机器学习实战 - 决策树

借用目前百科的解释：决策树(Decision Tree)是在已知各种情况发生概率的基础上，通过构成决策树来求取净现值的期望值大于等于零的概率，评价项目风险，判断其可行性的决策分析方法，是直观运用概率分析的一种图解法。由于这种决策分支画成图形很像一棵树的枝干，故称决策树。

在构建决策树的过程中，其伪代码可表示如下：

检测数据集中的每个子项是否属于同一分类：
    if so return 类标签
    else
        寻找划分数据集的最好的特征
        划分数据集
        创建分支节点
            for 每个划分的子集
                调用本函数并增加返回结果到分支节点中
        return 分支节点

那么当数据中存在多个特征的时候，我们如何选取最合适的特征进行分类呢？比如下图：

我们如何选择“不浮出水面是否可以生存”和“是否有脚蹼”，我们首先选择哪个特征进行分类呢？这里我们就要介绍一个一个叫“信息增益”的属性，我们划分数据是为了使无序的数据更加有序，组织杂乱无章数据的一种方法是使用信息论度量信息，在信息论中，划分数据之前之后信息发生的变成称之为“信息增益”，那么我们现在就要计算信息增益，信息增益最高的特征就是最好的选择。
信息增益的度量方式成为香农熵简称“熵”，其计算公式为
在每次遍历选取特征时，我们除开此特征之后计算其熵值，每个特征都要遍历，然后看哪个特征的熵值最小，就选取此特征进行划分，一直遍历到只有一个数据或者所有的数据分类便签都是一样的为止。那么，为什么要选取计算得到的新熵值最小的呢？因为熵值越小代表数据的混乱程度越低， 反之，熵值越大，代表数据的混乱程度越高，我们进行数据划分为了就是使数据的混乱程度小。

（这里使用的是Python3.6，如果python2.7出现中文问题可以在最前面加上一句#encoding=utf-8）：
trees.py

from math import log
import operator


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

"""计算香农熵"""
def calcShannonEnt(dataSet):
    length = len(dataSet)
    classCount = {}
    for i in range(length):
        if dataSet[i][-1] not in classCount.keys():
            classCount[dataSet[i][-1]] = 0
        classCount[dataSet[i][-1]] += 1
    shannonEnt = 0.0
    for classify in classCount:
        prob = float(classCount[classify]) / length
        shannonEnt -= prob * log(prob, 2)
    return shannonEnt

"""划分数据集, 根据axis轴的value值划分"""
def splitDataSet(dataSet, axis, value):
    returnDataSet = []
    for data in dataSet:
        if data[axis] == value:
            reducedFeatVec = data[:axis]
            reducedFeatVec.extend(data[axis + 1:])
            returnDataSet.append(reducedFeatVec)
    return returnDataSet

"""根据计算的熵最小的特征进行划分数据集"""
def chooseBestFeatureToSplit(dataSet):
    featureNum = len(dataSet[0]) - 1
    length = len(dataSet)
    """ 之所以要获得初始的香农熵, 是方便后续的比较, 对于不同的数据初始的熵值不一样, 难以初始化 事后仔细考虑了一下, 发现还有另外一个比较方法, 如下： baseEntropy = calcShannonEnt(dataSet) bestFeature = -1 bestShannonEnt = baseEntropy 这里不同 for i in range(featureNum): featureList = [example[i] for example in dataSet] uniqueFeature = set(featureList) newShannonEnt = 0.0 for feature in uniqueFeature: returnDataSet = splitDataSet(dataSet, i, feature) prob = len(returnDataSet) / length newShannonEnt += prob * calcShannonEnt(returnDataSet) if newShannonEnt < bestShannonEnt: 这里不同 bestShannonEnt =newShannonEnt 这里不同 bestFeature = i return bestFeature """
    baseEntropy = calcShannonEnt(dataSet)
    bestFeature = -1
    bestShannonEnt = 0.0
    for i in range(featureNum):
        featureList = [example[i] for example in dataSet]
        uniqueFeature = set(featureList)
        newShannonEnt = 0.0
        for feature in uniqueFeature:
            returnDataSet = splitDataSet(dataSet, i, feature)
            prob = len(returnDataSet) / length
            newShannonEnt += prob * calcShannonEnt(returnDataSet)
        if baseEntropy - newShannonEnt > bestShannonEnt:
            bestShannonEnt = baseEntropy - newShannonEnt
            bestFeature = i
    return bestFeature

