Fully-Connected Spatial-Temporal Graph for Multivariate Time-Series Data

TL;DR

This work tackles the challenge of modeling fully connected spatial-temporal dependencies in multivariate time-series data by introducing FC-STGNN, which constructs a fully-connected ST graph across all sensor patches and applies a moving-pooling GNN to learn local ST patterns. The FC graph construction uses dot-product similarities of sensor embeddings across patches and a temporal-distance decay matrix to emphasize temporally proximal interactions, addressing correlations between Different sEnsors at Different Timestamps (DEDT). The FC graph convolution employs a moving window with a multi-layer MPNN and temporal pooling to produce high-level sensor features, and multiple parallel layers capture diverse ST perspectives before a final MLP mapping. Extensive experiments on CMAPSS, UCI-HAR, and ISRUC-S3 demonstrate superior performance over SOTA methods in RUL, HAR, and SSC tasks, with favorable model complexity and inference speed. This approach offers a scalable and effective framework for learning rich ST representations in real-world MTS applications, with the code available at the authors’ repository.

Abstract

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.

Figures (8)

• Figure 1: ST graphs are constructed from MTS data, creating separate graphs for each timestamp, to capture ST dependencies. In step 1, GNN captures the spatial dependency within each graph, e.g., [$x^1_{T-1}$, $x^2_{T-1}$, $x^3_{T-1}$]. In step 2, temporal encoders capture temporal dependencies for the corresponding sensors across different timestamps, e.g., [$x^2_{T-1}$, $x^2_{T}$, $x^2_{T+1}$]. However, this method overlooks the correlations between different sensors at different timestamps, e.g., $x^3_{T-1}$ and $x^2_T$, failing to model comprehensive ST dependencies.
• Figure 2: Overall structure of FC-STGNN. Beginning with an MTS sample, each sensor's signals are segmented into multiple patches, as shown in the example with three patches (each containing four sensors). Sensor-level features are then learned through an encoder within each patch. Then, the features from different patches are further encoded with positional encoding, followed by FC graph construction and convolution. (1) FC graph construction: This involves fully connecting the sensors across patches by calculating their dot products, enabling the additional connections of DEDT. To refine the full connections of sensors across patches, a decay matrix is introduced by considering their temporal distances. (Note: Due to space constraints, only one sensor exhibits fully-connected weights in this example). (2) FC graph convolution: Moving windows with specific sizes traverse along patches (e.g., two in this example). Graph convolution is then applied to the FC graph within each window. Following the update of each sensor's features by capturing the comprehensive ST dependencies within each window, a temporal pooling operation is employed to learn high-level sensor features for each window. After multiple parallel layers, we concatenate the features, followed by an output layer to obtain final representations for downstream tasks.
• Figure 3: Decay matrix to improve the adjacent matrix.
• Figure 4: Three windows obtained by moving along patches.
• Figure 5: Sensitivity analysis for No. of parallel layers.