# Independent Random Recurrent Neural Networks for Infrared Spatial Point Targets Classification
## 3 Classification of IR Radiation Intensity Sequence Based on IRRNN
### Classification Algorithm Based on IRRNN
#### 3.3.2 Bi-Direction Extension Structure of IRRNN  
When the infrared radiation intensity time series of the spatial point target is processed according to the IRRNN structure of the previous section, only the data information before time step step t is used for the classification of decision processing at the current time, and the data information after time step t cannot be utilized. In fact, for the time series classification task of the spatial point target of this paper, due to the periodicity and continuity of the target motion, the sample data information before and after the current time step t is very important for the classification decision of the current time. Therefore, this paper proposes a Bi-direction IRRNN model, which makes the sample information change from the original forward-only transmission to a bidirectional network structure that can be forward and reverse. The sample information before and after time step t can be applied in the decision of the current state. The network structure of the bidirectional IRRNN (B-IRRNN) is shown in Figure 6. As shown, there are two hidden layers that are independent of each other, and the input data is processed simultaneously in forward and backward manners. Then the output obtained is the weighted sum of results in two directions. It can be seen as a combination of two unidirectional RNNs networks, in particular, the hidden layer transmission of the two networks is reversed, and the output is determined by the results of the two networks together. As shown in Figure 6, in the forward transmission layer, the hidden layer state \(\overset{\rightarrow}{\mathbf{h}}\) is recursively calculated from \(t=1\) to T, and the corresponding output is \(\overset{\leftarrow}{\mathbf{y}}\). In the backward transmission layer, the hidden layer state \(\overset{\leftarrow}{\mathbf{h}}\) is inversely recursively calculated from \(t=\) T to 1, and the corresponding output is \(\overset{\leftarrow}{\mathbf{y}}\). The final output is the weighted sum of the two output values. Therefore, the calculation formula of the B-IRRNN model is:  
\[ \begin{gathered}\overset{\rightarrow}{\mathbf{x}}_{t}=o\Big{(} \mathbf{x}_{t}+\beta\sum_{t=1}^{t-1}\mathbf{w}_{i}\overset{\rightarrow}{ \mathbf{y}}_{i}\Big{)}\overset{\leftarrow}{\mathbf{x}}_{t}=o\Big{(}\mathbf{x }_{t}+\beta\sum_{t=1}^{t-1}\mathbf{w}_{i}\overset{\leftarrow}{\mathbf{y}}_{ i}\Big{)}\\ \overset{\rightarrow}{\mathbf{h}}_{t}=f_{\text{fl}}\Bigg{(} \overset{\rightarrow}{\mathbf{W}}\overset{\rightarrow}{\mathbf{W}}\overset{ \rightarrow}{\mathbf{w}}\overset{\rightarrow}{\mathbf{w}}+\overset{ \rightarrow}{\mathbf{w}}\overset{\rightarrow}{\mathbf{h}}_{t-1}+\overset{ \rightarrow}{\mathbf{B}}^{\text{H}}\Bigg{)}\overset{\leftarrow}{\mathbf{h}}_{ t}=f_{\text{fl}}\Bigg{(}\overset{\leftarrow}{\mathbf{W}}\overset{\leftarrow}{ \mathbf{w}}\overset{\leftarrow}{\mathbf{x}}_{t}+\overset{\leftarrow}{\mathbf{w}} \overset{\leftarrow}{\mathbf{w}}\overset{\leftarrow}{\mathbf{h}}_{t-1}+ \overset{\leftarrow}{\mathbf{B}}^{\text{H}}\Bigg{)}\\ \overset{\rightarrow}{\mathbf{y}}_{t}=\alpha_{1}\overset{ \rightarrow}{\mathbf{y}}_{t}+\alpha_{2}\overset{\leftarrow}{\mathbf{y}}_{t}, \end{gathered}  \tag{18}\]  
where \(\alpha_{1}\) and \(\alpha_{2}\) are the weighting coefficients of the output, and \(\alpha_{1}+\alpha_{2}=1\) is required. Considering that the information before and after the current time is equally important in the time series of the infrared radiation intensity of the target, the equal weight addition is used here, so \(\alpha_{1}=\alpha_{2}=0.5\).