决策树练习

数据预处理分析，最后面附有决策树算法的实现
原始数据：
原数据地址

计算第一次决策如果
分别对在14天各个属性下是否进行施肥的统计情况且计算该属性的基尼指数，同一种属性不同表现的基尼指数表示为M，加权平均之后为节点的基尼指数，用N表示
天气：

#encoding = utf-8
import pandas as pd

Base_file = pd.read_excel('Data.xlsx')
Base_file.head(15)
#Base_file.head()
Weather_Sunny = Base_file[Base_file['天气'] == '晴天']['是否施肥'].value_counts()
#print(Weather_Sunny)['否' '否' '否' '是' '是']
Weather_Rainy = Base_file[Base_file['天气'] == '雨天']['是否施肥'].value_counts()
Weather_Overcast = Base_file[Base_file['天气'] == '阴天']['是否施肥'].value_counts()
Weather_Overcast['否'] = 0
Weather_df = pd.DataFrame([
    pd.Series([Weather_Sunny['是'], Weather_Sunny['否']], index = ['是', '否']),
    pd.Series([Weather_Rainy['是'], Weather_Rainy['否']], index = ['是', '否']),
    pd.Series([Weather_Overcast['是'], Weather_Overcast['否']], index = ['是', '否'])
], index=['晴天', '雨天', '阴天'])
Weather_df.head()

晴天：M1 = 2 * 2/5 * (1 - 2/5) = 0.444444445
雨天：M2 = 2 * 3/5 * (1 - 3/5) = 0.48
阴天：M3 = 0
N1 = 5/14 * M1 + 5/14 * M2 = 0.343
温度：

Hot = Base_file[Base_file['温度'] == '炎热']['是否施肥'].value_counts()
Cool = Base_file[Base_file['温度'] == '温']['是否施肥'].value_counts()
Cold = Base_file[Base_file['温度'] == '冷']['是否施肥'].value_counts()
Temperature_df = pd.DataFrame([
    pd.Series([Hot['是'], Hot['否']], index = ['是', '否']),
    pd.Series([Cool['是'], Cool['否']], index = ['是', '否']),
    pd.Series([Cold['是'], Cold['否']], index = ['是', '否'])
], index = ['炎热', '温', '冷'])
Temperature_df.head()

炎热：M1 = 2 * 2/4 * (1 - 2/4) = 0.5
温 ： M2 = 2 * 2/6 * (1 - 2/6) = 0.44444445
冷： M3 = 2 * 3/4 * (1 - 3/4) = 0.375
N2 = 4/14 * M1 + 6/14 * M2 + 4/14 * M3 = 0.440

湿度：

Humidity_high = Base_file[Base_file['湿度'] == '高']['是否施肥'].value_counts()
Humidity_mid = Base_file[Base_file['湿度'] == '中']['是否施肥'].value_counts()
Humidity_df = pd.DataFrame([
    pd.Series([Humidity_high['是'], Humidity_high['否']], index = ['是', '否']),
    pd.Series([Humidity_mid['是'], Humidity_mid['否']], index = ['是', '否'])
], index = ['高', '中'])
Humidity_df.head()

高：M1 = 2 * 3/4 * (1 - 3/4) = 0.375
中：M2 = 2 * 6/7 * (1 - 6/7) = 0.245
N3 = 1/2 * M1 + 1/2 * M2 = 0.310

风力：

Wind_strong = Base_file[Base_file['风力'] == '强风']['是否施肥'].value_counts()
Wind_weak = Base_file[Base_file['风力'] == '弱风']['是否施肥'].value_counts()
Wind_df = pd.DataFrame([
   pd.Series([Wind_strong['是'], Wind_strong['否']], index = ['是', '否']),
   pd.Series([Wind_weak['是'], Wind_weak['否']], index = ['是', '否'])
], index = ['强风', '弱风'])
Wind_df.head()

强风：M1 = 2 * 3/6 * (1 - 3/6) = 0.5
弱风：M2 = 2 * 6/8 * (1 - 6/8) = 0.375
N4 = 6/14 * M1 + 8/14 * M2 = 0.429
因为N2 > N4 > N1 > N3，所以第一次决策应根据湿度来分类：

