# Scalable inference of spatial regions and temporal signatures from time series

arXiv: https://arxiv.org/abs/2605.05008 · HTML: https://mlsanity.com/paper/2605.05008/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 69 references that are in the map.
- First posted on arXiv 6 May 2026.

## Builds on (most cited first, 17 of 17)

- [Bayesian stochastic blockmodeling](https://mlsanity.com/paper/1705.10225/) (2017)
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- [Representative community divisions of networks](https://mlsanity.com/paper/2105.04612/) (2021)
- [Spatial regionalization based on optimal information compression](https://mlsanity.com/paper/2111.01813/) (2021)
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- [Unsupervised Discretization by Two-dimensional MDL-based Histogram](https://mlsanity.com/paper/2006.01893/) (2020)
- [Information theoretic network approach to socioeconomic correlations](https://mlsanity.com/paper/2009.13825/) (2020)
- [Ordered community detection in directed networks](https://mlsanity.com/paper/2203.16460/) (2022)
- [Bayesian contiguity constrained clustering, spanning trees and dendrograms](https://mlsanity.com/paper/2302.12546/) (2023)
- [Mutual information and the encoding of contingency tables](https://mlsanity.com/paper/2405.05393/) (2024)
- [Differentially Describing Groups of Graphs](https://mlsanity.com/paper/2201.04064/) (2021)
- [Compressing network populations with modal networks reveals structural diversity](https://mlsanity.com/paper/2209.13827/) (2022)
- [Identifying hubs in directed networks](https://mlsanity.com/paper/2312.03347/) (2023)
- [Fast nonparametric inference of network backbones for weighted graph sparsification](https://mlsanity.com/paper/2409.06417/) (2024)
- [Transfer entropy for finite data](https://mlsanity.com/paper/2506.16215/) (2025)

## Abstract (arXiv)

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.