Feature Selection Techniques – Backward Elimination

March 30, 2020 admin Feature Selection Techniques 0

300320201313

In backward elimination, we start with all the features and removes the least significant feature at each iteration which improves the performance of the model. We repeat this until no improvement is observed on removal of features.

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='')

data source: https://www.kaggle.com/uciml/breast-cancer-wisconsin-data

In [3]:
df = pd.read_csv ('/home/wojciech/Pulpit/6/Breast_Cancer_Wisconsin.csv')
green(df.shape)
df.head(3)

(569, 33)
Out[3]:
id diagnosis radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavity_mean concave points_mean … texture_worst perimeter_worst area_worst smoothness_worst compactness_worst concavity_worst concave points_worst symmetry_worst fractal_dimension_worst Unnamed: 32
0 842302 M 17.99 10.38 122.8 1001.0 0.11840 0.27760 0.3001 0.14710 … 17.33 184.6 2019.0 0.1622 0.6656 0.7119 0.2654 0.4601 0.11890 NaN
1 842517 M 20.57 17.77 132.9 1326.0 0.08474 0.07864 0.0869 0.07017 … 23.41 158.8 1956.0 0.1238 0.1866 0.2416 0.1860 0.2750 0.08902 NaN
2 84300903 M 19.69 21.25 130.0 1203.0 0.10960 0.15990 0.1974 0.12790 … 25.53 152.5 1709.0 0.1444 0.4245 0.4504 0.2430 0.3613 0.08758 NaN

3 rows × 33 columns

Deleting unneeded columns

In [4]:
df['concave_points_worst'] = df['concave points_worst']
df['concave_points_se'] = df['concave points_se']
df['concave_points_mean'] = df['concave points_mean']

del df['Unnamed: 32']
del df['diagnosis']
del df['id']
In [5]:
df.isnull().sum()
Out[5]:
radius_mean                0
texture_mean               0
perimeter_mean             0
area_mean                  0
smoothness_mean            0
compactness_mean           0
concavity_mean             0
concave points_mean        0
symmetry_mean              0
fractal_dimension_mean     0
radius_se                  0
texture_se                 0
perimeter_se               0
area_se                    0
smoothness_se              0
compactness_se             0
concavity_se               0
concave points_se          0
symmetry_se                0
fractal_dimension_se       0
radius_worst               0
texture_worst              0
perimeter_worst            0
area_worst                 0
smoothness_worst           0
compactness_worst          0
concavity_worst            0
concave points_worst       0
symmetry_worst             0
fractal_dimension_worst    0
concave_points_worst       0
concave_points_se          0
concave_points_mean        0
dtype: int64
In [6]:
import seaborn as sns

sns.heatmap(df.isnull(),yticklabels=False,cbar=False,cmap='viridis')
Out[6]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fba4f05f3d0>

Deletes duplicates

there were no duplicates

In [7]:
green(df.shape)
df.drop_duplicates(keep='first', inplace=True)
blue(df.shape)

(569, 33)
(569, 33)
In [8]:
blue(df.dtypes)

radius_mean                float64
texture_mean               float64
perimeter_mean             float64
area_mean                  float64
smoothness_mean            float64
compactness_mean           float64
concavity_mean             float64
concave points_mean        float64
symmetry_mean              float64
fractal_dimension_mean     float64
radius_se                  float64
texture_se                 float64
perimeter_se               float64
area_se                    float64
smoothness_se              float64
compactness_se             float64
concavity_se               float64
concave points_se          float64
symmetry_se                float64
fractal_dimension_se       float64
radius_worst               float64
texture_worst              float64
perimeter_worst            float64
area_worst                 float64
smoothness_worst           float64
compactness_worst          float64
concavity_worst            float64
concave points_worst       float64
symmetry_worst             float64
fractal_dimension_worst    float64
concave_points_worst       float64
concave_points_se          float64
concave_points_mean        float64
dtype: object
In [9]:
df.columns
Out[9]:
Index(['radius_mean', 'texture_mean', 'perimeter_mean', 'area_mean',
       'smoothness_mean', 'compactness_mean', 'concavity_mean',
       'concave points_mean', 'symmetry_mean', 'fractal_dimension_mean',
       'radius_se', 'texture_se', 'perimeter_se', 'area_se', 'smoothness_se',
       'compactness_se', 'concavity_se', 'concave points_se', 'symmetry_se',
       'fractal_dimension_se', 'radius_worst', 'texture_worst',
       'perimeter_worst', 'area_worst', 'smoothness_worst',
       'compactness_worst', 'concavity_worst', 'concave points_worst',
       'symmetry_worst', 'fractal_dimension_worst', 'concave_points_worst',
       'concave_points_se', 'concave_points_mean'],
      dtype='object')

