# Feature Selection Techniques (by filter methods): numerical_ input, categorical output

In this case, statistical methods are used:
We always have continuous and discrete variables in the data set.
This procedure applies to the relations of discrete independent variables in relation to discrete result variables.
Below I show the analysis of numerical variables when the resulting value is discrete.

How to Choose a Feature Selection Method For Machine Learning

In [1]:
import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
from sklearn.preprocessing import LabelEncoder, OneHotEncoder
import warnings
warnings.filterwarnings("ignore")
from sklearn.model_selection import train_test_split
from sklearn.svm import SVC
from sklearn.metrics import confusion_matrix
np.random.seed(123)

In [2]:
##  colorful prints
def black(text):
print('33[30m', text, '33[0m', sep='')
def red(text):
print('33[31m', text, '33[0m', sep='')
def green(text):
print('33[32m', text, '33[0m', sep='')
def yellow(text):
print('33[33m', text, '33[0m', sep='')
def blue(text):
print('33[34m', text, '33[0m', sep='')
def magenta(text):
print('33[35m', text, '33[0m', sep='')
def cyan(text):
print('33[36m', text, '33[0m', sep='')
def gray(text):
print('33[90m', text, '33[0m', sep='')

In [3]:
df = pd.read_csv ('/home/wojciech/Pulpit/1/AirQualityUCI.csv', sep=';',nrows=1000)
green(df.shape)

(1000, 17)

Out[3]:
Date Time CO(GT) PT08.S1(CO) NMHC(GT) C6H6(GT) PT08.S2(NMHC) NOx(GT) PT08.S3(NOx) NO2(GT) PT08.S4(NO2) PT08.S5(O3) T RH AH Unnamed: 15 Unnamed: 16
0 10/03/2004 18.00.00 2,6 1360 150 11,9 1046 166 1056 113 1692 1268 13,6 48,9 0,7578 NaN NaN
1 10/03/2004 19.00.00 2 1292 112 9,4 955 103 1174 92 1559 972 13,3 47,7 0,7255 NaN NaN
2 10/03/2004 20.00.00 2,2 1402 88 9,0 939 131 1140 114 1555 1074 11,9 54,0 0,7502 NaN NaN

### Usuwanie niepotrzebnych kolumn¶

In [4]:
del df['Unnamed: 15']
del df['Unnamed: 16']


### Kasuje brakujące rekordy¶

In [5]:
green(df.shape)
df.isnull().sum()
df = df.dropna(how='any')
blue(df.shape)
blue(df.isnull().sum())

(1000, 15)
(1000, 15)
Date             0
Time             0
CO(GT)           0
PT08.S1(CO)      0
NMHC(GT)         0
C6H6(GT)         0
PT08.S2(NMHC)    0
NOx(GT)          0
PT08.S3(NOx)     0
NO2(GT)          0
PT08.S4(NO2)     0
PT08.S5(O3)      0
T                0
RH               0
AH               0
dtype: int64


### Kasuje duplikaty¶

nie było duplikatów

In [6]:
green(df.shape)
df.drop_duplicates(keep='first', inplace=True)
blue(df.shape)

(1000, 15)
(1000, 15)


### Z daty wyciągam dzień tygodnia, miesiąc, oraz godzinę jako zmienne ciągłe¶

In [7]:
df['Date'] = pd.to_datetime(df.Date)
df['day'] = df['Date'].dt.weekday
df['month'] = df['Date'].dt.month
df['hour'] = df['Time'].str.slice(0,2)

Out[7]:
Date day month hour
0 2004-10-03 6 10 18
1 2004-10-03 6 10 19
2 2004-10-03 6 10 20
In [8]:
del df['Date']
del df['Time']


### Kasuje zmienną -200 oznaczającą błąd danych¶

In [9]:
df[['CO(GT)', 'PT08.S1(CO)', 'NMHC(GT)', 'C6H6(GT)', 'PT08.S2(NMHC)',
'NOx(GT)', 'PT08.S3(NOx)', 'NO2(GT)', 'PT08.S4(NO2)', 'PT08.S5(O3)',
'T', 'RH', 'AH', 'day', 'month', 'hour']] = df[['CO(GT)', 'PT08.S1(CO)', 'NMHC(GT)', 'C6H6(GT)', 'PT08.S2(NMHC)',
'NOx(GT)', 'PT08.S3(NOx)', 'NO2(GT)', 'PT08.S4(NO2)', 'PT08.S5(O3)',
'T', 'RH', 'AH', 'day', 'month', 'hour']].replace(-200,np.NaN)

