MNT-TNN: spatiotemporal traffic data imputation via compact multimode nonlinear transform-based tensor nuclear norm

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Yihang Lu, Mahwish Yousaf, Xianwei Meng, Enhong Chen

Published: 01 Nov 2025, Last Modified: 28 Nov 2025Transportation Research Part C: Emerging TechnologiesEveryoneRevisionsCC BY-SA 4.0
Abstract: Highlights•A Novel Tensor-Based Method for Traffic Data Imputation: We introduce the Multimode Nonlinear Transformed Tensor Nuclear Norm (MNT-TNN), a new method specifically designed for imputing missing values in spatiotemporal traffic data. This approach rigorously extends the single-mode transform in the traditional TTNN framework to a multimode one, which more effectively captures the complex spatiotemporal correlations and low-rankness inherent in traffic tensors. The proposed method is generic and extendable, making it valuable for both theoretical and practical advancements across diverse domains.•Advanced Optimization and an Augmented Framework: To solve the resulting nonconvex optimization problem, we employ a proximal alternating minimization (PAM) algorithm that comes with theoretical convergence guarantees. Additionally, we propose the Augmented Transform-based Tensor Nuclear Norm Families (ATTNNs) framework, which significantly boosts imputation performance, especially at very high missing data rates.•Demonstrated State-of-the-Art Performance: Through extensive experiments on three real-world traffic datasets (CHSP, PEMS04, and PEMS-BAY), our proposed MNT-TNN and ATTNNs methods consistently outperform existing state-of-the-art imputation techniques. Our methods show particular strength in scenarios with high missing rates and in datasets with significant spatial dependencies.•Robustness Compared to Deep Learning Approaches: Further studies show that our optimization-based methods are more robust and practical in scenarios with limited data compared to leading deep learning models. While DL models struggle with instability and high data demands, MNT-TNN provides reliable performance without the need for extensive training data.•Identified Applicability and Future Directions: We provide a clear analysis of the method’s limitations, noting its prime suitability for tensors with strong spatial correlations and its reduced effectiveness for non-random missing patterns. Future work will focus on improving computational efficiency and extending the framework to other data types.