## 4 Methodology
### Multi-Perspective Hypergraph Construction
#### 4.1.2 Geospatial Context Hypergraph  
The construction of the geographical view hypergraph is a sophisticated process that entails the formulation of a hypergraph designed to represent the geographical relationships among different locations while adhering to specific spatial constraints. Formally, we denote a geospatial context hypergraph as \(\mathcal{G}_{G}=(\mathcal{V}_{G},\mathcal{E}_{G},\mathbf{H}_{G},\mathbf{W}_{G})\), where \(\mathcal{V}_{G}\) represents the set of locations. Locations that are within a predefined distance threshold, calculated using the Haversine distance, are connected via hyperedges. These hyperedges capture the spatial relationships between geographically close locations, reflecting the proximity effect in user preferences. Within this hypergraph \(\mathcal{G}_{G}\), a hyperedge is established to connect locations that lie within a predetermined distance threshold \(\Delta_{d}\). This threshold is critical for accurately capturing the proximity of interactions and is derived from the Haversine distance metric \(d_{H}\), which is mathematically expressed as follows:  
\[d_{H}(l_{i},l_{j})=2R\cdot\arcsin\left(\sqrt{\sin^{2}\Bigl{(}\frac{\phi_{i}- \phi_{j}}{2}\Bigr{)}+\cos(\phi_{i})\cos(\phi_{j})\sin^{2}\Bigl{(}\frac{\lambda_ {i}-\lambda_{j}}{2}\Bigr{)}}\right), \tag{3}\]  
where \((l_{i},l_{j})\) represents two locations,, \((\phi_{i},\phi_{j})\) denotes latitudes of locations \((l_{i},l_{j})\), \((\lambda_{i},\lambda_{j})\) signifies longitudes of locations \((l_{i},l_{j})\), and \(R=6371 km\) is the Earth's radius.  
In our model, we utilize the Haversine distance metric to capture geographical proximity between locations, as it accurately accounts for the curvature of the Earth. Unlike the Euclidean norm, which assumes a flat plane and is suitable only for small-scale distances, the Haversine distance calculates the shortest path along the surface of a sphere, making it ideal for modeling real-world spatial relationships between locations. This ensures that the proximity relationships between locations are represented more realistically, especially for large geographical areas.  
Consequently, the incidence matrix \(\mathbf{H}_{G}\in\mathbb{R}^{|\mathcal{L}|\times|\mathcal{E}_{G}|}\) serves as a crucial role in depicting the geographical interactions among locations. Specifically, if the Haversine distance between \(l_{i}\) and \(l_{j}\) satisfies the condition \(d_{H}(l_{i},l_{j})\leq\Delta_{d}\), we designate \(\mathbf{H}_{G}(i,j)=1\). Conversely, if the distance exceeds the threshold, we set \(\mathbf{H}_{G}(i,j)=0\). This binary representation encapsulates the existence of geographical relationships and enables the exploration of patterns in spatial clustering that significantly influence user behaviors and preferences.  
The proposed geospatial context hypergraph \(\mathcal{G}_{G}\) is not merely a mathematical construct, and it embodies critical geographical influences that play a vital role in shaping user preferences in real-world contexts. By integrating this spatial dimension, we can elucidate how users traverse their environments, uncovering visitation patterns often dictated by geographical proximity. This structure thus effectively reflects user geographical preferences, allowing us to analyze how proximity impacts user decision-making processes when selecting the next locations.  
So far, we have constructed two hypergraphs from diverse perspectives, namely the collective preference hypergraph \(\mathcal{G}_{C}\) and the geospatial context hypergraph \(\mathcal{G}_{G}\). Next, we will propose a disentangled hypergraph representation learning network to explicitly model and derive enriched representations of locations. Employing a disentangled learning framework, we can isolate the contributions of each viewpoint, facilitating a comprehensive understanding of user dynamic visit preferences.