# Enhancing the Recommendation of Learning Resources for Learners via an Advanced Knowledge Graph
## 3 Materials and Methods
### Prediction Layer
#### 3.4.3 Concatenation Aggregation  
Concatenation aggregation concatenates the vector representations in a set into a single vector representation and then applies a nonlinear transformation to it. The specific operation is as follows:  
\[agg_{concat}^{(o)}=\sigma\Big{(}\text{W}_{\text{a}}\cdot\Big{(}e_{o}^{(i_{1} )}\parallel e_{o}^{(i_{2})}\parallel\cdots\parallel e_{o}^{(i_{n})}\Big{)}+z _{a}\Big{)}, \tag{21}\]  
where \(e_{o}^{(i_{k})}\in\tau_{o}\), and \(\parallel\) denotes the concatenation operation.  
Since the aggregated vector representations of the learner and the learning resource require the same dimensions for further computation, we select a balanced combination of multiple representations for the aggregator. We use \(e_{l}\) to denote the aggregated vector of the learner and \(e_{s}\) to denote the aggregated vector of the learning resource. Finally, we compute the inner product of the representations to predict the learner's preference score for the learning resource.  
\[\hat{y}_{ls}=e_{l}^{T}e_{s}, \tag{22}\]  
KGNN-LS [18] is a method that applies a trainable function to compute user-specific item embeddings. It then utilizes a graph neural network to generate personalized item embeddings. Additionally, label smoothing is employed to regularize the edge weights, thereby enhancing the inductive bias.  
KGAT [6] is also an advanced propagation-based model that integrates a UIG and KG into a homogeneous unified graph called a CKG. Compared to KGCN, KGAT utilizes an attention mechanism to distinguish the importance of neighbors in the CKG during the propagation process.  
CKAN [7] is an advanced propagation-based model that utilizes a heterogeneous propagation strategy to explicitly encode these two types of information and applies a knowledge-aware attention mechanism to distinguish the contributions of different knowledge neighbors.  
KGIN [34] is proposed to explore the intentions behind user-item interactions using auxiliary item knowledge. Each intent is modeled as a careful combination of KG relationships, encouraging the independence of different intents to achieve better model capability and interpretability. A new information aggregation scheme is designed for the GNN, which recursively integrates sequences of relationships with long-range connectivity.  
CAKR [35] is a new method that optimizes feature interaction between items and their corresponding entities in the knowledge graph and includes a feature crossover unit incorporating an attention mechanism to enhance the recommendation performance.  
KGG [36] is a recommendation method that combines users' local interest features and global interest features, efficiently exploring users' preference levels toward target users by learning users' local and global interest features through a knowledge graph convolutional neural network and a generative adversarial network.  
KCNR [37] is a knowledge-aware enhanced network for domain-informed recommendation, which acquires different knowledge neighbors by propagating within the knowledge graph and utilizes a knowledge-aware attention network to distinguish and aggregate the contributions of different neighbors in the knowledge graph, thereby enriching user profiles. The information complementarity module automatically shares potential interactive features between items and entities, achieving information complementarity between items and entities.  
KGIE [38] is a novel graph neural network recommendation model based on interactive embeddings, which utilizes the knowledge graph and user-item interaction matrix to extract latent information, improves the aggregation method, and optimizes overall performance. The interactive embeddings are merged with users through a convolutional neural network and independently participate in the aggregation of domain information, providing more contextual information for recommendations.