决策树算法详解

import math from collections import Counter def entropy(labels): """计算信息熵""" n = len(labels) if n == 0: return 0 counts = Counter(labels) return -sum((c/n) * math.log2(c/n) for c in counts.values()) def best_split(X, y, features): """选择最佳分裂特征（基于信息增益）""" base_ent = entropy(y) best_ig, best_feat = -1, None for feat in features: values = set(row[feat] for row in X) weighted_ent = 0 for val in values: sub_y = [y[i] for i, row in enumerate(X) if row[feat] == val] weighted_ent += (len(sub_y) / len(y)) * entropy(sub_y) ig = base_ent - weighted_ent if ig > best_ig: best_ig, best_feat = ig, feat return best_feat def build_tree(X, y, features, depth=0, max_depth=10): """递归构建决策树""" # 停止条件：纯节点、无特征、达到最大深度 if len(set(y)) == 1: return y[0] if not features or depth >= max_depth: return Counter(y).most_common(1)[0][0] feat = best_split(X, y, features) if feat is None: return Counter(y).most_common(1)[0][0] tree = {feat: {}} values = set(row[feat] for row in X) remaining = [f for f in features if f != feat] for val in values: sub_X = [row for row in X if row[feat] == val] sub_y = [y[i] for i, row in enumerate(X) if row[feat] == val] tree[feat][val] = build_tree(sub_X, sub_y, remaining, depth+1, max_depth) return tree def predict(tree, sample): """用决策树预测单个样本""" if not isinstance(tree, dict): return tree feat = list(tree.keys())[0] val = sample.get(feat) subtree = tree[feat].get(val) if subtree is None: return None # 未知特征值 return predict(subtree, sample) # 使用示例 data = [ {'天气': '晴', '湿度': '高', '风力': '弱'}, {'天气': '晴', '湿度': '高', '风力': '强'}, {'天气': '阴', '湿度': '高', '风力': '弱'}, {'天气': '雨', '湿度': '高', '风力': '弱'}, {'天气': '雨', '湿度': '正常', '风力': '弱'}, ] labels = ['不打球', '不打球', '打球', '打球', '打球'] features = ['天气', '湿度', '风力'] tree = build_tree(data, labels, features, max_depth=5) print(tree) print(predict(tree, {'天气': '晴', '湿度': '正常', '风力': '弱'}))

from sklearn.tree import DecisionTreeClassifier from sklearn.model_selection import train_test_split from sklearn.metrics import accuracy_score, classification_report from sklearn.datasets import load_iris # 加载数据 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 ) # 训练决策树 clf = DecisionTreeClassifier( criterion='gini', # 'gini' 或 'entropy' max_depth=4, # 最大深度 min_samples_split=5, # 内部节点最少样本数 min_samples_leaf=2, # 叶节点最少样本数 random_state=42 ) clf.fit(X_train, y_train) # 预测与评估 y_pred = clf.predict(X_test) print(f"Accuracy: {accuracy_score(y_test, y_pred):.4f}") print(classification_report(y_test, y_pred, target_names=iris.target_names))

from sklearn.tree import DecisionTreeRegressor from sklearn.metrics import mean_squared_error, r2_score import numpy as np # 回归树用法完全类似，只是 criterion 不同 reg = DecisionTreeRegressor( criterion='squared_error', # 也支持 'friedman_mse', 'absolute_error' max_depth=5, min_samples_leaf=5, random_state=42 ) reg.fit(X_train, y_train) y_pred = reg.predict(X_test) print(f"MSE: {mean_squared_error(y_test, y_pred):.4f}") print(f"R^2: {r2_score(y_test, y_pred):.4f}")

# 查看各特征的重要性 import pandas as pd importances = clf.feature_importances_ feat_imp = pd.DataFrame({ 'feature': iris.feature_names, 'importance': importances }).sort_values('importance', ascending=False) print(feat_imp)

# 使用 CCP 后剪枝 # 1. 获取不同 alpha 值对应的剪枝路径 path = clf.cost_complexity_pruning_path(X_train, y_train) ccp_alphas = path.ccp_alphas # 2. 对每个 alpha 训练决策树 clfs = [] for alpha in ccp_alphas: c = DecisionTreeClassifier(ccp_alpha=alpha, random_state=42) c.fit(X_train, y_train) clfs.append(c) # 3. 评估训练集和测试集准确率，选择最佳 alpha train_scores = [c.score(X_train, y_train) for c in clfs] test_scores = [c.score(X_test, y_test) for c in clfs] best_idx = np.argmax(test_scores) best_alpha = ccp_alphas[best_idx] print(f"Best alpha: {best_alpha:.4f}, Test Accuracy: {test_scores[best_idx]:.4f}")

import matplotlib.pyplot as plt from sklearn.tree import plot_tree fig, ax = plt.subplots(figsize=(20, 10)) plot_tree( clf, feature_names=iris.feature_names, class_names=iris.target_names, filled=True, # 按类别填充颜色 rounded=True, # 圆角方框 fontsize=10, ax=ax ) plt.tight_layout() plt.savefig('decision_tree.png', dpi=150) plt.show()

from sklearn.tree import export_graphviz import graphviz # 导出 DOT 格式 dot_data = export_graphviz( clf, feature_names=iris.feature_names, class_names=iris.target_names, filled=True, rounded=True, special_characters=True ) # 渲染为图片 graph = graphviz.Source(dot_data) graph.render('iris_tree', format='png', cleanup=True) # 保存为 iris_tree.png graph # 在 Jupyter Notebook 中直接显示

from sklearn.tree import export_text # 纯文本形式打印决策树规则 tree_rules = export_text(clf, feature_names=iris.feature_names) print(tree_rules) # 输出类似： # |--- petal length (cm) <= 2.45 # | |--- class: setosa # |--- petal length (cm) > 2.45 # | |--- petal width (cm) <= 1.75 # | | |--- class: versicolor # | |--- petal width (cm) > 1.75 # | | |--- class: virginica