前面在Python编程实现基于基尼指数进行划分选择的决策树（CART决策树）算法中实现了基础的不进行剪枝操作的CART决策树，但是在现实情况中决策树很容易出现过拟合的现象。剪枝（pruning）是决策树学习中对付过拟合的一种常用的方法。决策树剪枝的基本策略有预剪枝和后剪枝。本文主要是对预剪枝的实现。预剪枝是指在决策树的生成过程中，对每个结点在划分前后先进行评估，如果当前结点的划分不能带来决策树泛化性能的提升，则停止划分，并将当前结点标记为叶结点。通俗来讲就是对每个结点比较对这个结点进行划分和不对这个结点进行划分这两种情况下决策树在测试数据集上的正确率，选择正确率大的那种方式。
下面是预剪枝CART决策树的Python代码实现，在实现的时候为了省劲儿，使用了之前写的不剪枝的CART决策树里面的一些函数，所以代码有点冗余，以后有时间的话再重新整理修改一下。如果在阅读中发现任何问题，欢迎通过QQ进行交流。
# 预剪枝的CART决策树
from Ch04DecisionTree import TreeNode
from Ch04DecisionTree import Dataset
from Ch04DecisionTree import cart
def current_accuracy(tree_node=TreeNode.TreeNode(), test_data=[], test_label=[]):
"""
计算当前决策树在训练数据集上的正确率
:param tree_node: 要判断的决策树结点
:param test_data: 测试数据集
:param test_label: 测试数据集的label
:return:
"""
root_node = tree_node
while not root_node.parent is None:
root_node = root_node.parent
accuracy = 0
for i in range(0, len(test_label)):
this_label = cart.classify_data(root_node, test_data[i])
if this_label == test_label[i]:
accuracy += 1
# print(str(tree_node.index) + " 处，分对了"+str(accuracy))
return accuracy / len(test_label)
def finish_node(current_node=TreeNode.TreeNode(), data=[], label=[], test_data=[], test_label=[]):
"""
完成一个结点上的计算
:param current_node: 当前计算的结点
:param data: 数据集
:param label: 数据集的 label
:param test_data: 测试数据集
:param test_label: 测试数据集的label
:return:
"""
n = len(label)
# 判断当前结点中的数据是否属于同一类
one_class = True
this_data_index = current_node.data_index
for i in this_data_index:
for j in this_data_index:
if label[i] != label[j]:
one_class = False
break
if not one_class:
break
if one_class:
current_node.judge = label[this_data_index[0]]
return
rest_title = current_node.rest_attribute # 候选属性
if len(rest_title) == 0: # 如果候选属性为空，则是个叶子结点。需要选择最多的那个类作为该结点的类
label_count = {}
temp_data = current_node.data_index
for index in temp_data:
if label_count.__contains__(label[index]):
label_count[label[index]] += 1
else:
label_count[label[index]] = 1
final_label = max(label_count)
current_node.judge = final_label
return
# 先为当前结点添加一个临时判断，如果需要添加孩子结点，就再把它恢复成None
data_count = {}
for index in current_node.data_index:
if data_count.__contains__(label[index]):
data_count[label[index]] += 1
else:
data_count[label[index]] = 1
before_judge = max(data_count, key=data_count.get)
current_node.judge = before_judge
before_accuracy = current_accuracy(current_node, test_data, test_label)
title_gini = {} # 记录每个属性的基尼指数
title_split_value = {} # 记录每个属性的分隔值，如果是连续属性则为分隔值，如果是离散属性则为None
for title in rest_title:
attr_values = []
current_label = []
for index in current_node.data_index:
this_data = data[index]
attr_values.append(this_data[title])
current_label.append(label[index])
temp_data = data[0]
this_gain, this_split_value = cart.gini_index(attr_values, current_label, cart.is_number(temp_data[title])) # 如果属性值为数字，则认为是连续的
title_gini[title] = this_gain
title_split_value[title] = this_split_value
best_attr = min(title_gini, key=title_gini.get) # 基尼指数最小的属性名
current_node.attribute_name = best_attr
current_node.split = title_split_value[best_attr]
rest_title.remove(best_attr)
a_data = data[0]
if cart.is_number(a_data[best_attr]): # 如果是该属性的值为连续数值
split_value = title_split_value[best_attr]
small_data = []
large_data = []
for index in current_node.data_index:
this_data = data[index]
if this_data[best_attr] <= split_value:
small_data.append(index)
else:
large_data.append(index)
small_str = '<=' + str(split_value)
large_str = '>' + str(split_value)
small_child = TreeNode.TreeNode(parent=current_node, data_index=small_data, attr_value=small_str,
rest_attribute=rest_title.copy())
large_child = TreeNode.TreeNode(parent=current_node, data_index=large_data, attr_value=large_str,
rest_attribute=rest_title.copy())
# 也需要先给子节点一个判断
small_data_count = {}
for index in small_child.data_index:
if small_data_count.__contains__(label[index]):
small_data_count[label[index]] += 1
else:
small_data_count[label[index]] = 1
small_child_judge = max(small_data_count, key=small_data_count.get)
small_child.judge = small_child_judge # 临时添加的一个判断
large_data_count = {}
for index in large_child.data_index:
if large_data_count.__contains__(label[index]):
large_data_count[label[index]] += 1
else:
large_data_count[label[index]] = 1
large_child_judge = max(large_data_count, key=large_data_count.get)
large_child.judge = large_child_judge # 临时添加的一个判断
current_node.children = [small_child, large_child]