因为此次分类之后，然未出现叶子节点，所以需要分别对第二排的两个节点进行分类，过程与第一次决策类似，计算各个属性下是否进行施肥的统计情况且计算该属性的基尼指数
左右节点的数据分别如下：

Base_file = pd.read_excel('Data.xlsx')
Base_file.head(15)
Temperature_df_high = Base_file[Base_file['湿度'] == '高']
Temperature_df_high.head(14)

先对左边节点分析：
天气：

Weather_Sunny = Temperature_df_high[Temperature_df_high['天气'] == '晴天']['是否施肥'].value_counts()
Weather_Sunny['是'] = 0
#print(Weather_Sunny)['否' '否' '否' '是' '是']
Weather_Rainy = Temperature_df_high[Temperature_df_high['天气'] == '雨天']['是否施肥'].value_counts()
Weather_Overcast = Temperature_df_high[Temperature_df_high['天气'] == '阴天']['是否施肥'].value_counts()
Weather_Overcast['否'] = 0
Weather_df = pd.DataFrame([
    pd.Series([Weather_Sunny['是'], Weather_Sunny['否']], index = ['是', '否']),
    pd.Series([Weather_Rainy['是'], Weather_Rainy['否']], index = ['是', '否']),
    pd.Series([Weather_Overcast['是'], Weather_Overcast['否']], index = ['是', '否'])
], index=['晴天', '雨天', '阴天'])
Weather_df.head()

晴天：M1 = 0
雨天：M2 = 0.5
阴天：M3 = 0
N1 = 2/7 * M2 = 0.143
温度：

Hot = Temperature_df_high[Temperature_df_high['温度'] == '炎热']['是否施肥'].value_counts()
Cool = Temperature_df_high[Temperature_df_high['温度'] == '温']['是否施肥'].value_counts()
Cold = Temperature_df_high[Temperature_df_high['温度'] == '冷']['是否施肥'].value_counts()
Cold['是'] = 0
Cold['否'] = 0
Temperature_df = pd.DataFrame([
    pd.Series([Hot['是'], Hot['否']], index = ['是', '否']),
    pd.Series([Cool['是'], Cool['否']], index = ['是', '否']),
    pd.Series([Cold['是'], Cold['否']], index = ['是', '否'])
], index = ['炎热', '温', '冷'])
Temperature_df.head()

炎热：M1 = 0.44444444445
温： M2 = 0.5
冷： M3 = 0
N2 = 3/7 * M1 + 4/7 * M3 = 0.476

风力：

Wind_strong = Temperature_df_high[Temperature_df_high['风力'] == '强风']['是否施肥'].value_counts()
Wind_weak = Temperature_df_high[Temperature_df_high['风力'] == '弱风']['是否施肥'].value_counts()
Wind_df = pd.DataFrame([
    pd.Series([Wind_strong['是'], Wind_strong['否']], index = ['是', '否']),
    pd.Series([Wind_weak['是'], Wind_weak['否']], index = ['是', '否'])
], index = ['强风', '弱风'])
Wind_df.head()

强风：M1 = 0.44444444445
弱风：M2 =0.5
N3 = 3/7 * M1 + 4/7 * M2 = 0.476

N1 > N2 = N3
所以左边的节点来说应该根据天气情况来分类
对右边节点分析：
天气：

Weather_Sunny = Temperature_df_mid[Temperature_df_mid['天气'] == '晴天']['是否施肥'].value_counts()
Weather_Sunny['否'] = 0
Weather_Rainy = Temperature_df_mid[Temperature_df_mid['天气'] == '雨天']['是否施肥'].value_counts()
Weather_Overcast = Temperature_df_mid[Temperature_df_mid['天气'] == '阴天']['是否施肥'].value_counts()
Weather_Overcast['否'] = 0
Weather_df = pd.DataFrame([
   pd.Series([Weather_Sunny['是'], Weather_Sunny['否']], index = ['是', '否']),
   pd.Series([Weather_Rainy['是'], Weather_Rainy['否']], index = ['是', '否']),
   pd.Series([Weather_Overcast['是'], Weather_Overcast['否']], index = ['是', '否'])
], index=['晴天', '雨天', '阴天'])
Weather_df.head()

