# Visual Data and Pattern Analysis for Smart Education:
## 4 Proposed Methods
### Federated Learning-Based Authentication
Based on the acquisition results mentioned above, the weekly engagement status of the students is computed using the Majority Voting Multi-Objective Clustering (MV-MOC) method. In this context, the multiple objectives pertain to the students' weekly academic and behavioural status, encompassing interactiveness, academic emotions, and behaviours, respectively. Multi-Objective Optimisation: MV-MOC extends conventional clustering by optimising multiple objectives concurrently. Each objective corresponds to a distinct clustering solution, and the algorithm aims to find a compromise among these objectives. Pareto Front: The Pareto Front is a set of solutions that are not dominated. A solution is considered non-dominant if it cannot be improved on one objective without negatively impacting another. The Pareto front illustrates the trade-offs between these objectives. Majority Voting: MV-MOC assigns data points to clusters based on the consensus of multiple clustering solutions using majority voting. The diversity between Solutions X and Y, based on their cluster assignments, can be calculated. This can be achieved using the Jaccard Index (J), which measures the dissimilarity or diversity between two sets, X and Y.

\[\delta_{2}(\beta) \rightarrow (\alpha) \tag{2}\]0

Here, \(X\cap Y\) represents the number of data points assigned to the same cluster in both Solution \(X\) and Solution \(Y\) (the intersection of sets \(X\) and \(Y\)), while \(X\cap Y\) represents the total number of unique data points assigned to clusters in Solutions \(X\) and \(Y\) (the union of sets \(X\) and \(Y\)). The Pareto Dominance Test is performed to determine whether Solution \(X\) dominates Solution \(Y\) based on multiple objectives. Solution \(X\) is considered to dominate Solution \(Y\) if it is equal to or better than Solution \(Y\) in all objectives. This dominance check can be expressed for each objective \(i\) as follows:

\[\delta_{2}(\beta) \rightarrow (\alpha) \tag{2}\]1

Here, \(f_{i}(S_{X})\) represents the value of objective \(i\) in Solution \(X\), and \(f_{i}(S_{Y})\) represents the value of objective \(i\) in Solution \(Y\). For Solution \(X\) to dominate Solution \(Y\), this inequality must hold for all objectives \(i\). If it holds for at least one objective, Solution \(X\) is considered to dominate or be equivalent for some objectives, but not all. In summary, these equations are used to analyse the diversity between two clustering solutions (Diversity Calculation) and to check if one solution dominates another based on multiple objectives (Pareto Dominance Check). In the final step of the MV-MOC algorithm, the number of times each data point has been assigned to each cluster across all Pareto front solutions is calculated. Subsequently, each data point is assigned to the cluster that receives the majority of votes, determining its final assignment. Optionally, the quality of the clustering solution can be evaluated using cluster validity \(\
ot{i}\) indices, such as the silhouette score, which measures how well the data points are clustered. \(\hat{\kappa}\) represents the Pareto front solutions. The process for the Majority Voting Multi-Objective Clustering (MV-MOC) is detailed in Pseudocode 3, which outlines the steps for clustering data based on multiple objectives and determining the engagement status of students. To ensure that the algorithm does not operate indefinitely, a termination condition is imposed based on either a fixed number of iterations or convergence. Ultimately, the final clustering solution consists of clusters obtained through majority voting based on Pareto-front solutions, enabling the effective classification of data points according to their engagement status or other relevant objectives. Concerning these objectives, the majority voting method clusters students into classes, such as engaged and non-engaged students. To clarify, students exhibiting good behaviour and positive academic emotions but lower levels of interactiveness would be categorised as engaged students, and vice versa.