# Cross-Domain Fake News Detection Through Fusion of Evidence from Multiple Social Media Platforms
## 3 System Architecture
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline News item: & \multicolumn{2}{c}{**Twitter**} & \multicolumn{2}{c}{**Reddit**} & \multicolumn{1}{c}{**Correlation, C**} \\ \hline
**Comments,**\(c_{int}\) & **Encoded** & **Probability,** & **Comments,**\(c_{int}\) & **Encoded** & **Probability,** & \\  & **comments,**\(c_{int}\) & \(p_{t-typ}^{c}\)\(\leftarrow\)\(M_{2}(c_{t})\) & **Comments,**\(c_{std}\) & **comments,**\(c_{std}\) & \(p_{t-typ}^{c}\)\(\leftarrow\)\(M_{2}(c_{t})\) \\ \hline Doesn’t account & & & & & \([-5.89307308\times 10^{-1},\) & \\ schedule [PERSON] chooses play. I & \([-0.51961124,\) & & & \([-5.89307308\times 10^{-1},\) & \\ mean didn’t & \(0.36066872,\) & & & \(6.89936399\times 10^{-1},\) & \\ bypass French & \(1.1010087,\ldots 1\) & & & topic / \(r\)/ tennis & \(5.71980417\times 10^{-1},\) & \(0.91\) \\ prioritise & & & & \(\ldots\)] & \\ grasscourt season. & & & & & \\ \hline Managed clinch & & & & & \\ important & \([-7.77983904\times 10^{-1},\) & & & add categorie & \\ must-win match & \(2.72371382\times 10^{-1},\) & & & \"Mental Strength\" & \([-5.32212585\times 10^{-1},\) & \(-\)**0.61** \\ fired isner. respect & \(7.28409469\times 10^{-1},\) & & & seeing [PERSON] & 3.82354587\(\times 10^{-1},\) & \\ man’s name & & & \"Saving BPs\" & 1.10202396\(\times\)\(10^{-1},\) & \\  & & & & horrendous BP & \\  & & & conversion rate & & \\  & & & doesn’t fit. & & \\ \hline Goat here, shit & \([5.41974604\times 10^{-1},\) & & & \([1.14744902\times 10^{-1},\) & \\ man & \(7.15636134\times 10^{-1},\) & & \(0.99\) & Needs Nadals bald & \(8.40671659\times 10^{-1},\) & \\  & \(2.83419457\times 10^{-3},\) & & patch & \(6.28644377\times 10^{-2},\) & \\  & \(\ldots\) & & & \(\ldots\)] & \\ \hline. &. &. &. &. &. \. &. &. &. &. &. \. &. &. &. &. &. \. &. &. &. &. &. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Calculation of correlation values from the comments of multiple platforms. The justification of this equation for uncertainty, \(U\), is linked to [PERSON]'s information theory, which quantifies uncertainty as a measure of unpredictability in probabilistic systems. When the correlation (\(C\)) between two social media platforms is zero (\(C=0\)), the platforms exhibit no relationship, leading to maximum uncertainty (\(U=1\)), consistent with the concept of maximum entropy in the absence of information. As the absolute correlation (\(|C|\)) increases, uncertainty decreases, reflecting stronger consistency in evidence across platforms. The term \(1-|C|\) models this reduction linearly, while the logarithmic components \(\log(|C|,10)\cdot\log(|C|,10)\) amplify the sensitivity to weak correlations (\(|C|\to 0\)), where the lack of agreement leads to higher uncertainty. The normalization factor \(\log(0.001,10)\) ensures \(U\) remains bounded and interpretable. This formulation is an adaptation of entropy-based principles commonly applied in communication systems [65], making it suitable for modeling uncertainty in cross-platform fake news detection. We have used the same uncertainty calculation method across different social media platforms for all comments to ensure fairness and comparability in the analysis. Support and non-support probability calculation: assessing the level of support, \(p^{sup}\), or non-support, \(p^{-sup}\), expressed in comments is another key factor for evaluating the credibility of information or detecting fake news. Support probability means the probability of news being fake in the presence of uncertainty and the inverse for non-support. For any comment, the general rule is this:  
\[p^{sup}+p^{-sup}+U=1 \tag{2}\]  
So, the calculation of support probability for Twitter follows as:  
\[p^{\sup}_{i-tw}= \begin{cases}0,&\text{when }U\approx 1\\ \min\biggl{(}\left\{p^{c}_{i-tw}\right\}^{n}_{i,tw=1},1-U\biggr{)},&\text{ otherwise}\end{cases}  \tag{3}\]  
Figure 2: Relationship between uncertainty and correlation. Similarly, the support probability for Reddit is defined as:  
\[p_{i\_r\_d}^{\sup}=