  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.
