PaperlayerView exact revision on arXiv

Source-linked AI summary

Relative Transitions, Not Absolute Destinations: A Transfer-and-Ground Framework for Target-Trajectory-Free Human Mobility Generation

Yidi Wang, Yunhe Zhang, Bangchao Deng, Dingqi Yang, Pengyang Wang

arXiv:2610.02033v1cs.LG

TL;DR

Trajectory generators usually need observations from their deployment city, limiting use where only a POI map is available. Nomad learns relative transitions from source cities and grounds them on target POIs; across 14 transfers, it outperforms adaptation baselines in fidelity and utility, with average error reductions of about 15% and 3%, respectively.

  • Problem

    Most trajectory generators assume deployment-city trajectories, while target-trajectory-free generation permits only target POIs and excludes target trajectories and trajectory-derived statistics.

    Source: §1 · pp. 1–2, §2.1 · p. 3

  • Method

    Nomad learns a source-city prior over context-conditioned semantic and geographic displacements and elapsed time, then grounds sampled transitions on target POIs with a behavior graph and exploration–return walk.

    Source: §1 · p. 2, §3.2 · p. 5, §3.3 · p. 5

  • Results

    Across 14 transfers, Nomad outperforms adaptation baselines in distributional fidelity and downstream utility, lowering average error over the best baseline of each metric by about 15% and about 3%, respectively.

    Source: §4.2 · p. 6, §5 · p. 9

  • Takeaways & Limitations

    Controlled analyses find that relative transitions contain less city-specific information than absolute destinations, supporting representation-level transfer without assuming full mobility-distribution invariance.

    Source: §1 · p. 2, §2.2 · p. 3

    The representation-level transferability analysis is conditional on a cross-city translation-alignment assumption.

    Source: §2.2 · p. 3

Abstract

from arXiv · show

Individual mobility trajectories support urban analysis and location-based services, yet most trajectory generators require observations from their deployment city. This assumption excludes precisely the cities where trajectories are unavailable even though points of interest (POIs) and their attributes can be obtained from public maps. We study target-trajectory-free generation: learning from POIs and trajectories in source cities while utilizing only POI coordinates and categories in a target city, with no target trajectory or trajectory-derived statistic available for training, model selection, or generation. Existing trajectory generators typically predict absolute destinations, entangling reusable movement behavior with city-specific POI identities and spatial layouts. Our core insight is to replace this city-bound output with context-conditioned relative transitions. We propose Nomad, a transfer-and-ground framework that separates learning how people move from determining where those movements are realized. Specifically, a history-conditioned flow-matching model learns from source trajectories a transition prior over semantic displacement between POI contexts, geographic displacement, and elapsed time; at inference, a behavior graph and an exploration--return walk ground sampled transitions onto the target POI map. This factorization enables a direct test of representation level transferability without assuming invariance of the full mobility distribution. Extensive experiments across ten cities and 14 transfers show that Nomad outperforms adaptation baselines in trajectory fidelity and downstream utility, lowering the average error over the best baseline of each metric by about 15% in distributional fidelity and about 3% in downstream utility.

1 Introduction

The introduction frames target-trajectory-free generation as learning from source-city trajectories while using only a target city’s POI map. Nomad models relative transitions and grounds them on target POIs, with experiments and controlled analyses supporting transfer across cities.

1 Introduction

  • Target-trajectory-free generation asks whether a source-trained model can generate target-city trajectories using its POI map alone, without target trajectories or trajectory-derived statistics.The target city’s POIs and attributes can be obtained from public maps, while trajectories may be inaccessible or unavailable.Source: §1 · pp. 1–2
  • Existing generators commonly predict absolute destinations tied to a city’s POI vocabulary, which target-specific output probabilities cannot be learned when target trajectories are absent.Cross-city methods may still require target observations, a shared grid, city-specific embeddings, or a target output layer.Source: §1 · p. 2
  • Relative transitions carry less city-specific information than absolute destinations, as transition distributions are consistent across NYC and Tokyo at the level of place-function semantics.The cities differ in spatial layout and POI popularity.Source: §1 · p. 2, Figure 1 · p. 2
  • Nomad transfers a source-learned prior over context-conditioned relative transitions, then grounds sampled transitions on target POIs using a behavior graph and an exploration–return walk.The prior models semantic displacement, geographic displacement, and elapsed time.Source: §1 · p. 2
  • Across 10 cities and 14 source-to-target transfers, Nomad improves trajectory fidelity by about 15% and downstream train-on-synthetic–test-on-real utility by about 3% over six baselines.The reported gains are over six baselines.Source: §1 · p. 2

2 Preliminary

The preliminary section defines generation with source-city trajectories but only a target-city POI set, then characterizes transferable moves as embedding displacements under a translation-alignment assumption.

