Multivariate Time Series Classification with Hierarchical Variational Graph Pooling

In recent years, multivariate time-series classification (MTSC) has attracted considerable attention owing to the advancement of sensing technology. Existing deep-learning-based MTSC techniques, which mostly rely on convolutional or recurrent neural networks, focus primarily on the temporal dependency of a single time series. Based on this, complex pairwise dependencies among multivariate variables can be better described using advanced graph methods, where each variable is regarded as a node in the graph, and their dependencies are regarded as edges. Furthermore, current spatial-temporal modeling (e.g., graph classification) methodologies based on graph neural networks (GNNs) are inherently flat and cannot hierarchically aggregate node information. To address these limitations, we propose a novel graph-pooling-based framework, MTPool, to obtain an expressive global representation of MTS. We first convert MTS slices into graphs using the interactions of variables via a graph structure learning module and obtain the spatial-temporal graph node features via a temporal convolutional module. To obtain global graph-level representation, we design an "encoder-decoder"-based variational graph pooling module to create adaptive centroids for cluster assignments. Then, we combine GNNs and our proposed variational graph pooling layers for joint graph representation learning and graph coarsening, after which the graph is progressively coarsened to one node. Finally, a differentiable classifier uses this coarsened representation to obtain the final predicted class. Experiments on ten benchmark datasets showed that MTPool outperforms state-of-the-art strategies in the MTSC task.