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《机器学习实战》第三章中使用python画决策树

plotNode

import matplotlib.pyplot as plt

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('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()

plotNode的功能是画结点和线，箭头是从 parentPt 指向 centerPt 的

plotMidText

该函数用于在线的中间写入数字

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)

plotTree 和 createPlot

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':
            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()

xOff

xOff和yOff用来记录当前要画的叶子结点的位置。

画布的范围x轴和y轴都是0到1，我们希望所有的叶子结点平均分布在x轴上。totalW记录叶子结点的个数，那么 1/totalW 正好是每个叶子结点的宽度

如果叶子结点的坐标是 1/totalW , 2/totalW, 3/totalW, …, 1 的话，就正好在宽度的最右边，为了让坐标在宽度的中间，需要减去0.5 / totalW 。所以createPlot函数中，初始化 plotTree.xOff 的值为-0.5/plotTree.totalW。这样每次 xOff + 1/totalW ，正好是下1个结点的准确位置

yOff

yOff的初始值为1，每向下递归一次，这个值减去 1 / totalD

cntrPt

cntrPt用来记录当前要画的树的树根的结点位置

在plotTree函数中，它是这样计算的

cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)

numLeafs记录当前的树中叶子结点个数。我们希望树根在这些所有叶子节点的中间。

plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW

这里的 1.0 + numLeafs 需要拆开来理解，也就是

plotTree.xOff +  float(numLeafs)/2.0/plotTree.totalW +1.0/2.0/plotTree.totalW

plotTree.xOff +  1/2 * float(numLeafs)/plotTree.totalW + 0.5/plotTree.totalW

因为xOff的初始值是-0.5/plotTree.totalW ，是往左偏了0.5/plotTree.tatalW 的，这里正好加回去。这样cntrPt记录的x坐标正好是所有叶子结点的中心点