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

TL;DR

This paper introduces a novel time-varying low-rank autoregression model for discovering interpretable dynamic patterns in complex spatiotemporal data, effectively capturing nonstationary behaviors and enabling pattern extraction.

Contribution

The paper develops a tensor-parameterized, time-varying reduced-rank VAR model that simultaneously achieves model compression and pattern discovery in spatiotemporal data.

Findings

Effective modeling of diverse nonlinear dynamical systems

Automatic extraction of spatial patterns via spatial modes

Revelation of complex temporal behaviors through temporal modes

Abstract

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.