Step Forward, Step Backward and Exhaustive Feature Selection | Wrapper Method | KGP Talkie

Published by Srishailam Sri on

Wrapping method

Uses of Wrapping method

  • Use combinations of variables to determine predictive power.
  • To find the best combination of variables.
  • Computationally expensive than filter method.
  • To perform better than filter method.
  • Not recommended on high number of features.
image.png

Forward Step Selection

In this wrapping method, it selects one best feature every time and finally it combines all the best features for the best accuracy.

image.png

Backward Step Selection

It is reverse process of Forward Step Selection method, intially it takes all the features and remove one by one every time. Finally it left with required number of features for the best accuracy.

image.png

Exhaustive Feature Selection

  • It is also called as subset selection method.
  • It fits the model with each possible combinations of N features.
    ( y = B0, y = B0 + B1.X1, y = C0 + C1.X2 )
  • It requires massive computational power.
  • It uses test error to evaluate model performance.

Drawback

It is a slower method compared to step forward and back ward methods.

Use of mlxtend in Wrapper Method

!pip install mlxtend
Requirement already satisfied: mlxtend in c:\users\srish\appdata\roaming\python\python38\site-packages (0.17.3)
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Requirement already satisfied: six>=1.5 in e:\callme_conda\lib\site-packages (from python-dateutil>=2.6.1->pandas>=0.24.2->mlxtend) (1.15.0)

More Information Available at http://rasbt.github.io/mlxtend/

How it works

Sequential feature selection algorithms are a family of greedy search algorithms that are used to reduce an initial d-dimensional feature space to a k-dimensional feature subspace where k < d.

In a nutshell, SFAs remove or add one feature at the time based on the classifier performance until a feature subset of the desired size k is reached. There are 4 different flavors of SFAs available via the SequentialFeatureSelector:

  • Sequential Forward Selection (SFS)
  • Sequential Backward Selection (SBS)
  • Sequential Forward Floating Selection (SFFS)
  • Sequential Backward Floating Selection (SBFS)

Step Forward Selection (SFS)

Importing required libraries

import numpy as np
import pandas as pd
import seaborn as sns
import matplotlib.pyplot as plt
%matplotlib inline
from sklearn.model_selection import train_test_split
from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier
from sklearn.metrics import roc_auc_score
from mlxtend.feature_selection import SequentialFeatureSelector as SFS
from sklearn.datasets import load_wine
from sklearn.preprocessing import StandardScaler

We are going to wine dataset. We can load this dataset from sklearn.

data = load_wine()

Let’s get the keys of this dataset.

data.keys()
dict_keys(['data', 'target', 'frame', 'target_names', 'DESCR', 'feature_names'])

Let’s get the description of the wine dataset.

print(data.DESCR)
.. _wine_dataset:

Wine recognition dataset
------------------------

**Data Set Characteristics:**

    :Number of Instances: 178 (50 in each of three classes)
    :Number of Attributes: 13 numeric, predictive attributes and the class
    :Attribute Information:
 		- Alcohol
 		- Malic acid
 		- Ash
		- Alcalinity of ash  
 		- Magnesium
		- Total phenols
 		- Flavanoids
 		- Nonflavanoid phenols
 		- Proanthocyanins
		- Color intensity
 		- Hue
 		- OD280/OD315 of diluted wines
 		- Proline

    - class:
            - class_0
            - class_1
            - class_2
		
    :Summary Statistics:
    
    ============================= ==== ===== ======= =====
                                   Min   Max   Mean     SD
    ============================= ==== ===== ======= =====
    Alcohol:                      11.0  14.8    13.0   0.8
    Malic Acid:                   0.74  5.80    2.34  1.12
    Ash:                          1.36  3.23    2.36  0.27
    Alcalinity of Ash:            10.6  30.0    19.5   3.3
    Magnesium:                    70.0 162.0    99.7  14.3
    Total Phenols:                0.98  3.88    2.29  0.63
    Flavanoids:                   0.34  5.08    2.03  1.00
    Nonflavanoid Phenols:         0.13  0.66    0.36  0.12
    Proanthocyanins:              0.41  3.58    1.59  0.57
    Colour Intensity:              1.3  13.0     5.1   2.3
    Hue:                          0.48  1.71    0.96  0.23
    OD280/OD315 of diluted wines: 1.27  4.00    2.61  0.71
    Proline:                       278  1680     746   315
    ============================= ==== ===== ======= =====

    :Missing Attribute Values: None
    :Class Distribution: class_0 (59), class_1 (71), class_2 (48)
    :Creator: R.A. Fisher
    :Donor: Michael Marshall (MARSHALL%[email protected])
    :Date: July, 1988

This is a copy of UCI ML Wine recognition datasets.
https://archive.ics.uci.edu/ml/machine-learning-databases/wine/wine.data

The data is the results of a chemical analysis of wines grown in the same region in Italy by three different cultivators. There are thirteen differentmeasurements taken for different constituents found in the three types of wine.

