## 5 Experiments
### Performance Comparsion  
Tables 2 and 3 provide an in-depth comparison of our MPHCL model when benchmarked against ten baseline models. The consistent differences in computation results between NYC and TKY can primarily be attributed to the differences in urban density, geographical layout, cultural and behavioral variations, and data sparsity. These factors influence how well the model can generalize to each city's unique characteristics, leading to the observed performance differences. Figures 6 and 7 are visual representations of Tables 2 and 3. Early methods, such as NeuNext and LSTPM, focus on sequence modeling based on LSTM architectures augmented with temporal and spatial gating mechanisms. While these models are effective in capturing short-term and long-term user interests to some extent, they do not explicitly model spatial relations or collaborative signals between users. Consequently, their performance remains suboptimal. On the NYC dataset, NeuNext achieves Recall@10 of 0.2549 and MRR of 0.2355, while LSTPM shows marginal improvement with Recall@10 of 0.2671 and MRR of 0.2460. These results reflect their limited representational power in capturing complex behavioral patterns. To overcome the weaknesses of purely sequential models, a second group of models such as EEDN, STAN, and GETNext integrates graph-based or attention-based mechanisms. These approaches incorporate spatial and semantic contexts more effectively. For instance, GETNext utilizes a global trajectory flow graph to model transitions between location predictions, which leads to improved performance with Recall@10 reaching 0.3739 on the NYC dataset. However, these models still operate largely within conventional graph frameworks, restricting their ability to capture high-order relationships and resulting in a plateau in performance around the 0.37-0.38 mark for Recall@10. This demonstrates that while adding attention or spatial graph structures improves results, these gains remain limited due to the inherent modeling constraints. Recent advances such as MSTHN, SLS-REC, and STHGCN further push the boundaries by incorporating hypergraph structures, enabling them to model high-order collaborative signals among location predictions and users more effectively. These models interpret user sessions or trajectory clusters as hyperedges, allowing them to capture rich interactions that are otherwise lost in traditional graphs. For example, STHGCN achieves Recall@10 of 0.4377 and MRR of 0.3709 on NYC, which represents a significant improvement over earlier graph-based approaches. Nonetheless, these models often focus on a single perspective, \begin{table}
\begin{tabular}{c c c c c c} \hline
**Models** & **Recall@5** & **Recall@10** & **NDCG@5** & **NDCG@10** & **MRR** \\ \hline NeuNext & 0.2354 & 0.2549 & 0.2271 & 0.2356 & 0.2355 \\ LSTPM & 0.2489 & 0.2671 & 0.2434 & 0.2469 & 0.2460 \\ LightGCN & 0.3238 & 0.3458 & 0.2950 & 0.3029 & 0.3012 \\ EEDN & 0.3432 & 0.3754 & 0.3036 & 0.3153 & 0.3071 \\ STAN & 0.3531 & 0.3832 & 0.3030 & 0.3147 & 0.3085 \\ GETNext & 0.3546 & 0.3739 & 0.3034 & 0.3154 & 0.3091 \\ CTRNext & 0.3581 & 0.3872 & 0.3083 & 0.3091 & 0.3115 \\ MSTHN & 0.3589 & 0.3842 & 0.3187 & 0.3199 & 0.3275 \\ SLS-REC & 0.4067 & 0.4389 & 0.3621 & 0.3721 & 0.3605 \\ STHGCN & 0.4093 & 0.4377 & 0.3631 & 0.3732 & 0.3709 \\
**MPHCL** & **0.4350** & **0.4786** & **0.3823** & **0.3965** & **0.3865** \\ \hline \end{tabular}
\end{table} 
Table 2: Performance comparison with baselines on NYC dataset.