上一篇我们介绍的K邻近算法可以解决很多分类的问题，但它的最大的缺点是无法给出数据内在的含义，决策树的主要优势在数据形式非常易于理解。
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，可以处理不相关数据特征。
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
工作原理
在构造决策树时，我们需要解决的第一个问题就是，当前数据集上哪个特征在划分数据分类时起决定性作用。为了找到决定性的特征，划出最好的结果，我们必须评估每一个特征。完成测试之后，原始数据集就被划分为几个数据子集。
这些数据子集会分布在第一个决策点的所有支点上，如果某个分支下的数据属于同一个类型，则无需对数据进行进一步分割。如果数据子集内的数据不属于同一类型，则需要重复划分数据子集的过程，划分方法与原始数据集的划分方法一致
直到所有具有相同类型的数据均在一个数据子集内
创建分支的伪代码函数
检测数据集中每个子项是否属于同一分类：
if so return 类标签
Else
寻找划分数据集的最好特征
划分数据集
创建分支点
for 每个划分的子集
调用函数createBranch并增加返回结果到分支节点中
return 分支节点
算法流程
收集数据
准备数据
分析数据
训练算法
测试算法
使用算法
决策树实现代码
import matplotlib.pyplot as plt decisionNode = dict(boxstyle="sawtooth", fc="0.8") leafNode = dict(boxstyle="round4", fc="0.8") arrow_args = dict(arrowstyle="<-") def getNumLeafs(myTree): numLeafs = 0 firstStr = myTree.keys()[0] secondDict = myTree[firstStr] 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 numLeafs += getNumLeafs(secondDict[key]) else: numLeafs +=1 return numLeafs def getTreeDepth(myTree): maxDepth = 0 firstStr = myTree.keys()[0] secondDict = myTree[firstStr] 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 thisDepth = 1 + getTreeDepth(secondDict[key]) else: thisDepth = 1 if thisDepth > maxDepth: maxDepth = thisDepth return maxDepth 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 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):#if the first key tells you what feat was split on numLeafs = getNumLeafs(myTree) #this determines the x width of this tree depth = getTreeDepth(myTree) firstStr = myTree.keys()[0] #the text label for this node should be this 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':#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 dict def createPlot(inTree): 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)) plotTree.totalD = float(getTreeDepth(inTree)) plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0; plotTree(inTree, (0.5,1.0), '') plt.show() #def createPlot(): # fig = plt.figure(1, facecolor='white') # fig.clf() # createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses # 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() 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] #createPlot(thisTree)