Bayesian Robust Tensor Decomposition Based on MCMC Algorithm for Traffic Data Completion

Data loss is a common problem in intelligent transportation systems (ITSs). And the tensor-based interpolation algorithm has obvious superiority in multidimensional data interpolation. In this paper, a Bayesian robust tensor decomposition method (MBRTF) based on the Markov chain Monte Carlo (MCMC) algorithm is proposed. The underlying low CANDECOMP/PARAFAC (CP) rank tensor captures the global information, and the sparse tensor captures local information (also regarded as anomalous data), which achieves a reliable prediction of missing terms. The low CP rank tensor is modeled by linear interrelationships among multiple latent factors, and the sparsity of the columns on the latent factors is achieved through a hierarchical prior approach, while the sparse tensor is modeled by a hierarchical view of the Student-t distribution. It is a challenge for traditional tensor-based interpolation methods to maintain a stable performance under different missing rates and nonrandom missing (NM) scenarios. The MBRTF algorithm is an effective multiple interpolation algorithm that not only derives unbiased point estimates but also provides a robust method for the uncertainty measures of these missing values.