## 3 The Proposed Model
### Image Classification Using Optimal CLSTM Model
In SOA, all the seekers have a central location vector \(\overset{\rightharpoonup}{c}\), viz., the initial position for finding upcoming solutions, and it is regarded as estimated value \(Ex\). Furthermore, all the seekers have a searching radius \(\overset{\rightharpoonup}{r}\) regarded as the \(En^{\prime}\), a trust level \(\mu\) as membership degree, and a searching direction \(\overset{\rightharpoonup}{d}\). Next, the seeker with some level of trust followed a potential direction and randomly moves towards the second point (novel candidate solution) in some searching radius from their existing location. In every time step \(t\), the search decision-making is carried out for evaluating the four variables, and the seeker moves toward the novel location \(\overset{\rightharpoonup}{x}(t+1)\). The updating location from the central location can be defined as \(y\)-conditional cloud generator [23]:  
\[\overset{\rightharpoonup}{x}_{ij}(t+1)=\overset{\rightharpoonup}{c}_{ij}(t)+ \overset{\rightharpoonup}{d}_{ij}(t)\times\overset{\rightharpoonup}{r}_{ij}(t) \times\sqrt{-\ln(\mu_{i})} \tag{17}\]  
Here \"\(i\)\" refers to the subscript index of seeker, and \"\(j\)\" indicates the subscript index of parameter dimension. The pseudo-code of the SOA is given in Algorithm 1. ```
\(t\gets 0\)  Initialized generation of \(S\) position \(\{x_{i}(t)|x_{i}(t)=(x_{i1},x_{i2},\ldots,x_{iD}),\;i=1,\ldots,S,\;t=0\}\) Uniformly and randomly in the parameters. Estimate all the seekers: Compute the fitness. Searching techniques provide search variables involving central location vector, searching direction, searching radius, and trust degree. Update new location of all the seekers is evaluated. \(t\gets t+1\)  When \(t<T_{\text{max}}\), then Go to 3; otherwise, End. ```  
**Algorithm 1**Pseudocode of SOA  
Instinctively, central location vector \(\overset{\rightharpoonup}{c}\) is fixed to existing location \(\overset{\rightharpoonup}{x}(t)\). Similar to particle swarm optimization (PSO), all the seekers contain a memory stored in its optimal location \(\overset{\rightharpoonup}{p}\) and a global optimal location \(g\) accomplished by communicating with neighboring seekers. Every seeker is categorized into \(k\) class in the subscript index, and the seeker in a similar class belongs to virtual neighbors. Therefore, \(\overset{\rightharpoonup}{g}\) is established in the virtual neighbors. \[\overset{\rightharpoonup}{c}=\overset{\rightharpoonup}{x}(t)+r_{1}\varnothing_ {1}\Big{(}\overset{\rightharpoonup}{p}(t)-\overset{\rightharpoonup}{x}(t) \Big{)}+r_{2}\varnothing_{2}\Big{(}\overset{\rightharpoonup}{g}(t)- \overset{\rightharpoonup}{x}(t)\Big{)} \tag{18}\]  
Now \(r_{1}\), \(r_{2}\) indicates the cognitive and social learning rates, correspondingly. \(\varnothing_{1}\) and \(\varnothing_{2}\) denotes the real number randomly and uniformly selected within the range of \([0,1]\). In every experiment carried out in the study, \(r_{1}=1\), \(r_{2}=1\), and \(k=3\). Generally, all the seekers have four significant directions, named local spacial direction \(\overset{\rightharpoonup}{d}_{ls}\), local temporal direction \(\overset{\rightharpoonup}{d}_{lt}\), global spacial direction \(\overset{\rightharpoonup}{d}_{gs}\), and global temporal direction \(\overset{\rightharpoonup}{d}_{gt}\), correspondingly. \[\overset{\rightharpoonup}{d}_{lt}=\left\{ \begin{array}{c}sign\left(\overset{ \rightharpoonup}{x}(t)-\overset{\rightharpoonup}{x}(t-1)\right)\;if\;fit\Big{(} \overset{\rightharpoonup}{x}(t)\Big{)}\geq fit\Big{(}\overset{\rightharpoonup}{x} (t-1)\Big{)}\\ sign\left(\overset{\rightharpoonup}{x}(t-1)-\overset{\rightharpoonup}{x}(t) \Big{)}\;if\;fit\Big{(}\overset{\rightharpoonup}{x}(t)\Big{)}<fit\Big{(} \overset{\rightharpoonup}{x}(t-1)\Big{)}\end{array} \right.