A Bayesian Robust Tensor Ring Decomposition Model with Gaussian-Wishart Prior for Missing Traffic Data Completion

The rapid development of Intelligent Transportation Systems (ITS) is often hindered by missing data due to technical or equipment failures, impacting data analysis and application. To address this issue and leverage the advantages of tensor completion methods in multidimensional data imputation, we propose a Bayesian Robust Tensor Ring Decomposition Model with Gaussian-Wishart priors (BRTRC). The BRTRC model structures traffic data into tensor formats such as “road segment × day × time of day” and “road segment × week × day of the week × time of day.” Using tensor ring decomposition, the model reduces tensor complexity and redundancy. To approximate real values more accurately, Gaussian-Wishart priors are applied to the horizontal and frontal slices of the core factors and conjugate priors are set on the hyperparameters, allowing automatic characterisation of data changes in Bayesian modelling to avoid overfitting. Additionally, the BRTRC model introduces a sparse tensor to identify outliers in the data and employs a variational Bayesian inference method to estimate model parameters and latent variables. Experiments on two real traffic datasets demonstrate that the BRTRC model effectively imputes traffic data under both random and non-random missing patterns, robustly identifies and removes outliers and improves data quality and reliability. Extending the model to the fourth order shows superior performance in recovering high-dimensional characteristics of intersecting data compared to other models.