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决策树

  • 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： 可能过度匹配
  • 适用数据类型： 数值型和标称型

可用来帮助理解数据中蕴含的知识信息，从不熟悉的数据集合中提取规则。如应用于专家系统。

过程：

在所有特征上尝试划分并计算信息增益，按信息增益最大的特征进行划分，然后在子集上重复上述过程，直到所有特征都被用完或者每个分支下的所有实例都具有同一分类。如果所有特征都被用完而类标签仍不唯一，则一般通过多数表决确定类标签。

整体看好象是贪心算法。。。

信息论、香农熵、信息熵、信息增益

可通过谷歌以上词语了解相关概念。

另，可了解基尼不纯度。





In [1]:



    


from math import log
def calcShannonEnt(dataSet):
    numEntries = len(dataSet)
    labelCounts = {}
    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
        shannonEnt -= prob * log(prob, 2)
    return shannonEnt



    











In [2]:



    


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



    











In [3]:



    


myDat, labels = createDataSet()



    











In [4]:



    


myDat



    


















    
Out[4]:








[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]

















In [5]:



    


calcShannonEnt(myDat)



    


















    
Out[5]:








0.9709505944546686

















In [6]:



    


myDat[0][-1] = 'maybe'



    











In [7]:



    


myDat



    


















    
Out[7]:








[[1, 1, 'maybe'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]

















In [8]:



    


calcShannonEnt(myDat)



    


















    
Out[8]:








1.3709505944546687

















In [9]:



    


def splitDataSet(dataSet, axis, value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet



    











In [10]:



    


myDat, labels=createDataSet()



    











In [11]:



    


myDat



    


















    
Out[11]:








[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]

















In [12]:



    


splitDataSet(myDat, 0, 1)



    


















    
Out[12]:








[[1, 'yes'], [1, 'yes'], [0, 'no']]

















In [13]:



    


splitDataSet(myDat, 0, 0)



    


















    
Out[13]:








[[1, 'no'], [1, 'no']]

















In [14]:



    


def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0
    bestFeature = -1
    for i in range(numFeatures):
        featList = [example[i] for example in dataSet]
        uniqueVals = set(featList)
        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
        if infoGain > bestInfoGain:
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature



    











In [15]:



    


chooseBestFeatureToSplit(myDat)



    


















    
Out[15]:








0

















In [16]:



    


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.items(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]



    











In [17]:



    


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(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[:]
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value), subLabels)
    return myTree



    











In [18]:



    


myTree = createTree(myDat, labels)



    











In [19]:



    


myTree



    


















    
Out[19]:








{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}

















In [20]:



    


%matplotlib inline



    











In [21]:



    


import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['SimHei'] #用来正常显示中文标签
plt.rcParams['axes.unicode_minus'] = False #用来正常显示负号
decisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
arrow_args = dict(arrowstyle="<-")
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)
def createPlot():
    fig = plt.figure(1, facecolor='white')
    fig.clf()
    createPlot.ax1 = plt.subplot(111, frameon=False)
    plotNode(u'决策节点', (0.5, 0.1),(0.1, 0.5), decisionNode)
    plotNode(u'叶节点', (0.8, 0.1), (0.3, 0.8), leafNode)
    plt.show()



    











In [22]:



    


createPlot()



    


















    
























In [23]:



    


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



    











In [24]:



    


def retrieveTree(i):
    return myTree



    











In [25]:



    


getNumLeafs(myTree)



    


















    
Out[25]:








3

















In [26]:



    


getTreeDepth(myTree)



    


















    
Out[26]:








2

















In [27]:



    


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, 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, parentPt, nodeTxt)
    plotNode(firstStr, cntrPt, parentPt, 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()



    











In [28]:



    


createPlot(myTree)



    


















    
























In [29]:



    


def myCreatePlot(inTree):
    fig = plt.figure(1, facecolor = 'white')
    fig.clf()
    #axprops = dict(xticks=[], yticks=[])
    createPlot.ax1 = plt.subplot(111, frameon=True)
    plotTree.totalW = float(getNumLeafs(inTree)) + 1
    plotTree.totalD = float(getTreeDepth(inTree))
    plotTree.xOff = 0.0 #-0.5 / plotTree.totalW
    print(plotTree.totalW)
    print(plotTree.xOff)
    plotTree.yOff = 1.0
    plotTree(inTree, (0.5, 1.0), '')
    plt.show()



    











In [30]:



    


myCreatePlot(myTree)



    


















    






4.0
0.0










    
























In [31]:



    


newTree = {'no surfacing':{0:'no', 1:{'flippers':{0:'no', 1:'yes'}}, 3:'maybe'}}



    











In [32]:



    


myCreatePlot(newTree)



    


















    






5.0
0.0










    
























In [33]:



    


createPlot(newTree)



    


















    
























In [34]:



    


newNewTree={'no surfacing':{0:'no', 1:{'flippers':{0:'no', 1:{'haha':{0:'yes', 1:{'hey':{0:'yes', 1:{'aha':{0:'yes', 1:'no'}}}}}}}}, 3:'maybe'}}



    











In [35]:



    


myCreatePlot(newNewTree)



    


















    






8.0
0.0










    
























In [36]:



    


createPlot(newNewTree)



    


















    
























In [37]:



    


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



    











In [38]:



    


myDat, labels = createDataSet()



    











In [39]:



    


labels



    


















    
Out[39]:








['no surfacing', 'flippers']

















In [40]:



    


myTree



    


















    
Out[40]:








{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}

















In [41]:



    


classify(myTree, labels, [1, 0])



    


















    
Out[41]:








'no'

















In [42]:



    


classify(myTree, labels, [1, 1])



    


















    
Out[42]:








'yes'

















In [43]:



    


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)



    











In [44]:



    


storeTree(myTree, 'myTree')



    











In [45]:



    


grabTree('myTree')



    


















    
Out[45]:








{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}

















In [46]:



    


fr = open('Ch03/lenses.txt')
lenses = [inst.strip().split('\t') for inst in fr.readlines()]



    











In [47]:



    


lensesLabels = ['age', 'prescript', 'astigmatic', 'tearRate']



    











In [48]:



    


lensesTree = createTree(lenses, lensesLabels)



    











In [49]:



    


lensesTree



    


















    
Out[49]:








{'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'}}

















In [50]:



    


createPlot(lensesTree)



    


















    
























In [ ]:

Content source: maxuewei2/machine-learning-in-action

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