首先是對於決策樹的個人理解：
通過尋找最大資訊增益（或最小資訊熵）的分類特徵，從部分已知類別的資料中提取分類規則的一種分類方法。
資訊熵：

其中，log底數為2，額，好吧，圖片我從百度截的。。
這裡只解釋到它是一種資訊的期望值，深入的請看維基百科

資訊增益：劃分資料集前後的資訊發生的變化（原書定義）
實際應用想要找到具有最大資訊增益的分類樹結構，就是使原始資料的資訊熵減去分類後的資訊熵的差值最大，原始資料的資訊熵可以理解為常數，那麼想要最大資訊增益，也就是要尋找一種分類方法，是按照分類方法分類後的資料集的資訊熵最小。（另：也可以選擇“不純度”或“錯誤率”作為評估引數，不純度，維基百科下，錯誤率就是字面意思）
所以找到最優分類樹結構程式碼如下：

def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0; bestFeature = -1
    for i in range(numFeatures):        #iterate over all the features
        featList = [example[i] for
 
 example in dataSet]#create a list of all the examples of this feature
        uniqueVals = set(featList)       #get a set of unique values
        newEntropy = 0.0
        for value in uniqueVals:
            subDataSet = splitDataSet(dataSet, i, value)
            prob = len(subDataSet)/float(len(dataSet))
            newEntropy += prob * calcShannonEnt(subDataSet)     
        infoGain = baseEntropy - newEntropy     #calculate the info gain; ie reduction in entropy
 

        if (infoGain > bestInfoGain):       #compare this to the best gain so far
            bestInfoGain = infoGain         #if better than current best, set to best
            bestFeature = i
    return bestFeature     

按照“尋找最大資訊增益的方式”，找到對於已知類別的一批資料（訓練集）的最優決策樹，然後用這個樹結構去分類未知資料（測試集），整體程式碼如下：

#!/usr/bin/env python
# coding=utf-8
'''
Created on Oct 12, 2010
Decision Tree Source Code for Machine Learning in Action Ch. 3
@author: Peter Harrington
'''
from math import log
import operator

def createDataSet():
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing','flippers']
    #change to discrete values
    return dataSet, labels

def calcShannonEnt(dataSet):
    # 計算香儂熵
    numEntries = len(dataSet)
    labelCounts = {}
    # 儲存特徵的字典
    for featVec in dataSet: #the the number of unique elements and their occurance
        currentLabel = featVec[-1]
        # 取最後一個元素，即該組特徵的label
        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
        # 如果沒有，增加新key，value初始化為0
        labelCounts[currentLabel] += 1
        # 對應key的值累計
    shannonEnt = 0.0
    for key in labelCounts:
        prob = float(labelCounts[key])/numEntries
        shannonEnt -= prob * log(prob,2) #log base 2
        # shannon公式：shanonEnt ＝（負的）求和（i.prob*log(i.prob,2))
    return shannonEnt

def splitDataSet(dataSet, axis, value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
            reducedFeatVec.extend(featVec[axis+1:])
            # 簡單的分片，除去分類特徵，餘下的新增到容器中
            retDataSet.append(reducedFeatVec)
    return retDataSet

def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0]) - 1      #the last column is used for the labels
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain = 0.0; bestFeature = -1
    for i in range(numFeatures):        #iterate over all the features
        featList = [example[i] for example in dataSet]#create a list of all the examples of this feature
        uniqueVals = set(featList)       #get a set of unique values
        newEntropy = 0.0
        for value in uniqueVals:
            subDataSet = splitDataSet(dataSet, i, value)
            prob = len(subDataSet)/float(len(dataSet))
            newEntropy += prob * calcShannonEnt(subDataSet)     
        infoGain = baseEntropy - newEntropy     #calculate the info gain; ie reduction in entropy
        if (infoGain > bestInfoGain):       #compare this to the best gain so far
            bestInfoGain = infoGain         #if better than current best, set to best
            bestFeature = i
    return bestFeature                      #returns an integer

def majorityCnt(classList):
    classCount={}
    for vote in classList:
        if vote not in classCount.keys(): classCount[vote] = 0
        classCount[vote] += 1
    sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]

def createTree(dataSet,labels):
    classList = [example[-1] for example in dataSet]
    if classList.count(classList[0]) == len(classList): 
        return classList[0]#stop splitting when all of the classes are equal
    if len(dataSet[0]) == 1: #stop splitting when there are no more features in dataSet
        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[:]       #copy all of labels, so trees don't mess up existing labels
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
    return myTree                            

def classify(inputTree,featLabels,testVec):
    firstStr = inputTree.keys()[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)
    key = testVec[featIndex]
    valueOfFeat = secondDict[key]
    if isinstance(valueOfFeat, dict): 
        classLabel = classify(valueOfFeat, featLabels, testVec)
    else: classLabel = valueOfFeat
    return classLabel

def storeTree(inputTree,filename):
    import pickle
    fw = open(filename,'w')
    pickle.dump(inputTree,fw)
    fw.close()

def grabTree(filename):
    import pickle
    fr = open(filename)
    return pickle.load(fr)

if __name__ == '__main__':
    (dataSet, labels) = createDataSet();
    print dataSet;print labels
    shannonEnt = calcShannonEnt(dataSet)
    print shannonEnt
    myTree = createTree(dataSet,labels )
    print 'mytree:'
    print myTree
    (dataSet, labels) = createDataSet();
    print classify(myTree,labels, [1,1])
    import treePlotter
    # treePlotter.createPlot(myTree)
    fr = open('lenses.txt')
    lenses = [inst.strip().split('\t') for inst in fr.readlines()]
    lensesLabels = ['age','prescript','astigmatic','tearRate']
    lensesTree = createTree(lenses,lensesLabels)
    print lensesTree
    treePlotter.createPlot(lensesTree)

部分地方加入了中文註釋，原著的那幾行英文註釋很好就沒有再換成中文的。
之前沒有詳細看過決策樹，以為它就是把分類邏輯變為樹結構，多個if else，說說個人學習後，對於決策樹的理解：
1.還是覺得它就是多個if else，樹結構也可以這麼理解吧
2.構建的過程或者說收斂條件是：最大資訊增益（最小資訊熵）
3.優點：可讀性強，邏輯簡單易懂，計算步驟不超過樹的深度；缺點：極易過擬合，得到的樹結構泛性不強
4.正因為過度追求最優解，導致決策樹往往會過擬合，原著是通過構建以後的合併細小或相近分支，也就是“後置裁剪”，但是這樣時間上有浪費，代表的是K-Fold Cross Validation，不斷裁剪，評估當前的錯誤率，有點類似於整體求解後，再反過來找恰當的“early stop”；另一種就是著名的隨機森林，系統複雜了，效果確實會好，額，隨機森林具體的以後深度學習下補上。
下面是原著利用matplolib畫圖的程式碼：

'''
Created on Oct 14, 2010

@author: Peter Harrington
'''
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)