Scalable Low-Rank Autoregressive Tensor Learning for Spatiotemporal Traffic Data Imputation

Missing value problem in spatiotemporal traffic data has long been a challenging topic, in particular for large-scale and high-dimensional data with complex missing mechanisms and diverse degrees of missingness. Recent studies based on tensor nuclear norm have demonstrated the superiority of tensor learning in imputation tasks by effectively characterizing the complex correlations/dependencies in spatiotemporal data. However, despite the promising results, these approaches do not scale well to large tensors. In this paper, we focus on addressing the missing data imputation problem for large-scale spatiotemporal traffic data. To achieve both high accuracy and efficiency, we develop a scalable autoregressive tensor learning model---Low-Tubal-Rank Autoregressive Tensor Completion (LATC-Tubal)---based on the existing framework of Low-Rank Autoregressive Tensor Completion (LATC), which is well-suited for spatiotemporal traffic data that characterized by multidimensional structure of location$\times$ time of day $\times$ day. In particular, the proposed LATC-Tubal model involves a scalable tensor nuclear norm minimization scheme by integrating linear unitary transformation. Therefore, the tensor nuclear norm minimization can be solved by singular value thresholding on the transformed matrix of each day while the day-to-day correlation can be effectively preserved by the unitary transform matrix. Before setting up the experiment, we consider two large-scale 5-minute traffic speed data sets collected by the California PeMS system with 11160 sensors. We compare LATC-Tubal with state-of-the-art baseline models, and find that LATC-Tubal can achieve competitively accuracy with a significantly lower computational cost. In addition, the LATC-Tubal will also benefit other tasks in modeling large-scale spatiotemporal traffic data, such as network-level traffic forecasting.