极度随机树ExtraTreesClassifier

                            极度随机树ExtraTreesClassifier

1 声明

本文的数据来自网络，部分代码也有所参照，这里做了注释和延伸，旨在技术交流，如有冒犯之处请联系博主及时处理。

2 极度随机树ExtraTreesClassifier简介

Extremely Randomized Trees Classifier(极度随机树) 是一种集成学习技术，它将森林中收集的多个去相关决策树的结果聚集起来输出分类结果。极度随机树的每棵决策树都是由原始训练样本构建的。在每个测试节点上，每棵树都有一个随机样本，样本中有k个特征，每个决策树都必须从这些特征集中选择最佳特征，然后根据一些数学指标(一般是基尼指数)来拆分数据。这种随机的特征样本导致多个不相关的决策树的产生。

在构建森林的过程中，对于每个特征，计算用于分割特征决策的数学指标（如使用基尼指数）的归一化总缩减量，这个值称为基尼要素的重要性。基尼重要性按降序排列后，可根据需要选择前k个特征。

3 极度随机树ExtraTreesClassifier代码示例

import pandas as pd
import matplotlib.pyplot as plt
from sklearn.ensemble import ExtraTreesClassifier
 
import  matplotlib
# 自定义字体，以兼容中文显示
myfont = matplotlib.font_manager.FontProperties(fname='C:\Windows\Fonts\STKAITI.TTF')
df_pre = pd.read_csv('../input/PlayTennis.txt',sep="\t")
# 拆分X(自变量)和y(因变量)
 
#X = df.drop('Play Tennis', axis=1)
df=df_pre.drop('Day', axis = 1)
#分类类型转数值型，通过字典映射转换
weather_mapper = {'Sunny': 1, 'Overcast': 2,'Rain':3}
df['Outlook'].replace(weather_mapper, inplace=True)
 
temperature_mapper = {'Hot': 1, 'Mild': 2,'Cool':3}
df['Temperature'].replace(temperature_mapper, inplace=True)
 
humidity_mapper = {'High': 1, 'Normal': 2}
df['Humidity'].replace(humidity_mapper, inplace=True)
 
wind_mapper = {'Weak': 1, 'Strong': 0}
df['Wind'].replace(wind_mapper, inplace=True)
 
playTennis_mapper={"Yes":1,"No":0}
df['PlayTennis'].replace(playTennis_mapper, inplace=True)
print(df.head())
y = df['PlayTennis']
X = df.loc[ :,'Outlook':'Wind']
#X = df.drop('PlayTennis', axis = 1)
#print(X.head())
 
# 5棵树、2个特征、评判指标是熵
extra_tree_forest = ExtraTreesClassifier(n_estimators=5,
                                         criterion='entropy', max_features=2)
extra_tree_forest.fit(X, y)
 
# 计算每个特征的重要性水平
feature_importance = extra_tree_forest.feature_importances_
 
# 标准化特征的重要性水平
feature_importance_normalized = np.std([tree.feature_importances_ for tree in
                                        extra_tree_forest.estimators_],
                                       axis=0)
#画图
# Plotting a Bar Graph to compare the models
plt.bar(X.columns, feature_importance_normalized)
plt.xlabel('特征',fontproperties = myfont)
plt.ylabel('特征重要性',fontproperties = myfont)
plt.title('特征重要性比较',fontproperties = myfont)
plt.show()

4 计算示意:

熵公示:

其中c为唯一类标签的个数，p i为所属分类的行占比。

-- 构造数据
CREATE TABLE PlayTennis(
DayNo varchar(10),	
Outlook	varchar(10),	
Temperature	varchar(10),	
Humidity varchar(10),	
Wind varchar(10),	
PlayTennis varchar(10)
);
 
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D1','Sunny','Hot','High','Weak','No');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D2','Sunny','Hot','High','Strong','No');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D3','Overcast','Hot','High','Weak','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D4','Rain','Mild','High','Weak','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D5','Rain','Cool','Normal','Weak','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D6','Rain','Cool','Normal','Strong','No');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D7','Overcast','Cool','Normal','Strong','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D8','Sunny','Mild','High','Weak','No');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D9','Sunny','Cool','Normal','Weak','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D10','Rain','Mild','Normal','Weak','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D1','Sunny','Mild','Normal','Strong','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D12','Overcast','Mild','High','Strong','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D13','Overcast','Hot','Normal','Weak','Yes');
insert into `PlayTennis`(`DayNo`,`Outlook`,`Temperature`,`Humidity`,`Wind`,`PlayTennis`) values ('D14','Rain','Mild','High','Strong','No');
 
-- 计算熵
WITH CTE1 AS
(
SELECT  DISTINCT COUNT(PlayTennis)OVER(PARTITION BY PlayTennis) gp,tatal
FROM PlayTennis,(SELECT COUNT(*) tatal FROM PlayTennis) A
)
 
SELECT SUM(-(gp/tatal)*LOG(2,gp/tatal)) entropy_s  FROM
(
 
SELECT gp,tatal
FROM CTE1
 )A
 
-- 0.940285959354754

假设第一棵决策树选择了特征Outlook 和Temperature，则

-- 计算OutLook特征的信息增益
WITH CTE2 AS
(
 
SELECT  DISTINCT COUNT(PlayTennis)OVER(PARTITION BY Outlook,PlayTennis
ORDER BY PlayTennis) gp,
COUNT(1)OVER(PARTITION BY Outlook ) num,
Outlook,PlayTennis,
(SELECT COUNT(*) tatal FROM PlayTennis) tatal
FROM PlayTennis
)
 
SELECT 0.940285959354754-SUM(-(num/tatal)*(gp/num)*LOG(2,gp/num)) Gain_S_OutLook
FROM CTE2
 
-- 0.246749820735977

同理

第二棵决策树选择了特征Temperature 和Wind，则Gain计算如下：

第三棵决策树选择了特征Outlook和Humidity，则Gain计算如下：

第四棵决策树选择了特征Temperature和Humidity，则Gain计算如下：

第五棵决策树选择了特征Wind 和 Humidity，则Gain计算如下：

则各个特征的gain(信息增益)汇总如下：

Outlook:0.246+0.246= 0.492

Temperature:0.029+0.029+0.029 = 0.087

Humidity:=0.151+0.151+0.151 = 0.453

Wind:0.048+0.048 = 0.096

所以极度随机树来确定的最重要变量是特征 Outlook。

注:因特征选择的随机性，这里计算的特征重要水平可能有差异。

5 总结

Refer ：

https://www.geeksforgeeks.org/ml-extra-tree-classifier-for-feature-selection/

https://machinelearningmastery.com/extra-trees-ensemble-with-python/