Dynamic graph-based bilateral recurrent imputation network for multivariate time series

Multivariate time series imputation using graph neural networks (GNNs) has gained significant attention, where the variables and their correlations are depicted as the graph nodes and edges, offering a structured way to understand the intricacies of multivariate time series. On this basis, existing GNNs typically make the assumption of static correlations between variables, using a graph with fixed edge weights to model multivariate relationships. However, the static assumption is usually inconsistent with the dynamic nature of real-world data, where correlations between variables tend to change over time. In this paper, we propose a dynamic graph-based bilateral recurrent imputation network (DGBRIN) to address the above issue. Specifically, for each segment of a multivariate time series captured within a sliding window, we construct a specialized graph to capture the localized, dynamic correlations between variables. To this end, we design a dynamic adjacency matrix learning (DAML) module, which integrates temporal dependencies through an information fusion layer and mine localized monotonic correlations between variables using the Spearman rank correlation coefficient. These correlations are represented in segment-specific adjacency matrices. Subsequently, the adjacency matrices and time series are fed into a hybrid graph-based bilateral recurrent network for missing value imputation, which combines the advantages of recurrent neural networks and graph convolutional networks to effectively capture temporal dependencies and merge the correlation information between variables. We conduct experiments on eight real-world time series. The results demonstrate the effectiveness of the proposed model.