决策树python实现

决策树python实现

算法构造

算法优缺点

  • 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。

算法流程

  • 收集数据:可以使用任何方法。
  • 准备数据:树构造算法只适用于标称型数据,因此数值型数据必须离散化。
  • 分析数据:可以使用任何方法,构造树完成之后,我们应该检查图形是否符合预期。
  • 训练算法:构造树的数据结构。
  • 测试算法:使用经验树计算错误率。
  • 使用算法:此步骤可以适用于任何监督学习算法,而使用决策树可以更好地理解数据的内在含义。

信息增益

# 计算给定数据集的香农熵
from math import log

def calcShannonEnt(dataSet):
    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:
        prob = float(labelCounts[key])/numEntries
        shannonEnt -= prob * log(prob,2) #log base 2
    return shannonEnt


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
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
calcShannonEnt(myDat)
0.9709505944546686

熵越高,则混合的数据也越多,我们可以在数据集中添加更多的分类,观察熵是如何变化的。这里我们增加第三个名为maybe的分类, 测试熵的变化:

myDat[0][-1] = 'maybe'
calcShannonEnt(myDat)
1.3709505944546687

划分数据集

# 按照给定特征划分数据集
# /*
# * dataSet: 待划分的数据集
# * axis: 划分数据的特征
# * 需要返回的特征的值
# */
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
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
splitDateSet(myDat, 0, 1) # 以第一个特征,特征值为1划分的结果
[[1, 'yes'], [1, 'yes'], [0, 'no']]
splitDateSet(myDat, 0, 0) # 以第一个特征,特征值为0划分的结果
[[1, 'no'], [1, 'no']]
# 选择最好的数据集划分方式
def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
    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
            bestInfoGain = infoGain         #if better than current best, set to best
            bestFeature = i
    return bestFeature                      #returns an integer
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
bestFeature = chooseBestFeatureToSplit(myDat)
print("bestFeature is {}".format(bestFeature))
bestFeature is 0

递归构造决策树

# 多数表决决定该叶子节点分类
import operator
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]
# 创建树的函数代码
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              
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
createTree(myDat, labels)
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}

在python中使用Matplotlib注解绘制树形图

Matplotlib提供了一个非常有用的注解工具annotations

# 使用文本注解绘制树节点
import matplotlib.pyplot as plt

#解决中文显示问题
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['axes.unicode_minus'] = False

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

def plotNode(nodeText, centerPt, parentPt, nodeType):
    createPlot.ax1.annotate(nodeText, xy=parentPt, xycoords='axes fraction',
                            xytext=centerPt, textcoords="axes fraction",
                            va="center", ha="center", bbox=nodeType, arrowprops=arrow_args)


def createPlot():
    fig =plt.figure(1, facecolor="white")
    fig.clf()
    createPlot.ax1 = plt.subplot(111, frameon=False)
    plotNode('决策节点', (0.5, 0.1), (0.1, 0.5), decisionNode)
    plotNode('叶节点', (0.8, 0.1), (0.3, 0.8), leafNode)
    plt.show()
createPlot()

决策树python实现_第1张图片

# 获取叶节点的数目和数的层数
def getNumLeafs(myTree):
    numLeafs = 0
    firstStr = list(myTree.keys())[0]
    secondDict = myTree[firstStr]
    for key in secondDict.keys():
        if type(secondDict[key]).__name__ == 'dict':
            numLeafs += getNumLeafs(secondDict[key])
        else:
            numLeafs += 1
    return numLeafs


def getTreeDepth(myTree):
    maxDepth = 0
    firstStr = list(myTree.keys())[0]
    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 maxDepth


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

    return listOfTrees[i]
retrieveTree(1)
{'flippers': {0: 'no',
  1: {'no surfacing': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'yes'}}}}
myTree = retrieveTree(0)
getNumLeafs(myTree)
3
getTreeDepth(myTree)
2
# plotTree函数
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, parentPr, nodeTxt):
    numLeafs = getNumLeafs(myTree)
    depth = getTreeDepth(myTree)
    firstStr = list(myTree.keys())[0]
    cntrpt = (plotTree.xoff + (1.0 + float(numLeafs)) / 2.0 / plotTree.totalW, plotTree.yoff)
    plotMidText(cntrpt, parentPr, nodeTxt)
    plotNode(firstStr, cntrpt, parentPr, decisionNode)
    secondDict = myTree[firstStr]
    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


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()
myTree = retrieveTree(1)
createPlot(myTree)

决策树python实现_第2张图片

myTree['flippers'][0] = 'maybe'
createPlot(myTree)

决策树python实现_第3张图片

测试和存储分类器

测试算法:使用决策树执行分类

# 使用决策树的分类函数
def classify(inputTree, featLabels, testVec):
    firstStr = list(inputTree.keys())[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)
    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
myDat, labels = createDataSet()
labels
['no surfacing', 'flippers']
myTree = retrieveTree(0)
myTree
{'flippers': {0: 'no', 1: {'no surfacing': {0: 'no', 1: 'yes'}}}}
classify(myTree, labels, [1, 0])
'no'
classify(myTree, labels, [1, 1])
'yes'

使用算法:决策树的存储

# 使用pickle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)
myTree
{'flippers': {0: 'no', 1: {'no surfacing': {0: 'no', 1: 'yes'}}}}
storeTree(myTree, 'data/classifierStorage.txt')
grabTree('data/classifierStorage.txt')
{'flippers': {0: 'no', 1: {'no surfacing': {0: 'no', 1: 'yes'}}}}

实例:使用决策树预测隐形眼镜类型

  • 收集数据:提供的文本文件。
  • 准备数据:解析tab键分隔的数据行。
  • 分析数据:快速检查数据,确保正确地解析数据内容,使用createPlot()函数绘制最终的树形图。
  • 训练算法:使用3.1节的createTree()函数。
  • 测试算法:编写测试函数验证决策树可以正确分类给定的数据实例。
  • 使用算法:存储树的数据结构,以便下次使用时无需重新构造树。
data = open('data/lenses.txt')
lenses = [inst.strip().split('\t') for inst in data.readlines()]
lensesLabels = ['age', 'prescript', 'astigmatic', 'tearRate']
lensesTree  = createTree(lenses, lensesLabels)
lensesTree
{'tearRate': {'normal': {'astigmatic': {'no': {'age': {'pre': 'soft',
      'presbyopic': {'prescript': {'hyper': 'soft', 'myope': 'no lenses'}},
      'young': 'soft'}},
    'yes': {'prescript': {'hyper': {'age': {'pre': 'no lenses',
        'presbyopic': 'no lenses',
        'young': 'hard'}},
      'myope': 'hard'}}}},
  'reduced': 'no lenses'}}
createPlot(lensesTree)

决策树python实现_第4张图片

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