Let’s go ahead and get the data in x and y vectors.

X = pd.DataFrame(data.data)
y = data.target
X.columns = data.feature_names
X.head()
alcoholmalic_acidashalcalinity_of_ashmagnesiumtotal_phenolsflavanoidsnonflavanoid_phenolsproanthocyaninscolor_intensityhueod280/od315_of_diluted_winesproline
014.231.712.4315.6127.02.803.060.282.295.641.043.921065.0
113.201.782.1411.2100.02.652.760.261.284.381.053.401050.0
213.162.362.6718.6101.02.803.240.302.815.681.033.171185.0
314.371.952.5016.8113.03.853.490.242.187.800.863.451480.0
413.242.592.8721.0118.02.802.690.391.824.321.042.93735.0

Now we will chech whether null values present in the dataset by using isnull.sum().

X.isnull().sum()
alcohol                         0
malic_acid                      0
ash                             0
alcalinity_of_ash               0
magnesium                       0
total_phenols                   0
flavanoids                      0
nonflavanoid_phenols            0
proanthocyanins                 0
color_intensity                 0
hue                             0
od280/od315_of_diluted_wines    0
proline                         0
dtype: int64

Let’s go ahead do the train,test and split for this dataset. Have a look at the following code.

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.2, random_state = 0)
X_train.shape, X_test.shape
((142, 13), (36, 13))

Let’s go ahead and start working for the Step Forward Feature Selection(SFS).

Step Forward Feature Selection (SFS)

Here, we are using SequentialFeatureSelector() and passing Random Forest Classifier in this we are passing number of estimators, random_state and number of jobs.

k number of features are the required number of features.
In this case, since it is forward step method, forward is equal to True.
For verbose it is for log here we are using 2.
Cross validation set,here we are choosing as 4.
Number of jobs means how many cores we will use, here -1 means use all the available core in this system.

sfs = SFS(RandomForestClassifier(n_estimators=100, random_state=0, n_jobs = -1),
         k_features = 7,
          forward= True,
          floating = False,
          verbose= 2,
          scoring= 'accuracy',
          cv = 4,
          n_jobs= -1
         ).fit(X_train, y_train)
[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   5 out of  13 | elapsed:    4.2s remaining:    6.8s
[Parallel(n_jobs=-1)]: Done  13 out of  13 | elapsed:    5.8s finished

[2020-08-06 12:56:29] Features: 1/7 -- score: 0.7674603174603174[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of  12 | elapsed:    1.5s remaining:    3.1s
[Parallel(n_jobs=-1)]: Done  12 out of  12 | elapsed:    3.2s finished

[2020-08-06 12:56:33] Features: 2/7 -- score: 0.9718253968253968[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   2 out of  11 | elapsed:    2.3s remaining:   10.6s
[Parallel(n_jobs=-1)]: Done   8 out of  11 | elapsed:    2.8s remaining:    1.0s
[Parallel(n_jobs=-1)]: Done  11 out of  11 | elapsed:    4.7s finished

[2020-08-06 12:56:37] Features: 3/7 -- score: 0.9859126984126985[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   7 out of  10 | elapsed:    2.2s remaining:    0.9s
[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    4.5s finished

[2020-08-06 12:56:42] Features: 4/7 -- score: 0.9789682539682539[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of   9 | elapsed:    2.3s remaining:    2.8s
[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    4.1s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    4.1s finished

[2020-08-06 12:56:46] Features: 5/7 -- score: 0.9720238095238095[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   3 out of   8 | elapsed:    2.1s remaining:    3.6s
[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    2.9s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    2.9s finished

[2020-08-06 12:56:49] Features: 6/7 -- score: 0.9789682539682539[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of   7 | elapsed:    2.3s remaining:    1.7s
[Parallel(n_jobs=-1)]: Done   7 out of   7 | elapsed:    2.7s finished

