## 3 Methodology
### Binarization of EOSA (BEOSA)
#### 3.3.1 Transformation of Method  
We proposed four transformation functions to position infected individuals \(ind_{i}\) in the discrete space. These functions follow the popular S-functions and V-functions categories, so that two functions are described for the latter and two for the former. Equations (4) and (5) contain the S1 and S2 functions which belong to the S-transform function, while Equations (6) and (7) contain the V1 and V2 functions which belong to the V-function family. \[S1=\ \frac{1}{1+e^{\left(-\sqrt{2}\right)}} \tag{4}\]  
\[S2=\ 1-\frac{1}{1+e^{x}} \tag{5}\]  
\[V1=\ \left|\frac{x}{\sqrt{2+x^{2}}}\right| \tag{6}\]  
\[V2=\left|\tan x\right| \tag{7}\]  
In Figure 3, the behavior of the transform functions is plotted to show that they are truly able to generate patterns similar to the class of function they belong to. For instance, the (a) part of the figure shows that the two S-functions result in an S-shaped pattern when the function is applied to values \([-6,6]\), while a V-shaped pattern is reported for the V-functions when they are applied to the same values. Note that these functions confine their output on the y-axis to values between \([0,1]\), which is the aim of using the transform functions. Figure 1: Representation of the search space for all individuals in the population, with an illustration of the binarization procedure of feature indicators for each individual. Figure 2: Identification of selected features as obtainable in every instance of the entire dataset. The aim of applying these transform functions is to ensure that they can help transfer the composition of feature positions in an individual to either 0 or 1. Additionally, these functions can increase the probability of changing the natural composition of that individual, so that they become a potential solution for solving feature selection problems. This is illustrated using Equations (8) and (9). The first part of the two equations controls the selection of either the S1 or S2 function when applying the S-function and the use of either T1 or T2 when applying the V-function. A determinant factor is used to guide this decision, so that if \(rand(0|1)\), the function generates 1, and the S2 or T2 function is called as appropriate; otherwise, the S1 or T1 function is called. In the second part of the two equations, the value of the \(k^{th}\) position in the representation of individual \(ind_{i}\) is modified to be 1 when \(r>S\left(ind_{i}^{k}\right)\) for S-functions and \(r>T\left(ind_{i}^{k}\right)\) for T-functions; otherwise, 0 is assigned to the \(k^{th}\) position whereby k lies between \(0\leq k<D\), and \(r\) is a randomly generated between \([0,1]\). \[S\left(ind_{i}^{k}\right),\ T\left(ind_{i}^{k}\right)= \begin{cases}S2\left(ind _{i}^{k}\right),T2\left(ind_{i}^{k}\right)&rand(0|1)==1\\ S1\left(ind_{i}^{k}\right),T1\left(ind_{i}^{k}\right)&rand(0|1)==0\end{cases}  \tag{8}\]  
\[ind_{i}^{k}= \begin{cases}1&r>S\left(ind_{i}^{k}\right)\mid r>T\left(ind_{i}^{k} \right)\\ 0&otherwise\end{cases}  \tag{9}\]  
A flowchart of the process of applying the transform functions to achieve the translation of the BEOSA from the continuous space to the discrete space is illustrated in Figure 4. The optimization process begins with a population described as the susceptible group. Based on the natural phenomenon of the EOSA method, some individuals are exposed to the virus, thereby leading to some of them being allocated to the infected subgroup. It is these infected individuals that are optimized for a number of iterations. It is expected that during the iteration, almost all the members of the susceptible subgroup will move to the infected subgroup. For each \(ind_{i}\) in the \(I\) subgroup, the \(k^{th}\) position is mutated using either of the S-functions or V-functions, depending on the satisfiability of the \(pos(i)<THRESHOLD\) criteria. Note that the \(pos(i)\) function computes the current position and displacement of individual \(ind_{i}\).