2.1 Problem Formulation

  • A POI has geographic coordinates and a category, while a trajectory is a time-ordered sequence of timestamped POI visits.POIs in a city are connected in a graph by spatially or semantically related edges.Source: §2.1 · pp. 2–3
  • The task learns from source-city POIs and trajectories to generate target-POI trajectories, excluding the target trajectory set and statistics derived from it.The output should be distributionally close to real target-city trajectories.Source: §2.1 · p. 3

2.2 Transferability of Transitions

  • A transition is a move between consecutive check-ins, represented by change in place context, geographic displacement, and elapsed time.A trajectory can therefore be read as a chain of transitions.Source: §2.2 · p. 3
  • Under translation alignment, embedding displacement is transferable and complete: every transferable transition representation is a function of that displacement.Functionally corresponding POIs are assumed to differ by a shared offset in the learned space.Source: §2.2 · pp. 3–4
  • The transfer guarantee is conditional: it does not assert that real cities necessarily admit a representation aligned up to a shift.The claim concerns what displacement preserves once the encoder aligns cities under the assumption.Source: §2.2 · pp. 3–4

3 Methodology

Nomad aligns POIs across source cities, learns history-conditioned relative transitions, then grounds sampled moves on the target POI map through a behavior graph and exploration–return walk.

3.1 Cross-City POI Alignment

  • A multi-relational POI graph and category, link, and contrastive objectives align functionally similar places into a city-agnostic embedding space.The graph combines spatial and categorical neighborhoods; the shared space provides the precondition for extracting movement knowledge across cities.Source: §3.1 · p. 4

3.2 Flow Matching in the Transition Space

  • Each transition combines the difference between consecutive POI embeddings with encoded geographic displacement and elapsed time, rather than an absolute destination.Because the channels are differences, the representation records what kind of move occurred rather than where; history conditioning supplies the move’s trajectory context.Source: §3.2 · pp. 4–5
  • A flow-matching generator learns to sample transitions by transporting noise toward source-trajectory transitions, conditioned on trajectory history.At inference, integrating the learned velocity from noise yields a transition conditioned on a target-city POI, without retraining on target trajectories.Source: §3.2 · p. 5

3.3 Grounding in Unseen Cities

  • Behavior-graph induction samples transitions from each target POI and snaps them to target candidates by semantic and geographic displacement, estimating successor probabilities.Retaining high-probability successors creates a directed weighted graph over target POIs.Source: §3.3 · p. 5
  • A source-pretrained Pointer Network chooses whether to return to a previously visited POI or explore an outgoing behavior-graph edge, using walk history.Generation starts from a target POI and timestamp, then repeats these decisions to produce a trajectory of target-city POIs with coordinates and times.Source: §3.3 · pp. 5–6

4 Experiments

Across the reported transfers, Nomad performs best on downstream utility and distributional fidelity, while analyses examine component effects, target-data adaptation, cross-city representations, and sampling budgets.

4.1 Experimental Settings

  • Evaluation compares six adaptation baselines using downstream prediction and recommendation gaps plus distributional measures of OD flow, distance, speed, and time-category visits.The prediction and recommendation gaps are averaged into Pred-MAPE, Pred-MSPE, Rec-MAPE, and Rec-MSPE; distributional metrics include OD-Sim and three Jensen-Shannon divergences.Source: §4.1.2 · p. 6, §4.1.1 · p. 6

4.2 Main Results

  • Across all 14 transfer settings, Nomad lowers average error over the best baseline of each metric by about 15% on distributional fidelity and about 3% on downstream utility.Source: §4.2 · p. 6

4.3 Ablation Study

  • Removing any of five modules degrades performance; flow matching most affects distributional metrics, while the copy-gate, autoregressive mask, graph encoder, and history condition have distinct effects.Without the copy-gate, distribution metrics barely move but recommendation error rises; removing the autoregressive mask increases prediction error, and dropping the graph encoder or history condition raises errors across the board.Source: §4.3.1 · p. 6, Table 2 · p. 8

