ID3决策树搭建

import numpy as np
import pandas as pd
from sklearn.tree import DecisionTreeClassifier, export_text
from sklearn.preprocessing import LabelEncoder

# 1. 准备数据（论坛客户流失数据）
data = {
    'gender': ['男', '女', '男', '女', '男', '女', '男', '女', '男', '女'],
    'Activity_info': ['高', '中', '低', '高', '中', '低', '高', '中', '低', '高'],
    'churn': ['否', '否', '是', '否', '是', '是', '否', '是', '是', '否']
}
df = pd.DataFrame(data)

print("=== 原始数据 ===")
print(df)

# 2. 计算信息熵
def entropy(labels):
    """计算信息熵"""
    _, counts = np.unique(labels, return_counts=True)
    probabilities = counts / len(labels)
    return -np.sum(probabilities * np.log2(probabilities))

# 3. 计算条件熵
def conditional_entropy(feature, labels):
    """计算条件熵"""
    unique_values = np.unique(feature)
    total = len(labels)
    cond_ent = 0
    for value in unique_values:
        subset = labels[feature == value]
        weight = len(subset) / total
        cond_ent += weight * entropy(subset)
    return cond_ent

# 4. 计算信息增益
def information_gain(feature, labels):
    """计算信息增益"""
    return entropy(labels) - conditional_entropy(feature, labels)

# 5. 计算各特征的信息增益
labels = df['churn'].values
print(f"\n=== 信息熵 ===")
print(f"H(D) = {entropy(labels):.4f}")

print(f"\n=== 各特征的信息增益 ===")
for feature_name in ['gender', 'Activity_info']:
    feature = df[feature_name].values
    ig = information_gain(feature, labels)
    print(f"{feature_name}: 信息增益 = {ig:.4f}")

# 6. 构建ID3决策树
# 编码
le_gender = LabelEncoder()
le_activity = LabelEncoder()
le_churn = LabelEncoder()

X = np.column_stack([
    le_gender.fit_transform(df['gender']),
    le_activity.fit_transform(df['Activity_info'])
])
y = le_churn.fit_transform(df['churn'])

# 创建决策树（criterion='entropy'表示使用信息增益，即ID3）
clf = DecisionTreeClassifier(criterion='entropy', random_state=42)
clf.fit(X, y)

# 7. 查看决策树结构
print(f"\n=== 决策树结构 ===")
tree_text = export_text(clf, 
                       feature_names=['gender', 'Activity_info'],
                       class_names=le_churn.classes_)
print(tree_text)

# 8. 预测新样本
new_sample = np.array([[0, 0]])  # 男, 高活跃
prediction = clf.predict(new_sample)
print(f"\n新样本预测: {le_churn.inverse_transform(prediction)[0]}")