In [10]:
df.isnull().sum()

Out[10]:
CO(GT)             0
PT08.S1(CO)       27
NMHC(GT)         274
C6H6(GT)           0
PT08.S2(NMHC)     27
NOx(GT)          206
PT08.S3(NOx)      27
NO2(GT)          206
PT08.S4(NO2)      27
PT08.S5(O3)       27
T                  0
RH                 0
AH                 0
day                0
month              0
hour               0
dtype: int64
In [11]:
del df['NMHC(GT)']
green(df.shape)
df.isnull().sum()
df = df.dropna(how='any')
blue(df.shape)
blue(df.isnull().sum())

(1000, 15)
(768, 15)
CO(GT)           0
PT08.S1(CO)      0
C6H6(GT)         0
PT08.S2(NMHC)    0
NOx(GT)          0
PT08.S3(NOx)     0
NO2(GT)          0
PT08.S4(NO2)     0
PT08.S5(O3)      0
T                0
RH               0
AH               0
day              0
month            0
hour             0
dtype: int64


# Zamieniam zmienne na wartości numeryczne¶

In [12]:
blue(df.dtypes)

CO(GT)            object
PT08.S1(CO)      float64
C6H6(GT)          object
PT08.S2(NMHC)    float64
NOx(GT)          float64
PT08.S3(NOx)     float64
NO2(GT)          float64
PT08.S4(NO2)     float64
PT08.S5(O3)      float64
T                 object
RH                object
AH                object
day                int64
month              int64
hour              object
dtype: object


### Macierz korelacji¶

In [13]:
df['CO(GT)'] = df['CO(GT)'].str.replace(',', '.')

In [14]:
df['C6H6(GT)'] = df['C6H6(GT)'].str.replace(',', '.')

In [15]:
df['T'] = df['T'].str.replace(',', '.')

In [16]:
df['RH'] = df['RH'].str.replace(',', '.')

In [17]:
df['AH'] = df['AH'].str.replace(',', '.')

In [18]:
df[['CO(GT)', 'PT08.S1(CO)', 'C6H6(GT)', 'PT08.S2(NMHC)',
'NOx(GT)', 'PT08.S3(NOx)', 'NO2(GT)', 'PT08.S4(NO2)', 'PT08.S5(O3)',
'T', 'RH', 'AH', 'day', 'month', 'hour']] = df[['CO(GT)', 'PT08.S1(CO)', 'C6H6(GT)', 'PT08.S2(NMHC)',
'NOx(GT)', 'PT08.S3(NOx)', 'NO2(GT)', 'PT08.S4(NO2)', 'PT08.S5(O3)',
'T', 'RH', 'AH', 'day', 'month', 'hour']].astype(float)

In [19]:
CORREL = df.corr()
plt.figure(figsize=(10,6))
sns.heatmap(CORREL, annot=True, cbar=False, cmap="coolwarm")

Out[19]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fcdc2507d90>

### Koduje zmienną kategoryczną wynikową – C6H6(GT)¶

In [20]:
print('max:',df['C6H6(GT)'].max())
print('min:',df['C6H6(GT)'].min())

sns.distplot(np.array(df['C6H6(GT)']))

max: 39.2
min: 0.5

Out[20]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fcdbef8a810>
In [21]:
df['C6H6(GT)'] = df['C6H6(GT)'].apply(lambda x: 1 if x > 10 else 0)
df['C6H6(GT)'].value_counts()

Out[21]:
0    446
1    322
Name: C6H6(GT), dtype: int64
In [22]:
df['C6H6(GT)'] = pd.Categorical(df['C6H6(GT)']).codes
df['C6H6(GT)'].value_counts()

Out[22]:
0    446
1    322
Name: C6H6(GT), dtype: int64

# Model regresji liniowej bez redukcji zmiennych¶

In [23]:
blue(df.dtypes)

CO(GT)           float64
PT08.S1(CO)      float64
C6H6(GT)            int8
PT08.S2(NMHC)    float64
NOx(GT)          float64
PT08.S3(NOx)     float64
NO2(GT)          float64
PT08.S4(NO2)     float64
PT08.S5(O3)      float64
T                float64
RH               float64
AH               float64
day              float64
month            float64
hour             float64
dtype: object

In [24]:
X = df.drop('C6H6(GT)', axis=1)
y = df['C6H6(GT)']


