entry-and-exit rate measurement from trajectories

Existing evaluation metrics for visual object tracking lack a comparable, continuous-time measure for the trajectory function of time (FoT), relying instead on discrete-frame assessments that fail to characterize arbitrary-time states or disentangle distinct error types (e.g., localization, false positives, missed detections). Method: We propose Star-ID—the first spatiotemporally aligned trajectory integral distance—defining a rigorous, comparable FoT metric over continuous spacetime. Star-ID strictly distinguishes temporally aligned versus misaligned trajectory segments and analytically decouples detection and localization errors. It introduces time-averaged metrics and a theoretical error decomposition model, supported by a multi-object numerical validation framework. Contribution/Results: We provide formal theoretical analysis and demonstrate—via both single- and multi-object simulations—that Star-ID significantly enhances physical interpretability and fine-grained discriminative power in tracking evaluation, enabling precise, continuous-time performance assessment.

This study addresses the challenge of systematically evaluating stay-point detection algorithms under noisy trajectory conditions, which has been hindered by the absence of publicly available benchmark datasets with ground-truth annotations. To bridge this gap, we construct the first large-scale synthetic trajectory dataset annotated with real-world stay points and propose both a novel unsupervised and a supervised detection algorithm. Leveraging this dataset alongside a noise-robustness evaluation framework, we conduct a comprehensive assessment of nine representative algorithms. Our results reveal that state-of-the-art methods suffer significant performance degradation under realistic noise, whereas the proposed approaches substantially improve detection accuracy, with the supervised variant notably outperforming existing baselines.

This study addresses the challenges of interpreting tourist behavior from GPS trajectories, which are often hindered by ambiguous activity sequences, substantial noise, and irregular sampling. To overcome these issues, the authors propose a rhythm-consistent semi-Markov generative model for synthetic trajectory creation. The method employs a probabilistic event–POI soft-matching mechanism to map staypoints to candidate points of interest (POIs), thereby constructing semantic stay sequences based on the MID10 POI taxonomy. It further integrates hourly category distributions, time-conditioned transition matrices, and category-dependent dwell-time models to capture human mobility rhythms. Experimental results demonstrate that the generated trajectories closely reproduce the temporal and categorical characteristics of real-world data, effectively quantifying how changes in POI configurations influence spatiotemporal visitation intensity. This approach transcends the limitations of conventional hard-matching strategies and static models, enabling interpretable transportation and geographic scenario simulations.

This work addresses the high cost and limited scalability of traditional turning movement count methods, which rely on manual annotation and camera calibration. The authors propose an unsupervised pipeline that automatically generates persistent polygonal entry and exit zones solely from vehicle trajectory start and end points, leveraging spatial clustering without requiring human intervention, camera calibration, or prior intersection knowledge. This approach introduces reusable spatial regions for the first time, enabling cross-camera deployment and substantially reducing computational overhead. Integrated with object detection, multi-object tracking, and systematic parameter optimization, the method achieves efficient trajectory classification. Evaluated on 25 real-world cameras—including 16 unseen scenarios—it attains a median classification error of approximately 3% and meets engineering standards under the GEH metric, demonstrating superior stability and efficiency compared to existing baselines.

To address the challenge of jointly detecting spatiotemporal change points and identifying spatial clusters in large-scale spatiotemporal count data, this paper proposes a doubly fused penalized Poisson regression model—the first to achieve simultaneous and consistent estimation of temporal breakpoints and spatially abrupt clusters. Methodologically, we design a dual structured penalty that jointly enforces temporal jumps and spatial proximity, and develop an iterative soft-thresholding optimization algorithm. Theoretically, we establish an asymptotic statistical inference framework and rigorously prove consistency and asymptotic normality of the estimators. Extensive simulations and real-world applications—including disease outbreak monitoring and urban anomaly detection—demonstrate that our method significantly outperforms existing approaches in localization accuracy and cluster identification precision, while exhibiting strong robustness and linear scalability with respect to sample size.

Existing research struggles to characterize the dynamic life cycle of individual metro travel behavior over multi-year horizons, often limited to static clustering or short-term behavioral analysis. This study proposes a state-based life cycle framework that integrates a hidden semi-Markov model (HSMM) with discrete-time survival analysis, jointly modeling state evolution and system entry/exit events for the first time. Leveraging four years of smart card data from Shanghai Metro, the framework identifies five robust travel states and reveals that exit risk depends solely on the current state, whereas re-entry risk decays sharply with increasing inactivity duration, exhibiting asymmetric temporal dynamics. The approach not only constructs a directed hierarchy of state transitions centered on occasional usage but also provides theoretical grounding and empirical support for targeted user retention strategies.

This study addresses the challenge of accurately characterizing individual activity spaces from sparse and irregularly sampled GPS data. The authors propose a modeling framework grounded in object-based spatial statistics, which integrates temporal distributions over GIS road networks and place polygons to construct a time-weighted estimator that effectively distinguishes between stationary and mobile behaviors. The approach further incorporates map-enhanced trajectory clustering and a stability metric for robust activity inference. Theoretical analysis provides error bounds accounting for both measurement inaccuracies and entity misclassification from multiple sources. Experimental results demonstrate that the method reliably identifies stable anchor locations and interpretable travel corridors, with both synthetic and real-world datasets confirming the superiority of the time-weighted strategy under irregular sampling conditions.

This study addresses the challenge of accurately modeling spatiotemporal active mobility patterns—such as walking and cycling—in urban environments while preserving individual privacy. The authors propose a macroscopic activity-based modeling framework leveraging non-intrusive sensor data, introducing an innovative “attendance function” to characterize individuals’ spatiotemporal travel behavior between activities. By reformulating aggregate count decomposition as a statistical inference problem, the method employs a Poisson count model, maximum likelihood estimation, and an efficient EM algorithm to enable scalable inference of unknown subpopulation sizes without requiring individual-level trajectories. Theoretical analysis and empirical results demonstrate that the framework effectively balances privacy preservation, computational efficiency, and modeling accuracy, successfully reconstructing fine-grained mobility patterns from aggregated observations.

This study investigates whether parameters in stochastic transport models can be uniquely identified from aggregate count data alone and examines the value of individual trajectory data in mitigating structural non-identifiability. By integrating lattice-based random walk models with both population counts and individual trajectories, the work employs multiscale modeling, mean-field PDE approximations, likelihood-based inference, and identifiability analysis to systematically uncover the inherent limitations of count-only data. The findings demonstrate that incorporating trajectory information substantially enhances parameter identifiability and estimation accuracy, offering theoretical guidance for optimal experimental design. The impact of various trajectory sampling strategies on practical identifiability is quantified, and all algorithms are made publicly available to support reproducible research.

Real-world urban trajectory data are often sparse and discontinuous due to low sampling rates and insufficient spatial coverage, hindering their utility for high-precision location-based services. To address this challenge, this work proposes TRACE, a diffusion-based generative model that introduces a State Propagation Diffusion Model (SPDM). By incorporating a memory mechanism during the denoising process, SPDM effectively leverages historical intermediate states to faithfully reconstruct missing trajectory segments under complex spatiotemporal patterns. The model supports end-to-end training and achieves state-of-the-art performance across multiple real-world datasets, improving trajectory reconstruction accuracy by over 26% compared to existing methods while maintaining computationally feasible inference costs.