Sector-wise Directional POI Aggregation

• The paper introduces an approach that partitions a 150 m radius around intersections into 8 angular sectors to capture POI attributes like distance, bearing, density, and presence.
• It combines these sector-specific descriptors with graph embeddings and transformer-based sequence modeling to enhance intersection-centric mobility prediction.
• Empirical results demonstrate up to 17 percentage points improvement in accuracy and high robustness to GPS perturbations and POI noise.

Searching arXiv for the cited papers to ground the article in current preprints. Sector-wise directional POI aggregation is a local spatial representation in which the neighborhood around a target location is partitioned into angular sectors and summarized with category-specific cues. In the explicit formulation introduced for intersection-centric next-step prediction, the target is a road intersection rather than a POI token, the neighborhood is a circular region around the node, and the output is a fixed-dimensional descriptor encoding distance, bearing, density, and presence information for surrounding POIs (Ren et al., 2 Aug 2025). This formulation is distinct from non-directional spatial analytic windows over circular neighborhoods (Shi et al., 2020), from sector-level aggregation of POI mobility by economic activity (Leslie et al., 16 Jun 2025), and from radial accessibility measures that aggregate over all directions equally (Fanelli et al., 2024).

1. Problem setting and conceptual scope

In the intersection-centric formulation, the motivation for sector-wise directional POI aggregation is the limitation of closed-world next-POI prediction. The cited framework represents trajectories on a city road-intersection graph, with nodes $V$ as intersections and edges $E$ as road segments, and frames prediction over the one-hop neighbor set $C(V_T)=N(V_T)$ of the current intersection $V_T$ (Ren et al., 2 Aug 2025). This replaces prediction over a fixed POI vocabulary with prediction over reachable intersections, which is topologically grounded and does not require a closed-world POI inventory.

Within that setting, POIs are not prediction targets. They are environmental context attached to graph nodes. The aggregation is therefore semantic rather than destination-enumerative: it summarizes the local urban environment around an intersection so that semantically similar but directionally distinct one-hop choices can be separated. The paper explicitly argues that human mobility is often open-ended, that a sizeable fraction of locations are visited only once or are previously unseen, and that directionality matters because two neighboring intersections may be semantically similar but differ by outgoing road direction (Ren et al., 2 Aug 2025).

A broader interpretation is that sector-wise directional POI aggregation belongs to a family of local-support methods in which computation is restricted to spatially delimited regions rather than performed globally. A plausible implication is that the method is best understood not as a POI recommendation heuristic, but as a node-centric contextual encoding for mobility forecasting on constrained transport topologies.

2. Geometric sectorization around the target intersection

For each intersection $v$, the method considers a circular neighborhood of radius

$R = 150 \text{ m}$

and partitions that disk into

$S = 8$

equal angular sectors, so that each sector spans $360^\circ/8 = 45^\circ$ (Ren et al., 2 Aug 2025). POIs inside the disk are assigned to sectors according to their bearing from the node, written through angular-bin membership as $\theta_i \in \mathrm{bin}_k$.

This construction gives the descriptor directional sensitivity. The paper states that the sectorization captures the anisotropy of urban space, aligns with outgoing road bearings, and helps distinguish one-hop candidates that are topologically similar but differ by direction (Ren et al., 2 Aug 2025). The neighborhood is therefore not treated as a single bag of POIs. Instead, the same local support is decomposed into wedge-shaped subregions whose occupancy patterns become features.

The contrast with isotropic radial methods is sharp. In the city-accessibility framework based on the radial distribution function, POIs are counted in concentric shells around each hexagon center, and the analysis is explicitly radial rather than sectoral; the method uses circular shells aggregated over all directions equally and does not implement north/south/east/west or angular bins (Fanelli et al., 2024). Sector-wise directional POI aggregation can thus be situated as an angular refinement of radius-based neighborhood analysis.

3. Descriptor construction, statistics, and normalization

For each category $c \in C$, where $E$0, the model computes a 14-dimensional summary $E$1 from POIs within radius $E$2. Concatenating across categories yields the node descriptor

$E$3

since $E$4 (Ren et al., 2 Aug 2025). The 14 dimensions are described as coming from category-wise circular statistics, angular sector densities, and a presence indicator.

The explicit circular-statistics terms are

$E$5

and

$E$6

Here $E$7 is the resultant-length statistic, capturing how concentrated the POIs are in one direction (Ren et al., 2 Aug 2025). The paper also states that the summary includes distance information through circular statistics over the POI set $E$8 inside radius $E$9, and characterizes the overall cue set as “distance, bearing, density, and presence cues” (Ren et al., 2 Aug 2025).

The sector-density component is defined per category and sector by

$C(V_T)=N(V_T)$0

The presence cue is binary: it is 1 if there is at least one POI of category $C(V_T)=N(V_T)$1 within radius $C(V_T)=N(V_T)$2, and 0 otherwise (Ren et al., 2 Aug 2025). This allows the model to distinguish empty categories from categories with sparse support.

The paper further specifies three implementation details. First, a per-feature binary mask is included for empty categories and sectors. Second, z-score normalization is fitted on the training set. Third, the features are precomputed offline and cached (Ren et al., 2 Aug 2025). Those choices make the descriptor a fixed, engineered node attribute rather than a representation learned directly from raw coordinates during sequence-model training.

4. Fusion with graph structure and sequence modeling

The node descriptor is combined with a structural graph representation. Each intersection $C(V_T)=N(V_T)$3 has a structural embedding obtained using Node2Vec, a POI descriptor built from sector-wise directional aggregation, and a planar coordinate $C(V_T)=N(V_T)$4 (Ren et al., 2 Aug 2025). The temporal encoder is a CfC-LNN branch that consumes differenced features, including

$C(V_T)=N(V_T)$5

with zeros at $C(V_T)=N(V_T)$6, and then mixes the recurrent state with the structural embedding through a gated fusion stage (Ren et al., 2 Aug 2025).

