上一篇博客主要介紹了決策樹的原理，這篇主要介紹他的實現，代碼環境python 3.4，實現的是ID3算法，首先為了后面matplotlib的繪圖方便，我把原來的中文數據集變成了英文。

原始數據集：

變化后的數據集在程序代碼中體現，這就不截圖了

構建決策樹的代碼如下：

#coding :utf-8'''2017.6.25 author :Erin    function: "decesion tree" ID3   '''import numpy as npimport pandas as pdfrom math import logimport operator def load_data():  #data=np.array(data) data=[['teenager' ,'high', 'no' ,'same', 'no'],   ['teenager', 'high', 'no', 'good', 'no'],   ['middle_aged' ,'high', 'no', 'same', 'yes'],   ['old_aged', 'middle', 'no' ,'same', 'yes'],   ['old_aged', 'low', 'yes', 'same' ,'yes'],   ['old_aged', 'low', 'yes', 'good', 'no'],   ['middle_aged', 'low' ,'yes' ,'good', 'yes'],   ['teenager' ,'middle' ,'no', 'same', 'no'],   ['teenager', 'low' ,'yes' ,'same', 'yes'],   ['old_aged' ,'middle', 'yes', 'same', 'yes'],   ['teenager' ,'middle', 'yes', 'good', 'yes'],   ['middle_aged' ,'middle', 'no', 'good', 'yes'],   ['middle_aged', 'high', 'yes', 'same', 'yes'],   ['old_aged', 'middle', 'no' ,'good' ,'no']] features=['age','input','student','level'] return data,features def cal_entropy(dataSet): ''' 輸入data ,表示帶最后標簽列的數據集 計算給定數據集總的信息熵 {'是': 9, '否': 5} 0.9402859586706309 '''  numEntries = len(dataSet) labelCounts = {} for featVec in dataSet:  label = featVec[-1]  if label not in labelCounts.keys():   labelCounts[label] = 0  labelCounts[label] += 1 entropy = 0.0 for key in labelCounts.keys():  p_i = float(labelCounts[key]/numEntries)  entropy -= p_i * log(p_i,2)#log(x,10)表示以10 為底的對數 return entropy def split_data(data,feature_index,value): ''' 劃分數據集 feature_index：用于劃分特征的列數，例如“年齡” value:劃分后的屬性值：例如“青少年” ''' data_split=[]#劃分后的數據集 for feature in data:  if feature[feature_index]==value:   reFeature=feature[:feature_index]   reFeature.extend(feature[feature_index+1:])   data_split.append(reFeature) return data_splitdef choose_best_to_split(data):  ''' 根據每個特征的信息增益，選擇最大的劃分數據集的索引特征 '''  count_feature=len(data[0])-1#特征個數4 #print(count_feature)#4 entropy=cal_entropy(data)#原數據總的信息熵 #print(entropy)#0.9402859586706309  max_info_gain=0.0#信息增益最大 split_fea_index = -1#信息增益最大，對應的索引號  for i in range(count_feature):    feature_list=[fe_index[i] for fe_index in data]#獲取該列所有特征值  #######################################  '''  print('feature_list')  ['青少年', '青少年', '中年', '老年', '老年', '老年', '中年', '青少年', '青少年', '老年',  '青少年', '中年', '中年', '老年']  0.3467680694480959 #對應上篇博客中的公式 =（1）*5/14  0.3467680694480959  0.6935361388961918  '''  # print(feature_list)  unqval=set(feature_list)#去除重復  Pro_entropy=0.0#特征的熵  for value in unqval:#遍歷改特征下的所有屬性   sub_data=split_data(data,i,value)   pro=len(sub_data)/float(len(data))   Pro_entropy+=pro*cal_entropy(sub_data)   #print(Pro_entropy)     info_gain=entropy-Pro_entropy  if(info_gain>max_info_gain):   max_info_gain=info_gain   split_fea_index=i return split_fea_index    ##################################################def most_occur_label(labels): #sorted_label_count[0][0] 次數最多的類標簽 label_count={} for label in labels:  if label not in label_count.keys():   label_count[label]=0  else:   label_count[label]+=1  sorted_label_count = sorted(label_count.items(),key = operator.itemgetter(1),reverse = True) return sorted_label_count[0][0]def build_decesion_tree(dataSet,featnames): ''' 字典的鍵存放節點信息，分支及葉子節點存放值 ''' featname = featnames[:]    ################ classlist = [featvec[-1] for featvec in dataSet] #此節點的分類情況 if classlist.count(classlist[0]) == len(classlist): #全部屬于一類  return classlist[0] if len(dataSet[0]) == 1:   #分完了,沒有屬性了  return Vote(classlist)  #少數服從多數 # 選擇一個最優特征進行劃分 bestFeat = choose_best_to_split(dataSet) bestFeatname = featname[bestFeat] del(featname[bestFeat])  #防止下標不準 DecisionTree = {bestFeatname:{}} # 創建分支,先找出所有屬性值,即分支數 allvalue = [vec[bestFeat] for vec in dataSet] specvalue = sorted(list(set(allvalue))) #使有一定順序 for v in specvalue:  copyfeatname = featname[:]  DecisionTree[bestFeatname][v] = build_decesion_tree(split_data(dataSet,bestFeat,v),copyfeatname) return DecisionTree