机器学习使用决策树

一：

简单例子理解决策树概念

二：决策树的一般流程

三：信息增益

划分数据集的大原则是：将无序的数据变得更加有序。我们可以使用多种方法划分数据集，
但是每种方法都有各自的优缺点。组织杂乱无章数据的一种方法就是使用信息论度量信息，信息
论是量化处理信息的分支科学。我们可以在划分数据之前使用信息论量化度量信息的内容。
在划分数据集之前之后信息发生的变化称为信息增益，知道如何计算信息增益，我们就可以
计算每个特征值划分数据集获得的信息增益，获得信息增益最高的特征就是最好的选择。
在可以评测哪种数据划分方式是最好的数据划分之前，我们必须学习如何计算信息增益。集
合信息的度量方式称为香农熵或者简称为熵，这个名字来源于信息论之父克劳德•香农。

期中n为分类的数目。

四：可视化

matplotlib可视化例子：

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()createPlot()

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(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 getNumLeafs(myTree):    numLeafs = 0    firstSides = list(myTree.keys())    firstStr = firstSides[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    firstSides = list(myTree.keys())    firstStr = firstSides[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]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)    firstSides = list(myTree.keys())    firstStr = firstSides[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.totalDprint(retrieveTree(1))myTrees = retrieveTree(0)print(getNumLeafs(myTrees))print(getTreeDepth(myTrees))createPlot(myTrees)