Rail transit OD-matrix completion via manifold regularized tensor factorisation

Urban rail transit has become an indispensable mode in major cities worldwide regarding the advantages of large capacity, high speed, punctuality, and environmental protection. Origin-destination (OD) matrix data is crucial to the organisation of rail train operation and management. Nevertheless, rail transit OD matrices are inevitably suffered from data loss problems due to the data transmission and acquisition failures. Tensor completion is a state-of-the-art method for missing data imputation. In this paper, a novel tensor completion method for OD- matrix completion is proposed. To this end, an OD-matrix tensor is established to represent OD information, and the similarity matrix of OD-matrix tensor for each dimension is extracted as a piece of auxiliary information expressing underlying multi-mode relationships of OD data. Finally, a manifold regularised tensor factorisation is applied to impute the missing OD data, in which the Graph Laplacians inferred from similarity weight matrices are used as regularisation priors on factorisation factors. The proposed model is applied to a case study of the metro line in Xi'an, China. The experimental results indicate that the proposed method outperforms baselines. It can accurately impute missing data within the OD matrices and work well even when the missing ratio is up to 80%.