机器学习算法-决策树（续）Python实现

决策树算法的理论部分参考：决策树理论

决策树算法实现一共分为以下几个部分：

• 加载数据集部分
• 熵的计算
• 按照给定特征划分数据集
• 根据信息增益的最大值的属性作为划分属性
• 递归构建决策树
• 样本的分类

创建分支节点伪代码函数createBranch()如下所示：

检测数据集的每个子项是否属于同一类：    if so return 类标签;    else        寻找划分数据集的最好特征        划分数据集        创建分支节点            for 每个分支节点                调用函数createBranch并增加返回结果到分支节点中        return 分支节点 

下面来介绍每个部分如何实现。

1.加载数据

创建一个构造数据集的函数，所有的代码均写在一个py文件里面。

def createDataSet():    dataSet = [[1, 1, 'yes'],               [1, 1, 'yes'],               [1, 0, 'no'],               [0, 1, 'no'],               [0, 1, 'no']]    labels = ['no surfacing','flippers']   #the label of each feature    #change to discrete values    return dataSet, labels

2.计算给定数据集的香农熵

def calcShannonEnt(dataSet):    n = len(dataSet) #calculate the size of dataset    labelCounts = {}    # create dictionary "count"     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:        prob = float(labelCounts[key])/n #notice transfering to float first          shannonEnt -= prob * log(prob,2) #log base 2    return shannonEnt

3.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]     #chop out axis used for splitting            reducedFeatVec.extend(featVec[axis+1:])            retDataSet.append(reducedFeatVec)    return retDataSet

可以根据这个来统计出某个特征的正样本和负样本的个数。

4.选择最好的数据集划分方式

计算出每种特征的信息增益值，然后选择出信息增益最大的作为划分属性。

def chooseBestFeatureToSplit(dataSet):    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels    baseEntropy = calcShannonEnt(dataSet)  #calculate the info of 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:         # calculate the info of each feature            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

这个函数会返回一个最佳的特征，作为划分的特征。下面根据这个特征来构建数，然后再迭代计算信息增益，获得新的特征，进行新的划分。

选择出最好的划分特征。

5.递归构建树

创建树的函数代码

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]#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  

6.执行数据分类

使用决策树的分类函数

def classify(inputTree,featLabels,testVec):    firstStr = inputTree.keys()[0]    secondDict = inputTree[firstStr]    featIndex = featLabels.index(firstStr)    key = testVec[featIndex]    valueOfFeat = secondDict[key]    if isinstance(valueOfFeat, dict):         classLabel = classify(valueOfFeat, featLabels, testVec)    else: classLabel = valueOfFeat    return classLabel

测试

附件：决策树源码

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