晴天：M1 = 0
雨天：M2 = 0.444444444445
阴天：M3 = 0
N1 = 3/7 * M2 = 0.190

温度：

Hot = Temperature_df_mid[Temperature_df_mid['温度'] == '炎热']['是否施肥'].value_counts()
Hot['否'] = 0
Cool = Temperature_df_mid[Temperature_df_mid['温度'] == '温']['是否施肥'].value_counts()
Cool['否'] = 0
Cold = Temperature_df_mid[Temperature_df_mid['温度'] == '冷']['是否施肥'].value_counts()

Temperature_df = pd.DataFrame([
  pd.Series([Hot['是'], Hot['否']], index = ['是', '否']),
  pd.Series([Cool['是'], Cool['否']], index = ['是', '否']),
  pd.Series([Cold['是'], Cold['否']], index = ['是', '否'])
], index = ['炎热', '温', '冷'])
Temperature_df.head()

炎热：M1 = 0
温： M2 = 0
冷： M3 = 2 * 3/4 * (1 - 3/4) = 0.375
N2 = 3/7 * M3 = 0.214

风力：

Wind_strong = Temperature_df_mid[Temperature_df_mid['风力'] == '强风']['是否施肥'].value_counts()
Wind_weak = Temperature_df_mid[Temperature_df_mid['风力'] == '弱风']['是否施肥'].value_counts()
Wind_weak['否'] = 0
Wind_df = pd.DataFrame([
    pd.Series([Wind_strong['是'], Wind_strong['否']], index = ['是', '否']),
    pd.Series([Wind_weak['是'], Wind_weak['否']], index = ['是', '否'])
], index = ['强风', '弱风'])
Wind_df.head()

强风：M1 = 2 * 2/3 * (1 - 2/3) = 0.44444445
弱风：M2 = 0
N3 = 3/7 * M2 = 0.190

N1 = N3 > N2
这里可以有两种分类决策方法，这里选择使用天气属性对右边节点进行分类，结合对左边节点的分析，对第二层的分类如下：

经过第二次分类之后，出现了叶子节点，只剩下两个节点需要继续分类，且只剩下温度和风力两个属性，下面是第二次分类之后的左右两个节点数据：

Weather_df_Rainy1 = Base_file[Base_file['湿度'] == '高'][Base_file['天气'] == '雨天']
Weather_df_Rainy1.head()
Weather_df_Rainy2 = Base_file[Base_file['湿度'] == '中'][Base_file['天气'] == '雨天']
Weather_df_Rainy2.head()

对于左边节点：
温度：

Hot = Weather_df_Rainy1[Weather_df_Rainy1['温度'] == '炎热']['是否施肥'].value_counts()
Hot['是'] = 0
Hot['否'] = 0
Cool = Weather_df_Rainy1[Weather_df_Rainy1['温度'] == '温']['是否施肥'].value_counts()
Cold = Weather_df_Rainy1[Weather_df_Rainy1['温度'] == '冷']['是否施肥'].value_counts()
Cold['是'] = 0
Cold['否'] = 0

Temperature_df = pd.DataFrame([
    pd.Series([Hot['是'], Hot['否']], index = ['是', '否']),
    pd.Series([Cool['是'], Cool['否']], index = ['是', '否']),
    pd.Series([Cold['是'], Cold['否']], index = ['是', '否'])
], index = ['炎热', '温', '冷'])
Temperature_df.head()