After sequence encoding, the model appends candidate-specific states for one-hop neighbors and processes the resulting token sequence with Transformer layers, followed by a relation-aware Transformer layer with bearing-biased self-attention (Ren et al., 2 Aug 2025). In that attention mechanism, the bias depends on the bearing $C(V_T)=N(V_T)$7 between nodes and is learned from $C(V_T)=N(V_T)$8; the paper also states that the bias is row-centered for numerical stability. Learned type embeddings distinguish observed-history tokens from candidate tokens, and the attention mask blocks candidate-to-candidate attention so that candidates attend to history only (Ren et al., 2 Aug 2025).

Within this architecture, the POI aggregation module supplies the main semantic context. The structural embedding supplies graph-topological regularities, while the bearing-aware attention supplies directional relational bias. A plausible implication is that the method distributes contextual information across three complementary levels: static local environment, static network structure, and dynamic trajectory-conditioned relation modeling.

5. Relation to adjacent aggregation paradigms

The closest database-style precursor is the spatial analytic window model. That framework extends relational analytic/window aggregation to spatial data through two window types: a kNN window formalized as

$C(V_T)=N(V_T)$9

and a range window formalized as

$V_T$0

with per-POI aggregates such as SUM(number_of_visits) computed over the centered local neighborhood (Shi et al., 2020). The paper explicitly notes that direction is not considered in n-dimensional space because there is no natural “preceding/following” notion, but also identifies the radius-based circular window as the natural base case from which sector windows can be derived. This suggests that sector-wise directional POI aggregation can be interpreted as a directional specialization of centered range-window aggregation, obtained by adding an angular constraint to a disk window.

A distinct but related notion of sector-wise aggregation appears in high-resolution mobility data organized by economic activity. That dataset aggregates weekly visitor counts, travel distances, and dwell times across POIs grouped by NAICS sector, yielding sector-by-week summaries rather than device-level traces or OD matrices (Leslie et al., 16 Jun 2025). The aggregation is sectoral in the economic sense, not sectoral in the angular sense. Its closest directional proxy is the distance from home CBG to the POI. Accordingly, it provides sector-wise mobility signals, but not angular partitions around individual POIs or intersections.

Another neighboring line of work uses the radial distribution function to infer a city’s core-periphery structure from POI distributions. There, accessibility is derived from shell densities around hexagon centers via $V_T$1 and compressed into an $V_T$2-value using the first crossing where $V_T$3 (Fanelli et al., 2024). Because the shells are isotropic, directional asymmetry is averaged out. Sector-wise directional POI aggregation departs from this isotropic design by keeping angular orientation explicit.

An instructive cross-domain analogy comes from mmWave massive MIMO. In that setting, a single base station is interpreted as non-overlapping virtual angular sectors, and user-channel estimation and transmission are performed independently and in parallel per sector; users sharing the same pilot dimension can still be resolved if they are not simultaneously visible in the same sector (Li et al., 2016). This suggests a general sectorization principle: locality is imposed in angle space so that conflicts become sector-local rather than global. In the POI setting, the analogous operation is not pilot resolution but environmental feature localization around an intersection.

6. Empirical behavior, robustness, and methodological boundaries

The reported empirical results tie the POI aggregation module directly to predictive performance. The full model outperforms six state-of-the-art baselines by up to 17 percentage points in accuracy at one hop and 10 percentage points in MRR (Ren et al., 2 Aug 2025). Under perturbation, it loses only 2.4 percentage points in accuracy at one under 50 meter GPS perturbation and 8.9 percentage points in accuracy at one hop under 25 percent POI noise, which the paper characterizes as high resilience.

The hyperparameter studies identify a preferred spatial support and angular resolution. Radius is tuned over

$V_T$4

and the best result occurs at $V_T$5 m with Test@1 $V_T$6 and MRR $V_T$7 (Ren et al., 2 Aug 2025). The number of sectors is swept over

$V_T$8

and the best setting is $V_T$9, again with Test@1 $v$0 and MRR $v$1. The paper attributes this to a trade-off: too few sectors cause directional aliasing and merge distinct bearings, while too many sectors increase sparsity and estimation variance.

The feature-branch ablation assigns particular weight to the POI descriptor. Removing all POI inputs causes the largest drop, with Acc@1 falling by 32.8 points; removing differenced POI features causes a further loss of 3.4 points; removing geometric deltas lowers Acc@1 by 8.9 points; and removing Node2Vec lowers Acc@1 by 19.3 points (Ren et al., 2 Aug 2025). The paper interprets these results as evidence that the sector-wise POI descriptor is the main semantic cue.

Several boundaries remain explicit in the surrounding literature. The spatial-window framework provides solutions only for constant-memory aggregates and excludes MIN/MAX from that class (Shi et al., 2020). The sectoral mobility dataset warns that dwell time should not be overinterpreted as a single behavior type and that aggregation at the 2-digit NAICS level can mask heterogeneity present at the 4-digit level (Leslie et al., 16 Jun 2025). The RDF-based accessibility method depends on city boundaries, hexagonal resolution, and isotropic shells, and it does not implement angular decomposition (Fanelli et al., 2024). Taken together, these points indicate that sector-wise directional POI aggregation is most precisely characterized as a node-local, angularly resolved contextual encoding: it is neither a generic substitute for all spatial aggregation nor a complete model of mobility behavior, but a specific representation for direction-sensitive prediction on road graphs (Ren et al., 2 Aug 2025).