详解机器学习的决策树算法(DT)-以及划分数据集的ID3算法

1：什么是决策树
顾名思义：决策树就是根据已有的条件进行决策从而产生的一棵树。
比如，这就是一颗决策树，根据不同的取值决定不同的走向

2、那么如何根据现有的属性来决定谁是第一个节点，谁是第二个节点呢，这里就要用到ID3算法了
Id3 算法大家可以搜一下，就是利用信息熵来计算的，根据信息增益每次找到最合适的来当树根，这样，就会更符合实际情况

3、有了建树的方法，接下来就是进行建树，建树是递归建立的，代码在底下，大家可以自己理解一下

4：最后利用输入训练数据进行训练，然后对测试数据进行树上的查找，从而进行预测

import numpy
from math import log
import operator
import treePlotter

# 计算熵的函数
def calcShannonEnt(dataSet):
    numEntries = len(dataSet)
    labelCounts = {}
    for featVec in dataSet: #the the number of unique elements and their occurance
        currentLabel = featVec[-1]
        if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
        labelCounts[currentLabel] += 1
    shannonEnt = 0.0
    for key in labelCounts:
        prob = float(labelCounts[key])/numEntries
        shannonEnt -= prob * log(prob,2) #log base 2
    return shannonEnt

# 创建数据集
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

# 测试
# dataSet , labels =createDataSet()
# ans = calcShannonEnt(dataSet)
# 熵越高，混合的数据就越多
# print(ans)

# 划分数据集，没有计算熵，直接分类
def splitDataSet(dataSet, axis, value):
    # 参数： 待划分的数据集，划分数据集的特征的列，按照该列进行分类的值，如果该列中有符合这个value的值，那么就会被分为一类
    # 注意：python 语言在函数中传递的是列表的引用，在函数内部对列表对象的修改，
    #   将会直接影响列表对象，所以，这里重新声明了一个列表
    retDataSet = []
    # dataSet中的数据也是列表
    for featVec in dataSet:
        # 讲符合特征的数据抽取出来
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]     #chop out axis used for splitting
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

# 通过计算熵来进行分类，调用上面计算熵的函数和朴素分类的算法
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.items(), key=operator.itemgetter(1), reverse=True)
    return sortedClassCount[0][0]


# 递归构造决策树,ID3  算法
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

# 划分数据集测试
dataSet , labels =createDataSet()
# ans =  splitDataSet(dataSet,0,0)        # 对dataset进行分类，按照地0列，值为0的进行归类
# print(ans)
# ans =  chooseBestFeatureToSplit(dataSet)
# print("对结果影响最大的一列是："+str(ans))

# 构造决策树
myTree = createTree(dataSet,labels)
# print(myTree)

# 使用matplotlib 绘制树
#####################     省略

# 测试算法：使用决策树进行分类
# 使用决策树的分类函数
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

# 使用pickle 模块存储决策树
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)

本来想利用决策树优化手写数字的识别，但是暂时没写出来。。。还是不太回写。。。后期再发吧。。

参考文献-machine learning -peter harrington