Multistage Graph Convolutional Network With Spatial Attention for Multivariate Time Series Imputation

In multivariate time series (MTS) analysis, data loss is a critical issue that degrades analytical model performance and impairs downstream tasks such as structural health monitoring (SHM) and traffic flow monitoring. In real-world applications, MTS is usually collected by multiple types of sensors, making MTS and correlations between variates heterogeneous. However, existing MTS imputation methods overlook the heterogeneous correlations by manipulating heterogeneous MTS as a homogeneous entity, leading to inaccurate imputation results. Besides, correlations between different data types vary due to ever-changing environmental conditions, forming dynamic correlations in MTS. How to properly learn the hidden correlation from heterogeneous MTS for accurate data imputation remains unresolved. To solve the problem, we propose a multistage graph convolutional network with spatial attention (MSA-GCN). In the first stage, we decompose heterogeneous MTS into several clusters with homogeneous data collected from identical sensor types and learn intracluster correlations. Then, we devise a GCN with spatial attention to explore dynamic intercluster correlations, which is the second stage of MSA-GCN. In the last stage, we decode the learned features from previous stages via stacked convolutional neural networks. We jointly train these three-stage models to predict the missing data in MTS. Leveraging this multistage architecture and spatial attention mechanism makes MSA-GCN effectively learn heterogeneous and dynamic correlations among MTS, resulting in superior imputation performance. We tested MSA-GCN with the monitoring data from a large-span bridge and Wetterstation weather dataset. The results affirm its superiority over baseline models, demonstrating its enhanced accuracy in reducing imputation errors across diverse datasets.