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.

翻译：多元时间序列（MTS）数据在多个应用领域至关重要。由于其序列性和多源（多传感器）特性，MTS数据天然具有时空依赖关系，包括时间戳间的时间相关性和每个时间戳内传感器之间的空间相关性。为有效利用这些信息，基于图神经网络的方法（GNNs）已被广泛采用。然而，现有方法分别捕获空间依赖性和时间依赖性，未能捕捉不同时间戳上不同传感器（DEDT）之间的相关性。忽视此类相关性阻碍了MTS数据中时空依赖关系的全面建模，从而限制了现有GNNs学习有效表征的能力。为解决这一局限，我们提出了一种名为全连接时空图神经网络（FC-STGNN）的新方法，包括两个关键组件：全连接图构建和全连接图卷积。在图构建方面，我们设计了一种衰减图，基于传感器的时间距离连接所有时间戳上的传感器，从而通过考虑DEDT之间的相关性全面建模时空依赖关系。此外，我们设计了带有移动池化GNN层的全连接图卷积，以有效捕获时空依赖关系来学习有效表征。大量实验表明，与最先进的方法相比，FC-STGNN在多个MTS数据集上具有显著有效性。