金融网站框架模板,在线设计海报的网站,个人网站制作多少钱,兰州响应式网站建设基尼系数实现决策树
基尼指数 Gini ( D ) 1 − ∑ k 1 K ( ∣ C k ∣ ∣ D ∣ ) 2 \operatorname{Gini}(D)1-\sum_{k1}^{K}\left(\frac{\left|C_{k}\right|}{|D|}\right)^{2} Gini(D)1−k1∑K(∣D∣∣Ck∣)2
特征 A A A条件下集合 D D D的基尼指数#xff1a; Gi…基尼系数实现决策树
基尼指数 Gini ( D ) 1 − ∑ k 1 K ( ∣ C k ∣ ∣ D ∣ ) 2 \operatorname{Gini}(D)1-\sum_{k1}^{K}\left(\frac{\left|C_{k}\right|}{|D|}\right)^{2} Gini(D)1−k1∑K(∣D∣∣Ck∣)2
特征 A A A条件下集合 D D D的基尼指数 Gini ( D , A ) ∣ D 1 ∣ ∣ D ∣ Gini ( D 1 ) ∣ D 2 ∣ ∣ D ∣ Gini ( D 2 ) \operatorname{Gini}(D, A)\frac{\left|D_{1}\right|}{|D|} \operatorname{Gini}\left(D_{1}\right)\frac{\left|D_{2}\right|}{|D|} \operatorname{Gini}\left(D_{2}\right) Gini(D,A)∣D∣∣D1∣Gini(D1)∣D∣∣D2∣Gini(D2)
import numpy as npdef calculate_gini(labels):# 计算标签的基尼系数_, counts np.unique(labels, return_countsTrue)probabilities counts / len(labels)gini 1 - np.sum(probabilities ** 2)return ginidef calculate_gini_index(data, labels, feature_index, threshold):# 根据给定的特征和阈值划分数据left_mask data[:, feature_index] thresholdright_mask data[:, feature_index] thresholdleft_labels labels[left_mask]right_labels labels[right_mask]# 计算左右子集的基尼系数left_gini calculate_gini(left_labels)right_gini calculate_gini(right_labels)# 计算基尼指数total_gini calculate_gini(labels)left_weight len(left_labels) / len(labels)right_weight len(right_labels) / len(labels)gini_index (left_weight * left_gini) (right_weight * right_gini)return gini_indexdef find_best_split(data, labels):num_features data.shape[1]best_gini_index float(inf)best_feature_index -1best_threshold Nonefor feature_index in range(num_features):feature_values data[:, feature_index]unique_values np.unique(feature_values)for threshold in unique_values:gini_index calculate_gini_index(data, labels, feature_index, threshold)if gini_index best_gini_index:best_gini_index gini_indexbest_feature_index feature_indexbest_threshold thresholdreturn best_feature_index, best_thresholddef create_decision_tree(data, labels):# 基本情况如果所有标签都相同则返回一个叶节点其中包含该标签if len(np.unique(labels)) 1:return {label: labels[0]}# 找到最佳的划分特征best_feature_index, best_threshold find_best_split(data, labels)# 创建一个新的内部节点其中包含最佳特征和阈值node {feature_index: best_feature_index,threshold: best_threshold,left: None,right: None}# 根据最佳特征和阈值划分数据left_mask data[:, best_feature_index] best_thresholdright_mask data[:, best_feature_index] best_thresholdleft_data data[left_mask]left_labels labels[left_mask]right_data data[right_mask]right_labels labels[right_mask]# 递归创建左右子树node[left] create_decision_tree(left_data, left_labels)node[right] create_decision_tree(right_data, right_labels)return nodedef predict(node, sample):if label in node:return node[label]feature_value sample[node[feature_index]]if feature_value node[threshold]:return predict(node[left], sample)else:return predict(node[right], sample)# 示例数据集
data np.array([[1, 2, 0],[1, 2, 1],[1, 3, 1],[2, 3, 1],[2, 3, 0],[2, 2, 0],[1, 1, 0],[1, 1, 1],[2, 1, 1],[1, 3, 0]
])labels np.array([0, 1, 1, 1, 0, 0, 0, 1, 1, 1])# 创建决策树
decision_tree create_decision_tree(data, labels)# 测试数据
test_data np.array([[1, 2, 0],[2, 1, 1],[1, 3, 1],[2, 3, 0]
])# 预测结果
for sample in test_data:prediction predict(decision_tree, sample)print(f样本: {sample}, 预测标签: {prediction})
