用python实现C4.5算法生成决策树
时间: 2023-11-25 15:06:06 浏览: 50
好的,下面我将为您介绍如何用Python实现C4.5算法生成决策树。
C4.5算法是一种基于熵增益的决策树算法,它的核心思想是通过计算每个特征对应的信息增益比来选择最优特征进行划分。下面是具体的实现过程:
1. 定义节点类和决策树类
```python
class Node:
def __init__(self, feature=None, label=None, children=None):
self.feature = feature # 划分该节点的特征
self.label = label # 叶子节点的标签
self.children = children or {} # 子节点
class DecisionTree:
def __init__(self, epsilon=0.1):
self.epsilon = epsilon # 停止划分的阈值
self.root = None # 决策树的根节点
```
2. 构建决策树
```python
def build_tree(self, data, labels):
self.root = self.build_tree_recursive(data, labels)
def build_tree_recursive(self, data, labels):
# 如果数据集为空,返回None
if len(data) == 0:
return None
# 如果所有样本属于同一类别,返回叶子节点
if len(set(labels)) == 1:
return Node(label=labels[0])
# 如果特征集合为空,返回叶子节点,标记为样本数最多的类别
if len(data[0]) == 0:
label = max(set(labels), key=labels.count)
return Node(label=label)
# 选择最优特征
best_feature, best_gain_ratio = self.choose_best_feature(data, labels)
# 如果信息增益比小于阈值,返回叶子节点,标记为样本数最多的类别
if best_gain_ratio < self.epsilon:
label = max(set(labels), key=labels.count)
return Node(label=label)
# 递归构建子树
children = {}
for value in set([sample[best_feature] for sample in data]):
sub_data, sub_labels = self.split_data(data, labels, best_feature, value)
children[value] = self.build_tree_recursive(sub_data, sub_labels)
return Node(feature=best_feature, children=children)
```
3. 选择最优特征
```python
def choose_best_feature(self, data, labels):
num_features = len(data[0])
base_entropy = self.calc_shannon_entropy(labels)
best_feature = -1
best_gain_ratio = 0
# 计算每个特征对应的信息增益比
for i in range(num_features):
feature_values = [sample[i] for sample in data]
unique_values = set(feature_values)
new_entropy = 0
# 计算该特征下每个取值对应的信息熵
for value in unique_values:
sub_data, sub_labels = self.split_data(data, labels, i, value)
prob = len(sub_data) / float(len(data))
new_entropy += prob * self.calc_shannon_entropy(sub_labels)
# 计算信息增益比
info_gain = base_entropy - new_entropy
intrinsic_value = self.calc_intrinsic_value(feature_values)
gain_ratio = info_gain / intrinsic_value
# 选择信息增益比最大的特征
if gain_ratio > best_gain_ratio:
best_feature = i
best_gain_ratio = gain_ratio
return best_feature, best_gain_ratio
```
4. 划分数据集
```python
def split_data(self, data, labels, feature_idx, value):
sub_data = []
sub_labels = []
for i in range(len(data)):
if data[i][feature_idx] == value:
sub_data.append(data[i][:feature_idx] + data[i][feature_idx+1:])
sub_labels.append(labels[i])
return sub_data, sub_labels
```
5. 计算信息熵和属性固有值
```python
def calc_shannon_entropy(self, labels):
num_samples = len(labels)
label_counts = {}
# 计算每个类别出现的次数
for label in labels:
label_counts[label] = label_counts.get(label, 0) + 1
# 计算信息熵
entropy = 0
for label in label_counts:
prob = label_counts[label] / float(num_samples)
entropy -= prob * math.log(prob, 2)
return entropy
def calc_intrinsic_value(self, feature_values):
num_samples = len(feature_values)
value_counts = {}
# 计算每个取值出现的次数
for value in feature_values:
value_counts[value] = value_counts.get(value, 0) + 1
# 计算属性固有值
iv = 0
for value in value_counts:
prob = value_counts[value] / float(num_samples)
iv -= prob * math.log(prob, 2)
return iv
```
以上就是用Python实现C4.5算法生成决策树的全部过程,您可以根据需要进行调整和优化。
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