# Visual Data and Pattern Analysis for Smart Education:
## 4 Proposed Methods
### Federated Learning-Based Authentication
Accuracy

Certainly, a simple linear equation can be used to represent the link between the number of training epochs and accuracy (\(\forall\)):

\[\delta_{2}(\beta) \rightarrow (\alpha) \tag{2}\]6

Here, \(\mathcal{E}\) represents the number of training epochs, and the rate of change in accuracy per epoch is given by \(\wp\). It indicates how much accuracy increases with each additional epoch. \(\mathcal{I}\) is the starting accuracy, often known as the intercept, which represents the accuracy at epoch 0. Figure 2 and Table 2 present the number of epochs vs. accuracy. As the number of epochs increases, the accuracy rate also increases. Choosing five epochs as a comparison point in machine learning model training can indicate early performance, assess model efficiency, and benchmark against standard practices. It also highlights resource efficiency, as fewer epochs mean less computational time and energy usage. For example, in several epochs (e.g., 5), the accuracy of the proposed method reaches 65%, while existing methods, such as PCT, achieve 15%, MST-FaDe achieves 25%, Fuzzy SVM achieves 35%, and AISAR achieves 45%. With a higher number of epochs (e.g., 25), the proposed method attains an accuracy level of 73%, while PCT reaches 39%, MST-FaDe reaches 49%, Fuzzy SVM reaches 59%, and AISAR reaches 61%. Ultimately, the proposed method demonstrates a higher accuracy level compared to existing ones. #### 5.1.2 No of Epochs vs. F1-Score

Certainly, the relationship between the number of training epochs and the F1-Score can be succinctly explained through a simple equation. The F1-Score is a widely used metric for evaluating the balance between precision and recall in classification problems. The formula is traditionally expressed as:

\[\delta_{2}(\beta) \rightarrow (\alpha) \tag{2}\]7

The F1-Score (F) is the harmonic mean of precision (E) and recall (K)). Precision (E) is defined as the ratio of true positives to the sum of true positives and false positives, while recall (K) is defined as the ratio of true positives to the sum of true positives and false negatives. Consequently, the F1-Score provides a single value that encapsulates model performance, considering both false positives and false negatives. This offers a balanced perspective, particularly useful in scenarios with uneven class distributions. Table 3 represents numerical outcomes, and Figure 3 illustrates the relationship between the number of epochs and the F1-score. As the number of epochs increases, the F1-score correspondingly rises. In the proposed method, F1-scores of 50%, 65%, and 95% are achieved with 5, 25, and 50 epochs, respectively. Conversely, the PCT method yields F1-scores of 42%, 52%, and 76%; the MST-FaDe method yields F1-scores of 43%, 57%, and 79%; and the fuzzy SVM method yields F1-scores of 45%, 62%, and 80% for the same respective epochs. Meanwhile, AISAR registers F1-scores of 46%, 63%, and 81% for the corresponding epochs. Existing approaches demonstrate lower F1-scores when compared to the proposed method. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Number of** \\ **Epochs** \\ \end{tabular} } & \multicolumn{5}{c}{**Accuracy**} \\ \cline{2-5}  & **PCT** & **MST-FaDe** & **Fuzzy SVM** & **AISAR** & **Proposed** \\ \hline
5 & 15 & 25 & 35 & 45 & 65 \\ \hline
10 & 17 & 29 & 37 & 41 & 66 \\ \hline
15 & 22 & 32 & 42 & 43 & 68 \\ \hline
20 & 36 & 46 & 56 & 58 & 71 \\ \hline
25 & 39 & 49 & 59 & 61 & 73 \\ \hline
30 & 41 & 51 & 61 & 63 & 78 \\ \hline
35 & 43 & 53 & 63 & 68 & 82 \\ \hline
40 & 49 & 59 & 69 & 71 & 85 \\ \hline
45 & 51 & 61 & 71 & 77 & 92 \\ \hline
50 & 60 & 65 & 75 & 79 & 97 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Numeric results of accuracy. Figure 2: Number of epochs vs. accuracy.