4.3.1 Ablation of Different Modules.

  • As target trajectories are added for adaptation, distributional errors steadily fall and utility errors trend downward, with a small target fraction bringing most settings near the in-domain lower bound.Metropolis differs: its larger POI vocabulary means utility error continues to decrease as more target data is added.Source: §4.3.2 · p. 6, Figure 3 · p. 7

4.4.1 Visualization of Cross-city Transitions and Destinations.

  • Under matched time-of-day and destination-category contexts, NYC and Tokyo destination embeddings separate by city, while relative-transition embeddings nearly overlap.The passage relates this contrast to an approximately constant translation between functionally equivalent POIs, which cancels in the displacement.Source: §4.4.1 · pp. 7–8, Figure 4 · p. 8

4.4.2 Analysis of Sampling Budgets.

  • Increasing flow steps improves distributional fidelity up to metric-specific plateaus, while utility changes little with the number of steps.Distance divergence drops sharply from N=5 to N=20 and then stays flat; OD-Sim reaches its lowest value near N=40.Source: §4.4.2 · p. 8, Figure 5 · p. 8
  • Increasing transition samples K densifies the behavior graph and improves downstream prediction, but slightly degrades OD-Sim as origin-destination structure becomes more diverse.The reported trade-off is better prediction and fine distance at a small cost to the OD match.Source: §4.4.2 · p. 8

5 Conclusion

The conclusion presents Nomad as a transfer-and-ground approach to target-trajectory-free generation, using relative transitions and target POI grounding. Experiments across fourteen transfers and controlled analyses support its performance and representation-level findings.

5 Conclusion

  • Nomad models relative transitions with a flow-matching prior and grounds them on target POIs using a behavior graph and pointer network.The conclusion contrasts this approach with modeling absolute destinations.Source: §5 · p. 9
  • Experiments across fourteen transfers report that Nomad outperforms adaptation baselines in distributional fidelity and downstream utility.Source: §5 · p. 9
  • Controlled analyses find that relative transitions contain less city-specific information under matched contexts.Source: §5 · p. 9

A.1 Proof of Theorem 2.7

The proof establishes transferability of displacement under the stated shift assumption and characterizes transferable functions of two POI embeddings as functions of their difference.

A.1 Proof of Theorem 2.7

  • Under Assumption 2.5, the shared city offset cancels in the displacement between functionally corresponding POIs, establishing Eq. (2).Source: §A.1 · p. 11
  • Conversely, invariance to every shared offset implies that a transferable function of two embeddings factors through their difference.The proof constructs the difference-only function as F̃(u)=F(0,u).Source: §A.1 · p. 11
  • A source-fitted distribution over displacement describes corresponding target moves when cities satisfy the assumption; the proof applies the same reasoning to time gaps and ground displacements.Source: §A.1 · p. 11

A.2 Corollary and the Proof

The appendix explains why context is needed alongside displacement and situates trajectory generation and cross-city transfer methods that still depend on city-specific trajectories or target observations.

A.2 Corollary and the Proof

  • A displacement-only distribution cannot encode a move’s starting place, direction preference, or return preference, while conditioning on a transferable context preserves transferability and allows anchor- and history-dependent preferences.The method therefore conditions the generator on trajectory context and handles revisiting with a separate history-conditioned module.Source: §A.2 · p. 11

B.1 Human Trajectory Generation

  • Trajectory generators spanning classical activity models, adversarial or imitation learning, diffusion, and LLM-based approaches are described as trained and generated within one city using its historical trajectories.Source: §B.1 · p. 11

B.2 Cross-City Transfer for Mobility

  • Cross-city transfer work commonly adapts on target observations or uses a target-specific location space; cited trajectory-generation methods still require target-city trajectories.Source: §B.2 · p. 11

C.1 Datasets Details

The evaluation uses Foursquare check-ins from ten cities across three regions, forming 14 source-to-target transfers. Trajectories are daily user check-in sequences, with city-group-specific density filters.

C.1 Datasets Details

  • 10 cities across three regions provide the public Foursquare check-in data for 14 source-to-target transfers.The cities include NYC and Tokyo, plus Japanese and Turkish clusters.Source: §C.1 · p. 11
  • A trajectory is one user’s time-ordered check-ins within a local day, truncated at fifteen steps.Source: §C.1 · p. 11
  • NYC and Tokyo days require at least three check-ins, while days in the Japanese and Turkish clusters require at least six.The paper presents four transfer pairs in Section 4.2 and reports the other ten in Appendix E.1.Source: §C.1 · p. 11

C.2 Ablation Variants

Five ablation variants test the roles of graph propagation, flow matching, revisits, autoregressive masking, and history conditioning in Nomad.

