# Visual Data and Pattern Analysis for Smart Education:
## 4 Proposed Methods
### Federated Learning-Based Authentication
Throughout the online course, through multiple distributed interactions, Intelligent Software Agents (ISAs) are responsible for capturing students' academic behaviours, interactivity, emotions, and other relevant behaviours, as well as CIs' behaviours and teaching styles. This information is utilised to determine the weekly engagement status of the students. To be more specific, the responsibilities of ISAs are outlined below:

#### 4.2.1 Student Interactiveness Acquisition

Data quality in an e-learning environment, especially regarding emotional data collected through cameras, is critical. Encouraging camera use, while ensuring informed consent and privacy, involves establishing clear guidelines on camera positioning, lighting, and background. Additionally, setting minimum technical standards for camera resolution and internet connectivity is essential. To technologically enhance data quality, implementing real-time feedback mechanisms is crucial. These mechanisms alert students when the camera is off or if the video quality is compromised due to inadequate lighting or incorrect angles. Furthermore, employing pre-processing algorithms, such as brightness and contrast adjustments, noise reduction, and image stabilisation, can significantly improve the clarity of facial features, ensuring a more accurate analysis of student emotions. During online courses, course instructors (CIs) engage with students through various methods, such as posing questions, conducting seminars, and administering short quizzes related to lectures, among other interactive activities. Based on these daily interactions, Intelligent Software Agents (ISAs) evaluate the students' levels of interactivity each week, categorising them into two classes: \"highly interactive\" and \"less interactive\". This evaluation employs the threshold-based Shannon entropy (TSE) method, which quantifies the frequency of interactions exceeding a predefined threshold, thereby assessing engagement levels. Shannon entropy, denoted as \(\mathrm{H}(\varkappa)\), measures the uncertainty in a dataset. It is calculated for a discrete random variable \(\varkappa\) with probability distribution \(\mathrm{P}(\varkappa)\) using the formula:

\[\mathrm{H}(\varkappa)=-\sum_{\varkappa}\mathrm{P}(\varkappa)\cdot\log_{2}( \mathrm{P}(\varkappa)) \tag{9}\]

Here, \(x\) represents the possible values of \(\varkappa\), and \(\mathrm{P}(\varkappa)\) is the probability of each value occurring. TSE specifically focuses on values exceeding a specified threshold, represented as \(\upsilon\). The unit of Shannon entropy is bits when using the base-2 logarithm (\(\log_{2}\)). To compute TSE (H), it first establishes the probability distribution for interactions surpassing the threshold and then employs the Shannon entropy formula. \[\mathfrak{H}=H(\varkappa>\upsilon) \tag{10}\]

Here, \(\varkappa>\upsilon\) represents the set of values exceeding the threshold value. \(\mathrm{H}\) (\(\varkappa>\upsilon\)) denotes the Shannon entropy for values greater than the threshold. TSE is calculated and then utilised to determine each student's interactiveness grade for the week. For instance, if TSE is below a certain threshold, the student could be categorised as \"less interactive\" (represented as \(\varrho_{\mathrm{low}}\)), whereas if TSE is above the threshold, the student could be classified as \"highly interactive\" (represented as \(\varrho_{\mathrm{high}}\)). The process for calculating the Threshold-based Shannon Entropy (TSE) is outlined in Pseudocode 2. This pseudocode details the steps involved in determining student interactiveness based on daily interaction data and a specified threshold.