## 3 The Proposed Model
### Feature Selection Using SFSA Technique  
In this work, the SFSA technique is applied to select a subset of features. SFSA is based on the specific development marvel of a random fractal and basically uses two processes afterward for population initialization: (1) diffusion and (2) update to enhance the searching [24]. In the arithmetical modeling of the SFSA, the finest solution is only preferred from the diffusion method to generate novel arrangements, while overlooking discrete arrangements. The procedure for making a new arrangement is characterized as Gaussian walks \((Gw)\) that are determined in the following:  
\[Gw_{1}=Gaussian\left(\mu_{G},\ \sigma\right)+\left(rand(0,1)\times P_{B}-rand \ (0,1)\times P_{i}\right) \tag{2}\]  
\[Gw_{2}=Gaussian(\mu_{P},\ \delta) \tag{3}\]  
The expression: \(rand(0,\ 1)\) refers to an arbitrary value that lies between zero and one, \(P_{i}\) and \(P_{B}\) denotes the \(i\)-\(th\) solutions and every particle diffuses around its position and completes correspondingly; \(\mu_{G}\) and \(\mu_{P}\) indicates the Gaussian means walk that is equivalent to \(|P_{i}|\) and \(|P_{B}|\) correspondingly; \(\delta\) denotes the standard deviation that is calculated by:  
\[\delta\bigg{|}\frac{\log(g)}{g}(P_{i}-P_{B})\bigg{|} \tag{4}\]  
In Equation (4), \(g\) represents the iteration count. In the optimization technique, \(g\) is increased but lesser than ending criteria \(G_{max}\), \(\delta\) are attuned dynamically. All the particles are diffused around their current situation by using the Gaussian walk until a predetermined extreme dissemination number YD is obtained. Based on the following equation, many generated solutions are attained:  
\[P_{ij}=LB_{ij}+rand(0,1)\times\left(LIB_{ij}-LB_{ij}\right),j=1,2,3,\ldots,Y_{D} \tag{5}\]  
In Equation (5), \(UB_{ij}\) and \(LB_{ij}\) refers to the upper as well as lower limits of \(j\)-th values of solution \(i;y_{D}\) denotes the maximal diffusion count of solutions generated by the SFSA. Then, the quality of solution has been calculated and the optimal solution \(P_{B}\) is defined. In this step, two methods are used: initially update the solution of (p) probability according to the value of \(Pa<rand\ (0,1)\) as follows:  
\[P_{a}=\frac{rank(P_{i})}{N_{D}} \tag{6}\]  
\[P^{\prime}_{ij}=P_{aj}-rand(0,1)\times(P_{a1}-P_{a2}) \tag{7}\]  
In Equation (7), rank (p) refers to the rank of \(i^{th}\) solutions amongst different arrangements in the population; \(P^{\prime}_{i}\) indicates the new solution of the \(i\)-\(th\) solution; \(P_{a1}\) and \(P_{a2}\) signifies the random solution of population. Next, improve the exploration accordingly and apply the variations to the solution based on discrete solutions from the population. The reconstructing error is minimalized by the Gradient Descent mechanism. The weight in Equations (10) and (11) need to be upgraded based on the following equations, where 0 indicates the learning rate:  
\[W=W-\alpha\frac{\partial L(x,z)}{\partial W}. \tag{13}\]  
\[b=b-\alpha\frac{\partial L(x,z)}{\partial b}. \tag{14}\]  
\[b^{\prime}=b^{\prime}-\alpha\frac{\partial L(x,z)}{\partial b^{\prime}}. \tag{15}\]  
Once the layer is pre-trained, the network enters the supervised finetuning phase. In the supervised finetuning phase, add an LR layer to the resultant layer. In this work, probability that the \(x\) input vector (Layer 4) belonging to \(i\)-\(th\) class is determined in the above equation, where \(y\) represents the predicted class of input vector \(x\). \(W\) and \(b\) denote the weight matrices and the bias vector, correspondingly, \(W_{j}\) and \(W_{j}\) denote the \(i^{th}\) and \(j^{th}\) row of matrixes \(W\), correspondingly, \(b_{i}\) and \(b_{j}\) denote the \(i^{th}\) and \(j^{th}\) elements of vector \(b\), correspondingly, and \(softmax\) refers to the nonlinearity function. The class with the maximum probability was assumed as the prediction label \(y_{pred}\) of \(x\) input vector, as determined in Equation (17).