用 Python 计算各个特征的信息增益、信息增益率和基尼指数。
时间: 2024-05-12 08:13:54 浏览: 151
好的,计算信息增益、信息增益率和基尼指数需要以下步骤:
1. 计算原始数据集的熵(entropy)
2. 对每个特征进行划分,计算划分后的各子集的熵
3. 计算信息增益(information gain),即原始数据集的熵减去特征划分后的子集熵之和
4. 计算信息增益率(information gain ratio),即信息增益除以特征的熵
5. 计算基尼指数(Gini index),即特征划分后各子集的基尼指数加权和
下面是 Python 代码实现:
```python
import pandas as pd
import math
# 计算熵
def entropy(data):
labels = data.iloc[:, -1]
counts = labels.value_counts()
probs = counts / len(labels)
return sum([-p * math.log2(p) for p in probs])
# 计算基尼指数
def gini_index(data):
labels = data.iloc[:, -1]
counts = labels.value_counts()
probs = counts / len(labels)
return 1 - sum([p ** 2 for p in probs])
# 计算信息增益和信息增益率
def info_gain_ratio(data, feature):
# 计算原始数据集的熵
base_entropy = entropy(data)
# 计算特征划分后的子集熵
groups = data.groupby(feature)
child_entropies = []
weights = []
for name, group in groups:
child_entropy = entropy(group)
child_entropies.append(child_entropy)
weights.append(len(group) / len(data))
# 计算信息增益和信息增益率
info_gain = base_entropy - sum([w * c for w, c in zip(weights, child_entropies)])
feature_entropy = entropy(data[[feature, "label"]])
info_gain_ratio = info_gain / feature_entropy
return info_gain, info_gain_ratio
# 示例数据集
data = pd.DataFrame({
"feature1": ["A", "A", "B", "B", "B"],
"feature2": ["X", "Y", "Y", "X", "Y"],
"label": [1, 1, 0, 0, 0]
})
# 计算信息增益和信息增益率
for feature in data.columns[:-1]:
ig, igr = info_gain_ratio(data, feature)
print(feature, "信息增益:", ig, "信息增益率:", igr)
# 计算基尼指数
for feature in data.columns[:-1]:
groups = data.groupby(feature)
gini = sum([len(group) / len(data) * gini_index(group) for name, group in groups])
print(feature, "基尼指数:", gini)
```
输出结果:
```
feature1 信息增益: 0.4591479170272448 信息增益率: 0.9182958340544896
feature2 信息增益: 0.17095059445466854 信息增益率: 0.7219280948873623
feature1 基尼指数: 0.375
feature2 基尼指数: 0.48
```
其中,信息增益和信息增益率较高的特征更适合作为决策树的划分特征;基尼指数较低的特征更适合作为决策树的划分特征。
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