## 3 Proposed Method  
### System Model  
This paper presents a GCN-LSTM framework for EEG-based epilepsy seizure detection. The proposed GCN-LSTM model comprises four modules: a graph construction module, a graph convolution module, an LSTM-based temporal information processing module, and a classification module. The specific model architecture is shown in Figure 1.  
Firstly, it is necessary to process raw data into a graph data structure acceptable to graph neural networks, which involves constructing a graph with three key components: nodes, features, and edges. The nodes represent the channels in the collected data, and the edges represent the adjacency relationship between the channels. In practical operations, time-frequency features are extracted from the raw data, and the graph's connectivity is defined based on the Pearson matrix. When the value exceeds 0.8, it is typically assumed that these two variables exhibit high correlation, implying a correlation between features of this channel and the existence of a connection relationship. Consequently, we can define the edge relationship between two channels and obtain the graph's adjacency matrix and degree matrix through channels. Early research directly multiplied the adjacency matrix \(A\) with the feature matrix \(H\): \(H^{(l+1)}=\sigma(AH^{l}W^{l})\), where \(l\) represents the 1 layer and \(W\) represents the weight parameter, without considering the self-influence of nodes. Simultaneously, the adjacency matrix \(A\) remains unnormalized, leading to nodes with more neighboring nodes exerting greater influence on other nodes. Subsequent studies have addressed this issue. Based on the adjacency matrix and degree matrix, it is straightforward to derive the graph's Laplacian matrix. The calculation formula is \(L=D-A\), where L denotes the Laplacian matrix, \(D\) represents the degree matrix, and \(A\) stands for the adjacency matrix.  
Figure 1: GCN-LSTM consists of four modules: a graph building block, a graph convolution block, LSTM module and Prediction block. The output of this model is a predictive label with probability.  
However, the issue of excessive influence due to each node possessing numerous adjacent points persists. To address this, the Laplacian matrix is optimized as follows: \(L_{sym}=D^{-\frac{1}{2}}*\hat{A}*D^{\frac{1}{2}}\). Here, \(\hat{A}=A+I\), where \(I\) represents the identity matrix, and the graph convolution process becomes \(H^{(l+1)}=\sigma(D^{-\frac{1}{2}}\hat{A}D^{\frac{1}{2}}W^{l})\). Following the symmetric normalization of the Laplacian matrix, the graph convolutional kernel can be derived through the process of feature decomposition as demonstrated in Section 3.3: \(g_{\theta}\approx\sum_{K=0}^{K}\theta_{k}T_{k}(\hat{L})\), where \(T_{k}()\) is the Chebyshev polynomial of order k, \(\theta_{k}\) is the corresponding coefficient (the parameter iteratively updated in training), and \(\hat{L}\) is the diagonal matrix of the eigenvalues of re-scaled, and the reason for this shift transformation is that the input of the Chebyshev polynomial is between [-1,1]. with the convolutional kernel matrix containing the weight information of each node's neighboring nodes. After undergoing two graph convolutions and a \(1*1\) dimension increase, the result of the convolution is processed using MaxPool2d maximum pooling. MaxPool2d maximum pooling represents the maximum pooling layer designed for two-dimensional input feature maps. Compared with the fixed pooling operation, the adaptive pooling operation, AdaptiveAvgPool2d, average pooling can dynamically adjust the size of the feature map to adapt to input feature maps of different sizes and different network structures. For the second convolution, AdaptiveAvgPool2d average pooling is applied following the activation of the function using Relu. Subsequently, this is fed into an LSTM network for feature extraction, with the probability value predicted by the Softmax output being utilized.