## 5 Results
If other proposed tables contain the same pair of communication (for example \([s_{1},r_{2}]\)), we only have to add the number of messages (from the proposed table) to the frequency messages table; see Table 7.  
The objective of the previous work is to identify whether or not there is communication between pairs, where **0** means there is not communication and **1** means that it is. In this work, we have estimated the frequency of communication among senders and recipients; see Table 7. Therefore, this is another contribution of the proposed TSDA-EM algorithm. Nevertheless, in order to compare the performance with previous works, we use Table 7 with binary values, i.e., we set **1** if there is communication and we set **0** otherwise. We have a dataset with the number of messages among senders \(S\) and recipients \(R\) for each faculty, which is our ground truth, also called real table [16]. So, the classification rate, specificity, and sensitivity were generated as follows with the real table versus frequency messages table (Table 7):  
* True positive (TP): number of messages in both cases is **1**. * False negative (FN): there is communication in the pair of communication but we could not determinate it. * True negative (TN): number of messages in both cells is **0**. * False positive (FP): there is not communication in the pair, but we have inferred a number of messages. \[Sensitivity=\frac{TP}{TP+FN} \tag{12}\]  
\[Specificity=\frac{TN}{TN+FP} \tag{13}\]  
\[Classification\ rate=\frac{TN+TP}{TN+TP+FN+FP} \tag{14}\] \begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline \(S^{\prime}\backslash R^{\prime}\) & \(r_{1}\) & \(r_{2}\) & \(r_{3}\) & \(r_{4}\) & \(r_{5}\) & \(r_{6}\) & \(r_{7}\) & \(\cdots\) & \(MS\) \\ \hline \(s_{1}\) & - & 5 & 0 & 0 & 0 & 0 & 0 & 0 & \(\cdots\) \\ \hline \(s_{2}\) & 0 & - & 0 & 0 & 0 & 0 & 0 & 0 & \(\cdots\) \\ \hline \(s_{3}\) & 0 & 0 & - & 0 & 0 & 0 & 1 & 0 & \(\cdots\) \\ \hline \(s_{4}\) & 0 & 0 & 0 & - & 0 & 0 & 0 & 0 & \(\cdots\) \\ \hline \(s_{5}\) & 0 & 0 & 0 & 1 & - & 3 & 0 & 0 & \(\cdots\) \\ \hline \(s_{6}\) & 0 & 0 & 0 & 0 & 0 & - & 0 & 0 & \(\cdots\) \\ \hline \(s_{7}\) & 0 & 0 & 0 & 0 & 0 & 0 & - & 0 & \(\cdots\) \\ \hline \(\vdots\) & 0 & 0 & 0 & 0 & 0 & 0 & - & \(\vdots\) \\ \hline \(MR\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) & \(\cdots\) \\ \hline \end{tabular}
\end{table} 
Table 7: Frequency messages table. Figure 8 shows the specificity rate for each faculty used in this proposal while Figure 9 shows the sensitivity for each faculty. In this way, we state TSDA-EM is better at inferring users who do not communicate for sure. Although the choice between having higher specificity or sensitivity depends on the context and the objectives of the problem. If we consider a scenario where it is more important to avoid errors in identifying negative cases, a high specificity should be prioritized. Conversely, if it is better to correctly detect all positive cases, sensitivity should be prioritized. After many tests, we notice a better classification rate for each faculty, but after some iteration, the rate does not increase. So checking the proposed tables, we found out that the program gets \"stuck.\" It generates the proposed tables in the best way that it can. That is, assigning values and completing tables. But it can not notice the wrong assigned values on  
Figure 8: Specificity rate for each faculty. Figure 9: Sensitivity rate for each faculty. the cells because apparently there is not any problem with the values on the cells. Look at Table 8 and compare it with Table 6.  
What is the difference between both tables? First, both tables are correct, but Table 8 is the real round. The difference is just one value at the cells \([s_{3},r_{4}]\) and \([s_{5},r_{7}]\). Pay attention to \(\lambda_{3,4}\) and \(\lambda_{5,7}\); see Table 5. How do we notice that the value is not in the correct cell?