Scalable inference of spatial regions and temporal signatures from time series

Traditional spatial regionalization methods rely on static snapshots, ignoring temporal dynamics, while time series clustering often forces spatial continuity through ad-hoc regularization and requires pre-specifying the number of regions. In a new paper on arXiv (2605.05008), Jiayu Weng and Alec Kirkley introduce a principled alternative: a fully nonparametric framework based on the minimum description length (MDL) principle from information theory. The algorithm jointly infers a spatial partition and a set of representative time series archetypes (termed 'drivers') that best compress a spatiotemporal dataset. Crucially, it does not require the user to fix the number of regions beforehand—the optimal partition emerges directly from the data. The method's runtime is log-linear in the number of time series, making it scalable to large datasets. This allows the model to handle massive sensor networks or satellite imagery archives without exponential complexity.

The researchers validated their approach on synthetic datasets, where it accurately recovered planted regional structures and underlying temporal drivers. They then applied it to large-scale empirical records of air quality measurements and vegetation indices (e.g., NDVI). The method extracted meaningful spatial regions and temporal signatures that align with known geographical and ecological patterns, demonstrating both interpretability and practical utility. By letting homogeneous regions and distinguishing temporal behaviors emerge from data, the framework offers a powerful tool for applications in environmental monitoring, urban planning, agriculture, and climate science. It empowers analysts to discover spatial divisions and their temporal signatures without imposing arbitrary boundaries or manual region counts.