## 4 Methodology
### Uni-Modal Representation Extraction
#### 4.1.4 Trend Module  
The dissemination of information on social media is affected by internal signals, such as user engagement with posts, as well as endogenous signals, such as sudden occurrences outside the platform. Our aim is to measure public reactions to the news contained in a tweet at that very moment and use it as an exogenous signal. Utilizing Google Trends, we were able to accomplish our objectives. The architecture of Trend Module is illustrated in Figure 12.  
**Exogenous features.** Using TF-IDF, we pulled out three relevant keywords from the title of the news. Not all of these were accurate, however, so we manually sorted through them to replace any unreasonable ones. To obtain their corresponding trending values, we used the Google Trends API to take data from 15 days prior to the date of the source tweet up until the day before. Finally, the geographical location was set to the United States area.  
One-dimensional convolutional neural network (1D-CNN) models can be used to encode trending values. 1D filters were employed in each convolutional layer to capture the local features of the input data, followed by a ReLU function for non-linear transformation of the data.  
Figure 12: The architecture of the trend component.  
\begin{table}
\begin{tabular}{l l l} \hline \hline  & **Feature** & **Description** \\ \hline \multirow{4}{*}{Statistical features} & _avg\_rt\_count_ & The average number of retweets of historical posts. \\  & _avg\_fluorite\_count_ & The average number of times the historical posts have been \\  & _avg\_time\_diff_ & The average time between posts of historical posts. \\  & _avg\_sentence\_count_ & The average sentence count of historical posts. \\  & _sensitive\_tweet\_ratio_ & The ratio of historical posts marked as sensitive. \\ \hline \multirow{4}{*}{Sentiment features} & _avg\_sentiment\_score_ & The average value of sentiment\_score from historical posts. \\  & _avg\_pos\_count_ & The average value of pos\_count from historical posts. \\ \cline{1-1}  & _avg\_neg\_count_ & The average value of neg\_count from historical posts. \\ \cline{1-1}  & _avg\_sentiment\_ratio_ & The average value of sentiment\_ratio from historical posts. \\ \hline \hline \end{tabular}
\end{table}
Table 5: User timeline features.  
The mathematical representation of the convolutional operation is given by  
\[\mathbf{c}_{i}=\sigma(\mathbf{x}_{i:i+h-1}*\mathbf{w}_{i}+\mathbf{b}),\mathbf{c}_{i}\in\mathbb{R}, \tag{7}\]  
in which \(\mathbf{w}_{i}\in\mathbb{R}^{h\times 1}\) denotes a filter that is applied to a window of \(h\) days' trending values to produce a new feature, \(i\) corresponds to the trending value index, and \(b\) is the bias. The convolution operator is represented by \(*\), and \(\sigma(\cdot)\) corresponds to the activation function. The feature \(\mathbf{c}_{i}\) is generated from windows of trending values \(\mathbf{x}_{i:i+h-1}\). This filter was applied to each possible window of trending values to produce a feature map, as shown in Equation (8).  
\[\mathbf{c}=[\mathbf{c}_{1},\mathbf{c}_{2},\dots,\mathbf{c}_{n-h+1}]. \tag{8}\]  
The model employed multiple filters (with a diverse range of window sizes) to extract multiple features. To capture the public's attention at different intervals, we set filter windows of 3, 5, and 7. We set up distinct numbers of layers for each branch of the window sizes so that the output size of the final layer was consistent; i.e., it had the same proportion of features regardless of time scale. Then, we applied channel-wise mean and concatenated the features from different time scales.  
The trend representation was obtained and further concatenated with statistical features and trend features, as shown in Table 6 below.