特征选择：方差选择法、卡方检验、互信息法、递归特征消除、L1范数、树模型

转载：https://www.cnblogs.com/jasonfreak/p/5448385.html

特征选择主要从两个方面入手：

• 特征是否发散：特征发散说明特征的方差大，能够根据取值的差异化度量目标信息.
• 特征与目标相关性：优先选取与目标高度相关性的.
• 对于特征选择，有时候我们需要考虑分类变量和连续变量的不同.

1.过滤法：按照发散性或者相关性对各个特征进行评分，设定阈值或者待选择阈值的个数选择特征

方差选择法：建议作为数值特征的筛选方法

计算各个特征的方差，然后根据阈值，选择方差大于阈值的特征

from sklearn.feature_selection import VarianceThreshold
from sklearn.datasets import load_iris
import pandas as pd

X,y = load_iris(return_X_y=True) 
X_df = pd.DataFrame(X,columns=list("ABCD"))

#建议作为数值特征的筛选方法，对于分类特征可以考虑每个类别的占比问题
ts = 0.5
vt = VarianceThreshold(threshold=ts)
vt.fit(X_df)

#查看各个特征的方差
dict_variance = {}
for i,j in zip(X_df.columns.values,vt.variances_):
    dict_variance[i] = j

#获取保留了的特征的特征名
ls = list()
for i,j in dict_variance.items():
    if j >= ts:
      ls.append(i)  
X_new = pd.DataFrame(vt.fit_transform(X_df),columns=ls)

卡方检验：建议作为分类问题的分类变量的筛选方法

经典的卡方检验是检验定性自变量对定性因变量的相关性。假设自变量有N种取值，因变量有M种取值，考虑自变量等于i且因变量等于j的样本频数的观察值与期望的差距，构建统计量：

 

from sklearn.feature_selection import VarianceThreshold,SelectKBest,chi2
from sklearn.datasets import load_iris
import pandas as pd


X,y = load_iris(return_X_y=True) 
X_df = pd.DataFrame(X,columns=list("ABCD"))

(chi2,pval) = chi2(X_df,y)

dict_feature = {}
for i,j in zip(X_df.columns.values,chi2):
    dict_feature[i]=j

#对字典按照values排序
ls = sorted(dict_feature.items(),key=lambda item:item[1],reverse=True)

#特征选取数量
k =2
ls_new_feature=[]
for i in range(k):
    ls_new_feature.append(ls[i][0])


X_new = X_df[ls_new_feature]

 互信息法：建议作为分类问题的分类变量的筛选方法

经典的互信息也是评价定性自变量对定性因变量的相关性的，为了处理定量数据，最大信息系数法被提出，互信息计算公式如下：

from sklearn.feature_selection import VarianceThreshold,SelectKBest,chi2
from sklearn.datasets import load_iris
import pandas as pd
from sklearn.feature_selection import mutual_info_classif

#用于度量特征和离散目标的互信息
X,y = load_iris(return_X_y=True) 
X_df = pd.DataFrame(X,columns=list("ABCD"))

feature_cat = ["A","D"]
discrete_features =  []
feature = X_df.columns.values.tolist()
for k in feature_cat:
    if k in feature:
        discrete_features.append(feature.index(k))
        


mu = mutual_info_classif(X_df,y,discrete_features=discrete_features, 
                         n_neighbors=3, copy=True, random_state=None)


dict_feature = {}
for i,j in zip(X_df.columns.values,mu):
    dict_feature[i]=j

#对字典按照values排序
ls = sorted(dict_feature.items(),key=lambda item:item[1],reverse=True)

#特征选取数量
k =2
ls_new_feature=[]
for i in range(k):
    ls_new_feature.append(ls[i][0])


X_new = X_df[ls_new_feature]

from sklearn.feature_selection import VarianceThreshold,SelectKBest,chi2
from sklearn.datasets import load_iris
import pandas as pd
from sklearn.feature_selection import mutual_info_classif,mutual_info_regression

#用于度量特征和连续目标的互信息
X,y = load_iris(return_X_y=True) 
X_df = pd.DataFrame(X,columns=list("ABCD"))

feature_cat = ["A","D"]
discrete_features =  []
feature = X_df.columns.values.tolist()
for k in feature_cat:
    if k in feature:
        discrete_features.append(feature.index(k))
        


mu = mutual_info_regression(X_df,y,discrete_features=discrete_features, 
                            n_neighbors=3, copy=True, random_state=None)


dict_feature = {}
for i,j in zip(X_df.columns.values,mu):
    dict_feature[i]=j

#对字典按照values排序
ls = sorted(dict_feature.items(),key=lambda item:item[1],reverse=True)

#特征选取数量
k =2
ls_new_feature=[]
for i in range(k):
    ls_new_feature.append(ls[i][0])


X_new = X_df[ls_new_feature]

 2.包装法

递归特征消除法：用一个基模型来进行多轮训练，每轮训练后，消除若干权值系数的特征，再基于新的特征集进行下一轮训练

 

from sklearn.datasets import load_iris
import pandas as pd
from sklearn.feature_selection import RFE,RFECV
from sklearn.ensemble import RandomForestClassifier

X,y = load_iris(return_X_y=True) 
X_df = pd.DataFrame(X,columns=list("ABCD"))

refCV = RFECV(estimator=RandomForestClassifier(), 
              step=0.5, 
              cv  =5, 
              scoring=None,
              n_jobs=-1)

refCV.fit(X_df,y)

#保留特征的数量
refCV.n_features_
#保留特征的False、True标记
refCV.support_
feature_new = X_df.columns.values[refCV.support_]
#交叉验证分数
refCV.grid_scores_ 

 3.嵌入的方法

基于L1范数：使用带惩罚项的基模型，除了筛选出特征外，同时也进行了降维 

from sklearn.datasets import load_iris
import pandas as pd
from sklearn.feature_selection import SelectFromModel
from sklearn.linear_model import LogisticRegression

X,y = load_iris(return_X_y=True) 
X_df = pd.DataFrame(X,columns=list("ABCD"))

sf = SelectFromModel(estimator=LogisticRegression(penalty="l1", C=0.1),
                     threshold=None, 
                     prefit=False, 
                     norm_order=1)

sf.fit(X_df,y)

X_new = X_df[X_df.columns.values[sf.get_support()]]

基于树模型的特征选择法：

树模型中GBDT也可用来作为基模型进行特征选择，使用feature_selection库的SelectFromModel类结合GBDT模型

from sklearn.datasets import load_iris
import pandas as pd
from sklearn.feature_selection import SelectFromModel
from sklearn.ensemble import GradientBoostingClassifier

X,y = load_iris(return_X_y=True) 
X_df = pd.DataFrame(X,columns=list("ABCD"))

sf = SelectFromModel(estimator=GradientBoostingClassifier(),
                     threshold=None, 
                     prefit=False, 
                     norm_order=1)

sf.fit(X_df,y)

X_new = X_df[X_df.columns.values[sf.get_support()]]