## 3 Materials and Methodology
### Finding the Predicted Target Module  
This proposed system predicts the learner's target module by processing both explicit and implicit signals using a hybrid model (XGBoost + GRU). Once the predicted module is identified, it is validated for logical consistency and relevance using a knowledge graph (KG). In Table 13, all of the modules are arranged in the order of complexity as a node with the target modules' information. The system predicts the target module in three main steps:  
* Step 1: Process explicit signals (XGBoost). * Input: Explicit signals such as pre-test scores, post-test scores, satisfaction ratings, and module preferences. * Processing: XGBoost uses tree-based methods to capture non-linear relationships and assigns a predicted score (\(\hat{y}_{\text{XGBoost}}\)) for each potential module as follows. * Objective function (\(\mathcal{L}(\theta)\): The objective function combines a loss function and a regularization term: \[\mathcal{L}(\theta)=\sum_{i=1}^{n}1(\text{x}_{i},\hat{\text{x}}_{i})+\sum_{k= 1}^{K}\Omega(\text{f}_{k})\] (7) where
* \(1(\text{x}_{i},\hat{\text{x}}_{i})\): Loss function. * \(\Omega(\text{f}_{k})=\gamma\text{T}+\frac{1}{2}\lambda\parallel w\parallel^{2}\): Regularization term. * T: The number of leaves in the tree. * w: Leaf weights. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Initial Module** & **Target Module 1** & **Target Module 2** & **Target Module 3** \\ \hline Data Structures & Algorithms & Trees & Graph Algorithms \\ Algorithms & Dynamic Programming & Graph Algorithms & Machine Learning \\ Binary Trees & Graph Algorithms & Advanced Trees & Segment Trees \\ Graph Algorithms & Shortest Path Algorithms & Network Flow & Advanced Graph Theory \\ SQL Basics & Database Optimization & Advanced SQL & Data Warehousing \\ Testing & Integration Testing & System Testing & Performance Testing \\ Networking & Operating Systems & Network Security & Cloud Networking \\ Machine Learning & Deep Learning & Natural Language Processing & Reinforcement Learning \\ Data Analytics & Big Data Analytics & Business Intelligence & Visualization Techniques \\ Operating Systems & Memory Management & Process Scheduling & Virtualization \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Knowledge graph structure. 2. Prediction (\(\hat{y}_{\rm i}\)): The final prediction is the sum of predictions from all trees: \[\hat{y}_{\rm i}=\sum_{k=1}^{K}f_{k}(x_{\rm i})\] (8) 3. Gradient and Hessian (\(g_{\rm i}\)): To optimize the loss, XGBoost computes: \[g_{\rm i}=\frac{\partial l(y_{\rm i},\hat{y}_{\rm i})}{\partial\hat{y}_{\rm i}},\quad h_{\rm i}=\frac{\partial^{2}l(y_{\rm i},\hat{y}_{\rm i})}{\partial\hat{ y}_{\rm i}^{2}}\] (9) 4. Tree-splitting gain (Gain): The gain from a split is calculated as follows: \[\text{Gain}=1/2((\text{G\_L2})/(\text{H\_L}+\lambda)+(\text{G\_R2})/(\text{H\_ R}+\lambda)-(\text{G\_L}+\text{G\_R})2/(\text{H\_L}+\text{H\_ R}+\lambda))-\gamma\] (10) where * \(\text{G\_L},\text{G\_R}\): Gradients for left and right nodes. * \(\text{H\_L},\text{H\_R}\): Hessians for left and right nodes. * Output: Probability or score indicating the relevance of each module. Step 2: Process implicit signals (GRU). * Input: Sequential data like time spent, retries, engagement trends, and clickstream data. * Processing: * GRU processes the temporal dependencies in the data, predicting a score (\(\hat{y}_{\text{GRU}}\)) for each module based on behavioural patterns as follows. 1. Update gate (\(z_{\rm t}\)): Determines how much of the previous hidden states to retain: \[z_{\rm t}=\sigma(W_{\rm z}x_{\rm t}+\text{U\_z}h_{\rm t-1}+b_{\rm z})\] (11) where * \(z_{\rm t}\): Update gate at time t. * \(x_{\rm t}\): Input at time t. * \(h_{\rm t-1}\): Previous hidden state. * \(W_{\rm z},\text{U\_z},\text{b\_z}\): Weights and bias. * \(\sigma\): Sigmoid activation function. 2.