决策树学习笔记

目录

• • 决策树简介
  • 构造决策树
    • 1 信息增益
    • 2 划分数据集
    • 3 递归创建树
  • demo预测隐形眼镜类型
    • 总结

1 决策树简介

决策树的一个重要任务是为了理解数据中所蕴含的知识信息，因此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，这些机器根据数据集创建规则的过程，就是机器学习的过程。

• 优点

  • 计算量简单，输出结果易于理解
  • 对中间值的缺少不敏感，比较适合处理有缺失属性值的样本，能够处理不相关的特征

• 缺点

  • 容易过拟合

• 适用范围

  • 数值型和标称型

2 构造决策树

在构造决策树时，我们需要解决的第一个问题是：当前的数据集上，那个特征在划分数据分类时起决定性作用。

2.1 信息增益

• 数据划分的最大原则：把无序数据变得尽可能有序。信息论中，用熵(entropy)量化信息的内容。
  

  H=−∑k=1np(xi)log2p(xi)
  p(xi)表示符号xi是该分类的概率

• 就算给定数据即的信息熵

def calcShannonEnt(dataSet):    numEntries = len(dataSet)    labelCounts = {}    # 为所有可能分配创建字典    for featVec in dataSet:         currentLabel = featVec[-1]        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0        labelCounts[currentLabel] += 1    shannonEnt = 0.0    # 用公式    for key in labelCounts:        prob = float(labelCounts[key])/numEntries        shannonEnt -= prob * log(prob,2) #log base 2    return shannonEnt

2.2 划分数据集

• 按照给定特征划分数据

def splitDataSet(dataSet, axis, value):    # dataSet：待划分的数据集。axis：划分数据集的特征。value：需要返回的特征值    # 创建新的list对象    retDataSet = []    for featVec in dataSet:        if featVec[axis] == value:            # 抽取            reducedFeatVec = featVec[:axis]            reducedFeatVec.extend(featVec[axis+1:])            retDataSet.append(reducedFeatVec)    return retDataSet

• 选择最好的数据集划分方式

def chooseBestFeatureToSplit(dataSet):    numFeatures = len(dataSet[0]) - 1    baseEntropy = calcShannonEnt(dataSet)    bestInfoGain = 0.0; bestFeature = -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        # 找到最好的信息增益        if (infoGain > bestInfoGain):            bestInfoGain = infoGain            bestFeature = i    return bestFeature

2.3 递归创建树

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):    # dataSet：数据集。labels：标签列表。    classList = [example[-1] for example in dataSet]    # 类别完全相同则停止    if classList.count(classList[0]) == len(classList):         return classList[0]    # 遍历完所有特征值时，返回出现次数最多的分类    if len(dataSet[0]) == 1:        return majorityCnt(classList)    bestFeat = chooseBestFeatureToSplit(dataSet)    bestFeatLabel = labels[bestFeat]    myTree = {bestFeatLabel:{}}    # 得到列表包含的所有属性的值    del(labels[bestFeat])    featValues = [example[bestFeat] for example in dataSet]    uniqueVals = set(featValues)    for value in uniqueVals:        subLabels = labels[:]        # 递归        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)    return myTree 

3 demo:预测隐形眼镜类型

def createPlot(inTree):    fig = plt.figure(1, facecolor='white')    fig.clf()    axprops = dict(xticks=[], yticks=[])    createPlot.ax1 = plt.subplot(111, frameon=False, **axprops)    plotTree.totalW = float(getNumLeafs(inTree))    plotTree.totalD = float(getTreeDepth(inTree))    plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0;    plotTree(inTree, (0.5,1.0), '')    plt.show()fr = open('lenses.txt')lenses = [inst.strip().split('\t') for inst in fr.readlines()]lensesLabels = ['age','prescript', 'astigmatic', 'tearRate']lensesTree = trees.createTree(lenses, lensesLabels)createPlot(lensesTree)

• 相关函数

#!/usr/bin/python# -*- coding:utf8 -*-decisionNode = dict(boxstyle="sawtooth", fc="0.8")leafNode = dict(boxstyle="round4", fc="0.8")arrow_args = dict(arrowstyle="<-")# 获取叶子结点数目def getNumLeafs(myTree):    numLeafs = 0    # 找到输入的第一个元素    firstSides = list(myTree.keys())    firstStr = firstSides[0]     secondDict = myTree[firstStr]    for key in secondDict.keys():        # 判断结点的数据类型是否为字典        if type(secondDict[key]).__name__=='dict':            numLeafs += getNumLeafs(secondDict[key])        else:   numLeafs +=1    return numLeafs# 获取树的深度def getTreeDepth(myTree):    maxDepth = 0    # firstStr = myTree.keys()[0]    firstSides = list(myTree.keys())    firstStr = firstSides[0]#找到输入的第一个元素    secondDict = myTree[firstStr]    for key in secondDict.keys():        if type(secondDict[key]).__name__=='dict':            thisDepth = 1 + getTreeDepth(secondDict[key])        else:   thisDepth = 1        if thisDepth > maxDepth: maxDepth = thisDepth    return maxDepthdef 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 )

# 在父子节点间填充文本信息    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, va="center", ha="center", rotation=30)def plotTree(myTree, parentPt, nodeTxt):    # 计算宽和高    numLeafs = getNumLeafs(myTree)      depth = getTreeDepth(myTree)    #找到输入的第一个元素    firstSides = list(myTree.keys())    firstStr = firstSides[0]    cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)    # 标记子节点属性值    plotMidText(cntrPt, parentPt, nodeTxt)    plotNode(firstStr, cntrPt, parentPt, decisionNode)    secondDict = myTree[firstStr]    # 减少y偏移    plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD    for key in secondDict.keys():        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))    plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalD

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总结

Matplotlib非常强大，画图甚至比MATLAB还好。

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