炎热：M1 = 0
温： M2 = 2 * 1/2 * (1 – 1/2) = 0.5
冷： M3 = 0
N1 = M2 = 0.5

风力：

Hot = Weather_df_Rainy1[Weather_df_Rainy1['温度'] == '炎热']['是否施肥'].value_counts()
Hot['是'] = 0
Hot['否'] = 0
Cool = Weather_df_Rainy1[Weather_df_Rainy1['温度'] == '温']['是否施肥'].value_counts()
Cold = Weather_df_Rainy1[Weather_df_Rainy1['温度'] == '冷']['是否施肥'].value_counts()
Cold['是'] = 0
Cold['否'] = 0

Temperature_df = pd.DataFrame([
   pd.Series([Hot['是'], Hot['否']], index = ['是', '否']),
   pd.Series([Cool['是'], Cool['否']], index = ['是', '否']),
   pd.Series([Cold['是'], Cold['否']], index = ['是', '否'])
], index = ['炎热', '温', '冷'])
Temperature_df.head()

强风：M1 = 0
弱风：M2 = 0
N2 = 0

N1 > N2
所以左边的节点应用风力属性继续往后分类
对右边节点分析：
温度：

Hot = Weather_df_Rainy2[Weather_df_Rainy2['温度'] == '炎热']['是否施肥'].value_counts()
Hot['是'] = 0
Hot['否'] = 0
Cool = Weather_df_Rainy2[Weather_df_Rainy2['温度'] == '温']['是否施肥'].value_counts()
Cool['否'] = 0
Cold = Weather_df_Rainy2[Weather_df_Rainy2['温度'] == '冷']['是否施肥'].value_counts()
Temperature_df = pd.DataFrame([
   pd.Series([Hot['是'], Hot['否']], index = ['是', '否']),
   pd.Series([Cool['是'], Cool['否']], index = ['是', '否']),
   pd.Series([Cold['是'], Cold['否']], index = ['是', '否'])
], index = ['炎热', '温', '冷'])
Temperature_df.head()

炎热：M1 = 0
温： M2 = 0
冷： M3 = 2 * 1/2 * (1 – 1/2) = 0.5
N1 = M3 = 0.5

风力：

Wind_strong = Weather_df_Rainy2[Weather_df_Rainy2['风力'] == '强风']['是否施肥'].value_counts()
Wind_strong['是'] = 0
Wind_weak = Weather_df_Rainy2[Weather_df_Rainy2['风力'] == '弱风']['是否施肥'].value_counts()
Wind_weak['否'] = 0
Wind_df = pd.DataFrame([
   pd.Series([Wind_strong['是'], Wind_strong['否']], index = ['是', '否']),
   pd.Series([Wind_weak['是'], Wind_weak['否']], index = ['是', '否'])
], index = ['强风', '弱风'])
Wind_df.head()

强风：M1 = 0
弱风：M2 = 0
N2 = 0

N1 > N2
所以右边边的节点应用风力属性继续往后分类，决策图如下：

可以看出第二次分类再经过风力的分类之后，此时决策树最后一排的节点全部变为了叶子节点，说明至此，分类完成。
算法实现：

#encoding = utf-8
import numpy as np
import pandas as pd
import operator

def CalcGiNiIndex(DataSet) :
    Num_length = len(DataSet)
    labelcounts = {
     }
    for feature in DataSet :
        currentlabel = feature[-1]
        #用字典统计类别及其数目
        if currentlabel not in labelcounts.keys() :
            labelcounts[currentlabel] = 1
        else :
            labelcounts[currentlabel] += 1
    GiNi_index = 0
    for key in labelcounts.keys() :
        #二分类求基尼指数：GiNi = 2 * p * （1 - p）
        GiNi_index = 2 * (float(labelcounts[key]) / Num_length) * (1 - float(labelcounts[key]) / Num_length)
    return GiNi_index

