机器学习实战-决策树
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第二章介绍的k-近邻算法可以完成很多分类任务,但是它最大的缺点就是无法给出数据内在的含义,决策树的主要优势在于数据形式非常容易理解。
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:可能会产生过度匹配的问题
适用数据类型:数值型和标称型
先计算给定数据集的香农熵
???CSDN的Markdown,第一行居然不居中?还是要加什么?
from math import logdef calcShannonEnt(dataSet): numEntries = len(dataSet) labelCounts = {} #为所有可能的分类创建字典 for featVec in dataSet: currentLabel = featVec[-1] if currentLabel not in labelCounts.keys():labelCounts[currentLabel] = 0 labelCounts[currentLabel] += 1 shannonEnt = 0.0 #计算熵 for key in labelCounts: prob = float(labelCounts[key])/numEntries #底数为2求对数 shannonEnt -= prob*log(prob,2) return shannonEntdef createDataSet(): dataSet = [[1,1,'yes'], [1,1,'yes'], [1,0,'no'], [0,1,'no'], [0,1,'no']] labels = ['no surfacing','flippers'] return dataSet,labels
测试数据集的熵
import treesreload(trees)myDat,labels = trees.createDataSet()
>>> myDat[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]>>> trees.calcShannonEnt(myDat)0.9709505944546686
熵越高,则混合的数据也越多
增加一个测试分类来测试熵的变化:
>>> myDat[0][-1]='maybe'>>> myDat[[1, 1, 'maybe'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]>>> trees.calcShannonEnt(myDat)1.3709505944546687
下面,开始划分数据集:
def splitDataSet(dataSet, axis, value): retDataSet = [] for featVec in dataSet: #将符合要求的数据集添加到列表中 if featVec[axis] == value: reducedFeatVec = featVec[:axis] reducedFeatVec.extend(featVec[axis+1:]) retDataSet.append(reducedFeatVec) return retDataSet
本段代码使用了三个输入参数:待划分的数据集,划分数据集的特征,需要返回的特征的值。
然后在Python命令提示符内输入下述命令:
>>> myDat[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]>>> trees.splitDataSet(myDat,0,1)[[1, 'yes'], [1, 'yes'], [0, 'no']]>>> trees.splitDataSet(myDat,0,0)[[1, 'no'], [1, 'no']]>>>
接下来我们开始遍历整个数据集,循环计算香农熵和splitDataSet()函数,找到最好的特征划分方式。
def chooseBestFeatureToSplit(dataSet): numFeatures = len(dataSet[0]) - 1 baseEntropy = calcShannonEnt(dataSet)#计算原始香农熵 bastInfoGain = 0.0;baseFeature = -1 for i in range(numFeatures): featList = [example[i] for example in dataSet] uniqueVals = set(featList)#创建分类标签集合 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
从列表中新建集合是Python语言得到列表中唯一元素的最快方法
下面开始测试上面代码的实际输出结果
>>> trees.chooseBestFeatureToSplit(myDat)0>>> myDat[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
代码告诉我们,第0个特征是最好的用于划分数据集的特征
下面我们开始采用递归的方式处理数据集
如果数据集已经处理了所有属性,但是类标签依然不是唯一的,此时我们需要决定如何定义该叶子节点,在这种情况下,我们通常会采用多数表决的方法决定该叶子节点的分类
import operatordef majorityCnt(classList): classCount = {} for vote in classList:#统计数据字典classList每一个类标签出现的频率 if vote not in classCount.keys(): classCount[vote] = 0 classCount[vote] += 1 sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgette(1), reverse=True)#排序 return sortedClassCount[0][0]#返回次数最多的
下面开始加入创建树的函数代码
def createTree(dataSet, labels):#数据集,标签列表 classList = [example[-1] for example in dataSet]#最后一个属性加入列表变量classList #类别完全相同则停止划分 if classList.count(classList[0]) == len(classList): return classList[0] if len(dataSet[0]) == 1:#遍历完所有特征,返回次数最多的类别 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
subLabels = labels[:],这行代码复制了类标签,并将其存储在新列表变量subLabels中。之所以这样做,是因为在Python语言中,函数参数是列表类型时,参数是按照引用方式传递的。为了保证每次调用函数createTree()时不改变原始列表的内容,使用新变量subLabels代替原始列表。
下面是测试实际输出结果
#trees-1.pyimport treesreload(trees)myDat,labels = trees.createDataSet()myTree = trees.createTree(myDat,labels)
>>> myTree{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}
下面开始学习使用Matplotlib画图
