# MVACLNet: A Multimodal Virtual Augmentation Contrastive Learning Network for Rumor Detection
## 3 Methodology
### Hierarchical Textual Feature Extraction Module
#### 3.3.2 Global-Level Textual Feature Extraction  
**Textual Continuous Feature Extraction**  
The continuous features of text reflect contextual information and semantic relationships, which can help the model understand the meaning of text and its emotions. We apply BiGRU on \(H^{t}\) to extract such continuous features, which can further capture their temporal and sequential characteristics:  
\[R^{gtc}=\left[ \begin{array}{c}r_{1}\\ r_{2}\\...\\ r_{n}\end{array} \right]=\text{BiGRU}(H^{t}), \tag{6}\]  
where \(R^{gtc}\in\mathbb{R}^{n\times d^{gtc}}\) represents the hidden state matrix of \(H^{t}\); \(r_{i}=[\overrightarrow{r_{i}},\overleftarrow{r_{i}}]\in\mathbb{R}^{d^{gtc}}\) denotes the hidden state of \(h_{i}^{t}\), which is formed by concatenating the forward hidden state \(\overrightarrow{r_{i}}\in\mathbb{R}^{d^{gtc}/2}\) of \(h_{i}^{t}\) and the backward hidden state \(\overleftarrow{r_{i}}\in\mathbb{R}^{d^{gtc}/2}\) of \(h_{i}^{t}\). Then, we concatenate \(\overleftarrow{r_{0}}\) and \(\overrightarrow{r_{n}}\) to obtain the global-level textual continuous feature representation \(F^{gtc}\in\mathbb{R}^{d^{gtc}}\):  
\[F^{gtc}=\text{concat}(\overleftarrow{r_{0}},\overrightarrow{r_{n}}). \tag{7}\]  
**Textual Non-Continuous Feature Extraction**  
Social texts often exhibit characteristics of discretization and fragmentation. To better extract these non-continuous features from \(T\), we transformed the feature extraction method into representation learning on a text graph. _Text Graph Construction._We converted each text into an independent heterogeneous text graph \(G^{t}(V^{t},E^{t})\) with corresponding feature matrix \(X^{t}\) and adjacency matrix \(A^{t}\), where\(V^{t}\) represents the set of nodes that includes a text node and multiple word nodes, and \(E^{t}\) represents the edge set that includes text-word edges and word-word edges. For constructing \(X^{t}\), we used pre-trained feature embeddings to initialize feature representations of word nodes. The initial feature representation of the text node was obtained by accumulating feature embeddings of non-repeating words it contains. Formally, \(X^{t}\in\mathbb{R}^{nt^{g}\times d^{gtnc}}\), where \(n^{tg}\) is the number of nodes in \(V^{t}\), and \(d^{gtnc}\) denotes the dimension of the feature representation of nodes. For constructing \(A^{t}\), we built weights of text-word and word-word edges based on word occurrence in texts and word co-occurrence in the whole corpus [41]. Here, we employ the term frequency-inverse document frequency (TF-IDF) and positive point-wise mutual information (PPMI), respectively, to calculate the weights of the edges between the text nodes and the word nodes and between the word nodes. Formally, the weight of the edge between node \(n_{i}\) and node \(n_{j}\) is defined as  
\[A^{t}_{i,j}=\left\{ \begin{array}{ll}\text{TF}-\text{IDF}(n_{i},n_{j})&\quad n _{i}\text{ is text, }\ n_{j}\text{ is word}\\ \text{PPMI}(n_{i},n_{j})&\quad n_{i},n_{j}\text{ are words}\\ 1&\quad n_{i}=n_{j}\end{array} \right.. \tag{8}\]  
The PPMI value between the word nodes is computed as  
\[\text{PPMI}(n_{i},n_{j})=\max(\log\frac{p(n_{i},n_{j})}{p(n_{i})p(n_{j})},0), \tag{9}\]  
\[p(n_{i},n_{j})=\frac{|W(n_{i},n_{j})|}{|W|}, \tag{10}\]  
\[p(n_{i})=\frac{|W(n_{i})|}{|W|}, \tag{11}\]  
where \(|W|\) is the total number of sliding windows in the corpus, \(|W(n_{i})|\) is the number of sliding windows containing \(n_{i}\), and \(|W(n_{i},n_{j})|\) is the number of sliding windows containing both \(n_{i}\) and \(n_{j}\). In particular, the statistical data used are based on the entire corpus rather than specific textual content. Text Graph Representation LearningAfter obtaining \(X^{t}\) and \(A^{t}\), we employed a two-layer GCN [42] on the constructed text graph \(G^{t}\) to perform graph representation learning to obtain hidden representations of all nodes:  
\[O^{gtnc}=\text{GCN}(X^{t},A^{t}), \tag{12}\]  
where \(O^{gtnc}\in\mathbb{R}^{nt^{g}\times d^{gtnc}}\).