else: # 如果该属性的值是离散值
best_titlevalue_dict = {} # key是属性值的取值，value是个list记录所包含的样本序号
for index in current_node.data_index:
this_data = data[index]
if best_titlevalue_dict.__contains__(this_data[best_attr]):
temp_list = best_titlevalue_dict[this_data[best_attr]]
temp_list.append(index)
else:
temp_list = [index]
best_titlevalue_dict[this_data[best_attr]] = temp_list
children_list = []
for key, index_list in best_titlevalue_dict.items():
a_child = TreeNode.TreeNode(parent=current_node, data_index=index_list, attr_value=key,
rest_attribute=rest_title.copy())
# 也需要先给子节点一个判断
temp_data_count = {}
for index in index_list:
if temp_data_count.__contains__(label[index]):
temp_data_count[label[index]] += 1
else:
temp_data_count[label[index]] = 1
temp_child_judge = max(temp_data_count, key=temp_data_count.get)
a_child.judge = temp_child_judge # 临时添加的一个判断
children_list.append(a_child)
current_node.children = children_list
current_node.judge = None
later_accuracy = current_accuracy(current_node, test_data, test_label)
# print(str(current_node.index)+"处，不剪枝的正确率是 "+str(later_accuracy) +"，剪枝的正确率是 "+str(before_accuracy))
if before_accuracy > later_accuracy:
current_node.children = None
current_node.judge = before_judge
# print(str(current_node.index)+"处进行剪枝")
return
else:
# print(current_node.to_string())
for child in current_node.children: # 递归
finish_node(child, data, label, test_data, test_label)
def precut_cart_tree(Data, title, label, test_data, test_label):
"""
生成一颗预剪枝 CART 决策树
:param Data: 训练数据集，每个样本是一个 dict(属性名：属性值)，整个 Data 是个大的 list
:param title: 每个属性的名字，如 色泽、含糖率等
:param label: 存储的是训练集每个样本的类别
:param test_data: 测试数据集
:param test_label: 测试数据集的标签
:return:
"""
n = len(Data)
rest_title = title.copy()
root_data = []
for i in range(0, n):
root_data.append(i)
root_node = TreeNode.TreeNode(data_index=root_data, rest_attribute=title.copy())
finish_node(root_node, Data, label, test_data, test_label)
return root_node
def run_test():
train_watermelon, test_watermelon, title = Dataset.watermelon2()
# 先处理数据
train_data = []
test_data = []
train_label = []
test_label = []
for melon in train_watermelon:
a_dict = {}
dim = len(melon) - 1
for i in range(0, dim):
a_dict[title[i]] = melon[i]
train_data.append(a_dict)
train_label.append(melon[dim])
for melon in test_watermelon:
a_dict = {}
dim = len(melon) - 1
for i in range(0, dim):
a_dict[title[i]] = melon[i]
test_data.append(a_dict)
test_label.append(melon[dim])
decision_tree = precut_cart_tree(train_data, title, train_label, test_data, test_label)
print('训练的决策树是:')
cart.print_tree(decision_tree)
print('\n')
test_judge = []
for melon in test_data:
test_judge.append(cart.classify_data(decision_tree, melon))
print('决策树在测试数据集上的分类结果是：', test_judge)
print('测试数据集的正确类别信息应该是： ', test_label)
accuracy = 0
for i in range(0, len(test_label)):
if test_label[i] == test_judge[i]:
accuracy += 1
accuracy /= len(test_label)
print('决策树在测试数据集上的分类正确率为：' + str(accuracy * 100) + "%")
if __name__ == '__main__':
run_test()
程序的在西瓜数据集2.0上的运行结果如下所示，可以看出进行预剪枝之后决策树在测试数据集上的正确率比不进行剪枝时有了明显的提升。
训练的决策树是:
--------------------------------------------
current index : 5;
data : [0, 1, 2, 3, 4, 5, 6, 7, 8, 9];
select attribute is : 色泽;
children : [6, 7, 8]
--------------------------------------------
--------------------------------------------
current index : 6;
parent index : 5;
色泽 : 青绿;
data : [0, 3, 5, 9];
label : 是
--------------------------------------------
--------------------------------------------
current index : 7;
parent index : 5;
色泽 : 乌黑;
data : [1, 2, 4, 7];
select attribute is : 根蒂;
children : [12, 13]
--------------------------------------------
--------------------------------------------
current index : 8;
parent index : 5;
色泽 : 浅白;
data : [6, 8];
label : 否
--------------------------------------------
--------------------------------------------
current index : 12;
parent index : 7;
根蒂 : 蜷缩;
data : [1, 2];
label : 是
--------------------------------------------
--------------------------------------------
current index : 13;
parent index : 7;
根蒂 : 稍蜷;
data : [4, 7];
label : 是
--------------------------------------------
决策树在测试数据集上的分类结果是： ['是', '否', '是', '是', '否', '否', '是']
测试数据集的正确类别信息应该是： ['是', '是', '是', '否', '否', '否', '否']
决策树在测试数据集上的分类正确率为：57.14285714285714%
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