# Markovian Reeb Graphs for Simulating Spatiotemporal Patterns of Life

arXiv: https://arxiv.org/abs/2510.03152 · HTML: https://mlsanity.com/paper/2510.03152/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 37 references that are in the map.
- First posted on arXiv 3 Oct 2025.

## Builds on (most cited first, 9 of 9)

- [DiffTraj: Generating GPS Trajectory with Diffusion Probabilistic Model](https://mlsanity.com/paper/2304.11582/) (2023)
- [SpaBERT: A Pretrained Language Model from Geographic Data for Geo-Entity Representation](https://mlsanity.com/paper/2210.12213/) (2022)
- [NUMOSIM: A Synthetic Mobility Dataset with Anomaly Detection Benchmarks](https://mlsanity.com/paper/2409.03024/) (2024)
- [Deep Activity Model: A Generative Approach for Human Mobility Pattern Synthesis](https://mlsanity.com/paper/2405.17468/) (2024)
- [Urban Anomalies: A Simulated Human Mobility Dataset with Injected Anomalies](https://mlsanity.com/paper/2410.01844/) (2024)
- [Metropolitan Scale and Longitudinal Dataset of Anonymized Human Mobility Trajectories](https://mlsanity.com/paper/2307.03401/) (2023)
- [The Patterns of Life Human Mobility Simulation](https://mlsanity.com/paper/2410.00185/) (2024)
- [ReeFRAME: Reeb Graph based Trajectory Analysis Framework to Capture Top-Down and Bottom-Up Patterns of Life](https://mlsanity.com/paper/2410.14913/) (2024)
- [ReeSPOT: Reeb Graph Models Semantic Patterns of Normalcy in Human Trajectories](https://mlsanity.com/paper/2405.00808/) (2024)

## Abstract (arXiv)

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.