MNT-TNN: Spatiotemporal Traffic Data Imputation via Compact Multimode Nonlinear Transform-based Tensor Nuclear Norm

Imputation of random or non-random missing data is a long-standing research topic and a crucial application for Intelligent Transportation Systems (ITS). However, with the advent of modern communication technologies such as Global Satellite Navigation Systems (GNSS), traffic data collection has outpaced traditional methods, introducing new challenges in random missing value imputation and increasing demands for spatiotemporal dependency modelings. To address these issues, we propose a novel spatiotemporal traffic imputation method, Multimode Nonlinear Transformed Tensor Nuclear Norm (MNT-TNN), grounded in the Transform-based Tensor Nuclear Norm (TTNN) optimization framework which exhibits efficient mathematical representations and theoretical guarantees for the recovery of random missing values. Specifically, we strictly extend the single-mode transform in TTNN to a multimode transform with nonlinear activation, effectively capturing the intrinsic multimode spatiotemporal correlations and low-rankness of the traffic tensor, represented as location $\times$ location $\times$ time. To solve the nonconvex optimization problem, we design a proximal alternating minimization (PAM) algorithm with theoretical convergence guarantees. We suggest an Augmented Transform-based Tensor Nuclear Norm Families (ATTNNs) framework to enhance the imputation results of TTNN techniques, especially at very high miss rates. Extensive experiments on real datasets demonstrate that our proposed MNT-TNN and ATTNNs can outperform the compared state-of-the-art imputation methods, completing the benchmark of random missing traffic value imputation.