"""获取出现次数最多的分类"""
def majorityCnt(dataSet):
    classCount = {}
    for value in majorityCnt:
        if value not in classCount.keys():
            classCount[value] = 0
        classCount += 1
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

"""递归创建树"""
def createTree(dataSet, labels):
    classList = [example[-1] for example in dataSet]
    if classList.count(classList[0]) == len(classList):
        return classList[0]
    if len(dataSet[0]) == 1:
        return majorityCnt(dataSet)
    bestFeatrue = chooseBestFeatureToSplit(dataSet)
    bestLabel = labels[bestFeatrue]
    del (labels[bestFeatrue])
    myTree = {bestLabel: {}}
    featureValues = [example[bestFeatrue] for example in dataSet]
    uniqueValues = set(featureValues)
    for feature in uniqueValues:
        subLabels = labels[:]
        myTree[bestLabel][feature] = createTree(splitDataSet(dataSet, bestFeatrue, feature), subLabels)
    return myTree

"""使用决策树进行分类"""
def classify(inputTree, featLabels, testVec):
    firstStr = list(inputTree.keys())[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)
    for key in secondDict.keys():
        if key == testVec[featIndex]:
            if type(secondDict[key]).__name__ == 'dict':
                classLabel = classify(secondDict[key], featLabels, testVec)
            else:
                classLabel = secondDict[key]
    return classLabel

"""将树存储在本地, python3的pickle存储的是二进制所以存储跟读取使用wb和rb"""
def storeTree(inputTree, filename):
    import pickle
    fw = open(filename, 'wb')
    pickle.dump(inputTree, fw)
    fw.close()

"""从本地获取出树, python3的pickle存储的是二进制所以存储跟读取使用wb和rb"""
def grabTree(filename):
    import pickle
    fw = open(filename, 'rb')
    return pickle.load(fw)

treePlotter.py

import matplotlib.pyplot as plt

dicisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
arrow_args = dict(arrowstyle="<-")

"""画箭头、文字、还有框框"""
def plotNode(nodeTxt, centerPt, parentPt, nodeType):
    createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction', xytext=centerPt,
                            textcoords='axes fraction', va="center", ha="center", bbox=nodeType,
                            arrowprops=arrow_args)

"""该函数是一个示例函数"""
def createPlot():
    fig = plt.figure(1, facecolor="white")
    fig.clf()
    createPlot.ax1 = plt.subplot(111, frameon=False)
    plotNode('decisionNode', (0.5, 0.1), (0.1, 0.5), dicisionNode)
    plotNode('leafNode', (0.8, 0.1), (0.3, 0.8), leafNode)
    plt.show()

"""递归得到树的叶子节点个数"""
def getLeafsNum(myTree):
    leafsNum = 0
    firstStr = list(myTree.keys())[0]
    secondDict = myTree[firstStr]
    for key in secondDict.keys():
        if type(secondDict[key]).__name__ == 'dict':
            leafsNum += getLeafsNum(secondDict[key])
        else:
            leafsNum += 1
    return leafsNum

"""递归得到树的深度"""
def getTreeDeapth(myTree):
    maxDeapth = 0
    firstStr = list(myTree.keys())[0]
    secondDict = myTree[firstStr]
    for key in secondDict.keys():
        if type(secondDict[key]).__name__ == 'dict':
            thisDeapth = 1 + getTreeDeapth(secondDict[key])
        else:
            thisDeapth = 1
        if thisDeapth > maxDeapth:
            maxDeapth = thisDeapth
    return maxDeapth


def retrieveTree(i):
    listOfTrees = [{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}},
                   {'no surfacing': {0: 'no', 1: {'flippers': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}}]
    return listOfTrees[i]

