代码注释：机器学习实战第9章 树回归

写在开头的话：在学习《机器学习实战》的过程中发现书中很多代码并没有注释，这对新入门的同学是一个挑战，特此贴出我对代码做出的注释，仅供参考，欢迎指正。

1、将CART算法用于回归

#coding:gbkfrom numpy import *#作用：从文件导入数据#输入：文件名#输出：数据矩阵def loadDataSet(fileName):    dataMat = []    fr = open(fileName)    for line in fr.readlines():        curLine = line. strip().split('\t')        fltLine = map(float, curLine)#将每行映射成浮点数        dataMat.append(fltLine)    return dataMat# 作用：从文件导入数据# 输入：数据矩阵，待切分特征值，阈值# 输出：切分后的数据集def binSplitDataSet(dataSet, feature, value):    # 书中最后有[0]，练习发现只会返回1*n矩阵，因此删掉    mat0 = dataSet[nonzero(dataSet[:, feature] > value)[0], :]# nonzero()返回的是列表的下标值    mat1 = dataSet[nonzero(dataSet[:, feature] <= value)[0], :]    return mat0, mat1# 作用：目标变量的均值# 输入：数据集# 输出：目标变量的均值def regLeaf(dataSet):    return mean(dataSet[:, -1])# 作用：目标变量的总方差# 输入：数据集# 输出：目标变量的总方差def regErr(dataSet):    return var(dataSet[:, -1]) * shape(dataSet)[0]#均方差乘以数据集中样本的个数，得总方差# 作用：找到数据的最佳二元切分方式# 输入：数据集，建立叶节点的函数，误差计算函数，包含树构建所需其他参数的元组# 输出：最佳切分特征和特征值def chooseBestSplit(dataSet, leafType = regLeaf, errType = regErr, ops = (1, 4)):    tolS = ops[0]#容许的误差下降值    tolN = ops[1]#切分的最少样本数    #如果所有值都相等则退出    if len(set(dataSet[:, -1].T.tolist()[0])) == 1:        return None, leafType(dataSet)    m, n = shape(dataSet)#数据集的行数和列数    S = errType(dataSet)#数据集的总方差    bestS = inf    bestIndex = 0    bestValue = 0    for featIndex in range(n-1):#最后一列为y值        #书中代码有错，需改成如下形式，转置后转换为列表        for splitVal in set(dataSet[:, featIndex].T.tolist()[0]):#对每个特征的特征值            mat0, mat1 = binSplitDataSet(dataSet, featIndex, splitVal)            # 有切分的数据集太小，跳过该种切分方式            if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):                continue            #切分后的总方差            newS = errType(mat0) + errType(mat1)            if newS < bestS:                bestIndex = featIndex                bestValue = splitVal                bestS = newS    #如果误差不大则退出    if (S - bestS) < tolS:        return None, leafType(dataSet)    mat0, mat1 = binSplitDataSet(dataSet, bestIndex, bestValue)    #如果切分出的数据集很小则退出    if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):        return None, leafType(dataSet)    return bestIndex, bestValue#作用：创建树#输入：数据集，建立叶节点的函数，误差计算函数，包含树构建所需其他参数的元组#输出：树def createTree(dataSet, leafType = regLeaf, errType = regErr, ops = (1, 4)):    feat, val = chooseBestSplit(dataSet, leafType, errType, ops)    if feat == None:        return val    retTree = {}    retTree['spInd'] = feat    retTree['spVal'] = val    lSet, rSet = binSplitDataSet(dataSet, feat, val)    retTree['left'] = createTree(lSet, leafType, errType, ops)    retTree['right'] = createTree(rSet, leafType, errType, ops)    return retTree#作用：测试输入变量是否是一棵树#输入：输入变量#输出：布尔类型的结果，是一棵树则返回Truedef isTree(obj):    return (type(obj).__name__ == 'dict')#如果是一棵树，则类型为'dict'即字典#作用：得到树的平均值#输入：树#输出：数的平均值def getMean(tree):    if isTree(tree['right']):        tree['right'] = getMean(tree['right'])    if isTree(tree['left']):        tree['left'] = getMean(tree['left'])    #如果左子树和右子树的样例个数不相等，意义是什么？    return (tree['left'] + tree['right']) / 2.0#作用：剪枝#输入：待剪枝的树，剪枝所需的测试数据#输出：剪好的树def prune(tree, testData):    if shape(testData)[0] == 0:#确认测试集是否为空        return getMean(tree)    #如果两个分支有一个是子树，则对测试数据进行划分    if (isTree(tree['right']) or isTree(tree['left'])):        lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])    # 对左子树进行剪枝    if isTree(tree['left']):        tree['left'] = prune(tree['left'], lSet)    # 对右子树进行剪枝    if isTree(tree['right']):        tree['right'] = prune(tree['right'], rSet)    #两个分支都不是子树    if not isTree(tree['left']) and not isTree(tree['right']):        lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])        #没有合并的误差        errorNoMerge = sum(power(lSet[:, -1] - tree['left'], 2)) + \                       sum(power(rSet[:, -1] - tree['right'], 2))        #有点疑问，如果左右子树样例个数不相等，则treeMean意义是什么？        treeMean = (tree['left'] + tree['right']) / 2.0        #合并后的误差        errorMerge = sum(power(testData[:, -1] - treeMean, 2))        if errorMerge < errorNoMerge:            print "merging"            return treeMean        else:            return tree    else:        return tree

