## 3 Proposed Method
### Dataset and Preprocessing
#### 3.2.4 Graph Construction  
In frequency-domain convolution of a graph, spatial topological information needs to be built into the graph data based on the collection locations of electrodes in different parts of the brain, so three parts of the graph need to be constructed: nodes, features, and edges. For EEG signals, the nodes of the graph are the channel dimensions of the EEG signal; the features are the data collected by the electrodes and the edges indicate the connection status between the nodes of the graph. Since the EEG collection points are similar to a sphere in the brain, and the distance between each collection point and its adjacent nodes is not the same, the weights of its adjacent nodes are different. The correlation features between nodes cannot be well extracted using simple convolution, so the Pearson correlation coefficient (PCC) matrix is used to describe the connection relationship between channels. Treat each channel as a set of vectors, calculate the PCC between the two vectors, and generate a correlation coefficient matrix. Based on PCC, a weighted adjacency matrix is established, and its calculation formula is as follows:  
\[A(i,j)=abs(PCC(x_{i},x_{j}))=abs(\frac{cov(x_{i},x_{j})}{c_{x_{i}}c_{x_{j}}})\]  
where abs () represents the absolute value function and cov() is the covariance, i.e., \(cov(x_{i},x_{j})=\frac{1}{n-1}\sum_{1}^{n}(X_{i}-\bar{X})(x_{j}-\bar{X}), \sigma_{x_{i}}=\sqrt{\sum_{i=1}^{n}(X_{i}-\bar{X})}\). In order to investigate the localization of seizure onset zone with epilepsy propagation networks based on graph convolutional networks, the experiment [28] processed the combination of high-frequency oscillation propagation networks and seizure propagation network through unsupervised and semi-supervised graph convolutional networks. The confidence coefficient of each electrode being located in the seizure onset zone was obtained, and electrodes closely related to the pathogenic epileptogenic network were located. In this article, EEG data are used to verify the correlation between the channels in the seizure area using a PCC matrix. It is evident from Figure 3 that FP1-F7, FP1-F3, FP2-F4, and FP2-F8 showed relatively distinct correlations at the same time, with an average value of 0.85 in the correlation matrix, while the rest were only 0.26. According to the relationship between Pearson values and correlation, when \(|r|\) is greater than 0.8, it can be considered that two variables are highly correlated; when \(0.5<|r|<0.8\), it can be considered that two variables are moderately correlated; when \(0.3<|r|<0.5\), it can be considered that two variables are weakly correlated; when \(|r|\) is less than 0.3, it can be considered that two variables are essentially uncorrelated. In this case, \(|r|\) refers to \(abs(PCC(x_{i},x_{j}))\). As can be seen from the electrode collection positions in Figure 3, the four channels are adjacent in physical space. Figure 3: Schematic diagram of peripheral electrode of epilepsy signal. **(a)** Raw EEG signal; **(b)** Correlation matrix. At 10 s, abnormal brain electrical fluctuations appeared near these four channels, as shown in Figure 4. Therefore, extracting the topology of the location will help us extract the characteristics of the information. The graph construction framework is based on time-frequency feature extraction. As shown in part 1 and part 2 of Figure 5. Part 1 is to convert the feature vector into the nodes of the graph; part 2 is to calculate the Pearson correlation matrix between each node and then obtain the adjacency matrix of the graph based on the nodes. Finally, the graph G = (V,E,X) is obtained. Among them, the feature extraction part is to preprocess the multi-channel EEG signal and then extract the features of the segmented raw data. In this experiment, features are extracted from both the time domain and the frequency domain. In the time domain, the data collected over a period of time are analyzed.