## 6 Discussion  
This study introduces the TSDA-EM algorithm as an improvement over previous approaches to infer communication patterns within an anonymous communication networks. Unlike many prior works that rely on assumptions of uniform communication behavior or homogeneous user groups, the method presented here is designed to accommodate variations in user interaction frequency and social network structures, thereby addressing some of the limitations in earlier algorithms.  
Table 9 provides a comparison between TSDA-EM and some of the methods described in the Related Works section of this article. The accuracy column shows there are two distinct sets of algorithms: the ones that achieve less than 65% accuracy and those with more than 90% of this same metric. TSDA-EM belongs to this latter group. Another classification can be made when comparing the number of friends that the Alice user is allowed to have in each study. Some only permit a restricted number, less than or equal to 25, while others have practically no restrictions about this parameter. When considering the previous two metrics, only BT-SDA [30] and TSDA-EM belong to both groups.  
The last column compares the threshold value for the mix network employed at each study. A small value implies that fewer messages need to be stored at the mix network before resending them to the intended users, which also means that it becomes easier to identify the relationship between sender and receiver. Conversely, larger values generate more data to be processed by the corresponding algorithm. Given that none of the algorithms in Table 9 are linear, the time and processing complexity rapidly increase with the threshold value. Although the threshold value used in the current study is not large, it is still within the range of other similar studies.  
The proposed TSDA-EM algorithm consistently produces favorable results in terms of accuracy while avoiding restrictions in the number of friends for the Alice user. It is  
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline \(\mathbf{S^{\prime}\backslash R^{\prime}}\) & \(\mathbf{r_{2}}\) & \(\mathbf{r_{4}}\) & \(\mathbf{r_{6}}\) & \(\mathbf{r_{7}}\) & \(\mathbf{MS}\) \\ \hline \(s_{1}\) & \(\mathbf{5}\) & \(\mathbf{0}\) & \(\mathbf{0}\) & \(\mathbf{0}\) & 5 \\ \hline \(s_{3}\) & \(\mathbf{0}\) & \(\mathbf{1}\) & \(\mathbf{0}\) & \(\mathbf{0}\) & 1 \\ \hline \(s_{5}\) & \(\mathbf{0}\) & \(\mathbf{0}\) & \(\mathbf{3}\) & \(\mathbf{1}\) & 4 \\ \hline \(MR\) & 5 & 1 & 3 & 1 & 10 \\ \hline \end{tabular}
\end{table}
Table 8: Real values for the first round of faculty 1.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Attack** & **Accuracy** & **Friends** & **Data Used** & **Mix Network Threshold** \\ \hline PMDA [29] & 62\% & No restrictions & Synthetic & 100 \\ \hline LSDA [32] & 90\% & 25 & Synthetic & 2–40 \\ \hline RSDA [31] & 50\% & 10 & Synthetic & 100–500 \\ \hline NSDA [34] & 63\% & 20 & Synthetic & 10 \\ \hline HSA [28] & 95\% & 23 & Synthetic & - \\ \hline BT-SDA [30] & 95\% & No restrictions & Synthetic & 20 \\ \hline
**TSDA-EM [this]** & **>94\%** & **No restrictions** & **Real data** & **10** \\ \hline \end{tabular} \({}^{a}\) [PERSON]’s friends only.  
\end{table}
Table 9: Comparison of SDA algorithms.  
important to remember that previous approaches have limited the complexity of user behaviors to create simplified and overly controlled test scenarios, while TSDA-EM has been rigorously tested across varied and more realistic datasets. Moreover, TSDA-EM does not require assumptions about message size, resulting in greater accuracy and robustness across these diverse datasets.