## 2 Methodology
### Graph Convolution Branch  
Numerous studies have shown that the classification accuracy can be effectively improved by combining the different features of images. Traditional CNN models can only convolve images in regular image regions using convolution kernels of a fixed size and weight, resulting in an inability to obtain global features and structural features of images. Therefore, it is often required to deepen the network layer to alleviate this problem. However, as the number of network layers deepens, the chance of overfitting increases subsequently, especially when processing data with a small amount of training samples such as HSIs. Such a result is unacceptable to us. Therefore, a GCN branch based on superpixel segmentation was constructed to obtain the structural features. Different from the CNN, the GCN is a method used for the graph structure. The GCN branch can extract the structure features and dependency relationship between the nodes from images. These features are different from the neighborhood spatial features in a local fine region extracted by the CNN branch. Finally, the property of the network can be enhanced by fusing the different features extracted from the two branches. The graph structure is a non-Euclidean structure that can be defined as \(\text{G}=(\text{V},\text{E})\), where V is the set of nodes and E is the set of edges. V and E are usually encoded into a degree matrix \(\mathbf{D}\) and node matrix \(\mathbf{A}\), where \(\mathbf{D}\) records the relationship between each pixel of the hyperspectral image and \(\mathbf{A}\) denotes the number of edges associated with each node. Because the degree of each graph node in the graph structure is not the same, the GCN cannot directly use the same-size local graph convolution kernel for all nodes similar to the CNN. Considering that the convolution in the spatial domain is equivalent to the product in the frequency domain, researchers hope to implement the convolution operation on topological graphs with the help of the theory of graph spectra, and they have proposed the frequency domain graph convolution method [31]. The Laplacian matrix of the graph structure is defined as \(\mathbf{L}=\mathbf{D}-\mathbf{A}\). The symmetric normalized Laplacian matrix is defined as:  
\[\mathbf{L}=\mathbf{I}_{N}-\mathbf{D}^{-1/2}\mathbf{A}\mathbf{D}^{-1/2} \tag{2}\]  
The graph convolution operation can be expressed by Equation (3). \[g_{\theta}\bullet x=\mathbf{U}g_{\theta}(\Lambda)\mathbf{U}^{\text{T}}x \tag{3}\]  
where \(\mathbf{U}\) is the orthogonal matrix composed of the feature vectors of the Laplacian matrix L by column, and \(g_{\theta}(\Lambda)\) is a diagonal matrix consisting of parameter \(\theta\), representing the parameter to be learned. The above is the general form of graph convolution, but Equation (3) is computationally intensive because the complexity of the eigenvector matrix \(\mathbf{U}\) is \(O(N^{2})\). Therefore, [PERSON] et al. [32] showed that this process can be obtained by fitting a Chebyshev polynomial, as in Equation (4). \[g_{\theta}\bullet x=\sum_{k=0}^{K}\Theta_{k}T_{k}\Big{(}\widetilde{L}\Big{)}x \tag{4}\]  
where \(\widetilde{L}=\frac{2}{\lambda_{\text{max}}}L-I_{N}\) and \(\lambda_{\text{max}}\) are the largest eigenvalues of \(L\). \(\Theta_{k}\) is the vector of the Chebyshev coefficients. In order to reduce the computational effort, the literature [33] only calculates up to K = 1. \(\lambda_{\text{max}}\) is approximated as two; then, we have:\[g\theta\bullet x\approx\theta\Big{(}\mathbf{I}_{N}+\mathbf{D}^{-1/2}\mathbf{A} \mathbf{D}^{-1/2}\Big{)}x \tag{5}\]  
In addition, self-normalization is introduced:  
\[\mathbf{I}_{N}+\mathbf{D}^{-1/2}\mathbf{A}\mathbf{D}^{-1/2}\rightarrow\widetilde {\mathbf{D}}^{-1/2}\widetilde{\mathbf{A}}\widetilde{\mathbf{D}}^{-1/2} \tag{6}\]  
where \(\widetilde{\mathbf{A}}=\mathbf{A}+\mathbf{I}_{N}\widetilde{\mathbf{D}}_{ii}= \sum\limits_{j}\widetilde{\mathbf{A}}_{ij}\).