Scalable inference of spatial regions and temporal signatures from time series

TL;DR

This paper introduces a scalable, nonparametric method for spatial regionalization of time series data that jointly infers regions and representative temporal archetypes based on data compression principles.

Contribution

It presents a novel framework utilizing the minimum description length principle to efficiently partition spatial domains and identify temporal drivers without prior assumptions.

Findings

Accurately recovers planted regional structures in synthetic data.

Extracts meaningful patterns from large-scale air quality and vegetation data.

Runs in log-linear time relative to the number of time series.

Abstract

Regionalization aims to partition a spatial domain into contiguous regions that share similar characteristics, enabling more effective spatial analysis, policy making, and resource management. Existing approaches for spatial regionalization typically rely on static spatial snapshots rather than evolving time series. Meanwhile, most time series clustering methods ignore spatial structure or enforce spatial continuity through ad hoc regularization, constraining the number of inferred regions a priori either explicitly or implicitly. Utilizing the minimum description length principle from information theory, here we propose an efficient and fully nonparametric framework for the regionalization of spatial time series. Our method jointly infers a spatial partition along with a set of representative time series archetypes ("drivers") that best compress a spatiotemporal dataset, with a runtime log-linear in the number of time series. We demonstrate that this method can accurately recover planted regional structure and drivers in synthetic time series, and can extract meaningful structural regularities in large-scale empirical air quality and vegetation index records. Our method provides a principled and scalable framework for spatially contiguous partitioning, allowing interpretable temporal patterns and homogeneous regions to emerge directly from the data itself.