### Python 实现决策树的示例代码 以下是基于给定引用以及专业知识构建的一个完整的 Python 决策树实现示例。此代码涵盖了创建数据集、计算熵、选择最优特征分裂点并最终生成决策树的过程。 #### 数据准备 首先定义一个简单的数据集用于演示决策树的学习过程： ```python def create_dataset(): dataset = [ [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no'] ] labels = ['feature_1', 'feature_2'] # 特征标签 return dataset, labels ``` #### 计算香农熵 (Shannon Entropy) 为了评估数据集中的不确定性，可以使用以下方法来计算香农熵： ```python from math import log def calc_shannon_entropy(dataset): num_entries = len(dataset) label_counts = {} for feature_vector in dataset: current_label = feature_vector[-1] if current_label not in label_counts.keys(): label_counts[current_label] = 0 label_counts[current_label] += 1 shannon_entropy = 0.0 for key in label_counts: prob = float(label_counts[key]) / num_entries shannon_entropy -= prob * log(prob, 2) # 使用log base 2 return shannon_entropy ``` #### 划分数据集 通过特定特征和其可能取值分割数据集的方法如下所示： ```python def split_dataset(dataset, axis, value): ret_dataset = [] for feature_vec in dataset: if feature_vec[axis] == value: reduced_feature_vec = feature_vec[:axis] reduced_feature_vec.extend(feature_vec[axis+1:]) ret_dataset.append(reduced_feature_vec) return ret_dataset ``` #### 选取最佳划分方式 利用信息增益挑选出能够最大化减少不确定性的特征作为节点的最佳划分依据： ```python def choose_best_splitting_feature(dataset): num_features = len(dataset[0]) - 1 # 减去最后一列分类标签 base_entropy = calc_shannon_entropy(dataset) best_info_gain = 0.0; best_feature_index = -1 for i in range(num_features): # 遍历所有特征 unique_values_for_this_feature = set([example[i] for example in dataset]) new_entropy = 0.0 for value in unique_values_for_this_feature: sub_dataset = split_dataset(dataset, i, value) probability_of_value = len(sub_dataset)/float(len(dataset)) new_entropy += probability_of_value * calc_shannon_entropy(sub_dataset) info_gain = base_entropy - new_entropy # 计算信息增益 if(info_gain > best_info_gain): # 更新最大信息增益及其对应的特征索引 best_info_gain = info_gain best_feature_index = i return best_feature_index # 返回具有最高信息增益的特征编号[^1]. ``` #### 构建决策树 递归地建立整个决策树结构直到满足停止条件为止： ```python def majority_count(class_list): class_count = {} for vote in class_list: if vote not in class_count.keys(): class_count[vote] = 0 class_count[vote] += 1 sorted_class_count = sorted(class_count.items(), key=lambda item:item[1], reverse=True) return sorted_class_count[0][0] def create_decision_tree(dataset, labels): class_list = [example[-1] for example in dataset] if class_list.count(class_list[0]) == len(class_list): return class_list[0] # 如果所有的类标签完全相同，则返回该类标签 if len(dataset[0]) == 1: # 当没有更多特征可供进一步划分时 return majority_count(class_list) # 返回出现次数最多的类别 best_feat_idx = choose_best_splitting_feature(dataset) best_feat_label = labels[best_feat_idx] decision_tree = {best_feat_label:{}} del(labels[best_feat_idx]) # 删除已使用的特征名 feat_values = [example[best_feat_idx] for example in dataset] unique_vals = set(feat_values) for val in unique_vals: sub_labels = labels[:] # 复制一份剩余的特征列表以防修改原表 decision_tree[best_feat_label][val] = create_decision_tree(split_dataset(dataset, best_feat_idx, val), sub_labels) return decision_tree # 返回构造完成后的决策树[^2]. ``` #### 可视化决策树（可选） 如果希望直观展示所得到的结果，还可以加入绘图功能： ```python import matplotlib.pyplot as plt def get_num_leaves(tree_dict): num_leaves = 0 first_str = list(tree_dict.keys())[0] second_dict = tree_dict[first_str] for key in second_dict.keys(): if type(second_dict[key]).__name__=='dict': num_leaves += get_num_leaves(second_dict[key]) else: num_leaves +=1 return num_leaves def plot_node(node_txt, center_pt, parent_pt, node_type): arrow_args = dict(arrowstyle="<-", color='black') font_size=12 create_plot.ax1.annotate(node_txt, xy=parent_pt, xycoords='axes fraction', xytext=center_pt, textcoords='axes fraction', va="center", ha="center", bbox=node_type, arrowprops=arrow_args ) def retrieve_tree(i): trees=[{'no surfacing': {0: 'no', 1: {'flippers': \ {0: 'no', 1: 'yes'}}}}, {'no surfacing': {0: 'no', 1: {'flippers': \ {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}} ] return trees[i] def create_plot(in_tree): fig = plt.figure(1, facecolor='white') fig.clf() axprops = dict(xticks=[], yticks=[]) create_plot.ax1 = plt.subplot(111, frameon=False, **axprops) total_width = float(get_num_leaves(in_tree)) total_depth = float(max_depth(in_tree)) x_off = -0.5/total_width; y_off = 1.0 plot_tree(in_tree, (0.5,1.0), '', total_width, total_depth) plt.show() def max_depth(tree_dict): depth = 0 first_str = list(tree_dict.keys())[0] second_dict = tree_dict[first_str] for key in second_dict.keys(): if isinstance(second_dict[key], dict): this_depth = 1 + max_depth(second_dict[key]) else: this_depth = 1 if this_depth > depth: depth = this_depth return depth decision_tree_example = retrieve_tree(0) create_plot(decision_tree_example) ``` 以上即为一个基本版的手动编写Python决策树模型流程概述与部分核心代码片段[^1].