2、模型树

#作用：将数据集格式化成目标变量Y和自变量X，并求回归系数向量#输入：数据集#输出：回归系数向量，自变量，目标变量def linearSolve(dataSet):    m, n = shape(dataSet)    X = mat(ones((m, n)))    Y = mat(ones((m, 1)))    X[:, 1:n] = dataSet[:, 0:n-1]#X[:, 0]为截距，均为1    Y = dataSet[:, -1]    xTx = X.T * X    if linalg.det(xTx) == 0.0:        raise NameError('This matrix is singular, cannot do inverse,\n\                        try increasing the second value of ops')    ws = xTx.I * (X.T * Y)    return ws, X, Y#作用：求数据集的回归系数向量#输入：数据集#输出：回归系数向量def modelLeaf(dataSet):    ws, X, Y = linearSolve(dataSet)    return ws#作用：求数据集的方差#输入：数据集#输出：数据集的方差def modelErr(dataSet):    ws, X, Y = linearSolve(dataSet)    yHat = X * ws    return sum(power(Y - yHat, 2))#作用：返回模型的浮点数#输入：模型，？#输出：模型的浮点数def regTreeEval(model, inDat):    return float(model)#作用：貌似没有出现过#输入：#输出：def modelTreeEval(model, inDat):    n = shape(inDat)[1]    X = mat(ones((1, n + 1)))    X[:, 1:n+1] = inDat    return float(X * model)#作用：预测测试数据在树中的值#输入：数，测试数据，树形式#输出：测试数据在树中的值def treeForeCast(tree, inData, modelEval = regTreeEval):    if not isTree(tree):        return modelEval(tree, inData)    if inData[tree['spInd']] > tree['spVal']:#inData[]值比根节点大，进入左子树        if isTree(tree['left']):            return treeForeCast(tree['left'], inData, modelEval)        else:            return modelEval(tree['left'], inData)    else:#inData[]值比根节点小，进入右子树        if isTree(tree['right']):            return treeForeCast(tree['right'], inData, modelEval)        else:            return modelEval(tree['right'], inData)#作用：预测测试数据集在树中的值#输入：数，测试数据集，树形式#输出：测试数据集在树中的值def createForeCast(tree, testData, modelEval = regTreeEval):    m = len(testData)    yHat = mat(zeros((m, 1)))    for i in range(m):        yHat[i, 0] = treeForeCast(tree, mat(testData[i]), modelEval)    return yHat

