## 3 The Proposed Model
### Image Classification Using Optimal CLSTM Model  
In the final stage, the optimal CLSTM model is utilized to recognize different types of classes that exist in the aerial images [22]. A recurrent neural network (RNN) is a kind of DL method which is depending on existing input and the preceding input. In general, it is suitable for the scenario where the dataset has a consecutive correlation. But while handling a longer series of datasets, there exists an exploiting and vanishing gradient problem. In order to resolve this problem, a long short term memory (LSTM) is utilized that has an internal memory state which adds forget gate. The gate controls the time dependency and the effects of preceding inputs. Bidirectional long short term memory (BiLSTM) and bidirectional RNN (BiRNN) are other variations that reflect preceding input and assume the upcoming input of a certain time frame. This work, can present the BiLSTM RNN and cascaded uni-directional LSTM models. The method comprises the initial layer of bi-directional RNN integrated with uni-directional RNN layer. The bi-directional LSTM comprises forward and backward tracks to learn patterns in two directions. \[O_{n}^{f1},\,h_{n}^{f1},\,i_{n}^{f1}=L^{f1}\Big{(}i_{n-1}^{f1},\,h_{n-1}^{f1},\,x _{n}\,:P^{f1}\Big{)}, \tag{12}\]  
\[O_{n}^{b1}\,\,h_{n}^{b1}\,\,i_{n}^{b1}=L^{b1}\,\left(i_{n-1}^{b1},\,h_{n-1}^{b1},\,x _{n}\,:P^{b1}\right), \tag{13}\]  
Equations (12) and (13) show the operation of forwarding and backward tracks. Figure 2 depicts the framework of LSTM. From the equation, \(O_{n}^{f1},\,h_{n}^{f1},\,i_{n}^{f1}\) and \(O_{n}^{b1},\,h_{n}^{b1},\,i_{n}^{b1}\) indicate the output, the hidden state, and the internal state of the existing state for forwarding and backward LSTM tracks correspondingly. \(x_{n}\) denotes the sequential input, \(P\) indicates the LSTM cell variable. The output from these two tracks is integrated as in Equation (14) and forwarded into the next layers. \[O_{n}^{1}=O_{n}^{f1}+O_{N-n+1}^{b1}. \tag{14}\]  
Bi-directional RNN and uni-directional RNN transform information into an abstract form and assist in learning spatial dependency. The output from the uni-directional layer can be attained by the following equation. \[O_{n}^{l},h_{n}^{l},\,i_{n}^{l}=\text{LSTM}^{l}\,\left(i_{n-1}^{l},\,h_{n-1}^{ l},\,O_{n}^{l-1};P^{l}\right), \tag{15}\]  
Now, the output from the lower layer \(O_{n-1}^{l-1}\) is integrated with preceding internal state \(i_{n-1}^{l}\) and hidden state \(h_{n-1}^{l}\) for obtaining output \(O_{n}^{l}\) of layer \(l\), and \(P^{l}\) indicates a variable of the LSTM cell. The input dataset comprises a series of instances \((x_{1},\,\,x_{2},\,\dots,\,x_{N})\), while every feature \(x_{n}\) is regarded at time \(n\)\((n=1,2,\,\dots,\,N)\). The information is mainly classified into windows of time segment \(N\) and fed into the cascading LSTM. We attain predicted score vectors for every time step \(\left(O_{1}^{L},\,O_{2}^{L},\,\dots,\,O_{N}^{L}\right)\) at the output. The entire prediction score can be attained by integrating the predictive score vector for the window \(N\). The combination of scores can be implemented by using the sum rule as demonstrated in Equation (16) that implements well than other methodologies. Finally, the predictive score is transformed into probability using a softmax layer over \(Y\). \[Y=\frac{1}{N}\sum_{(n=1)}^{N}O_{n}^{L}. \tag{16}\]  
Figure 2: Infrastructure of LSTM. We cascade LSTM to simulate incremental change of n time steps, and every LSTM is utilized for estimating the increment for one time step. In this work, \(\theta\)-increment learning method learns increment of parameters using the cascaded LSTM network to gain higher frequency approximation, and \(\theta\) represents the targeted parameter to be calculated. In order to optimally elect the hyperparameter values of the CLSTM model, the SOA is exploited.