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Synergistic Fusion of Topological Structure and Temporal Semantics of Mobility for Urban Region Embedding
Namwoo Kim, Jeeyun Chang, Kanghoon Lee, Yoonjin Yoon
TL;DR
Urban region embedding methods underuse mobility’s temporal dynamics and often miss signals that emerge only from jointly considering temporal and structural views. MoSS combines hourly mobility sequences, zigzag-persistence structure views, and multi-degree synergy interactions, achieving state-of-the-art performance across three tasks in New York City and Chicago using mobility alone. The paper concludes that temporal–topological pairing is a promising design pattern, while extensions to additional modalities, longer time scales, and cross-city transfer remain open.
Problem
Existing approaches under-model continuous mobility dynamics and evolving connectivity, while additive fusion misses higher-order signals arising from jointly considered views.
Method
MoSS combines a sequence stream for hourly inflow/outflow with a zigzag-persistence structure stream and fuses them using shared–private decomposition and multi-degree interactions.
Results
MoSS achieves state-of-the-art performance across crime, income, and service-call prediction in New York City and Chicago using mobility data alone, outperforming auxiliary-modality baselines.
Takeaways & Limitations
The temporal–topological pairing is presented as a general design pattern for urban region representation from mobility data.
Abstract
from arXiv · showhide
Urban region embeddings have shown promising results in diverse urban sensing tasks such as crime, income, and service-call prediction. Recent methods improve representation quality by integrating mobility data with auxiliary modalities, using cross-view attention or contrastive objectives to align heterogeneous features into a unified region representation. However, leveraging the temporal dynamics of human mobility remains under-explored. Regional inflow and outflow fluctuate throughout the day, and inter-region connections emerge, persist, and dissolve over time. Moreover, prevailing fusion strategies combine views additively and miss the joint signal that emerges only when views co-occur. To address these gaps, we propose Mobility Stream-Structure Synergy (MoSS), which derives complementary views from mobility data: a Sequence view that preserves each region's hourly inflow/outflow profile, and a Structure view based on zigzag persistence diagrams that capture how regional connectivity emerges, persists, and dissolves over time. A synergy module then extracts emergent representations from the co-occurrence of these views through multi-degree interactions, explicitly capturing higher-order signal across views. Extensive experiments on New York City and Chicago show that MoSS achieves state-of-the-art performance across three downstream tasks using mobility data alone, outperforming baselines that rely on auxiliary modalities.
I. INTRODUCTION
Urban region embeddings use mobility to represent interactions among regions, but existing methods under-model fine-grained temporal dynamics and evolving connectivity, while common fusion strategies miss higher-order cross-view signals. MoSS addresses these gaps with sequence and structure streams plus a synergy module, achieving state-of-the-art performance from mobility alone.
- Human mobility encodes regional functional organization because trips provide observable interactions between regions.
- Existing mobility methods model static graphs or independently processed snapshots, limiting their capture of temporal dependencies and evolving inter-region connectivity.
- Attention-based and contrastive fusion strategies combine views additively and can miss signals arising from the joint co-occurrence of temporal and structural patterns.
- MoSS derives sequence and structure views from one mobility stream and fuses them through shared–private decomposition and multi-degree interactions.The Sequence stream models hourly inflow and outflow with dilated convolutions, while the Structure stream uses zigzag persistence diagrams.
- MoSS achieves state-of-the-art urban region embedding on New York City and Chicago using mobility data alone, outperforming baselines using auxiliary modalities.
B. Multi-View Approaches in Urban Region Embedding
Multi-view urban representation methods often lack explicit higher-order interaction modeling, while topological tools provide a way to summarize structural change over time. The section introduces the topological foundations motivating MoSS’s use of zigzag persistence for evolving mobility connectivity.
- Attention, contrastive, and related multi-view fusion families remain limited in representing higher-order cross-view interactions.
- MoSS models pairwise and triple-wise multiplicative terms to represent signals emerging from the joint presence of multiple views.
- Persistent homology summarizes multi-scale data shape as persistence diagrams and can complement time-series or time-varying graph representations.
