## 5 SU-CMO-Based Hybrid Classification  
### Hybrid Classifiers  
LSTM classifier: It [24] includes a sequence of recurring LSTM cells. Each cell of LSTM encompassed 3 units, such as \"forget gate, the input gate, and the output gate\". Presume variables \(Z\) and \(D\) that indicate hidden and cell state in order. \((X_{t},D_{t-1},Z_{t-1})\) and \((Z_{t},D_{t})\) indicate input and output layers.  
At time \(t\), the output, input and forget gate implies \(O_{t},I_{t},F_{t}\) in that order. LSTM chiefly exploits \(F_{t}\) for sorting the data. The sorted data indicate specified partial features connected to the previous gaze direction; \(F_{t}\) is formulated as shown in Equation (9).  
\[F_{t}=\sigma(J_{IF}X_{t}+L_{IF}+J_{ZF}Z_{t-1}+L_{ZF}). \tag{9}\]  
In Equation (9), \((J_{ZF},L_{ZF})\) and \((J_{IF},L_{IF})\) points out weight and bias constraints to map hidden and input layers to forget gate and activation function is signified by \(\sigma\).  
Input gate is exploited by LSTM as revealed in Equations (10)-(12), wherein, \((J_{ZG},L_{ZG})\) and \((J_{IG},L_{IG})\) implies weight and bias constraints to map hidden and input layers to the cell gate respectively. \((J_{ZI},L_{ZI})\) and \((J_{II},L_{II})\) imply weight and bias constraints to map hidden and input layers to \(I_{t}\).  
\[G_{t}=\tanh(J_{IG}X_{t}+L_{IG}+J_{ZG}Z_{t-1}+L_{ZG}) \tag{10}\]  
\[I_{t}=\sigma(J_{II}X_{t}+L_{II}+J_{ZI}Z_{t-1}+L_{ZI}) \tag{11}\]  
\[D_{t}=F_{t}D_{t-1}+I_{t}G_{t} \tag{12}\]  
\[O_{t}=\sigma(J_{IO}X_{t}+L_{IO}+J_{ZO}Z_{t-1}+L_{ZO}) \tag{13}\]  
\[Z_{t}=O_{t}\tanh(D_{t}). \tag{14}\]  
In addition, the LSTM cell obtains the output hidden layer from the output gate as shown in Equations (13) and (14), in which, \((J_{ZO},L_{ZO})\) and \((J_{IO},L_{IO})\) represents weight and bias to map the hidden and input layer to \(O_{t}\). Accordingly, the weights of LSTM represented by \(J\) are optimally elected by the proposed SU-CMO model.  
Bi-GRU [25]: Depending upon RNN, 3 gates named \"forget gate, input gate, and output gate and memory cell\" are integrated with LSTM for controlling the flow of information across LSTM cells. Similarly, GRU deploys special gates, called reset and update gates, for lessening gradient dispersal with slighter computation losses. The update gate \((ut)\) substitutes forget and input gates of LSTM, portray the retention degree of prior data as revealed in Equation (15).  
\[ut=\mu(W_{u}*[R_{t-1},Fea_{t}]+f_{u}). \tag{15}\]  
In Equation (15), \(\mu\) points out the sigmoid activation function among 0 and 1, \(Fea_{t}\) stands for the input matrix at time step \(t\), \(R_{t-1}\) stands for the hidden state at the prior time step; \(t-1\) stands for the weight matrix of \(ut\) and \(f_{u}\) stands for the bias matrix of \(ut\). The reset gate \((rt)\) regulates how much chronological data have to be ignored, which is revealed in Equation (16), wherein, \(W_{r}\) characterize weight matrix of \(rt\) and \(f_{r}\) symbolize bias matrix of \(rt\).  
\[rt=\mu(W_{r}*[R_{t-1},Fea_{t}]+f_{r}). \tag{16}\]Subsequently, the candidate's hidden state is revealed in Equation (17), wherein, \(tanh\) stands for \(tanh\) activation function. \(f_{R}\) and \(W_{R}\) stand for bias matrix and weight matrix of new cell state, \({}^{*}\) stands for dot multiplication function. Thus, the output \(R_{t}\) implies linear interruption amid \(\left(\widetilde{R}_{t}\right)\) and \(R_{t-1}\) in Equation (18).  
\[\widetilde{R}_{t}=\tanh(W_{R}[R_{t-1}*rg,Fea_{t}]+f_{R}) \tag{17}\]  
\[R_{t}=(1-ut)*R_{t-1}+ut*\widetilde{R}_{t}. \tag{18}\]  
The forward GRU captures the previous details of input data and the backward GRU obtains the upcoming details of input data. The Bi-GRU is modeled as in Equation (19), wherein, \(\overset{\leftarrow}{R}_{t}\) and \(\overset{\rightarrow}{R}_{t}\) correspond to the hidden state of backward and forward GRU in that order, \(Ct\) corresponds to combining technique of outputs at two directions.  
\[Yt=Ct\left(\overset{\rightarrow}{R}_{t},\overset{\leftarrow}{R}_{t}\right). \tag{19}\]