## Podział na dane treningowe i testowe¶

In [25]:
from sklearn.model_selection import train_test_split

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.20, random_state=123,stratify=y)


## Definicje¶

In [26]:
# Classification Assessment
def Classification_Assessment(model ,Xtrain, ytrain, Xtest, ytest, y_pred):
import matplotlib.pyplot as plt
from sklearn import metrics
from sklearn.metrics import classification_report, confusion_matrix
from sklearn.metrics import confusion_matrix, log_loss, auc, roc_curve, roc_auc_score, recall_score, precision_recall_curve
from sklearn.metrics import make_scorer, precision_score, fbeta_score, f1_score, classification_report

print("Recall Training data:     ", np.round(recall_score(ytrain, model.predict(Xtrain)), decimals=4))
print("Precision Training data:  ", np.round(precision_score(ytrain, model.predict(Xtrain)), decimals=4))
print("----------------------------------------------------------------------")
print("Recall Test data:         ", np.round(recall_score(ytest, model.predict(Xtest)), decimals=4))
print("Precision Test data:      ", np.round(precision_score(ytest, model.predict(Xtest)), decimals=4))
print("----------------------------------------------------------------------")
print("Confusion Matrix Test data")
print(confusion_matrix(ytest, model.predict(Xtest)))
print("----------------------------------------------------------------------")
print(classification_report(ytest, model.predict(Xtest)))

y_pred_proba = model.predict_proba(Xtest)[::,1]
fpr, tpr, _ = metrics.roc_curve(ytest,  y_pred)
auc = metrics.roc_auc_score(ytest, y_pred)
plt.plot(fpr, tpr, label='Logistic Regression (auc = plt.xlabel('False Positive Rate',color='grey', fontsize = 13)
plt.ylabel('True Positive Rate',color='grey', fontsize = 13)
plt.legend(loc="lower right")
plt.legend(loc=4)
plt.plot([0, 1], [0, 1],'r--')
plt.show()
print('auc',auc)

In [27]:
blue(X.shape)
green(X_train.shape)
green(X_test.shape)

(768, 14)
(614, 14)
(154, 14)


# Modelu klasyfikacji bez wyboru funkcji¶

In [28]:
import numpy as np
from sklearn import model_selection
from sklearn.pipeline import make_pipeline
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import GridSearchCV

Parameteres = {'C': np.power(10.0, np.arange(-3, 3))}
LR = LogisticRegression(warm_start = True)
LR_Grid = GridSearchCV(LR, param_grid = Parameteres, scoring = 'roc_auc', n_jobs = -1, cv=2)

LR_Grid.fit(X_train, y_train)
y_pred_LRC = LR_Grid.predict(X_test)

In [29]:
Classification_Assessment(LR_Grid ,X_train, y_train, X_test, y_test, y_pred_LRC)

Recall Training data:      0.9728
Precision Training data:   0.9766
----------------------------------------------------------------------
Recall Test data:          0.9692
Precision Test data:       0.9844
----------------------------------------------------------------------
Confusion Matrix Test data
[[88  1]
[ 2 63]]
----------------------------------------------------------------------
precision    recall  f1-score   support

0       0.98      0.99      0.98        89
1       0.98      0.97      0.98        65

accuracy                           0.98       154
macro avg       0.98      0.98      0.98       154
weighted avg       0.98      0.98      0.98       154


auc 0.9789974070872948


# Redukcja zmiennych niezależnych za pomocą OLS¶

In [30]:
from statsmodels.formula.api import ols
import statsmodels.api as sm

model_fit = model.fit()

blue(model_fit.summary())

