## 3 Method
### Graph-Enhanced Structure for Event Fusion and Clustering
#### 3.4.1 Bilayer Graph-Enhanced Structure  
The event element map, abbreviated as \(G_{m}\), contains the components of all the events that involved the same person. Each node in \(G_{m}\) represents an event element that has been extracted by the scheme described in the previous section, Section 3.3. The elements are connected by undirected edges based on the correlation calculation of event element features. Let \(m\) denote an event element and \(m\) denote the corresponding event element feature vector. Then, \(m\) can be represented as  
\[m=(f,\rho,\tau,\mu) \tag{1}\]  
\(f\) is the vector feature, representing the textual feature of the event element, generated by the BERT pre-trained model. \(\rho\),\(\tau\), and \(\mu\) are numerical features. \(\rho\) is the part of speech obtained in a lexical analysis of event elements, including nouns, adverbs, verbs, adjectives, and others, which are coded 0, 1, 2, 3, and 4. \(\tau\) represents the named entity type of the event element, including the name of the person, the name of the organization, the place name, and others, coded 0, 1, 2, and 3. \(\mu\) is the semantic role of each event element, including the time, place, causer, patient, trigger word, and event description, encoded 0, 1, 2, 3, 4, and 5. Given two event elements \(m_{i}\) and \(m_{j}\), the correlation \(\varphi_{m}\big{(}\mathbf{m_{i}},\mathbf{m_{j}}\big{)}\) is calculated as below. \[\varphi_{m}\big{(}\mathbf{m_{i}},\mathbf{m_{j}}\big{)}=\omega_{\rho}Dif\big{(}\rho_{i},\rho_{j}\big{)}+\omega_{\tau}Dif\big{(}\tau_{i},\tau_{j}\big{)}+\omega_{\mu}Dif \big{(}\mu_{i},\mu_{j}\big{)}+\omega_{f}S_{f}\big{(}\mathbf{f_{i}},\mathbf{f_{j}}\big{)} \tag{2}\]  
\(Dif(x,y)\) is used to calculate the similarity for categorical features, including \(\rho\), \(\tau\), and \(\mu\):  
\[  
The event map \(Ge\) is constructed based on the event element map \(Gm\). We use \(e\) to denote an event and \(e\) to denote the corresponding feature vector. \(e\) is represented as  
\[e=(em,et) \tag{7}\]  
where \(em\) is the combination of the extended features of the corresponding event elements, and \(et\) denotes the original event text. \[em=\left(\overline{m}_{ei},\overline{m}_{tun},\overline{m}_{loc},\overline{m} _{ag},\overline{m}_{pa}\right) \tag{8}\]  
For two event feature vectors \(e_{i}\) and \(e_{j}\), the correlation of these two vectors is defined below. \[\varphi_{e}\big{(}e_{i},e_{j}\big{)}=\omega_{em}S_{em}\big{(}em_{i},em_{j} \big{)}+\omega_{et}S_{et}\big{(}et_{i},et_{j}\big{)} \tag{9}\]  
where \(S_{em}\big{(}em_{i},em_{j}\big{)}\) and \(S_{et}\big{(}et_{i},et_{j}\big{)}\) denote the similarity of the \(em\) component and the \(et\) component of these two event feature vectors, respectively. As \(em\) consists of five event element feature vectors, \(S_{em}\big{(}em_{i},em_{j}\big{)}\) is calculated based on the calculation of event element correlation, which is defined as follows:  
\[S_{em}\big{(}em_{i},em_{j}\big{)}=\sum_{k\in\{e_{i},m,loc,ag,pa\}}\omega_{m} \times\varphi_{m}\big{(}m_{i,k},m_{j,k}\big{)}+\omega_{mc}\times\varphi_{m} \big{(}mc_{i,k},mc_{j,k}\big{)} \tag{10}\]  
\(m_{i,k}\) and \(mc_{i,k}\) form \(\overline{m}_{i,k}\), where \(k\in\{ei,tm,loc,ag,pa\}\). This equation represents the weighted summation of the correlation of these five event element feature vectors, where each event element feature vector has two components, including the original feature vector and the environmental feature vector, i.e., \(\overline{m}_{i,k}=(m_{i,k},mc_{i,k})\). As \(et\) is the text that describes the event, we use Rouge-L to calculate the similarity \(S_{et}\big{(}et_{i},et_{j}\big{)}\). Similar to the event element map, we also define the environmental feature \(ec_{i}\) for each event \(e_{i}\) to capture the influence of related events on \(e_{i}\). Therefore, \(e_{i}\) is extended to \(\overline{e}_{i}=(em_{i},et_{i},ec_{i})\). \(ec_{i}\) is calculated as below.