C.2 Ablation Variants

  • The graph-encoder ablation replaces relation-aware message passing with a linear projection of raw POI features.It tests whether cross-city transfer benefits from graph propagation of geographic information.Source: §C.2 · p. 12
  • The flow-matching ablation uses a one-pass MSE regressor that predicts only the conditional mean transition and removes Euler sampling.Source: §C.2 · p. 12
  • The copy-gate ablation removes the revisit branch, leaving grounding as a pure behavior-graph walk.Source: §C.2 · p. 12
  • The autoregressive-mask ablation allows bidirectional attention, exposing the next-step ground truth that the mask otherwise blocks.Source: §C.2 · p. 12
  • The conditioning ablation samples the marginal transition distribution while retaining the current POI anchor during snapping.It tests history conditioning’s effect on sequence modeling.Source: §C.2 · p. 12

D Algorithm Analysis

Nomad’s three stages scale linearly with city POI count and generated trajectories, with behavior-graph construction dominating computation. Its flow-matching generation is faster than the listed baselines for 10k trajectories.

D Algorithm Analysis

  • Nomad’s encoder, behavior-graph construction, and grounding walk each scale linearly with city POI count; generation also scales linearly with the number of trajectories.Behavior-graph construction dominates cost, drawing K transitions for each POI.Source: D Algorithm Analysis · p. 12
  • A few integration steps and a single-pass grounding walk avoid diffusion-based generators’ long iterative denoising.Flow matching enables one-pass generation, while target-POI grounding adds lightweight nearest-neighbor matching and probability lookup.Source: D Algorithm Analysis · p. 12
  • 13.3 seconds for 10k trajectories compares with 17.0 for GTG, 53.0 for COLA, and 241.7 for MIRAGE.The comparison is generation time; Table 4 also reports training time per epoch.Source: D Algorithm Analysis · p. 12, Table 4 · p. 12

E.1 Full Results on All Transfers

Across the ten additional transfer pairs, Nomad shows broad fidelity gains, though utility rankings vary by pair and task. Negative aggregate gains coexist with strong distance, speed, and temporal-category results in some settings.

E.1 Full Results on All Transfers

  • Nomad has a positive average gain over the strongest metric-wise baselines on seven of ten additional pairs, with a gain reaching 24.43%.Source: §E.1 · pp. 12–13
  • Nomad records the lowest Distance error in nine of ten pairs, lowest Speed error in eight, and lowest Time-Cat error in nine.The reported fidelity measures reflect travel ranges, movement speeds, and temporal-category patterns.Source: §E.1 · p. 13
  • Nomad ranks first across all four downstream metrics on TKY→NYC and NGO→OSA, and is best or second-best on most utility measures in four other named pairs.The other pairs are OSA→NGO, OSA→KYO, IST→IZM, and IZM→IST.Source: §E.1 · p. 13
  • Negative aggregate gains on three pairs coexist with best Distance, Speed, and Time-Cat results, reflecting mismatches with pair-specific downstream or OD patterns.The three pairs are OSA→FUK, IST→IZM, and IST→BUR.Source: §E.1 · p. 13

E.2 Parameter Analysis

Nomad maintains competitive performance across broad parameter ranges in both transfer settings, rather than depending on a sharp optimum. The analysis also finds that selected hyperparameters generalize across the two city groups.

E.2 Parameter Analysis

  • Competitive performance holds across a broad range of parameter combinations in both transfer settings, rather than at a single sharp optimum.The sensitivity analyses cover ANK+BUR+IZM→IST and KYO+NGO→OSA.Source: §E.2 · p. 13, Figure 6 · p. 15, Figure 7 · p. 16
  • Overweighting category or link losses can degrade performance, while varying the return-gate weight causes only moderate changes.λcat weights category prediction for semantic alignment; λlink weights link reconstruction; and λgate balances return-gate and revisit-prediction objectives.Source: §E.2 · p. 13
  • Similar sensitivity patterns across the two city groups indicate that the selected hyperparameters generalize rather than being tailored to one transfer setting.Source: §E.2 · pp. 13–14
Loading 2610.02033v1…