"""在两个节点之间打印特征值, 这里是0|1"""
def plotMidText(cntrPt, parentPt, txtString):
    xMid = (parentPt[0] - cntrPt[0]) / 2.0 + cntrPt[0]
    yMid = (parentPt[1] - cntrPt[1]) / 2.0 + cntrPt[1]
    createPlot.ax1.text(xMid, yMid, txtString)


def plotTree(myTree, parentPt, nodeText):
    leafsNum = getLeafsNum(myTree)
    depth = getTreeDeapth(myTree)
    """ 得到一个字符串键值(第0个) {'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}} 则第一次得到的是no surfacing """
    firstStr = list(myTree.keys())[0]
    """当前节点的坐标"""
    cntrPt = (plotTree.xOff + (1.0 + float(leafsNum)) / 2.0 / plotTree.totalW, plotTree.yOff)
    """在两个节点之间画0|1"""
    plotMidText(cntrPt, parentPt, nodeText)
    plotNode(firstStr, cntrPt, parentPt, dicisionNode)
    """当前节点的子节点"""
    secondDict = myTree[firstStr]
    """因为画子节点所以y值要减小向下移"""
    plotTree.yOff = plotTree.yOff - 1.0 / plotTree.totalD
    for key in secondDict.keys():
        """如果子节点不是叶子节点, 就递归调用画子树"""
        if type(secondDict[key]).__name__ == 'dict':
            plotTree(secondDict[key], cntrPt, str(key));
        else:
            plotTree.xOff = plotTree.xOff + 1.0 / plotTree.totalW
            plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode)
            plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key))
    """画完当前子节点所以y值要增大向上移回去"""
    plotTree.yOff = plotTree.yOff + 1.0 / plotTree.totalD

"""绘制图形"""
def createPlot(inTree):
    """这里figure第一个参数是窗口的名字figure 1, facecoloe为背景色"""
    fig = plt.figure(1, facecolor='white')
    fig.clf()
    """axprops是横竖轴需要出现的坐标, 可以尝试axprops = dict(xticks=[0, 0.5, 1], yticks=[0, 1])"""
    axprops = dict(xticks=[], yticks=[])
    """ plt.subplot第一个参数其实是三个参数nmp, 表示分割成n*m个图, 当前图的编号是p frameon表示是否有方框包围坐标轴 最后一个是坐标的参数 """
    createPlot.ax1 = plt.subplot(111, frameon=False, **axprops)
    """宽度"""
    plotTree.totalW = float(getLeafsNum(inTree))
    """深度"""
    plotTree.totalD = float(getTreeDeapth(inTree))
    """ 当前递归到的叶子节点的上一个叶子节点的坐标 初始为第一个叶子节点的x坐标的上一个坐标, 也就是第一个叶子节点的x坐标-1/plotTree.totalW, 可以结合整个画图的过程理解一下，比较难解释 """
    plotTree.xOff = -0.5 / plotTree.totalW
    """初始y坐标"""
    plotTree.yOff = 1.0
    """画第一个图, 坐标是(0.5, 1.0)"""
    plotTree(inTree, (0.5, 1.0), '')
    plt.show()

下面是我的一些测试代码test.py

import trees
import treePlotter

# dataSet, labels = trees.createDataSet()

# shannonEnt = trees.calcShannonEnt(dataSet)

# print(trees.createTree(dataSet, labels))
#
# treePlotter.createPlot()

# myTree = treePlotter.retrieveTree(0)
# print(trees.classify(myTree, labels, [1, 0]))
# print(trees.classify(myTree, labels, [1, 1]))
# treePlotter.createPlot(myTree)

# trees.storeTree(myTree, 'classifierStorage.txt')
# print(trees.grabTree('classifierStorage.txt'))
#
# fr = open('lenses.txt')
# lenses = [inst.strip().split('\t') for inst in fr.readlines()]
# lensesLabels = ['age', 'prescript', 'astigmatic', 'tearRate']
# lensesTree = trees.createTree(lenses, lensesLabels)
# print(lensesTree)
# treePlotter.createPlot(lensesTree)

myDat, labels = trees.createDataSet()
print(trees.chooseBestFeatureToSplit(myDat))