Algorithm 1. Pseudocode of Proposed AREMFFS.

Input:

n: Total number of features in the dataset

N: Total Number of Filter Rank Method = |CS, REF, IG|

T1： Threshold value for optimal features selections = ${\left(\prod _{i=1}^n{X}_i\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}$$=\sqrt[n]{X_1{X}_2{X}_{3 }\dots X_n}$

${\mathrm{T}}_2: {\log }_{2}n$

A[]: Aggregators A = { min $\{R_1\left(a_{1\dots n}\right), R_2\left(a_{1\dots n}\right), \dots R_m\left(a_{1\dots n}\right)$},

max{$R_1\left(a_{1\dots n}\right), R_2\left(a_{1\dots n}\right), \dots R_m\left(a_{1\dots n}\right)$},mean{$\left(\sum _{i=1}^m{R}_i\left(a_{1\dots n}\right)\right)\times \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$}, }

P[]: Aggregated Features

$P_t^{\prime }[]$: Optimal Features Selected from Aggregated Rank List based on T

Output:

$M_t^{*}[]$ – Single rank list based on AREMFFS

// Multi-Filter Feature Selection Phase

1.  for $\mathrm{i}=1$ to N { do

2.          Generate Rank list Rn for each filter rank method i

3.        }

4. Generate Aggregated Rank list using Aggregator functions:

for i=1 to len$(A[ ]) \{ \mathrm{do}$

5.          $P_t^{*}\left[i\right]$ // Initialise variable to hold optimal features

6.          $P_i=A_i$

7.          for i =1 to $P_i\left[N_i\right]${ do

8.              $\mathrm{if} (P_i\left[i\right]\le$ T1)

9.                    $P_t^{*}\left[i\right]\leftarrow P_i\left[i\right]$$// \mathrm{append} \mathrm{optimal} \mathrm{features} \mathrm{from} P^{\prime }$ based on T

10.                     }

11.             }

//Ensemble Rank Aggregation Phase

12.   $\mathrm{for} \mathrm{each} \mathrm{feature}f \mathrm{in} P_t^{*}\left[i\right] s.t. i=1,\dots , A_n \{ do$// compute the frequency of each feature in the

aggregated lists

13.                            $\mathrm{if} feature f_j\in P_t^{*}\left[i\right]$

14.                               $j=count (f_{j })$

15.                            $\mathrm{if} \left(j \ge A_{n-1}\right)$

16.                                $\mathrm{M}[ ] \leftarrow feature f_j$   //append feature

}//select most occurring feature f in the aggregated list

17.   $\mathrm{for} \mathrm{i}=1 \mathrm{to} \mathrm{N}\{ do$

18.          Generate Rank list Rn for each filter rank method i

19.           $\mathrm{for} \mathrm{i}=1 \mathrm{to} R_n$ { do

20.                     $R_i{}^{\prime }\left[i\right] \leftarrow TopK features of R_n based on T_2$

21.                   }

22.           }

//Backtracking function Phase

23.    $\mathrm{for} \mathrm{i}=1 \mathrm{to} \mathrm{len}(M[ ])\{ do$

24.              $\mathrm{for} \mathrm{j}=1 \mathrm{to} R_i{}^{\prime }\left[N\right]$ { do

25.                           $\mathrm{if} (feature f_{i }\in R_i{}^{\prime }\left[j\right]$)

26.                                     $g=count \left(f_i\right)$

27.                         }

28.               $\mathrm{if} \left(g \ge R_{n-1}\right)$

29.                  $M_t^{*}[ ]\leftarrow feature f_i$

30.              }

31.  $\mathrm{return} M_t^{*}[ ]$