[2020-08-06 12:56:52] Features: 7/7 -- score: 0.9791666666666666
sfs.k_feature_names_
('alcohol',
 'ash',
 'magnesium',
 'flavanoids',
 'proanthocyanins',
 'color_intensity',
 'proline')
sfs.k_feature_idx_
(0, 2, 4, 6, 8, 9, 12)
sfs.k_score_
0.9791666666666666
pd.DataFrame.from_dict(sfs.get_metric_dict()).T
feature_idxcv_scoresavg_scorefeature_namesci_boundstd_devstd_err
1(6,)[0.7222222222222222, 0.8333333333333334, 0.742…0.76746(flavanoids,)0.06709010.04185330.024164
2(6, 9)[0.9444444444444444, 1.0, 0.9714285714285714, …0.971825(flavanoids, color_intensity)0.0314920.01964590.0113425
3(4, 6, 9)[0.9722222222222222, 1.0, 0.9714285714285714, …0.985913(magnesium, flavanoids, color_intensity)0.02258620.01409010.00813492
4(4, 6, 9, 12)[0.9722222222222222, 0.9722222222222222, 0.971…0.978968(magnesium, flavanoids, color_intensity, proline)0.01947140.0121470.00701308
5(2, 4, 6, 9, 12)[0.9444444444444444, 0.9722222222222222, 0.971…0.972024(ash, magnesium, flavanoids, color_intensity, …0.03149030.01964490.011342
6(2, 4, 6, 8, 9, 12)[0.9722222222222222, 0.9722222222222222, 0.971…0.978968(ash, magnesium, flavanoids, proanthocyanins, …0.01947140.0121470.00701308
7(0, 2, 4, 6, 8, 9, 12)[0.9444444444444444, 0.9722222222222222, 1.0, …0.979167(alcohol, ash, magnesium, flavanoids, proantho…0.03692010.02303210.0132976
sfs = SFS(RandomForestClassifier(n_estimators=100, random_state=0, n_jobs = -1),
         k_features = (1, 8),
          forward= True,
          floating = False,
          verbose= 2,
          scoring= 'accuracy',
          cv = 4,
          n_jobs= -1
         ).fit(X_train, y_train)
[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   5 out of  13 | elapsed:    2.4s remaining:    4.0s
[Parallel(n_jobs=-1)]: Done  13 out of  13 | elapsed:    4.8s finished

[2020-08-06 12:57:09] Features: 1/8 -- score: 0.7674603174603174[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of  12 | elapsed:    2.3s remaining:    4.7s
[Parallel(n_jobs=-1)]: Done  12 out of  12 | elapsed:    4.4s finished

[2020-08-06 12:57:13] Features: 2/8 -- score: 0.9718253968253968[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   2 out of  11 | elapsed:    1.9s remaining:    8.7s
[Parallel(n_jobs=-1)]: Done   8 out of  11 | elapsed:    2.3s remaining:    0.8s
[Parallel(n_jobs=-1)]: Done  11 out of  11 | elapsed:    4.3s finished

[2020-08-06 12:57:17] Features: 3/8 -- score: 0.9859126984126985[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   7 out of  10 | elapsed:    2.6s remaining:    1.0s
[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    4.4s finished

[2020-08-06 12:57:22] Features: 4/8 -- score: 0.9789682539682539[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of   9 | elapsed:    2.5s remaining:    3.1s
[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    4.3s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    4.3s finished

[2020-08-06 12:57:26] Features: 5/8 -- score: 0.9720238095238095[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   3 out of   8 | elapsed:    2.1s remaining:    3.5s
[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    2.5s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    2.5s finished

[2020-08-06 12:57:29] Features: 6/8 -- score: 0.9789682539682539[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of   7 | elapsed:    1.7s remaining:    1.3s
[Parallel(n_jobs=-1)]: Done   7 out of   7 | elapsed:    1.8s finished

[2020-08-06 12:57:31] Features: 7/8 -- score: 0.9791666666666666[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   3 out of   6 | elapsed:    1.9s remaining:    1.9s
[Parallel(n_jobs=-1)]: Done   6 out of   6 | elapsed:    1.9s finished

[2020-08-06 12:57:33] Features: 8/8 -- score: 0.9791666666666666

Let’s go ahead and see the accuracy with this 7 features.

sfs.k_score_
0.9859126984126985

Now, we can see here selected feature from this algorithm.

sfs.k_feature_names_
('magnesium', 'flavanoids', 'color_intensity')

Step Backward Selection (SBS)

Let’s go ahead work with the Step Backward Selection. Have a look at the following script.

