]) - 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) / baseEntropy
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.iteritems(), 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)
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調用方式：
import tree
mydat,mylab = tree.createDataSet()
mytree = tree.createTree(mydat,mylab)
print mytree
