决策树(ID3)

1信息增益

    划分数据的最大原则就是:将无序的数据变得更加有序。
    在划分数据集之前之后信息发生的变化称为信息增益,通过计算每个特征值划分数据集获得的信息增益,获得信息增益最高的特征就是最好的选择。
    度量集合信息的方式简称为熵。另一个度量集合无序程度的方法是基尼不纯度。

计算信息熵的代码实现
from math import log


def calShannonEnt(dataSet):
    '''
    计算给定数据集的熵
    :param dataSet:
    :return:
    '''
    numEntries = len(dataSet)
    labelCounts = {}
    # 为所有可能分类创建字典
    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  # 使用标签出现的频率计算类别出现的概率
        shannonEnt -= prob * log(prob, 2)  # 以2为底求对数
    return shannonEnt

    PS:熵定义为信息的期望值,

        如果待分类的事务可能划分在多个分类之中,则符合xi的信息的定义为:
                     其中p(xi)是选择该分类的概率。

        为了计算熵,我们需要计算所有类别所有可能值包含的信息期望,通过下面的公式得到:
                     其中n是分类的数目。

创建数据集
def createDataSet():
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing', 'flippers']
    return dataSet, labels

2划分数据集

按照给定特征划分数据集
def splitDataSet(dataSet, axis, value):
    '''
    :param dataSet:待划分的数据集
    :param axis: 划分数据集的特征
    :param value: 特征的返回值
    :return:
    '''
    retDateSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis + 1:])  # extend 合并列表方法 例:[1,2,3].extend([5,6,7]) => [1,2,3,4,5,6]
            retDateSet.append(reducedFeatVec)
    return retDateSet
选择最好的数据集划分方式
def chooseBestFeatureToSplit(dataSet):
    '''
    实现选取特征,划分数据集
    :param dataSet:
    :return: 最佳特征的index,用于划分数据集的特征
    '''
    numFeatures = len(dataSet[0]) - 1
    baseEntropy = calcShannonEnt(dataSet)  # 整个数据集的原始熵
    bestInfoGain, bestFeature = 0.0, -1
    for i in range(numFeatures):
        # 创建唯一的分类标签列表
        featList = [example[i] for example in dataSet]
        uniqueVals = set(featList)
        newEntropy = 0.0
        # 计算每种划分方式的信息熵
        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:
            # 计算最好的信息增益
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature

3递归构建决策树

多数表决方法决定叶子节点的分类
def majorityCnt(classList):
    '''
    :param classList: 分类名称列表
    :return:出现次数最多的分类名称
    '''
    classCount = {}
    for vote in classList:
        if vote not in classCount.keys(): classCount[vote] = 0
        classCount[vote] += 1
    sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]
创建树的函数代码
def createTree(dataSet, labels):
    '''
    :param dataSet:数据集
    :param labels: 标签列表(数据集中所有特征的标签)
    :return:
    '''
    classList = [example[-1] for example in dataSet]  # 数据集中所有类标签
    # 类别完全相同则停止继续划分
    if classList.count(classList[0]) == len(classList):
        return classList[0]
    # 遍历完所有特征时返回出现次数最多的
    if len(dataSet[0]) == 1:
        return majorityCnt(classList)
    bestFeat = chooseBestFeatureToSplit(dataSet)  # 最好特征
    bestFeatLabel = labels[bestFeat]
    myTree = {bestFeatLabel: {}}
    # 得到列表包含的所有属性值
    del labels[bestFeat]
    featVlaues = [example[bestFeat] for example in dataSet]
    uniqueVals = set(featVlaues)
    for value in uniqueVals:
        subLabels = labels[:]
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels)  # 递归调用createTree
    return myTree


if __name__ == '__main__':
    myData, labels = createDataSet()
    res = createTree(myData, labels)
    print(res)
    '''
    {'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}
    '''

4使用决策树执行分类

def classify(inputTree, featLabels, testVec):
    '''
    使用决策树的分类函数
    :param inputTree:
    :param featLabels:
    :param testVec:
    :return:
    '''
    firstStr = list(inputTree.keys())[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)  # 将标签字符串转换为索引
    for key in secondDict.keys():
        if testVec[featIndex] == key:
            if type(secondDict[key]).__name__ == 'dict':
                classLabel = classify(secondDict[key], featLabels, testVec)
            else:
                classLabel = secondDict[key]
    return classLabel

if __name__ == '__main__':
    myData, labels = trees.createDataSet()
    print(labels)
    myTree = trees.createTree(myData, labels.copy())  # 浅拷贝,否则labels会被修改
    print(myTree)
    print(trees.classify(myTree, labels, [1, 0]))
    print(trees.classify(myTree, labels, [1, 1]))

5决策树的存储,如何在硬盘上存储决策树分类器

# 使用pickles模块存储决策树
def storeTree(inputTree, filename):
    import pickle
    fw = open(filename, 'wb')
    pickle.dump(inputTree, fw)
    fw.close()


def grabTree(filename):
    import pickle
    fr = open(filename, 'rb')
    return pickle.load(fr)

if __name__ == '__main__':
    myData, labels = trees.createDataSet()
    myTree = trees.createTree(myData, labels.copy())
    trees.storeTree(myTree, 'classifierStorage.txt')
    res = trees.grabTree('classifierStorage.txt')
    print(res)
posted @ 2020-06-11 17:11  六神酱  阅读(333)  评论(0编辑  收藏  举报