Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria

Model selection in tensor decomposition is important for real applications if the rank of the original data tensor is unknown and the observed tensor is noisy. In the Tucker model, the minimum description length (MDL) or Bayesian information criteria have been applied to tensors via matrix unfolding, but these methods are sensitive to noise when the tensors have a multilinear low rank structure given by the Tucker model. In this study, we propose new methods for improving the MDL so it is more robust to noise. The proposed methods are justified theoretically by analyzing the “multilinear low-rank structure” of tensors. Extensive experiments including numerical simulations and a real application to image denoising are provided to illustrate the advantages of the proposed methods.