1.决策树的构造
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
# coding:utf-8# !/usr/bin/env python'''Created on Oct 12, 2010Decision Tree Source Code for Machine Learning in Action Ch. 3@author: Peter Harrington'''from math import logimport operator#通过是否浮出水面和是否有脚蹼，来划分鱼类和非鱼类def createDataSet(): dataSet = [[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']] labels = ['no surfacing','flippers'] #change to discrete values return dataSet, labelsdef calcShannonEnt(dataSet): #计算给定数据集的香农熵 numEntries = len(dataSet) #数据集中的实例总数 labelCounts = {} #为所有可能的分类创建字典，键是可能的特征属性，值是含有这个特征属性的总数 for featVec in dataSet: currentLabel = featVec[-1] if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0 labelCounts[currentLabel] += 1 #计算香农熵 shannonEnt = 0.0 #为所有的分类计算香农熵 for key in labelCounts: prob = float(labelCounts[key])/numEntries shannonEnt -= prob * log(prob,2) #以2为底求对数 #香农熵Ent的值越小，纯度越高，即通过这个特征属性来分类，属于同一类别的结点会比较多 return shannonEnt 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 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 integerdef 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): 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 def classify(inputTree,featLabels,testVec): firstStr = inputTree.keys()[0] secondDict = inputTree[firstStr] featIndex = featLabels.index(firstStr) key = testVec[featIndex] valueOfFeat = secondDict[key] if isinstance(valueOfFeat, dict): classLabel = classify(valueOfFeat, featLabels, testVec) else: classLabel = valueOfFeat return classLabeldef storeTree(inputTree,filename): import pickle fw = open(filename,'w') pickle.dump(inputTree,fw) fw.close() def grabTree(filename): import pickle fr = open(filename) return pickle.load(fr) if __name__ == '__main__': myDat,labels = createDataSet() print myDat print calcShannonEnt(myDat)
#通过是否浮出水面和是否有脚蹼，来划分鱼类和非鱼类def createDataSet(): dataSet = [[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']] labels = ['no surfacing','flippers'] #change to discrete values return dataSet, labelsdef calcShannonEnt(dataSet): #计算给定数据集的香农熵 numEntries = len(dataSet) #数据集中的实例总数 labelCounts = {} #为所有可能的分类创建字典，键是可能的特征属性，值是含有这个特征属性的总数 for featVec in dataSet: currentLabel = featVec[-1] if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0 labelCounts[currentLabel] += 1 #计算香农熵 shannonEnt = 0.0 #为所有的分类计算香农熵 for key in labelCounts: prob = float(labelCounts[key])/numEntries shannonEnt -= prob * log(prob,2) #以2为底求对数 #香农熵Ent的值越小，纯度越高，即通过这个特征属性来分类，属于同一类别的结点会比较多 return shannonEnt
myDat,labels = createDataSet()print myDatprint calcShannonEnt(myDat)
2.划分数据集
def splitDataSet(dataSet, axis, value): #按照给定特征划分数据集，axis表示根据第几个特征，value表示特征的值 retDataSet = [] #创建新的list对象 for featVec in dataSet: if featVec[axis] == value: reducedFeatVec = featVec[:axis] #切片 reducedFeatVec.extend(featVec[axis+1:]) #把序列添加到列表reducedFeatVec中 #print reducedFeatVec retDataSet.append(reducedFeatVec) #把对象reducedFeatVec（是一个list）添加到列表retDataSet中 return retDataSet
def chooseBestFeatureToSplit(dataSet): #选择最好的数据集划分方式 numFeatures = len(dataSet[0]) - 1 #特征的数量，最后一列是标签，所以减去1 baseEntropy = calcShannonEnt(dataSet) bestInfoGain = 0.0; bestFeature = -1 #信息增益和最好的特征下标 for i in range(numFeatures): #递归所有特征 featList = [example[i] for example in dataSet] #创建一个列表，包含第i个特征的所有值 uniqueVals = set(featList) #创建一个集合set，由不同的元素组成 newEntropy = 0.0 for value in uniqueVals: subDataSet = splitDataSet(dataSet, i, value) #按照所有特征的可能划分数据集 prob = len(subDataSet)/float(len(dataSet)) #计算所有特征的可能性 newEntropy += prob * calcShannonEnt(subDataSet) infoGain = baseEntropy - newEntropy #计算信息增益 if (infoGain > bestInfoGain): #比较不同特征之间信息增益的大小 bestInfoGain = infoGain #选取信息增益大的特征 bestFeature = i return bestFeature #返回特征的下标
3.递归构建决策树
def createTree(dataSet,labels): #创建决策树的函数，采用字典的表示形式 classList = [example[-1] for example in dataSet] if classList.count(classList[0]) == len(classList): #如果类别完全相同则停止继续划分 return classList[0] if len(dataSet[0]) == 1: #遍历完所有特征时返回出现次数最多的 return majorityCnt(classList) bestFeat = chooseBestFeatureToSplit(dataSet) #选择信息增益最大的特征下标 bestFeatLabel = labels[bestFeat] #选择信息增益最大的特征 myTree = {bestFeatLabel:{}} del(labels[bestFeat]) #从标签中删除已经划分好的特征 featValues = [example[bestFeat] for example in dataSet] #取得该特征的所有可能取值 uniqueVals = set(featValues) #建立一个集合 for value in uniqueVals: subLabels = labels[:] myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels) #递归createTree return myTree