#-*- coding=utf-8 -*-import matplotlib.pyplot as pltdecisionNode = 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("a decision node",(0.5,0.1),(0.1,0.5),decisionNode) plotNode("a leaf node",(0.8,0.1),(0.3,0.8),leafNode) plt.show()
>>> import treePlotter;treePlotter.createPlot()
下面开始获取叶节点的数目和树的层数
def getNumLeafs(myTree): numLeafs = 0 firstStr = 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 numLeafsdef getTreeDepth(myTree): maxDepth = 0 firstStr = 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 maxDepthdef 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]
>>> import treePlotter>>> treePlotter.retrieveTree(1){'no surfacing': {0: 'no', 1: {'flippers': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}}>>> myTree = treePlotter.retrieveTree(0)>>> treePlotter.getNumLeafs(myTree)3>>> treePlotter.getTreeDepth(myTree)2
更新部分代码,开始尝试画图
def plotMidText(cntrPt, parentPt, txtString):#计算父节点和子节点的中间位置 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): numLeafs = getNumLeafs(myTree) depth = getTreeDepth(myTree) firstStr = 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
并更新creaePlot()部分的代码
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))#宽度 plotTree.totalD = float(getTreeDepth(inTree))#高度 plotTree.xOff = -0.5/plotTree.totalW;plotTree.yOff = 1.0; plotTree(inTree, (0.5,1.0),'') plt.show()
开始画图
#treePlotter-1.pyimport treePlottermyTree=treePlotter.retrieveTree(0)treePlotter.createPlot(myTree)
接着添加字典的内容,重新绘制图片
>>> myTree['no surfacing'][3] = 'maybe'>>> myTree{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}, 3: 'maybe'}}>>> treePlotter.createPlot(myTree)
下面开始重点讲如何利用决策树执行数据分类
在执行数据分类时,需要使用决策树以及用于构造决策树的标签向量。然后,程序比较测试数据与决策树上的数值,递归执行该过程直到进入叶子节点;最后将测试数据定义为叶子节点所属的类型。
#使用决策树的分类函数#添加到trees.pydef classify(inputTree, featLabels, testVec): firstStr = inputTree.keys()[0] secondDict = inputTree[firstStr] featIndex = featLabels.index(firstStr)#将标签字符串转化为索引 for key in secondDict.keys(): if testVec[featIndex] == key: if type(secondDict[key]).__name__=='dict':#递归遍历 classLabel = classify(secondDict[key],featLabels,testVec) else: classLabel = secondDict[key] #key = testVec[featIndex] #valueOfFeat = secondDict[key] #if isinstance(valueOfFeat, dict):#是否是实例 # classLabel = classify(valueOfFeat, featLabels, testVec) #else: classLabel = valueOfFeat return classLabel
#trees-1import treesimport treePlottermyDat,labels = trees.createDataSet()myTree=treePlotter.retrieveTree(0)
>>> labels['no surfacing', 'flippers']>>> myTree{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}>>> trees.classify(myTree,labels,[1,0])'no'>>> trees.classify(myTree,labels,[1,1])'yes'
下面开始在硬盘上存储决策树分类器
#trees.pydef storeTree(inputTree,filename): import pickle#重点 fw = open(filename,'w') pickle.dump(inputTree,fw) fw.close()def grabTree(filename): import pickle fr = open(filename) return pickle.load(fr)
#tree-1.pyimport treesimport treePlottermyDat,labels = trees.createDataSet()myTree = trees.createTree(myDat,labels)trees.storeTree(myTree,'classifierStorage.txt')
>>> trees.grabTree('classifierStorage.txt'){'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}
import treesimport treePlottermyDat,labels = trees.createDataSet()myTree = trees.createTree(myDat,labels)fr=open('lenses.txt')lenses=[inst.strip().split('\t') for inst in fr.readlines()]lensesLabels=['age','prescript','astigmatic','tearRate']lensesTree = trees.createTree(lenses,lensesLabels)
>>> treePlotter.createPlot(lensesTree)
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