python实现id3算法

ID3算法是一种决策树学习算法，用于分类和预测。下面是Python实现ID3算法的基本步骤：

1. 导入相应的库：

import pandas as pd
import numpy as np
import math

2. 定义一个函数来计算数据集的熵：

def entropy(target_col):
    elements, counts = np.unique(target_col, return_counts=True)
    entropy = np.sum(
        [(-counts[i]/np.sum(counts)) * np.log2(counts[i]/np.sum(counts)) for i in range(len(elements))]
    )
    return entropy

3. 定义一个函数来计算数据集中每个特征的信息增益：

def info_gain(data, split_attribute_name, target_name="class"):
    total_ent = entropy(data[target_name])
    vals, counts = np.unique(data[split_attribute_name], return_counts=True)
    weighted_ent = np.sum(
        [(counts[i]/np.sum(counts)) * entropy(data.where(data[split_attribute_name] == vals[i]).dropna()[target_name])
         for i in range(len(vals))]
    )
    info_gain = total_ent - weighted_ent
    return info_gain

4. 定义一个函数来选择具有最高信息增益的特征：

def ID3(data, original_data, features, target_attribute_name="class", parent_node_class=None):
    if len(np.unique(data[target_attribute_name])) <= 1:
        return np.unique(data[target_attribute_name])[0]
    elif len(data) == 0:
        return np.unique(original_data[target_attribute_name])[
            np.argmax(np.unique(original_data[target_attribute_name], return_counts=True)[1])]
    elif len(features) == 0:
        return parent_node_class
    else:
        parent_node_class = np.unique(data[target_attribute_name])[
            np.argmax(np.unique(data[target_attribute_name], return_counts=True)[1])]
        item_values = [info_gain(data, feature, target_attribute_name) for feature in features]
        best_feature_index = np.argmax(item_values)
        best_feature = features[best_feature_index]
        tree = {best_feature: {}}
        features = [i for i in features if i != best_feature]
        for value in np.unique(data[best_feature]):
            sub_data = data.where(data[best_feature] == value).dropna()
            subtree = ID3(sub_data, original_data, features, target_attribute_name, parent_node_class)
            tree[best_feature][value] = subtree
        return tree

5. 最后，我们使用训练数据来构建一棵决策树：

def train_test_split(dataset, split_ratio=0.8):
    train_size = int(split_ratio * len(dataset))
    train_set = dataset.sample(train_size)
    test_set = dataset.drop(train_set.index)
    return train_set.reset_index(drop=True), test_set.reset_index(drop=True)

data = pd.read_csv("dataset.csv")
train_data, test_data = train_test_split(data)

tree = ID3(train_data, train_data, train_data.columns[:-1])

这样我们就可以得到一个基本的ID3算法实现。需要注意的是，这个实现并不包括一些优化技巧，例如剪枝等，因此在实际应用中可能需要进行一定的修改。