  Multivariate Time-Series (MTS) data is crucial in various application fields.
With its sequential and multi-source (multiple sensors) properties, MTS data
inherently exhibits Spatial-Temporal (ST) dependencies, involving temporal
correlations between timestamps and spatial correlations between sensors in
each timestamp. To effectively leverage this information, Graph Neural
Network-based methods (GNNs) have been widely adopted. However, existing
approaches separately capture spatial dependency and temporal dependency and
fail to capture the correlations between Different sEnsors at Different
Timestamps (DEDT). Overlooking such correlations hinders the comprehensive
modelling of ST dependencies within MTS data, thus restricting existing GNNs
from learning effective representations. To address this limitation, we propose
a novel method called Fully-Connected Spatial-Temporal Graph Neural Network
(FC-STGNN), including two key components namely FC graph construction and FC
graph convolution. For graph construction, we design a decay graph to connect
sensors across all timestamps based on their temporal distances, enabling us to
fully model the ST dependencies by considering the correlations between DEDT.
Further, we devise FC graph convolution with a moving-pooling GNN layer to
effectively capture the ST dependencies for learning effective representations.
Extensive experiments show the effectiveness of FC-STGNN on multiple MTS
datasets compared to SOTA methods. The code is available at
https://github.com/Frank-Wang-oss/FCSTGNN.