myDat,labels = createDataSet()myTree = createTree(myDat,labels)print myTree{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}} 
4.在Python中使用Matplotlib注解绘制树形图
myDat,labels = createDataSet()print myDatimport treePlottertreePlotter.createPlot(myTree) #绘制树形图
5.构造注解树
获取叶节点的数目和树的层数
import matplotlib.pyplot as pltdecisionNode = dict(boxstyle="sawtooth", fc="0.8")leafNode = dict(boxstyle="round4", fc="0.8")arrow_args = dict(arrowstyle="<-")def getNumLeafs(myTree): #获取叶子节点的数目 numLeafs = 0 firstStr = myTree.keys()[0] secondDict = myTree[firstStr] for key in secondDict.keys(): if type(secondDict[key]).__name__=='dict': #测试节点的数据类型是否为字典 numLeafs += getNumLeafs(secondDict[key]) #递归 else: numLeafs +=1 #如果不是字典，则说明是叶子节点 return numLeafsdef getTreeDepth(myTree): #获取树的层数 maxDepth = 0 firstStr = myTree.keys()[0] secondDict = myTree[firstStr] for key in secondDict.keys(): if type(secondDict[key]).__name__=='dict': #测试节点的数据类型是否为字典，如果不是字典，则说明是叶子节点 thisDepth = 1 + getTreeDepth(secondDict[key]) #递归 else: thisDepth = 1 if thisDepth > maxDepth: maxDepth = thisDepth return maxDepth
绘制树形图
def plotNode(nodeTxt, centerPt, parentPt, nodeType): #绘制带箭头的注解 #annotate参数：nodeTxt：标注文本，xy：所要标注的位置坐标，xytext：标注文本所在位置，arrowprops：标注箭头属性信息 createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction', xytext=centerPt, textcoords='axes fraction', va="center", ha="center", bbox=nodeType, arrowprops=arrow_args ) def plotMidText(cntrPt, parentPt, txtString): #在父子节点间填充文本信息 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): #if the first key tells you what feat was split on numLeafs = getNumLeafs(myTree) #计算宽与高 depth = getTreeDepth(myTree) firstStr = myTree.keys()[0] #the text label for this node should be this print plotTree.xOff cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff) print parentPt print cntrPt plotMidText(cntrPt, parentPt, nodeTxt) #标记子节点属性值 plotNode(firstStr, cntrPt, parentPt, decisionNode) secondDict = myTree[firstStr] plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD #减少y偏移 for key in secondDict.keys(): if type(secondDict[key]).__name__=='dict': #test to see if the nodes are dictonaires, if not they are leaf nodes plotTree(secondDict[key],cntrPt,str(key)) #recursion else: #it's a leaf node print the leaf node 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#if you do get a dictonary you know it's a tree, and the first element will be another dictdef createPlot(inTree): #绘制树形图，调用了plotTree() fig = plt.figure(1, facecolor='white') fig.clf() axprops = dict(xticks=[], yticks=[]) createPlot.ax1 = plt.subplot(111, frameon=False, **axprops) #no ticks #createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses plotTree.totalW = float(getNumLeafs(inTree)) #存储树的宽度 plotTree.totalD = float(getTreeDepth(inTree)) #存储树的深度 plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0; plotTree(inTree, (0.5,1.0), '') plt.show()
测试和存储分类器
1.测试算法：使用决策树执行分类
def classify(inputTree,featLabels,testVec): #使用决策树的分类函数 firstStr = inputTree.keys()[0] secondDict = inputTree[firstStr] featIndex = featLabels.index(firstStr) #将标签字符串转换为索引 key = testVec[featIndex] valueOfFeat = secondDict[key] if isinstance(valueOfFeat, dict): classLabel = classify(valueOfFeat, featLabels, testVec) else: classLabel = valueOfFeat return classLabel
myDat,labels = createDataSet() Labels = labels print "myDat=" print myDat print "labels=" print labels import treePlotter myTree = treePlotter.retrieveTree(0) #绘制树形图 print myTree print classify(myTree,Labels,[0,1])
2.使用算法：决策树的存储
def storeTree(inputTree,filename): #使用pickle模块存储决策树 import pickle fw = open(filename,'w') pickle.dump(inputTree,fw) fw.close() def grabTree(filename): #查看决策树 import pickle fr = open(filename) return pickle.load(fr)
myDat,labels = createDataSet() Labels = labels print "myDat=" print myDat print "labels=" print labels import treePlotter myTree = treePlotter.retrieveTree(0) #绘制树形图 print myTree storeTree(myTree,'classifierStorage.txt') print grabTree('classifierStorage.txt')
示例：使用决策树预测隐形眼镜类型
import treePlotter import simplejson import ch ch.set_ch() from matplotlib import pyplot as plt fr = open('lenses.txt') lenses = [inst.strip().split('\t') for inst in fr.readlines()] #读取一行数据，以tab键分割并去掉空格 lensesLabels = [u'年龄',u'近远视',u'散光',u'眼泪等级'] #使用unicode，不然编码会报错 lensesTree = createTree(lenses,lensesLabels) print simplejson.dumps(lensesTree, encoding="UTF-8", ensure_ascii=False) #使用simplejson模块输出对象中的中文 treePlotter.createPlot(lensesTree) 
