  Mining natural associations from high-dimensional spatiotemporal signals
plays an important role in various fields including biology, climatology, and
financial analysis. However, most existing works have mainly studied
time-independent signals without considering the correlations of spatiotemporal
signals that achieve high learning accuracy. This paper aims to learn graphs
that better reflect underlying data relations by leveraging the long- and
short-term characteristics of spatiotemporal signals. First, a spatiotemporal
signal model is presented that considers both spatial and temporal relations.
In particular, we integrate a low-rank representation and a Gaussian Markov
process to describe the temporal correlations. Then, the graph learning problem
is formulated as a joint low-rank component estimation and graph Laplacian
inference. Accordingly, we propose a low rank and spatiotemporal
smoothness-based graph learning method (GL-LRSS), which introduces a
spatiotemporal smoothness prior into time-vertex signal analysis. By jointly
exploiting the low rank of long-time observations and the smoothness of
short-time observations, the overall learning performance can be effectively
improved. Experiments on both synthetic and real-world datasets demonstrate
substantial improvements in the learning accuracy of the proposed method over
the state-of-the-art low-rank component estimation and graph learning methods.