                            OLS Regression Results
==============================================================================
Dep. Variable:               C6H6(GT)   R-squared:                       0.691
Method:                 Least Squares   F-statistic:                     120.2
Date:                Sat, 28 Mar 2020   Prob (F-statistic):          4.93e-181
Time:                        09:35:48   Log-Likelihood:                -96.437
No. Observations:                 768   AIC:                             222.9
Df Residuals:                     753   BIC:                             292.5
Df Model:                          14
Covariance Type:            nonrobust
=================================================================================
coef    std err          t      P>|t|      [0.025      0.975]
---------------------------------------------------------------------------------
const            -2.0863      0.283     -7.371      0.000      -2.642      -1.531
CO(GT)           -0.0003      0.000     -0.938      0.348      -0.001       0.000
PT08.S1(CO)      -0.0002      0.000     -1.127      0.260      -0.001       0.000
PT08.S2(NMHC)     0.0030      0.000      8.413      0.000       0.002       0.004
NOx(GT)          -0.0002      0.000     -0.395      0.693      -0.001       0.001
PT08.S3(NOx)      0.0007      0.000      5.578      0.000       0.000       0.001
NO2(GT)           0.0013      0.001      1.408      0.160      -0.001       0.003
PT08.S4(NO2)     -0.0007      0.000     -2.763      0.006      -0.001      -0.000
PT08.S5(O3)    3.589e-05   8.45e-05      0.425      0.671      -0.000       0.000
T                 0.0008      0.011      0.073      0.942      -0.021       0.022
RH               -0.0015      0.004     -0.392      0.695      -0.009       0.006
AH                0.4456      0.278      1.602      0.109      -0.100       0.992
day              -0.0008      0.005     -0.138      0.890      -0.011       0.010
month            -0.0009      0.004     -0.243      0.808      -0.008       0.006
hour             -0.0028      0.002     -1.495      0.135      -0.006       0.001
==============================================================================
Omnibus:                       43.664   Durbin-Watson:                   1.370
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.380
Skew:                           0.068   Prob(JB):                     0.000168
Kurtosis:                       2.276   Cond. No.                     8.46e+04
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 8.46e+04. This might indicate that there are
strong multicollinearity or other numerical problems.

In [31]:
p_values = model_fit.summary2().tables[1]['P>|t|']
## zaokrąglam

p_values = np.round(p_values, decimals=2)
p_values= p_values.sort_values()

plt.figure(figsize=(3,8))
p_values.plot(kind='barh')
plt.title('p-value for independent variables in OLS')
plt.grid(True)
plt.ylabel('independent variables')
plt.xlabel('p-value')
plt.xticks(rotation=90)

Out[31]:
(array([0. , 0.2, 0.4, 0.6, 0.8, 1. ]), <a list of 6 Text xticklabel objects>)

# Wybieramy zmienne z p-value < 0.1¶

In [32]:
df.columns

Out[32]:
Index(['CO(GT)', 'PT08.S1(CO)', 'C6H6(GT)', 'PT08.S2(NMHC)', 'NOx(GT)',
'PT08.S3(NOx)', 'NO2(GT)', 'PT08.S4(NO2)', 'PT08.S5(O3)', 'T', 'RH',
'AH', 'day', 'month', 'hour'],
dtype='object')
In [33]:
df2= df[['PT08.S4(NO2)','PT08.S3(NOx)','PT08.S2(NMHC)','AH','C6H6(GT)']]

In [34]:
y= y.to_frame()

Out[34]:
C6H6(GT)
0 1
1 0
2 0
3 0
In [35]:
fig = plt.figure(figsize = (20, 25))
j = 0
for i in df2.columns:
plt.subplot(6, 4, j+1)
j = 1+j
sns.distplot(df2[i][y['C6H6(GT)']==0], color='#999999', label = '0')
sns.distplot(df2[i][y['C6H6(GT)']==1], color='#ff0000', label = '1')
plt.legend(loc='best',fontsize=10)
fig.suptitle('Classification charts',fontsize=34,color='#ff0000',alpha=0.3)
fig.tight_layout()
plt.show()

In [36]:
def scientist_plot(data, y, AAA, Title):
fig = plt.figure(figsize = (20, 25))
j = 0
for i in df2.columns:
plt.subplot(6, 4, j+1)
j = 1+j
sns.distplot(data[i][y[AAA]==0], color='#999999', label = '0')
sns.distplot(data[i][y[AAA]==1], color='#274e13', label = '1')
plt.legend(loc='best',fontsize=10)
fig.suptitle(Title,fontsize=34,color='#274e13',alpha=0.5)
fig.tight_layout()
plt.show()

In [37]:
scientist_plot(df2, y, 'C6H6(GT)','Classification charts')

In [38]:
fig = plt.figure(figsize = (20, 25))
kot = ['#999999','#274e13']
sns.pairplot(data=df2[['PT08.S4(NO2)','PT08.S3(NOx)','PT08.S2(NMHC)','AH','C6H6(GT)']], hue='C6H6(GT)', dropna=True, height=2, palette=kot)
fig.suptitle('Classification charts',fontsize=34,color='#274e13',alpha=0.3)
fig.tight_layout()

<Figure size 1440x1800 with 0 Axes>