实现决策树的ID3算法

import pandas as pd 
import numpy as np 
from math import log
def entropy(ele):
    # ele:类别取值的列表
    # 计算列表中取值的概率分布
    probs=[ele.count(i)/len(ele) for i in set(ele)]
    # 计算信息熵
    entropy=-sum([prob*log(prob,2) for prob in probs])
    return entropy
# 划分函数
def df_split(df,col):
    '''
    df:待划分的训练数据
    col:划分数据的依据特征
    '''
    # 获取依据特征的不同取值
    unique_col_val=df[col].unique()
    # 创建划分结果的数据框字典
    res_dict={elem:pd.DataFrame for elem in unique_col_val}
    # 根据特征取值进行划分
    for key in res_dict.keys():
        res_dict[key]=df[:][df[col]==key]
    # 根据特征取值划分后的不同数据集字典
    return res_dict
 
# 选择最优参数
def choose_best_feature(df,label):
    '''
    df:待划分的训练数据
    label:训练标签
    max_value:最大信息增益值
    best_feature:最优参数
    max_splited:根据最优特征划分后的数据字典
    '''
    entropy_D=entropy(df[label].tolist())
    cols=[col for col in df.columns if col not in [label]]
    max_value,best_feature=-999,None
    max_splited=None
    # 遍历特征并根据特征取值划分
    for col in cols:
        splited_set=df_split(df,col)
        entropy_DA=0
        for subset_col,subset in splited_set.items():
            # 计算划分后的数据子集的标签信息熵
            entropy_Di=entropy(subset[label].tolist())
            # 计算当前特征的经验条件熵
            entropy_DA+=len(subset)/len(df)*entropy_Di
        # 计算当前特征的信息增益
        info_gain=entropy_D-entropy_DA
        if info_gain>max_value:
            max_value,best_feature=info_gain,col
            max_splited=splited_set
    return max_value,best_feature,max_splited
 
class ID3Tree:
    # 定义决策树的结点类
    class TreeNode:
        # 定义树节点
        def __init__(self,name):
            self.name=name
            self.connections={}
        # 定义树连接
        def connect(self,label,node):
            self.connections[label]=node
    def __init__(self,df,label):
        self.columns=df.columns
        self.df=df
        self.label=label
        self.root=self.TreeNode("Root")
    # 构建树的调用
    def construct_tree(self):
        self.construct(self.root,"",self.df,self.columns)
    # 决策树的构建方法
    def construct(self,parent_node,parent_label,subset_df,colums):
        # 选择最优特征
        max_value,best_feature,max_splited=choose_best_feature(subset_df[colums],self.label)
        if not best_feature:
            node=self.TreeNode(subset_df[self.label].iloc[0])
            parent_node.connect(parent_label,node)
            return 
        
        # 根据最有特征以及子节点构建树
        node=self.TreeNode(best_feature)
        parent_node.connect(parent_label,node)
        # 以A—Ai为新的特征集
        new_columns=[col for col in colums if col != best_feature]
        # 递归构造决策树
        for splited_value,splited_data in max_splited.items():
            self.construct(node,splited_value,splited_data,new_columns)
 
df=pd.read_csv(r'监督学习单模型\6.决策树\example_data.csv')
id3_tree=ID3Tree(df,'play')
id3_tree.construct_tree()