- Zigzag persistence permits alternating inclusion directions, enabling features that vanish and re-emerge to be tracked directly.
- A simplicial complex is a collection of subsets closed under taking subsets, with vertices, edges, and triangles representing increasing simplex dimensions.
- Betti numbers count independent holes in a simplicial complex, including connected components, loops, and enclosed cavities.
C. Persistent Homology
Persistent homology represents topological features by when they appear and disappear across a filtration. Zigzag persistence extends this to alternating inclusions, allowing transient mobility connections that vanish and re-emerge to be tracked.
- A filtration records each topological feature as a birth–death point (b, d), where b and d mark appearance and disappearance indices.
- Standard persistence cannot represent features that disappear and reappear because its filtration only grows monotonically.
- Zigzag persistence replaces one-way growth with inclusions in alternating directions, directly representing features that vanish and re-emerge.
- This extension matches urban mobility, where inter-regional edges are transient and regional roles depend on when connections appear and dissolve.
- MoSS applies zigzag persistence to evolving connectivity structures and combines the resulting structure view with temporal mobility semantics.
B. Sequence Stream
The Sequence stream encodes each region’s hourly inflow and outflow history with a dilated temporal convolutional network, while the structure construction supplies temporally varying connectivity information around each region.
- Sequence Stream: Each region’s normalized inflow and outflow series are stacked as a two-channel input spanning the full observation window.
- Sequence Stream: A single dilated temporal convolutional network jointly processes both flow directions through residual blocks with exponentially increasing dilation.
- Sequence Stream: The exponentially growing dilation spans daily and weekly periodicities with logarithmically many layers, followed by projection and max-pooling into a sequence-view embedding.
- Structure Construction: For each region, directional connectivity graphs contain edges where the region is the source or destination, capturing complementary functional roles.
- Structure Construction: The resulting graph sequences are converted into clique complexes and connected across consecutive times for zigzag persistence computation.
- Structure Construction: The structure stream restricts analysis to H0 because connected components directly capture whether mobility-neighborhood regions remain linked, merge, or disconnect.
E. Structure Stream: Persistence-diagram Encoder
The persistence-diagram encoder converts directional birth–death features and their lifespans into fixed-size embeddings while preserving the diagrams’ unordered-set structure.
- Persistence-Diagram Encoder: For each region and direction, zigzag persistence returns birth–death pairs with lifespans that describe connected-component emergence and disappearance over time.
- Persistence-Diagram Encoder: The encoder maps each directional persistence multiset to a fixed-size vector representation.
- Permutation Invariance: Because persistence points have no canonical order, the encoder is designed to be permutation-invariant.
- Permutation Invariance: A shared per-point transformation followed by coordinate-wise max-pooling produces an order-independent embedding of each diagram.
- Directional Outputs: The structure encoder outputs Vout and Vin, whose rows encode when connected components in each region’s neighborhood emerge, persist, and disappear.
F. Synergy Module
The synergy module separates shared and view-private information before combining private embeddings through low-rank multi-degree interactions, preserving both common content and higher-order cross-view signal.
- View Decomposition: MoSS forms three views per region: one sequence embedding and two directional persistence-diagram embeddings.
- View Decomposition: A shared–private decomposition separates each view into cross-view shared content and view-private information.
- View Decomposition: Central Moment Discrepancy aligns shared embeddings across views, while orthogonality penalties keep shared and private components distinguishable.
- Multi-Degree Interaction: Augmenting each private embedding with a constant unit lets one outer-product tensor encode first-, second-, and third-order interactions.
- Multi-Degree Interaction: A learned tensor projection combines the interaction tensor, while low-rank factorization reduces the parameter cost and yields a Hadamard-product formulation in rank space.
- Output Fusion: The final synergy output is recombined with the mean shared embedding across views.
G. Trip-distribution Loss
The trip-distribution loss supervises MoSS embeddings by matching predicted mobility transitions with the empirical OD distribution in both directions.
- The empirical OD distribution M is obtained from the observed OD matrix and supervises the learned embeddings.
