Gaussian Adaptive Patching Powered Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data

Multivariate Time-Series (MTS) data is crucial across diverse domains. With its sequential and multi-source (e.g., sensors) properties, MTS data inherently exhibits Spatial-Temporal (ST) dependencies, involving temporal correlations over time and spatial correlations between sensors. While Graph Neural Networks (GNNs) have been widely adopted to exploit these dependencies, existing methods typically capture spatial and temporal dependencies separately, overlooking correlations between Different sEnsors at Different Times (DEDT). Ignoring such correlations limits the comprehensive modeling of ST dependencies and hinders effective MTS representation learning. To address this, we propose a Fully-Connected Spatial-Temporal Graph Neural Network (FC-STGNN), which introduces two key components: FC graph construction and FC graph convolution. In graph construction, we design an FC graph that links all sensors at all times, with edge weights refined according to temporal distances. This design enables comprehensive modeling of ST dependencies by explicitly capturing correlations between DEDT. To exploit this graph, we introduce FC graph convolution with moving-pooling GNN layers, effectively capturing the ST dependencies for MTS representation learning. However, FC-STGNN relies on fixed-size patching, which may limit its ability to capture optimal local patterns for FC graph construction. To overcome this, we extend the framework to GAP-STGNN by incorporating Gaussian Adaptive Patching (GAP), dynamically learning patches with adaptive receptive fields to better capture local patterns. GAP further integrates an adaptive patch selection module that identifies informative patches while softly attenuating less relevant ones to maintain temporal continuity. Extensive experiments on multiple MTS datasets demonstrate that FC-STGNN and GAP-STGNN effectively capture comprehensive ST dependencies with improved FC graphs, achieving superior performance compared to SOTA methods. The code is available at https://github.com/Frank-Wang-oss/GAP-STGNN.