## 5 Experiments
### Performance Comparison (RQ1)  
We first compare the recommended performance of the proposed method with the existing methods on the two datasets. Table 2 shows the performance of different methods on Recall@20 and NDCG@20.  
As shown in the table, our proposed method outperforms all baselines in most cases on both datasets. This demonstrates that the integration of the VRKG-based global smoothing mechanism and the GAT-based local attention mechanism enables the model to capture complex user-item interactions more effectively, thereby enhancing recommendation performance. We perform the following analysis and discussion:  
First, the improvement can be attributed to the design of the Virtual Relational Knowledge Graph (VRKG), which consolidates numerous original relations in the knowledge graph into a small set of virtual relations. These virtual relations not only uncover semantically related edges but also help encode more informative and task-relevant knowledge for downstream recommendation. Additionally, the Local Weighted Smoothing (LWS) mechanism generates item embeddings by aggregating features from their neighbors, focusing on transforming relational knowledge into neighborhood-aware item representations. This design encourages closer proximity between semantically connected entities in the embedding space.  
Second, the Graph Attention Network (GAT) component enhances both user and item embeddings via a dynamic attention mechanism. The GAT can adaptively assign importance weights to neighboring nodes, for example by prioritizing recent interactions to reflect users' evolving preferences. Furthermore, it aggregates multi-hop semantic signals (e.g., connections via directors, actors, etc.) through stacked layers. Compared to traditional GCNs with fixed-weight aggregation, the GAT effectively suppresses noise propagation and improves embedding expressiveness. Importantly, the GAT and LWS are complementary: while LWS mitigates the sparsity of long-tail relations through virtual relation clustering, GAT refines fine-grained interaction modeling via attention-based aggregation. This synergistic architecture balances global semantic consistency and local behavioral dynamics, leading to both accuracy and adaptability in recommendation.  
Among the baselines, FM and NFM perform poorly on both datasets due to their inability to utilize external knowledge graph information, limiting their capacity to learn expressive item embeddings. Although CKE incorporates first-order knowledge via TransR, it lacks the capacity to model multi-hop semantics. In contrast, KGAT and KGIN apply GNN-based propagation to capture higher-order neighbor signals. However, the effectiveness  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & \multicolumn{2}{c}{**Last.FM**} & \multicolumn{2}{c}{**MovieLens-1M**} \\ \cline{2-5}  & **Recall20** & **NDCG20** & **Recall20** & **NDCG20** \\ \hline FM & 0.1402 & 0.0772 & 0.2911 & 0.2798 \\ NFM & 0.1497 & 0.0805 & 0.2759 & 0.2484 \\ CKE & 0.2695 & 0.1625 & 0.3130 & 0.2918 \\ KGAT & 0.2059 & 0.1671 & 0.2637 & 0.2305 \\ KGIN & 0.3549 & 0.2169 & 0.3150 & 0.1935 \\ VRKG4 Rec & 0.3878 & 0.2302 & 0.3412 & 0.3192 \\ LightGCN & 0.2246 & 0.1326 & 0.2730 & 0.2366 \\ Wide \& Deep & 0.1748 & 0.1103 & 0.2683 & 0.2305 \\ GLARA & 0.3953 & 0.2482 & 0.3627 & 0.3325 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Overall comparison of performance.  
of this propagation heavily depends on graph structure and domain characteristics--for instance, KGAT performs poorly on Last.FM, possibly due to over-smoothing or noise accumulation in sparse relational paths.  
Interestingly, CKE and KGIN exhibit dataset-specific performance trade-offs: KGIN outperforms CKE on Last.FM, while the opposite is observed on MovieLens-1M. This may be because the knowledge graph of MovieLens-1M primarily consists of shallow, one-hop triples, which TransR in CKE can exploit more effectively. In contrast, KGIN may introduce noise during multi-hop propagation, resulting in degraded performance.