Structure-sparse Tucker-based tensor optimization for traffic prediction

This study presents a structure-sparse Tucker-based tensor optimization model with orthogonality constraints for traffic prediction. The Tucker decomposition exploits low-rank structure to capture intrinsic spatiotemporal correlations in traffic flow data, while ℓ2,0-regularized terms on the factor matrices selectively preserves the historical features most critical for forecasting. A Toeplitz-structured sparsity prior and a complementary ℓ0-terms are embedded to implement anomaly detection of traffic data during the training. For this nonconvex and nonsmooth optimization problem, we develop a computationally efficient augmented Lagrangian method that is theoretically guaranteed to converge to a Karush-Kuhn-Tucker (KKT) point under mild assumptions. For the subproblem involving the factor matrices with group sparsity and orthogonality constraints, an inexact ‘two-step’ projection strategy is employed to obtain approximate solutions efficiently. To validate the effectiveness and practical applicability of the proposed approach, extensive numerical experiments are conducted on both synthetic data and real-world traffic datasets, and the results show that the proposed method consistently achieves strong predictive performance, highlighting its robustness and efficiency in handling spatiotemporal traffic data with inherent sparsity and anomalies.