本文将详细介绍C4.5算法在Python中的实现方法。
一、C4.5算法简介
C4.5算法是一种决策树学习算法，采用信息增益比来选择最优的划分属性。它通过对训练数据集进行递归划分，生成一棵决策树模型。C4.5算法的主要思想是以信息熵的减少作为选择最优划分属性的标准，同时考虑到属性的取值数目不同对信息增益的影响，引入了信息增益比来解决这个问题。
以下是C4.5算法的Python实现代码：
import math
def entropy(data):
n = len(data)
class_counts = {}
for row in data:
label = row[-1]
if label not in class_counts:
class_counts[label] = 0
class_counts[label] += 1
entropy = 0
for count in class_counts.values():
p = count / n
entropy -= p * math.log2(p)
return entropy
def information_gain(data, attribute_index):
original_entropy = entropy(data)
attribute_values = set([row[attribute_index] for row in data])
gain = original_entropy
for value in attribute_values:
subset = [row for row in data if row[attribute_index] == value]
p = len(subset) / len(data)
gain -= p * entropy(subset)
return gain / original_entropy
def choose_best_attribute(data, attributes):
best_gain = 0
best_attribute = None
for i, attribute in enumerate(attributes):
gain = information_gain(data, i)
if gain > best_gain:
best_gain = gain
best_attribute = attribute
return best_attribute
def create_decision_tree(data, attributes):
class_labels = set([row[-1] for row in data])
if len(class_labels) == 1:
return class_labels.pop()
if len(attributes) == 0:
class_counts = {}
for row in data:
label = row[-1]
if label not in class_counts:
class_counts[label] = 0
class_counts[label] += 1
return max(class_counts, key=class_counts.get)
best_attribute = choose_best_attribute(data, attributes)
decision_tree = {best_attribute: {}}
attribute_values = set([row[attributes.index(best_attribute)] for row in data])
for value in attribute_values:
subset = [row for row in data if row[attributes.index(best_attribute)] == value]
new_attributes = [attr for attr in attributes if attr != best_attribute]
decision_tree[best_attribute][value] = create_decision_tree(subset, new_attributes)
return decision_tree
二、C4.5算法步骤
1、计算数据集的熵值。
2、对于每个属性，计算其信息增益。
3、选择信息增益最大的属性作为划分属性。
4、根据划分属性的取值对数据集进行划分。
5、递归地对每个子数据集进行划分，直到满足终止条件。
三、C4.5算法实例
以下是一个使用C4.5算法进行鸢尾花分类的示例：
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score
iris = load_iris()
X_train, X_test, y_train, y_test = train_test_split(iris.data, iris.target, test_size=0.2, random_state=42)
attributes = ['sepal length', 'sepal width', 'petal length', 'petal width']
data = [list(row) + [target] for row, target in zip(X_train, y_train)]
decision_tree = create_decision_tree(data, attributes)
predictions = []
for sample in X_test:
node = decision_tree
while isinstance(node, dict):
attribute = list(node.keys())[0]
value = sample[attributes.index(attribute)]
node = node[attribute][value]
predictions.append(node)
accuracy = accuracy_score(y_test, predictions)
print("Accuracy:", accuracy)
四、总结
本文介绍了C4.5算法在Python中的实现方法，详细说明了算法的原理和步骤，并通过一个鸢尾花分类的实例演示了算法的应用。C4.5算法是一种经典的决策树学习算法，在实际应用中具有较好的效果。