The only thing change here compared to Step Forward Selection, keep forward as False.

sfs = SFS(RandomForestClassifier(n_estimators=100, random_state=0, n_jobs = -1),
         k_features = (1, 8),
          forward= False,
          floating = False,
          verbose= 2,
          scoring= 'accuracy',
          cv = 4,
          n_jobs= -1
         ).fit(X_train, y_train)
[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   5 out of  13 | elapsed:    2.2s remaining:    3.6s
[Parallel(n_jobs=-1)]: Done  13 out of  13 | elapsed:    4.6s finished

[2020-08-06 12:57:54] Features: 12/1 -- score: 0.9861111111111112[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of  12 | elapsed:    2.2s remaining:    4.5s
[Parallel(n_jobs=-1)]: Done  12 out of  12 | elapsed:    4.5s finished

[2020-08-06 12:57:58] Features: 11/1 -- score: 0.9861111111111112[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   2 out of  11 | elapsed:    2.2s remaining:   10.3s
[Parallel(n_jobs=-1)]: Done   8 out of  11 | elapsed:    2.7s remaining:    0.9s
[Parallel(n_jobs=-1)]: Done  11 out of  11 | elapsed:    4.1s finished

[2020-08-06 12:58:03] Features: 10/1 -- score: 0.9791666666666666[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   7 out of  10 | elapsed:    3.1s remaining:    1.3s
[Parallel(n_jobs=-1)]: Done  10 out of  10 | elapsed:    4.9s finished

[2020-08-06 12:58:08] Features: 9/1 -- score: 0.9861111111111112[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of   9 | elapsed:    2.1s remaining:    2.7s
[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    4.1s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   9 out of   9 | elapsed:    4.1s finished

[2020-08-06 12:58:12] Features: 8/1 -- score: 0.9859126984126985[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   3 out of   8 | elapsed:    2.2s remaining:    3.8s
[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    2.7s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   8 out of   8 | elapsed:    2.7s finished

[2020-08-06 12:58:15] Features: 7/1 -- score: 0.978968253968254[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of   7 | elapsed:    2.1s remaining:    1.6s
[Parallel(n_jobs=-1)]: Done   7 out of   7 | elapsed:    2.4s finished

[2020-08-06 12:58:17] Features: 6/1 -- score: 0.9859126984126985[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   3 out of   6 | elapsed:    1.7s remaining:    1.7s
[Parallel(n_jobs=-1)]: Done   6 out of   6 | elapsed:    1.8s finished

[2020-08-06 12:58:19] Features: 5/1 -- score: 0.9789682539682539[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   2 out of   5 | elapsed:    2.1s remaining:    3.2s
[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    2.1s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    2.1s finished

[2020-08-06 12:58:21] Features: 4/1 -- score: 0.9718253968253968[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   4 out of   4 | elapsed:    2.3s remaining:    0.0s
[Parallel(n_jobs=-1)]: Done   4 out of   4 | elapsed:    2.3s finished

[2020-08-06 12:58:24] Features: 3/1 -- score: 0.9718253968253968[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   3 out of   3 | elapsed:    2.3s finished

[2020-08-06 12:58:26] Features: 2/1 -- score: 0.9718253968253968[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.
[Parallel(n_jobs=-1)]: Done   2 out of   2 | elapsed:    2.2s finished

[2020-08-06 12:58:28] Features: 1/1 -- score: 0.7674603174603174
sbs = sfs
sbs.k_score_
0.9859126984126985

Let’s get the selected features.

sbs.k_feature_names_
('alcohol',
 'malic_acid',
 'ash',
 'alcalinity_of_ash',
 'magnesium',
 'flavanoids',
 'nonflavanoid_phenols',
 'color_intensity')

Exhaustive Feature Selection (EFS)

Let’s go ahead and learn about the Exhaustive Feature Selection(EFS).

from mlxtend.feature_selection import ExhaustiveFeatureSelector as EFS

It will start with the subset of minimum features to maximum subset of features.

efs = EFS(RandomForestClassifier(n_estimators=100, random_state=0, n_jobs=-1),
         min_features= 4,
          max_features= 5,
          scoring='accuracy',
          cv = None,
          n_jobs=-1
         ).fit(X_train, y_train)
Features: 2002/2002

So, while training with exauhstive feature selection with minimum subset of 4 and 5 it has trained for 2002 subsets.

C(13, 4) + C(13, 5) = 715 + 1287

715 + 1287
2002

Let’s find out best accuracy for EFS algorithm with the following code.

efs.best_score_
1.0

Now get the selected features for the best score.

efs.best_feature_names_
('alcohol', 'malic_acid', 'ash', 'alcalinity_of_ash')

Let’s get indices of selected features.

efs.best_idx_
(0, 1, 2, 3)
from mlxtend.plotting import plot_sequential_feature_selection as plot_sfs

Now, try to plot the graph of the performance with changing number of features.

plot_sfs(efs.get_metric_dict(), kind='std_dev')
plt.title('Performance of the EFS algorithm with changing number of features')
plt.show()

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