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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

arXiv:2609.08268v1cs.LGcs.AI

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.

    Source: A. Human Mobility in Urban Region… · p. 3, C. Persistent Homology · p. 4

  • 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.

    Source: §I · p. 2

  • 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.

    Source: §I · p. 2, E. Main Results · pp. 8–9

  • Takeaways & Limitations

    The temporal–topological pairing is presented as a general design pattern for urban region representation from mobility data.

    Source: §VI · p. 11

Abstract

from arXiv · show

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.Source: §I · p. 1
  • Existing mobility methods model static graphs or independently processed snapshots, limiting their capture of temporal dependencies and evolving inter-region connectivity.Source: §I · p. 1, A. Human Mobility in Urban Region… · p. 3
  • Attention-based and contrastive fusion strategies combine views additively and can miss signals arising from the joint co-occurrence of temporal and structural patterns.Source: §I · p. 2
  • 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.Source: §I · p. 2
  • MoSS achieves state-of-the-art urban region embedding on New York City and Chicago using mobility data alone, outperforming baselines using auxiliary modalities.Source: §I · p. 2

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.

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.

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.Source: B. Sequence Stream · p. 4
  • A single dilated temporal convolutional network jointly processes both flow directions through residual blocks with exponentially increasing dilation.Source: B. Sequence Stream · p. 4
  • The exponentially growing dilation spans daily and weekly periodicities with logarithmically many layers, followed by projection and max-pooling into a sequence-view embedding.Source: B. Sequence Stream · p. 4

Structure Construction

  • For each region, directional connectivity graphs contain edges where the region is the source or destination, capturing complementary functional roles.Source: C. Structure Stream:… · p. 4
  • The resulting graph sequences are converted into clique complexes and connected across consecutive times for zigzag persistence computation.Source: D. Structure Stream: Zigzag… · pp. 4, 6
  • The structure stream restricts analysis to H0 because connected components directly capture whether mobility-neighborhood regions remain linked, merge, or disconnect.Source: D. Structure Stream: Zigzag… · p. 6

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.Source: E. Structure Stream:… · p. 6
  • The encoder maps each directional persistence multiset to a fixed-size vector representation.Source: E. Structure Stream:… · p. 6

Permutation Invariance

  • Because persistence points have no canonical order, the encoder is designed to be permutation-invariant.Source: E. Structure Stream:… · p. 6
  • A shared per-point transformation followed by coordinate-wise max-pooling produces an order-independent embedding of each diagram.Source: E. Structure Stream:… · p. 6

Directional Outputs

  • The structure encoder outputs Vout and Vin, whose rows encode when connected components in each region’s neighborhood emerge, persist, and disappear.Source: E. Structure Stream:… · p. 6

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.Source: F. Synergy Module · p. 6
  • A shared–private decomposition separates each view into cross-view shared content and view-private information.Source: F. Synergy Module · pp. 6–7
  • Central Moment Discrepancy aligns shared embeddings across views, while orthogonality penalties keep shared and private components distinguishable.Source: F. Synergy Module · p. 7

Multi-Degree Interaction

  • Augmenting each private embedding with a constant unit lets one outer-product tensor encode first-, second-, and third-order interactions.Source: F. Synergy Module · p. 7
  • 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.Source: F. Synergy Module · p. 7

Output Fusion

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.Source: G. Trip-distribution Loss · p. 7
  • The synergy embedding Y is mapped to region representations Z through a two-layer MLP head before source and destination projection.Source: G. Trip-distribution Loss · p. 7
  • Predicted mobility distributions are computed and matched against empirical OD distributions in both directions using a dedicated loss.Source: G. Trip-distribution Loss · p. 7
  • The bidirectional loss includes terms involving source and destination transition probabilities and the empirical OD entries.Source: G. Trip-distribution Loss · p. 7

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.

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.

Implementation details

Baselines

  • MoSS is positioned alongside six representative baselines according to their input modalities and fusion strategies.Source: C. Baselines · p. 8, Table II · p. 8
  • The baselines include adaptive view weighting, multi-graph fusion, heterogeneous graph encoding, dual prediction, structure-aware contrastive learning, and disentangled attention-based fusion.Source: C. Baselines · p. 8

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.Source: D. Evaluation Protocol · p. 8

Main results

  • MoSS is compared with six baselines across crime, income, and service-call prediction in New York City and Chicago.Source: E. Main Results · p. 8
  • 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.Source: E. Main Results · p. 8
  • 12.0%: MoSS reduces crime RMSE on New York relative to HREP, from 88.43 to 77.82.Source: E. Main Results · p. 9
  • MoSS ranks first in mean performance across tasks and cities, indicating stable generalization across urban structures, targets, and scales.Source: E. Main Results · p. 9

Ablation study

  • Replacing the sequence stream, structure stream, shared–private decomposition, or synergy module produces downstream performance degradation.Source: F. Ablation Study · p. 9
  • 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.Source: F. Ablation Study · p. 9

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.Source: Figure 4 · p. 9, G. Hyperparameter Analysis · p. 9, Table III · p. 10

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.Source: G. Hyperparameter Analysis · p. 10

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.Source: G. Hyperparameter Analysis · p. 10

Efficiency

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.Source: §VI · p. 11

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