# 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  
#### 3.3.1 IRRNN Overall Structure and Algorithm  
Aiming at the sample dataset characteristics and classification requirements of the targets, this paper proposes an IRRNN model. On the one hand, to ensure that the periodic features of the sample sequence are preserved and not destroyed by truncation, we use the IndRNN structure, which has the ability to process longer sequences than the traditional RNNs structure. On the other hand, in order to improve the classification performance of the RNNs model, we use the RRNN model to map historical output information to the input layer through a random weight matrix. The spatial point targets generally have micro-motion forms such as precession or tumbling in the exo-atmosphere, so that the infrared radiation intensity sequences have periodic characteristics, and different shapes and micro-motion features will be fully embodied in the sequences, which makes the traditional feature extraction methods hard to extract. Therefore, the RNNs model is suitable for the classification of target infrared radiation intensity sequences. The length of each input sequence determines whether the feature information can be completely input to the neural network. IndRNN makes the training simpler and more efficient because of its independent structure. At the same time, it solves the problem of gradient explosion and vanishing and can input longer sequences. Therefore, we use the IndRNN structure to make the periodic characteristic information of the sequence not lost and can be used for subsequent classification. The infrared radiation intensity sequence of the spatial point target has high correlation in time, and the information before time step t has important reference value for the classification of current time. Therefore, we combine the historical output information before time step t by random weighting with the input data at time t and input it to the hidden layer for further processing. The structure of the IRRNN is as shown in the following Figure 5. First, the historical output information is weighted by the random weight matrix \(\mathbf{W}\) and combined with the input data of the current time together, and then becomes the new input data and enters the hidden layer. Then the neurons of the hidden layer are independent of each other, and the training is more efficient and stable and can effectively converge when the input sequence is long. To reflect the structure of the IndRNN, the connection of the hidden layer is represented by the symbol of the Hadamard product \(\odot\), and ReLU is used as the activation function. Since the network structure of IRRNN improves the structure of the input layer and the connection mode of the hidden layer only on the basis of the traditional RNNs, the other network structures remain unchanged, so according to the Equations (8) and (14), the IRRNN network can be obtained. The calculation model is  
\[ \begin{array}{l}\mathbf{x^{\prime}}_{t}=\sigma\Big{(}\mathbf{x}_{t}+\beta \mathbf{\sum}_{i=1}^{t-1}\mathbf{W}_{i}\mathbf{y}_{i}\Big{)};\\ \mathbf{a}_{t}=\mathbf{W}^{\text{HI}}\mathbf{\cdot}\mathbf{x^{\prime}}_{t}+ \mathbf{w}\odot\mathbf{h}_{t-1}+\mathbf{B}^{\text{H}};\\ \mathbf{h}_{t}=f_{h}(\mathbf{a}_{t});\\ \mathbf{b}_{t}=\mathbf{W}^{\text{OH}}\mathbf{\cdot}\mathbf{h}_{t}+\mathbf{B}^ {\text{O}};\\ \mathbf{y}_{t}=f_{o}(\mathbf{b}_{t}),\end{array}  \tag{17}\]  
where \(\odot\) indicates the Hadamard product, and other parameters are the same as Equation (14). In the formula, \(f_{h}(\cdot)\) and \(f_{o}(\cdot)\) are the activation function of the hidden layer and the output layer respectively. Because of the structure of IndRNN, \(f_{h}(\cdot)\) can be a unsaturated nonlinear function, so we choose ReLU as the activation function. And \(f_{o}(\cdot)\) still chooses Softmax as the activation function.