Robust Tensor Ring Decomposition for Urban Traffic Data Imputation

In urban transportation systems, missing data and noise contamination are almost inevitable. To address the challenge of imputing traffic data corrupted by noise and outliers in real-world scenarios, this paper proposes a novel algorithm based on spatiotemporal tensor completion. The proposed method transforms observed data into three-dimensional spatiotemporal tensors and utilizes tensor ring decomposition for data completion. Furthermore, spatial and temporal information is incorporated into the model by utilizing the graph Laplacian matrix. To handle outliers, they are treated as unknown parameters, and the ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>-norm is introduced to ensure their sparsity, thereby achieving the Spatio-Temporal Tensor Completion model with ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>-norm term (STTC-ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>). The solution to the model is derived using the alternating optimization framework with the alternating direction method of multipliers. Then, we discuss the convergence of the solution method. To further enhance the efficiency of our proposed method, we combine the unrolling algorithm with our iterative optimization model, creating a lightweight and efficient neural network tailored for tensor completion, called STTC-ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>-NN. Extensive experiments conducted on real datasets demonstrate the superiority of our proposed method over several state-of-the-art methods across various experimental scenarios. It is worth noting that STTC-ℓ<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub>-NN reduces computational time by one to two orders of magnitude compared to existing methods while maintaining or even improving imputation accuracy. The code is available at https://github.com/TCCofWANG/STTC-L0-and-STTC-L0-NN.