## 3 Materials and Methods
### Feature Fusing Based on Cross Attention Mechanism (SCF-Net)  
To utilize the inherent characteristics of SAR target data in the process of CIL, a feature fusion method based on the cross-attention mechanism is proposed, and by integrating these inherent characteristics, which are more stable compared to CNN features, a more balanced representation in terms of stability and plasticity is generated. As shown in Figure 3, for SAR targets, SAR raw data and its corresponding amplitude images are used to extract features, respectively. For the SAR amplitude image, the VGG16 network is modified to extract the CNN feature with less computation. We remove two conv 3-512 layers, one conv 3-256 layer, and all the fully connected layers. In order to apply cross attention mechanism to fusing the extracted CNN feature with electromagnetic attributed scattering center feature. The extracted CNN feature needs to be flattened to a size of \(8192\times 1\). Then, through a fully connected layer, the CNN feature is converted into a size of \(256\times 1\). For the SAR raw data of target, following the method in [33], we can extract the electromagnetic attributed scattering center feature (SC feature) vector, which is also with the size of \(256\times 1\). First of all, \(N_{sc}\) attributed scattering centers are estimated to obtain the parameter set. For scattering center \(i\), its parameter set \(\Phi_{i}\) can be estimated as follows:  
\[\hat{\Phi}_{i}=\underset{\Phi_{i}}{\text{argmin}}\left\|\overset{\rightharpoonup} {S}-\sum_{i}A_{i}\overset{\rightharpoonup}{\hat{\phi}_{i}}\right\|^{2} \tag{1}\]  
where \(\overset{\rightharpoonup}{S}\) is the SAR echo raw data that is transformed into a vector; \(A_{i}\) is the complex amplitude; and \(\phi_{i}\) can be calculate by Equation (2) and then be transformed into a vector as well. \[ \begin{split}\phi_{i}(f,\varphi)=\sin c\left[2\pi\frac{L_{i}}{c} f\sin(\varphi-\varphi_{0i})\right]\\ \times\exp\left[-j4\pi\frac{f}{c}(x_{i}\cos\varphi+y_{i}\sin \varphi)\right]\end{split}  \tag{2}\]  
where \(L_{i}\) is the length of attributed scattering center \(i\), \(c\), \(f\), and \(\varphi\) are the speed of light, frequency, and azimuth angle, respectively. Through iterative optimization in [50], the parameter set of the scattering center \(i\) can be obtained, which contains \(\left\{\hat{A}_{i},\hat{L}_{i},\hat{\varphi}_{i},\hat{x}_{i},\hat{y}_{i}\right\}\), where \"\(\cdots\)\" means optimized approximate results, \(\hat{x}_{i}\) and \(\hat{y}_{i}\) are the position coordinates of the scattering center \(i\), respectively. After estimating the parameters of the scattering centers, for each class that contains \(n\) samples, a parameter set with a size of \(n\times N_{sc}\times 6\), where \(\hat{A}_{i}\) is divided into \(\left[\hat{A}_{i}\right]_{real}\) and \(\left[\hat{A}_{i}\right]_{imag}\). \(\left[\hat{A}_{i}\right]_{real}\) and \(\left[\hat{A}_{i}\right]_{imag}\) are the real part and the imagery part of \(\hat{A}_{i}\), respectively. With the BOVW method, the parameters set of \(N_{sc}\) scattering centers of each target is transferred into the SC feature vector. The lower part of Figure 3 presents a comparison between our cross-attention structure and the conventional self-attention structure. The main difference between the two attention structures lies in the way Query--\(Q\), Key--\(K\), and Value--\(V\) are generated. In the conventional self-attentional structure, a single feature is input and projected  
Figure 3: Structure of our SCF-Net. through three different matrices \(W^{Q}\), \(W^{K}\), and \(W^{V}\) to obtain \(Q\), \(K\), and \(V\), which are then used for feature extraction. In contrast, to achieve better feature fusion, our method takes two heterogeneous representations extracted from the SAR image and SAR echo data as \(Q\), \(K\), and \(V\), respectively. This design emphasizes the interaction between the CNN-derived image features and the SC features.