Anantajit Subrahmanya

arXiv2025

Markovian Reeb Graphs for Simulating Spatiotemporal Patterns of Life

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.

cs.CV↗

arXiv2025

GPS-MTM: Capturing Pattern of Normalcy in GPS-Trajectories with self-supervised learning

Foundation models have driven remarkable progress in text, vision, and video understanding, and are now poised to unlock similar breakthroughs in trajectory modeling. We introduce the GPSMasked Trajectory Transformer (GPS-MTM), a foundation model for large-scale mobility data that captures patterns of normalcy in human movement. Unlike prior approaches that flatten trajectories into coordinate streams, GPS-MTM decomposes mobility into two complementary modalities: states (point-of-interest categories) and actions (agent transitions). Leveraging a bi-directional Transformer with a self-supervised masked modeling objective, the model reconstructs missing segments across modalities, enabling it to learn rich semantic correlations without manual labels. Across benchmark datasets, including Numosim-LA, Urban Anomalies, and Geolife, GPS-MTM consistently outperforms on downstream tasks such as trajectory infilling and next-stop prediction. Its advantages are most pronounced in dynamic tasks (inverse and forward dynamics), where contextual reasoning is critical. These results establish GPS-MTM as a robust foundation model for trajectory analytics, positioning mobility data as a first-class modality for large-scale representation learning. Code is released for further reference.

cs.LG↗