- The synergy embedding Y is mapped to region representations Z through a two-layer MLP head before source and destination projection.
- Predicted mobility distributions are computed and matched against empirical OD distributions in both directions using a dedicated loss.
- The bidirectional loss includes terms involving source and destination transition probabilities and the empirical OD entries.
H. Total Training Objective
MoSS is trained end-to-end with an objective that combines its predictive loss with alignment and orthogonality controls for cross-view representations.
- MoSS is trained end-to-end by minimizing a total objective.
- λalign and λorth control the strengths of cross-view shared alignment and dual orthogonality terms, respectively.
- Income is reported as the average of per-region median household income in the dataset statistics.
V. EXPERIMENTS
The experiments evaluate MoSS on real mobility data from New York City and Chicago across three regional prediction tasks, against representative multimodal embedding baselines.
- Experiments use real-world data from New York City and Chicago to evaluate MoSS.
- Hourly pickup–drop-off OD tensors are constructed for each region from taxi-trip records and used as MoSS input.
- The downstream tasks are crime prediction, income prediction, and service-call prediction.
- Implementation details: The structure component extracts one zigzag H0 persistence diagram for inflow and one for outflow per region.
- Baselines: MoSS is positioned alongside six representative baselines according to their input modalities and fusion strategies.
- Baselines: The baselines include adaptive view weighting, multi-graph fusion, heterogeneous graph encoding, dual prediction, structure-aware contrastive learning, and disentangled attention-based fusion.
D. Evaluation Protocol
The evaluation freezes region embeddings for cross-validated downstream regression and compares MoSS with six baselines, component ablations, and cross-city task performance.
- Evaluation protocol: Frozen region embeddings are evaluated with a Ridge regressor under 5-fold cross-validation using MAE, RMSE, and R2.
- Main results: MoSS is compared with six baselines across crime, income, and service-call prediction in New York City and Chicago.
- Main results: MoSS achieves state-of-the-art performance on every task for MAE, RMSE, and R2, with notable R2 gains on service-call and Chicago income prediction.
- Main results: 12.0%: MoSS reduces crime RMSE on New York relative to HREP, from 88.43 to 77.82.
- Main results: MoSS ranks first in mean performance across tasks and cities, indicating stable generalization across urban structures, targets, and scales.
- Ablation study: Replacing the sequence stream, structure stream, shared–private decomposition, or synergy module produces downstream performance degradation.
- Ablation study: Removing persistence-diagram views consistently degrades performance, while removing shared–private decomposition causes drops such as 0.723 →0.622 on NYC crime and 0.587 →0.208 on Chicago crime.
G. Hyperparameter Analysis
The analysis evaluates sensitivity to alignment and orthogonality weights, embedding dimension, and practical efficiency. Results show task- and city-dependent hyperparameter effects, alongside a parameter–training-cost trade-off.
- Sensitivity setup: The study varies alignment weight λalign, orthogonality weight λorth, and final embedding dimension H across NYC and CHI tasks.Each curve reports per-task R2, while downstream results use MAE, RMSE, and R2 evaluated with frozen embeddings and Ridge regression.
- Weight parameters: Crime is robust to both weight ranges, varying within 0.02 in R2 across both cities, whereas service call is most responsive.The two cities respond oppositely to λalign: CHI rises from 0.466 to 0.601, while NY declines from 0.465 to 0.426.
- Final embedding dimension: CHI’s three tasks peak at H = 144 and decline at H = 192, with H = 64 producing the worst performance.NY instead shows task-specific patterns: crime and income improve through H = 192, while service call peaks at H = 96 with R2 = 0.476.
- Efficiency: MoSS’s components increase per-epoch cost while keeping the model compact in parameters and contributing to its accuracy gains.The comparison measures trainable parameters and wall-clock time per epoch against six baselines on NYC and CHI.
- Overall assessment: The conclusion reports that MoSS uses mobility data alone, outperforms baselines using auxiliary modalities, and uses a fraction of the strongest baselines’ parameters.The stated future scope includes additional modalities, longer time scales, and cross-city transfer.