# Discovering Dynamic Patterns from Spatiotemporal Data with Time-Varying Low-Rank Autoregression

arXiv: https://arxiv.org/abs/2211.15482 · HTML: https://mlsanity.com/paper/2211.15482/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 28 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Online dynamic mode decomposition for time-varying systems](https://mlsanity.com/paper/1707.02876/) (2017)
- [High-dimensional vector autoregressive time series modeling via tensor decomposition](https://mlsanity.com/paper/1909.06624/) (2019)
- [Time-varying Autoregression with Low Rank Tensors](https://mlsanity.com/paper/1905.08389/) (2019)
- [Forecasting Sparse Movement Speed of Urban Road Networks with Nonstationary Temporal Matrix Factorization](https://mlsanity.com/paper/2203.10651/) (2022)
- [SamBaTen: Sampling-based Batch Incremental Tensor Decomposition](https://mlsanity.com/paper/1709.00668/) (2017)
- [OCTen: Online Compression-based Tensor Decomposition](https://mlsanity.com/paper/1807.01350/) (2018)

## Built on by (most cited first, 6 of 6)

- [Expand and Compress: Exploring Tuning Principles for Continual Spatio-Temporal Graph Forecasting](https://mlsanity.com/paper/2410.12593/) (2024)
- [Urban traffic analysis and forecasting through shared Koopman eigenmodes](https://mlsanity.com/paper/2409.04728/) (2024)
- [Spatiotemporal Regularized Tucker Decomposition Approach for Traffic Data Imputation](https://mlsanity.com/paper/2305.06563/) (2023)
- [Guaranteed Multidimensional Time Series Prediction via Deterministic Tensor Completion Theory](https://mlsanity.com/paper/2501.15388/) (2025)
- [Interpretable Time Series Autoregression for Periodicity Quantification](https://mlsanity.com/paper/2506.22895/) (2025)
- [Data-Driven Discovery of Mobility Periodicity for Understanding Urban Systems](https://mlsanity.com/paper/2508.03747/) (2025)

## Abstract (arXiv)

The problem of broad practical interest in spatiotemporal data analysis, i.e., discovering interpretable dynamic patterns from spatiotemporal data, is studied in this paper. Towards this end, we develop a time-varying reduced-rank vector autoregression (VAR) model whose coefficient matrices are parameterized by low-rank tensor factorization. Benefiting from the tensor factorization structure, the proposed model can simultaneously achieve model compression and pattern discovery. In particular, the proposed model allows one to characterize nonstationarity and time-varying system behaviors underlying spatiotemporal data. To evaluate the proposed model, extensive experiments are conducted on various spatiotemporal data representing different nonlinear dynamical systems, including fluid dynamics, sea surface temperature, USA surface temperature, and NYC taxi trips. Experimental results demonstrate the effectiveness of modeling spatiotemporal data and characterizing spatial/temporal patterns with the proposed model. In the spatial context, the spatial patterns can be automatically extracted and intuitively characterized by the spatial modes. In the temporal context, the complex time-varying system behaviors can be revealed by the temporal modes in the proposed model. Thus, our model lays an insightful foundation for understanding complex spatiotemporal data in real-world dynamical systems. The adapted datasets and Python implementation are publicly available at https://github.com/xinychen/vars.