精确建模人类移动性对城市规划、流行病学和交通管理至关重要。本文提出马尔可夫型 Reeb 图(Markovian Reeb Graphs),一种新颖框架,将 Reeb 图从描述性分析工具转变为面向时空轨迹的生成模型。该方法捕捉个体与群体层面的生命活动模式(Patterns of Life, PoLs),并生成能保持基础行为特征、同时嵌入随机变异性的逼真轨迹——其核心在于将概率转移嵌入 Reeb 图结构之中。我们提出了两种变体:面向个体智能体的序列型 Reeb 图(Sequential Reeb Graphs, SRGs)与融合个体及群体 PoLs 的混合型 Reeb 图(Hybrid Reeb Graphs, HRGs)。在 Urban Anomalies 和 Geolife 数据集上,我们基于五项移动性统计指标对其进行了评估。结果表明,HRGs 在各项指标上均展现出优异的保真度,且仅需规模适中的轨迹数据集,无需依赖特定辅助信息。本工作确立了马尔可夫型 Reeb 图作为轨迹仿真的一种有前景的框架,具有在各类城市环境中的广泛适用性。
Accurately modeling human mobility is critical for urban planning, epidemiology, and traffic management. In this work, we introduce Markovian Reeb Graphs, a novel framework that transforms Reeb graphs from a descriptive analysis tool into a generative model for spatiotemporal trajectories. Our approach captures individual and population-level Patterns of Life (PoLs) and generates realistic trajectories that preserve baseline behaviors while incorporating stochastic variability by embedding probabilistic transitions within the Reeb graph structure. We present two variants: Sequential Reeb Graphs (SRGs) for individual agents and Hybrid Reeb Graphs (HRGs) that combine individual with population PoLs, evaluated on the Urban Anomalies and Geolife datasets using five mobility statistics. Results demonstrate that HRGs achieve strong fidelity across metrics while requiring modest trajectory datasets without specialized side information. This work establishes Markovian Reeb Graphs as a promising framework for trajectory simulation with broad applicability across urban environments.