机器学习-决策树-蒲公英云

机器学习-决策树

此文章是《Machine Learning in Action》中决策树章节的学习笔记，
决策树可以使用不熟悉的数据集合，并从中提取出一系列规则，在这些机器根据数据集创建规则时，就是机器学习的过程。

优点：计算复杂度不高，输出结果易于理解，对中间值的缺失不敏感，可以处理不相关特征数据
缺点：可能会产生过度匹配问题
适用数据类型：数值型和标称型

1 香农熵
香农熵百度百科,信息量的度量就等于不确定性的多少。变量的不确定性越大，熵也就越大，把它搞清楚所需要的信息量也就越大。

# -*- coding: utf-8 -*-
''' Created on 2018年02月21日 @author: dzm '''
from math import log
def createDataSet():
    ''' 数据集， 第一列 不浮出水面是否可以生存 第二列 是否有脚蹼 第三列 属于鱼类 :return: '''
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing','flippers']
    #change to discrete values
    return dataSet, labels
def calcShannonEnt(dataSet):
    ''' 计算香农熵 :param dataSet: :return: '''
    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:
        # 计算分类的概率
        prob = float(labelCounts[key])/numEntries
        # 计算香农熵
        shannonEnt -= prob * log(prob,2) #log base 2
    return shannonEnt
if __name__ == '__main__':
    myDat, labels = createDataSet()
    print calcShannonEnt(myDat)

2 划分数据集

def splitDataSet(dataSet, axis, value):
    ''' 划分数据集 :param dataSet: 待划分的数据集 :param axis: 划分数据集的特征 :param value: 需要返回的特征值 :return: '''
    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
def chooseBestFeatureToSplit(dataSet):
    ''' 选择最好的数据集划分方式 :param dataSet: :return: '''
    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
    # 计算整个数据集的原始香农熵
    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
        # 讲每个特征对应的熵进行比较，选择熵值最小的，作为特征划分的索引值
            bestInfoGain = infoGain         #if better than current best, set to best
            bestFeature = i
    return bestFeature                      #returns an integer

3 决策树

def majorityCnt(classList):
    ''' :param classList: :return: '''
    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):
    ''' 构建决策树 :param dataSet: 数据集 :param labels: 标签列表，包含了数据集中所有特征的标签 :return: '''
    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]
    # 存储数据的信息
    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