三种决策树总结

import numpy as np

# 1. 三种决策树的划分标准计算
def entropy(labels):
    """熵"""
    _, counts = np.unique(labels, return_counts=True)
    probabilities = counts / len(labels)
    return -np.sum(probabilities * np.log2(probabilities))

def conditional_entropy(feature, labels):
    """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

def information_gain(feature, labels):
    """信息增益（ID3）"""
    return entropy(labels) - conditional_entropy(feature, labels)

def feature_entropy(feature):
    """特征熵"""
    return entropy(feature)

def information_gain_ratio(feature, labels):
    """信息增益率（C4.5）"""
    ig = information_gain(feature, labels)
    fe = feature_entropy(feature)
    return ig / fe if fe > 0 else 0

def gini(labels):
    """基尼值"""
    _, counts = np.unique(labels, return_counts=True)
    probabilities = counts / len(labels)
    return 1 - np.sum(probabilities ** 2)

def gini_index(feature, labels):
    """基尼指数（CART）"""
    unique_values = np.unique(feature)
    total = len(labels)
    gi = 0
    for value in unique_values:
        subset = labels[feature == value]
        weight = len(subset) / total
        gi += weight * gini(subset)
    return gi

# 2. 示例数据
labels = np.array(['A', 'A', 'A', 'B', 'B', 'B'])
feature = np.array(['alpha', 'alpha', 'alpha', 'alpha', 'beta', 'beta'])

# 3. 计算三种指标
print("=== 三种决策树划分标准 ===")
ig = information_gain(feature, labels)
igr = information_gain_ratio(feature, labels)
gi = gini_index(feature, labels)

print(f"ID3 - 信息增益: {ig:.4f} (越大越好)")
print(f"C4.5 - 信息增益率: {igr:.4f} (越大越好)")
print(f"CART - 基尼指数: {gi:.4f} (越小越好)")

# 4. 基尼值示例
print("\n=== 基尼值示例 ===")
datasets = {
    '10个红球': np.array(['红'] * 10),
    '5红5蓝': np.array(['红'] * 5 + ['蓝'] * 5),
    '4红3蓝3绿': np.array(['红'] * 4 + ['蓝'] * 3 + ['绿'] * 3),
    '10个不同类': np.array([str(i) for i in range(10)])
}

for name, data in datasets.items():
    g = gini(data)
    print(f"{name}: 基尼值 = {g:.4f}")

# 5. CART二叉树处理多分类
print("\n=== CART二叉树处理多分类 ===")
# 婚姻状况：结婚、单身、离异
labels_multi = np.array(['结婚', '结婚', '单身', '单身', '离异', '离异'])
feature_multi = np.array(['A', 'A', 'B', 'B', 'C', 'C'])

# 三种二分类方式
splits = [
    ('结婚 vs 其他', np.array([1, 1, 0, 0, 0, 0])),
    ('单身 vs 其他', np.array([0, 0, 1, 1, 0, 0])),
    ('离异 vs 其他', np.array([0, 0, 0, 0, 1, 1]))
]

for name, split in splits:
    gi = gini_index(split, labels_multi)
    print(f"{name}: 基尼指数 = {gi:.4f}")

# 6. 三种决策树特点总结
print("\n=== 三种决策树特点总结 ===")
print("ID3:")
print("  - 划分标准: 信息增益 (越大越好)")
print("  - 数据类型: 离散")
print("  - 缺点: 偏向取值多的特征")

print("\nC4.5:")
print("  - 划分标准: 信息增益率 (越大越好)")
print("  - 数据类型: 离散+连续")
print("  - 缺点: 不适合大数据集")

print("\nCART:")
print("  - 划分标准: 基尼指数 (越小越好)")
print("  - 数据类型: 离散+连续")
print("  - 任务: 分类+回归")
print("  - 特点: 二叉树")