决策树ID3算法

最新推荐文章于 2022-02-21 21:03:31 发布

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本文详细介绍如何从零开始构建决策树模型。首先介绍了数据预处理、离散化等准备工作，然后重点讲解了通过计算香农熵来评估数据集的不确定性，并以此为基础选择最佳划分特征。最后，通过递归构造决策树直至满足停止条件。

一、构造决策树步骤：

1.数据准备

数据离散化

2.划分数据

计算数据集香农熵
计算特征值信息增量，最大的为最好划分

3.递归构造决策树

二、代码模块

1.计算香农熵：

def calcShannonEnt(dataSet):
    numEntries = len(dataSet)
    labelCounts = {}
    for featVec in dataSet: #the the number of unique elements and their occurance
        currentLabel = featVec[-1]
        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
        labelCounts[currentLabel] += 1
    shannonEnt = 0.0
    for key in labelCounts:#公式：H=-∑（n）（i-1）p(xi)log2p(xi)
        prob = float(labelCounts[key])/numEntries #选择该分类概率p(xi)
        shannonEnt -= prob * log(prob,2) #log base 2
    return shannonEnt

2.划分数据集（按给定特征值划分）

def splitDataSet(dataSet, axis, value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

3.选择最好的数据集划分方式

选取特征值
划分数据
计算最好的划分数据特征

def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0; bestFeature = -1
    for i in range(numFeatures):        #iterate over all the features
        featList = [example[i] for example in dataSet]#create a list of all the examples of this feature
        uniqueVals = set(featList)       #get a set of unique values
        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     #calculate the info gain; ie reduction in entropy
        if (infoGain > bestInfoGain):       #compare this to the best gain so far
            bestInfoGain = infoGain         #if better than current best, set to best
            bestFeature = i
    return bestFeature                      #returns an integer

4.递归构造决策树

递归退出条件：

所有的类标签完全相同，直接返回该类标签
使用完了所有特征，但是还是不能将数据集划分成只包含唯一类别的分组（返回值:挑出出现次数最多的类别）

def createTree(dataSet,labels):
    classList = [example[-1] for example in dataSet] #all labels
    if classList.count(classList[0]) == len(classList): 
        return classList[0]#stop splitting when all of the classes are equal
    if len(dataSet[0]) == 1: #stop splitting when there are no more features in dataSet
        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[:]       #copy all of labels, so trees don't mess up existing labels
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
    return myTree