## 5 Experimental Setup
### Comparative Experiments  
We compare the GEVEHGAN model with six baseline methods, conducting ten repeated experiments for each model. The average values of AUC, AP, and Top@10 results from five repeated experiments are used as the final results. The experimental results are shown in Figure 4.  
In the comparative experiments, we evaluate the performance of the GEVEHGAN model against seven other baseline models on six datasets. The results show that the GEVEHGAN model outperforms all other baseline models. Specifically, compared with the best performance of the baseline models, the GEVEHGAN model shows an average improvement of 1.52%, 1.61%, and 2.18% in AUC, AP, and Top@K, respectively. Notably, the performance improvements in the IST and KL datasets are significant. This is likely due to the rich information available in these datasets, such as user, POI, and friend numbers, which provide sufficient resources for the GEVEHGAN model to effectively mine topological and semantic information. Figure 4: Performance comparison of eight recommendation models on six different datasets—analysis of AUC, AP, and TOP@10 metrics. (**a**) Shows the AUC performance of the eight recommendation models across six datasets. (**b**) Shows the AP performance of each model on the same datasets. (**c**) Shows the TOP@10 hit rate performance of these models across six datasets. With these metrics, we can comprehensively evaluate the strengths and weaknesses of each recommendation model in different scenarios. Among the seven models, Metapath2 vec shows a relatively average performance. As an unsupervised learning method that mines heterogeneous graphs through random walks and learns node relationships using the heterogeneous Skip-Gram model, Metapath2 vec fails to adequately consider the differences in node types and relationship types. It also does not fully exploit edge features, spatiotemporal information, or semantic information in the heterogeneous graph, limiting its performance in the friend link prediction task. GraphSAGE performs similarly to Metapath2 vec. Although GraphSAGE is a homogenous graph model, it aggregates neighbor information and stacks multiple layers to obtain higher-level node representations. Thus, it somewhat competes with Metapath2 vec's heterogeneous graph approach. However, the neighbor node sampling strategy of GraphSAGE reduces computational complexity but also limits its ability to fully leverage neighbor information. GCN and GAT show similar performance and outperform GraphSAGE, which is also a homogenous graph method. This may be because GCN and GAT are more refined in capturing relationships between nodes, allowing them to more effectively utilize information from the graph structure. In contrast, GraphSAGE's sampling strategy may lead to the loss of information. Heter-GCN shows a significant improvement over both homogenous graph methods and Metapath2 vec, demonstrating the importance of heterogeneous information in friend link prediction tasks. MAGNN AllSetTransformer performs even better than Heter-GCN. This may be because Heter-GCN fails to fully consider the rich spatiotemporal and semantic information in the LBSN data when constructing the heterogeneous graph. MAGNN, by incorporating metapaths and attention mechanisms, is able to capture higher-order interactions between nodes and better understand the importance of different nodes and metapaths, The higher-order set relationship modeling of hypergraphs connects multiple nodes through hyperedges, supporting cross-type and cross-hierarchy interaction propagation, further enhancing its performance in friend link prediction. In the comparison between the GEVEHGAN model and the other seven models, an in-depth qualitative analysis is conducted across multiple dimensions, including graph model construction, node embedding, and dimensionality reduction denoising, along with information aggregation and propagation.