# Cross-Domain Fake News Detection Through Fusion of Evidence from Multiple Social Media Platforms
## 3 System Architecture
These encoded comments were then processed through a machine learning model, \(M_{2}\), to calculate a probability for each comment. Mathematically, this is expressed generally for Twitter and Reddit as:  
\[p^{c}_{i\_{-tw}}\gets M_{2}(e_{i\_{-tw}})\]  
and  
\[p^{c}_{i\_{-nd}}\gets M_{2}(e_{i\_{-nd}})\]  
where \(p^{c}_{i\_{-tw}}\) and \(p^{c}_{i\_{-rd}}\) are the probability for the \(i\)-th comment on Twitter and Reddit, respectively. In Table 3, the original comments, their encoded vectors, and the computed probabilities are presented for both Twitter and Reddit. For instance, a Twitter comment 'Doesn't account schedule [PERSON] chooses play...' is encoded and the corresponding probability is 0.08, while a Reddit comment 'It 100 the time I topic /r/tennis' is encoded and has a probability of 0.91. After calculating all probabilities using Algorithm 1, the correlation between the probabilities is calculated. To calculate these probabilities, pairs are formed between Twitter and Reddit comments based on their timestamps. This means the first comment on Twitter is paired with the first comment on Reddit, and so on. Specifically, the Pearson correlation coefficient (\(C\)) is determined to evaluate the relationship between the sets of probabilities. \[\{p^{c}_{i\_{-tw}}\}\quad\text{and}\quad\{p^{c}_{i\_{-rd}}\}\]  
The correlation value (Table 3) of \(-0.61\) reveals a moderate-to-strong inverse relationship between comments on Twitter and Reddit, highlighting contrasting patterns of user engagement and interpretation across the two platforms. When comments on Twitter align positively with a news item, Reddit comments often challenge or refute it, and vice versa. This divergence reflects the distinct user behaviors and discussion dynamics unique to each platform--Twitter's real-time and concise communication contrasts with Reddit's preference for detailed and critical discussions. This negative correlation underscores the variability in how users interact with the same news item across platforms, shaped by their respective functional and cultural characteristics. Such findings reinforce the importance of cross-platform analysis in understanding how information is debated and interpreted, offering valuable insights into the mechanisms of news dissemination and the potential for misinformation to spread. Comment analysis with uncertainty: after calculating the correlation, the next step is uncertainty. This process is divided into three parts. First, we calculate the uncertainty based on the correlation between comments. Next, we compute both the support and non-support probabilities to quantify the likelihood of the news being fake or true in the presence of uncertainty. Finally, we fuse these decisions to arrive at a comprehensive conclusion. * Uncertainty calculation: analyzing comments from two social media platforms can introduce the possibility of uncertainty that needs to be addressed. Calculating the uncertainty associated with comment analysis provides a measure of the confidence or reliability of the analysis results. This information aids in interpreting the findings and making informed decisions or drawing accurate conclusions based on the analyzed comments with the presence of uncertainty. Here we measure uncertainty, U, as defined by the following equation: \[U= \begin{cases}1,&\text{if }C=0\\ \frac{(1-|C|)\cdot\text{log}(|C|,10)\cdot\text{log}(|C|,10)}{\text{log}(0,001,1 0)},&\text{otherwise}\end{cases} \] (1) Figure 2 illustrates the relationship between correlation (\(C\)) and uncertainty (\(U\)), and comes from Equation (1). When there is a positive or negative correlation, the level of uncertainty is relatively low. However, as \(C\) approaches zero, \(U\) increases significantly. When \(C=0\), the uncertainty reaches its maximum value of 1.