We choose the continuous variable – compactness_mean

In [10]:
print('max:',df['compactness_mean'].max())
print('min:',df['compactness_mean'].min())

sns.distplot(np.array(df['compactness_mean']))

max: 0.3454
min: 0.01938
Out[10]:
<matplotlib.axes._subplots.AxesSubplot at 0x7fba4bc79750>

Backward Elimination

In [18]:
x = df.drop('compactness_mean', axis=1) 
y = df['compactness_mean']  

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)
# Jeżeli się rzuca wtedy wycinamy stratify=y.
In [21]:
cols=list(x.columns)
pmax=1
while (len(cols)>0):
    p=[]
    x_1 = x[cols]
    x_1 = sm.add_constant(x_1)
    model=sm.OLS(y,x_1).fit()
    p=pd.Series(model.pvalues.values[1:],index=cols)
    pmax=max(p)
    features_with_p_max=p.idxmax()
    if(pmax>0.05):
        cols.remove(features_with_p_max)
    else:
        break
new_cols=cols
print(new_cols)

['radius_mean', 'perimeter_mean', 'area_mean', 'smoothness_mean', 'concavity_mean', 'symmetry_mean', 'fractal_dimension_mean', 'texture_se', 'compactness_se', 'concave points_se', 'fractal_dimension_se', 'radius_worst', 'perimeter_worst', 'compactness_worst', 'concavity_worst', 'symmetry_worst', 'fractal_dimension_worst', 'concave_points_se']
In [23]:
df2 = df[new_cols]
blue(df.shape)
df2.head(3)

(569, 33)
Out[23]:
radius_mean perimeter_mean area_mean smoothness_mean concavity_mean symmetry_mean fractal_dimension_mean texture_se compactness_se concave points_se fractal_dimension_se radius_worst perimeter_worst compactness_worst concavity_worst symmetry_worst fractal_dimension_worst concave_points_se
0 17.99 122.8 1001.0 0.11840 0.3001 0.2419 0.07871 0.9053 0.04904 0.01587 0.006193 25.38 184.6 0.6656 0.7119 0.4601 0.11890 0.01587
1 20.57 132.9 1326.0 0.08474 0.0869 0.1812 0.05667 0.7339 0.01308 0.01340 0.003532 24.99 158.8 0.1866 0.2416 0.2750 0.08902 0.01340
2 19.69 130.0 1203.0 0.10960 0.1974 0.2069 0.05999 0.7869 0.04006 0.02058 0.004571 23.57 152.5 0.4245 0.4504 0.3613 0.08758 0.02058

The Backward Elimination algorithm stated that reducing variables does not improve the model. Therefore, the number of variables was left unchanged.

OLS linear regression model for variables before reduction

In [12]:
blue(df.shape)

(569, 33)
In [13]:
X1 = df.drop('compactness_mean', axis=1) 
y1 = df['compactness_mean']
In [14]:
from statsmodels.formula.api import ols
import statsmodels.api as sm

model = sm.OLS(y1, sm.add_constant(X1))
model_fit = model.fit()

print('R2: #blue(model_fit.summary())

R2: 0.980200