def createDataSet() :
    DataSet = [['晴天', '炎热', '高', '弱风', '否'],
                 ['晴天', '炎热', '高', '强风', '否'],
                 ['阴天', '炎热', '高', '弱风', '是'],
                 ['雨天', '温', '高', '弱风', '是'],
                 ['雨天', '冷', '中', '弱风', '是'],
                 ['雨天', '冷', '中', '强风', '否'],
                 ['阴天', '冷', '中', '强风', '是'],
                 ['晴天', '温', '高', '弱风', '否'],
                 ['晴天', '冷', '中', '弱风', '是'],
                 ['雨天', '温', '中', '弱风', '是'],
                 ['晴天', '温', '中', '强风', '是'],
                 ['阴天', '温', '高', '强风', '是'],
                 ['阴天', '炎热', '中', '弱风', '是'],
                 ['雨天', '温', '高', '强风', '否']]
#     file = pd.read_excel('Data.xlsx')
#     DataSet = file.iloc[ : , 1 : ]
#     DataSet = np.array(DataSet)
    labels = ['天气', '温度', '湿度', '风力']
    
    return DataSet, labels

def splitDataSet(DataSet, axis, value): 
    #计算以某个特征分类后剩下的数据量。
    #axis表示第i个特征，value表示在改特征的情况下的具体表现，如天气特征有雨天。阴天等。
    retDataSet = []
    #创建一个新列表，准备提取数据
    for featVec in DataSet :
        #剔除在数据集中需要被分类的特征的列行
        if featVec[axis] == value :
            reducedFeatVec = featVec[ : axis]
            reducedFeatVec.extend(featVec[axis + 1 : ])
            retDataSet.append(reducedFeatVec)
    return retDataSet

def ChooseBestFeatureToSplit(DataSet) :
    #计算父亲节点的GiNi指数
    FatherGiNi = CalcGiNiIndex(DataSet)
    BestIoFoGain = 0
    BestFeature = -1
    numFeature = len(DataSet[0]) - 1
    #去掉最后一列
    for i in range(numFeature) :
        #每个特征下的具体表现形式
        featList = [example[i] for example in DataSet]
        uniqueVals = set(featList)#去重复
        newGiNi = 0
        for value in uniqueVals :
            #计算每一种表现形式GiNi指数的权重和
            subData = splitDataSet(DataSet, i, value)
            prob = len(subData) / float(len(DataSet))
            newGiNi += prob * CalcGiNiIndex(subData)
        infogain = FatherGiNi - newGiNi#计算信息增益
        if infogain > BestIoFoGain :
            #比较信息增益的大小，更新最佳分类的特征
            BestIoFoGain = infogain
            BestFeature = i
    return BestFeature

def majorityCnt(classList):    #按分类后类别数量排序，比如：最后分类为2yes1no，则判定为yes；
    classCount={
     }
    for vote in classList:
        if vote not in classCount.keys():
            classCount[vote]=0
        classCount[vote]+=1
    #字典逆序排序
    sortedClassCount = sorted(classCount.items(), key = lambda x : x[1], reverse=True)
    return sortedClassCount[0][0]

def createTree(DataSet, labels) :
    ConditionList = [example[-1] for example in DataSet]
    #list.count(element) 方法用于统计某个元素在列表中出现的次数。
    if ConditionList.count(ConditionList[0]) == len(ConditionList) :#yes or no
        return ConditionList[0]
    #dataSet[0]取矩阵第一行，dataSet[0][0]取矩阵第一行第一列元素
    #递归终止条件2：使用完所有特征，则返回最后出现次数最多的那个标签
    if len( DataSet[0] ) == 1:   
        return majorityCnt(classList)
    
     #以上两个终止条件都不满足，开始选择最优特征划分，已经有了一个方框，准备往方框中写入判断问题
    BestFeature = ChooseBestFeatureToSplit(DataSet)
    BestFeatLabel = labels[BestFeature]
    mytree = {
     BestFeatLabel : {
     }}
    #用过了该特征，将该特征从所有特征列表中删除
    del (labels[BestFeature])
    featValues = [example[BestFeature] for example in DataSet]
    uniqueVals = set(featValues)
    for value in uniqueVals:
        subLabels = labels[ : ]
        splitdata = splitDataSet(DataSet, BestFeature, value)
        #递归
        mytree[BestFeatLabel][value] = createTree(splitdata, subLabels)
    return mytree

DataSet, labels = createDataSet()# 创造示列数据
print(createTree(DataSet, labels))# 输出决策树模型结果