本文實(shí)例講述了基于Python實(shí)現(xiàn)的ID3決策樹(shù)功能。分享給大家供大家參考，具體如下：

ID3算法是決策樹(shù)的一種，它是基于奧卡姆剃刀原理的，即用盡量用較少的東西做更多的事。ID3算法，即Iterative Dichotomiser 3，迭代二叉樹(shù)3代，是Ross Quinlan發(fā)明的一種決策樹(shù)算法，這個(gè)算法的基礎(chǔ)就是上面提到的奧卡姆剃刀原理，越是小型的決策樹(shù)越優(yōu)于大的決策樹(shù)，盡管如此，也不總是生成最小的樹(shù)型結(jié)構(gòu)，而是一個(gè)啟發(fā)式算法。

如下示例是一個(gè)判斷海洋生物數(shù)據(jù)是否是魚(yú)類而構(gòu)建的基于ID3思想的決策樹(shù)

# coding=utf-8import operatorfrom math import logimport timedef createDataSet():  dataSet = [[1, 1, 'yes'],        [1, 1, 'yes'],        [1, 0, 'no'],        [0, 1, 'no'],        [0, 1, 'no'],        [0,0,'maybe']]  labels = ['no surfaceing', 'flippers']  return dataSet, labels# 計(jì)算香農(nóng)熵def calcShannonEnt(dataSet):  numEntries = len(dataSet)  labelCounts = {}  for feaVec in dataSet:    currentLabel = feaVec[-1]    if currentLabel not in labelCounts:      labelCounts[currentLabel] = 0    labelCounts[currentLabel] += 1  shannonEnt = 0.0  for key in labelCounts:    prob = float(labelCounts[key]) / numEntries    shannonEnt -= prob * log(prob, 2)  return shannonEntdef 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 retDataSetdef chooseBestFeatureToSplit(dataSet):  numFeatures = len(dataSet[0]) - 1 # 因?yàn)閿?shù)據(jù)集的最后一項(xiàng)是標(biāo)簽  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# 因?yàn)槲覀冞f歸構(gòu)建決策樹(shù)是根據(jù)屬性的消耗進(jìn)行計(jì)算的，所以可能會(huì)存在最后屬性用完了，但是分類# 還是沒(méi)有算完，這時(shí)候就會(huì)采用多數(shù)表決的方式計(jì)算節(jié)點(diǎn)分類def majorityCnt(classList):  classCount = {}  for vote in classList:    if vote not in classCount.keys():      classCount[vote] = 0    classCount[vote] += 1  return max(classCount)def createTree(dataSet, labels):  classList = [example[-1] for example in dataSet]  if classList.count(classList[0]) == len(classList): # 類別相同則停止劃分    return classList[0]  if len(dataSet[0]) == 1: # 所有特征已經(jīng)用完    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[:] # 為了不改變?cè)剂斜淼膬?nèi)容復(fù)制了一下    myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet,                                bestFeat, value), subLabels)  return myTreedef main():  data, label = createDataSet()  t1 = time.clock()  myTree = createTree(data, label)  t2 = time.clock()  print myTree  print 'execute for ', t2 - t1if __name__ == '__main__':  main()