## 3 The Proposed Model
### Image Classification  
In the final stage, the BGRCU is exploited for DR detection and classification. Gated recurrent unit (GRU) is making all the recurrent units for adaptably capture dependency of distinct time scales. Like the long short term memory (LSTM), the GRU is a gate unit that modulates the flow of data inside the memory [20], but without taking a discrete memory cell. The input to GRU in step \(t\) is \(D\) dimension vector \(x_{t}\in\mathbb{R}^{D}\). The hidden vector sequence \(h_{1}^{T}:=h_{1},\ldots,h_{T}\) was computed as iterating the subsequent formulas in \(t=1,\ldots,T\):  
\[z_{t}=\sigma(W_{z}x_{t}+U_{z}h_{t-1}+b_{z})\]  
\[r_{t}=\sigma(W_{r}x_{t}+U_{r}h_{t-1}+b_{r})\]  
\[\overline{h}=\sigma(W_{h}x_{t}+U_{h}(r_{t}E\odot h_{t-1})+b_{h})\]  
\[h_{t}=(1-z_{t})h_{t-1}+z_{t}\overline{h}_{t}\]  
The activation has been collected of the update gate \(z_{t}\), reset gate \(r_{t}\), candidate gate \(\overline{h}\), and resultant activation \(h_{t}\). \(W_{(\bullet)}\), \(U_{(\bullet)}\), and \(b_{(\bullet)}\) represent the suitable sized matrix and bias. The symbol \(\sigma\) represents the sigmoid activation and \(\odot\) denotes the elementwise multiplication. The BiGRU processes data from both directions with forward as well as backward hidden layers. Related to the unidirectional case the number of free parameters doubles. The outcome of both directions is then concatenated from the outcome. Assume \(\overrightarrow{h}_{1}^{T}\) remain the forwarding outcome of BGRU with procedure the input order \(x_{1}^{T}\) with \(t=1,\ldots,T\) and consider \(\overleftarrow{h}_{1}^{T}\) to be the equivalent backward outcome with processing the input order in the reverse direction with \(t=T,\ldots,1\). The outcome \(h_{1}^{T}\) of BGRU is the step-wise concatenation of forward as well as backward outputs \(h_{t}:=(\overrightarrow{h}_{t},\overleftarrow{h}_{t})\). An input to Gated Recurrent Convolutional Unit (GRCU) with \(C\) channel and input dimensional \(D\) is an order \(x_{1}^{T}\) of vectors \(x_{t}\in\mathbb{R}^{C\times D}\). The hidden vector order \(h_{1}^{T}\) has been calculated by iterating the subsequent formulas in \(t=1,\ldots,T\):  
\[z_{t}=\sigma(W_{z}*x_{t}+pool(U_{z}*h_{t-1})+b_{z})\]  
\[r_{t}=\sigma(W_{r}*x_{t}+pool(U_{t}*h_{t-1})+b_{r})\]  
\[\overline{h}_{t}=\sigma(W_{h}*x_{t}+pool(U_{h}*(r_{t}\odot h_{t-1}))+b_{h})\]  
\[h_{t}=(1-z_{t})h_{t-1}+z_{t}\overline{h}\]  
\(W_{(\bullet)}\in\mathbb{R}^{F\times C\times L}\) and \(U_{(\bullet)}\in\mathbb{R}^{F\times F\times L}\) are \(F\) features map of length \(L\). The max-pooling functions also take length \(L\) and \(b_{(\bullet)}\in\mathbb{R}^{F}\) are the bias. The GRCU utilizes a similar gating infrastructure as the BGRU, then every fully connected (FC) matrix multiplication was replaced with a convolutional matrix function afterward a max-pooling function with a similar filter length. Integrating GRCU as well as bidirectional recurrent neural network (RNN) outcomes from the BGRCU that were determined analogously to BGRU. In this study, the AOA assists in optimal hyperparameter tuning of the BGRCU model. AOA is a technique simulated by physics, in further detail Archimedes' law. This technique was established by [PERSON] in 2020 and goes into the class of meta-heuristics [21]. In the procedure of AOA, the upgrade of density and volume has been recognized for changing the acceleration dependent upon the collision model amongst objects that play a vital role from determine a new place of present solutions. The common steps of AOA are explained as:The initialized procedure purposes for initializing arbitrarily the real population which comprises \(N\) objects utilized in Equation (1).