import numpy as np
import math

#產生數據的函數
def createdatabase():
    dataSet = [[1,1,‘yes‘],[1,1,‘yes‘],[1,0,‘no‘],[0,1,‘no‘],[0,1,‘no‘]]
    labels = [[‘no surfacing‘],[‘flippers‘]]
    return dataSet,labels
dataSet,labels = createdatabase()
print(‘dataSet:‘,dataSet)
print()

#求數據的香農熵                    熵越大 混合的數據越多
 

def XN(dataSet):
    mydict = {}
    Sum = 0
    datasize = len(dataSet)
    for i in dataSet:
        mydict[i[-1]] = mydict.get(i[-1],0) + 1
    for key in mydict:
        P = mydict[key] / datasize
        Sum -= P * math.log(P,2)
    # print(‘dict:‘,mydict)
    # print(‘XN:‘,Sum)
    return
 
 Sum
# XN(dataSet)

def D_split(dataSet,axis,value):                #按某一列的某個值分數據    以dataset[axis]的value值分類  返回的數組比原數據少一列(少的axis這列)
    # print("data:{},axis:{},value:{}".format(dataSet,axis,value))
    result = []
    for i in dataSet:
        # print(i[axis],i[axis] == value,type(i[axis]))
        if
 
 i[axis] == value:
            # print(‘測試每行‘, i[axis])
            data1 = i[:axis]
            data2 = i[axis + 1:]
            data1.extend(data2)
            result.append(data1)
    return result
# partdata = D_split(dataSet,0,1)
#                                           partdata [[1, ‘yes‘], [1, ‘yes‘], [0, ‘yo‘]]

def chooseaxis(dataSet):                    #選擇最佳axis       返回最佳特征值的序號
    datasize = len(dataSet)                 #數據行數(長度)
    baseXN = XN(dataSet)                    #原始數據的熵值
    bestaxis = 0  # 最好的axis選擇默認為0
    for axis in range(len(dataSet[0]) - 1):                 #axis 為列號
        value_list = [row[axis] for row in dataSet]             #把該列的所有value組成一個列表
        value_list = set(value_list)                             #去重
        newXN = 0                                                #設置新熵值
        for value in value_list:
            partdata = D_split(dataSet,axis,value)
            P = len(partdata) / datasize                         #求該value的概率
            newXN += P * XN(partdata)
        # print(‘partdata:{},P:{},axis為:{},newXH:{}‘.format(partdata,P,axis,newXN))            # axis為:0,newXH:0.5509775004326937
                                                                    # axis為:1,newXH:0.8
        if newXN < baseXN:
            baseXN = newXN
            bestaxis = axis
    print(‘bestaxis:{},XN:{}‘.format(bestaxis,baseXN))           # bestaxis:0,XN:0.5509775004326937
    return bestaxis

def major(classlist):                           #少數服從多數函數   返回較多的類型
    classcount = {}
    for i in classlist:
        classcount[i] = classcount.get(i,0) + 1
    classcount = sorted(classcount,key=classcount.get)
    return classcount[-1]

classlist = [i[2] for i in dataSet]
print(‘classlist:‘,classlist)
# mydict = major(classlist)

def createtree(dataSet,labels):                       #構造樹
    classlist = [i[-1] for i in dataSet]
    if len(dataSet) == classlist.count(classlist[0]):
        return classlist[0]
    if len(dataSet[0]) == 1:
        return major(classlist)
    axis = chooseaxis(dataSet)
    label_choose = labels[axis]
    # print(‘label_choose‘,label_choose)
    del labels[axis]
    mytree = {label_choose[0]:{}}                                         #定義需要返回的樹 以當前分類特征為key
    for value in [row[axis] for row in dataSet]:
        newlables = labels[:]                                               #如果直接傳lables，列表元素傳值是傳的引用，會影響，所以這裏用切片切個一樣的副本，不能單純的‘=‘，不然還是引用
        mytree[label_choose[0]][value] = createtree(D_split(dataSet,axis,value),newlables)
    print("mytree:\n",mytree)
    return mytree
createtree(dataSet,labels)
# 結果如下：
# {‘no surfacing‘: {1: {‘flippers‘: {1: ‘yes‘, 0: ‘no‘}}, 0: ‘no‘}}

機器學習之--決策樹遞歸算法實現