## 2 Methods
### Spectral Graph Convolution  
After constructing the deep sequence correlation graph \(G_{d}\) and the feature correlation graph \(G_{f}\), we process the topological structures of both graphs \(G_{d}\) and \(G_{f}\) separately using two spectral graph convolution operations. Equation (6) describes the spectral graph convolution operations, where \(g_{d}\) denotes the graph convolution kernel from the deep sequence correlation graph \(G_{d}\), and \(g_{f}\) denotes the graph convolution kernel from the feature correlation graph \(G_{f}\); \(F\) represents the graph Fourier transform, and \(F^{-1}\) represents the inverse graph Fourier transform. \[g\Big{(}*_{[G_{d},G_{f}]}\Big{)}X_{i}=\Big{[}F(F(g_{d})\odot F(X_{i})),F^{-1} \Big{(}F\Big{(}g_{f}\Big{)}\odot F\Big{(}X_{i}^{T}\Big{)}\Big{)}\Big{]}, \tag{7}\]  
To facilitate understanding of Equation (7), the spectral graph convolution operations performed on \(G_{d}\) and \(G_{f}\) can be rewritten in terms of the eigendecomposition of a deep sequence Laplacian matrix \(L_{d}\) and a feature Laplacian matrix \(L_{f}\). The definitions of the Laplacian matrices \(L_{d}\) and \(L_{f}\) are given by Equation (8) and Equation (9), respectively. \[L_{d}=I_{d}-D_{d}^{-1/2}A_{d}D_{d}^{-1/2}, \tag{8}\]  
\[L_{f}=I_{f}-D_{f}^{-1/2}A_{f}D_{f}^{-1/2}, \tag{9}\]  
where \(I_{d}\in\mathbb{R}^{S\times S}\) and \(I_{f}\in\mathbb{R}^{F\times F}\) are identity matrices. \(D_{d}\) and \(D_{f}\) are diagonal matrices representing the node degrees in \(G_{d}\) and \(G_{f}\), respectively. Since the Laplacian matrices \(L_{d}\) and \(L_{f}\) are real symmetric matrices, their eigendecomposition can be expressed as in Equations (10) and (11). \[L_{d}=Q_{d}\wedge_{d}Q_{d}^{-1}=Q_{d}\wedge_{d}Q_{d}^{T}, \tag{10}\]  
\[L_{f}=Q_{f}\wedge_{f}Q_{f}^{-1}=Q_{f}\wedge_{f}Q_{f}^{T}, \tag{11}\]  
where \(Q_{d}\) and \(Q_{f}\) represent the eigenvectors of \(L_{d}\) and \(L_{f}\), respectively; and \(\wedge_{d}\) and \(\wedge_{f}\) represent the arrays of eigenvalues of \(L_{d}\) and \(L_{f}\), respectively. The spectral graph convolution operations performed on \(G_{d}\) and \(G_{f}\), rewritten in the form of eigendecomposition of the Laplacian matrices, can be expressed as Equation (12). \[g\Big{(}*_{[G_{d},G_{f}]}\Big{)}X_{i}=\bigg{[}Q_{d}\Big{(}Q_{d}^{T}g_{d}\odot Q _{d}^{T}X_{i}\Big{)},Q_{f}\bigg{(}Q_{f}^{T}g_{f}\odot\Big{(}X_{i}Q_{f}\Big{)} ^{T}\bigg{)}\bigg{]}, \tag{12}\]  
Equation (12) can also be expressed as Equation (13), where \(\theta_{d}\) represents the learnable parameters for the graph convolution kernel \(g_{d}\), and \(\theta_{f}\) represents those for \(g_{f}\). \[g\Big{(}*_{[G_{d},G_{f}]}\Big{)}X_{i}=\Big{[}Q_{d}g_{d,\theta_{d}}(\Lambda_{d} )Q_{d}^{T}X_{i},Q_{f}g_{f,\theta_{f}}(\Lambda_{f})Q_{f}^{T}X_{i}^{T}\Big{]}, \tag{13}\]  
By substituting Equations (10) and (11) into Equation (13), we can derive Equation (14). \[g\Big{(}*_{[G_{d},G_{f}]}\Big{)}X_{i}=\Big{[}g_{d,\theta_{d}}(L_{d})X_{i},g_{f, \theta_{f}}(L_{f})X_{i}^{T}\Big{]}, \tag{14}\]  
Since solving Equation (14) is computationally expensive, it is widely accepted to use the first-order Chebyshev polynomial approximation technique for spectral convolution operations [31]. Equation (15) provides the first-order Chebyshev polynomial approximation of Equation (14). Here, \(N=1\) represents the first-order approximation, and \(T_{N}(\cdot)\) is the \(N\)th-order Chebyshev polynomial. \[g\Big{(}*_{[G_{d},G_{f}]}\Big{)}X_{i}=\Bigg{[}\sum_{n=1}^{N}\theta_{d,N}T_{N}( L_{d})X_{i},\sum_{n=1}^{N}\theta_{f,N}T_{N}(L_{f})X_{i}^{T}\Bigg{]}, \tag{15}\]Substituting Equations (8) and (9) into Equation (15) yields Equation (16). Here, \(\Theta_{d}\in\mathbb{R}^{F\times F}\) represents the parameter matrix for the graph filter \(g_{d}\), while \(\Theta_{f}\in\mathbb{R}^{S\times S}\) represents the parameter matrix for the graph filter \(g_{f}\).