谷歌笔记本（可选）
from google.colab import drive drive.mount("/content/drive")
output Mounted at /content/drive
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：可能产生过度匹配的问题
- 适用数据类型：数值型和标称型
决策树的一般流程
（1）收集数据
（2）准备数据
（3）分析数据
（4）训练算法
（5）测试算法
（6）使用算法
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: currentLabel = featVec[-1] if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0 labelCounts[currentLabel] += 1 shannonEnt = 0 for key in labelCounts: prob = float(labelCounts[key]) / numEntries shannonEnt -= prob * log(prob, 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, labels
output ([[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']], ['no surfacing', 'flippers'])
calcShannonEnt(myDat)
output 0.9709505944546686
myDat[0][-1] = 'maybe' myDat
划分数据集
# 按照给定特征划分数据集 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
myDat, labels = createDataSet() splitDataSet(myDat, 0, 1)
output
[[1, 'yes'], [1, 'yes'], [0, 'no']]
myDat, labels = createDataSet() calcShannonEnt(myDat)
output
0.9709505944546686
# 选择最好的数据集划分方式 def chooseBestFeatureToSplit(dataSet): numFeatures = len(dataSet[0]) - 1 # 2 baseEntropy = calcShannonEnt(dataSet) # 0.9709505944546686 bestInfoGain = 0 bestFeature = -1 for i in range(numFeatures): featList = [example[i] for example in dataSet] uniqueVals = set(featList) newEntropy = 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
chooseBestFeatureToSplit(myDat)
output
0
递归构建决策树
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]
# 创建树的代码 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
myDat, labels = createDataSet() myTree = createTree(myDat, labels) myTree
output
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}
使用Matplotlib注解绘制树形图
Matplotlib注解
# 使用文本注解绘制树节点 import matplotlib.pyplot as plt import warnings warnings.filterwarnings("ignore") 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('leaf01', (0.5, 0.1), (0.1, 0.5), decisionNode) plotNode('leaf02', (0.8, 0.1), (0.3, 0.8), leafNode) plt.show()
createPlot()
output
构造注解树
# 获取叶节点的数目 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
# 获取树的层数 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 = [{'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]
retrieveTree(1)
output
{'no surfacing': {0: 'no',
1: {'flippers': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}}
myTree = retrieveTree(0) getNumLeafs(myTree)
output
3
getTreeDepth(myTree)
output
2
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): 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()
myTree = retrieveTree(0) createPlot(myTree)
output
myTree['no surfacing'][2] = 'maybe' myTree
output
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}, 2: 'maybe'}}
createPlot(myTree)
output
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() myTree = retrieveTree(0) classify(myTree, labels, [1,0])
output
'no'
classify(myTree, labels, [1,1])
output
'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
output
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}
storeTree(myTree, 'classifierStorage.txt') grabTree('classifierStorage.txt')
output
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}
