## 5 Experiments
### Hyperparameter Analysis  
We analyze the impact of the temperature hyperparameter \(\tau\) and the distance threshold \(\Delta_{d}\) on the model performance, measured by Recall@5, on both the NYC and TKY datasets. The temperature hyperparameter \(\tau\) is commonly used in contrastive learning frameworks (e.g., InfoNCE loss), where it controls the concentration level of the similarity distribution. Specifically, a smaller \(\tau\) sharpens the distribution, amplifying differences between similar and dissimilar pairs, while a larger \(\tau\) smooths it. In our case, we observe that the optimal value is \(\tau=0.5\), which balances these effects and leads to the highest recall performance across different distance thresholds. Figure 7: Performance comparison of different methods on TKY dataset. In Figure 9a, we observe that, when \(\tau=0.5\), Recall@5 reaches its peak for all values of \(\Delta_{d}\). Among these, \(\Delta_{d}=2.0 km\) yields the best performance. This can be attributed to the spatial characteristics of NYC, where location predictions are densely clustered, particularly in Manhattan. Hence, a relatively small distance threshold is sufficient to capture the relevant local geographical context. In contrast, Figure 9b shows that, while \(\tau=0.5\) is still optimal, the best-performing distance threshold is \(\Delta_{d}=2.5 km\), slightly larger than that of NYC. This is because the location predictions in Tokyo are more geographically dispersed across a wider urban area. As a result, a larger \(\Delta_{d}\) is necessary to incorporate a broader spatial context and effectively capture semantic relationships in the data. In summary, while the optimal temperature hyperparameter \(\tau\) remains consistent across datasets at \(\tau=0.5\), the optimal distance threshold \(\Delta_{d}\) varies due to differences in location prediction density and spatial distribution. NYC benefits from a smaller \(\Delta_{d}\) due to its compact urban layout, whereas TKY requires a larger threshold to accommodate its broader geographical spread. To investigate the sensitivity of our Disentangled Hypergraph Representation Learning Network to architectural configurations, we conduct a comprehensive evaluation over varying embedding dimensions \(d\in\{32,64,128,256\}\) and layer numbers \(L\in\{1,2,3,4\}\), as shown in Figure 10.  
Figure 8: CPU usage comparison of different models. (**a**) NYC dataset. (**b**) TKY dataset. Figure 9: The impact of the temperature hyperparameter \(\tau\) and distance threshold \(\Delta_{d}\). (**a**) NYC dataset. (**b**) TKY dataset. The performance surface formed by varying \(d\) and \(L\) reveals the following key observations:  
(1) On the NYC dataset, the model attains the maximum performance Recall@5 = 0.4350 at \((d=128,L=2)\). This setting, corresponding to an intermediate embedding size and a two-layer network, strikes an effective balance between representation capacity and overfitting risk. (2) On the TKY dataset, the optimal setting shifts slightly to a deeper architecture, Recall@5 = 0.3630 at \((d=128,L=3)\). Despite the difference in optimal depth, both datasets consistently favor an embedding dimension of \(d=128\), suggesting this size as a robust choice across domains. (3) We observe a non-monotonic relationship between both \(d\) and \(L\) with performance. When the embedding size is too small (e.g., \(d=32\)), the model suffers from insufficient representational capacity, leading to degraded performance due to its inability to capture complex hyper-relational patterns. As \(d\) increases, performance improves, peaking at \(d=128\), after which further increases (e.g., \(d=256\)) lead to a decline. This degradation for larger \(d\) is attributed to feature redundancy, which not only increases the computational cost but may also introduce noise, harming generalization. A similar pattern is observed with respect to network depth \(L\).