3、使用Python的Tkinter库创建GUI

#coding:gbkfrom numpy import *from Tkinter import *import regTreesimport matplotlibmatplotlib.use('TkAgg')from matplotlib.backends.backend_tkagg import FigureCanvasTkAggfrom matplotlib.figure import Figure#作用：重绘新面板#输入：容许的误差下降值，切分的最少样本数#输出：无def reDraw(tolS, tolN):    reDraw.f.clf()    reDraw.a = reDraw.f.add_subplot(111)    #检查复选框是否选中    if chkBtnVar.get():#复选框被选中，执行模型树        if tolN < 2:#切分的最少样本数不能少于2            tolN = 2        myTree = regTrees.createTree(reDraw.rawDat, regTrees.modelLeaf, regTrees.modelErr, (tolS, tolN))        yHat = regTrees.createForeCast(myTree, reDraw.testDat, regTrees.modelTreeEval)    else:#复选框没被选中，执行会归树        myTree = regTrees.createTree(reDraw.rawDat, ops = (tolS, tolN))        yHat = regTrees.createForeCast(myTree, reDraw.testDat)    #绘制sine.txt中的点    reDraw.a.scatter(reDraw.rawDat[:, 0], reDraw.rawDat[:, 1], s = 5)    #绘制得到的直线    reDraw.a.plot(reDraw.testDat, yHat, linewidth = 2.0)    reDraw.canvas.show()#作用：得到tolN和tolS的取值#输入：无#输出：无def getInputs():    # 得到tolN的取值    try:        tolN = int(tolNentry.get())    except:        tolN = 10        print "enter Integer for tolN"        tolNentry.delete(0, END)        tolNentry.insert(0, '10')    # 得到tolS的取值    try:        tolS = float(tolSentry.get())    except:        tolS = 1.0        print "enter Float for tolS"        tolSentry.delete(0, END)        tolSentry.insert(0, '1.0')    return tolN, tolS#作用：绘制新的树#输入：无#输出：无def drawNewTree():    tolN, tolS = getInputs()    reDraw(tolS, tolN)root = Tk()#绘制主面板reDraw.f = Figure(figsize = (5, 4), dpi = 100)reDraw.canvas = FigureCanvasTkAgg(reDraw.f, master = root)reDraw.canvas.show()reDraw.canvas.get_tk_widget().grid(row = 0, columnspan = 3)#创建退出按钮#Button(root, text = "Quit", fg = 'black', command = root.quit).grid(row = 1, column = 2)#插入标题标签#Label(root, text = "Plot Place Holder").grid(row = 0, columnspan = 3)#插入tolN标签Label(root, text = "tolN").grid(row = 1, column = 0)#插入tolN文本框tolNentry = Entry(root)tolNentry.grid(row = 1, column = 1)tolNentry.insert(0, '10')#插入tolS标签Label(root, text = "tolS").grid(row = 2, column = 0)#插入tolS文本框tolSentry = Entry(root)tolSentry.grid(row = 2, column = 1)tolSentry.insert(0, '1.0')#创建ReDraw按钮Button(root, text = "ReDraw", command = drawNewTree).grid(row = 1, column = 2, rowspan = 3)#创建按钮勾选状态变量chkBtnVar = IntVar()#创建Model Tree按钮chkBtn = Checkbutton(root, text = "Model Tree", variable = chkBtnVar)chkBtn.grid(row = 3, column = 0, columnspan = 2)#sine.txt中的数据集reDraw.rawDat = mat(regTrees.loadDataSet('exp2.txt'))#sine.txt第一行即x轴的最大值到最小值reDraw.testDat = arange(min(reDraw.rawDat[:, 0]), max(reDraw.rawDat[:, 0]), 0.01)reDraw(1.0, 10)root.mainloop()