Zhang, L.Wei, W.Shi, Q.Shen, C.van den Hengel, A.Zhang, Y.2021-05-172021-05-172020IEEE Transactions on Neural Networks and Learning Systems, 2020; 31(1):4170-41842162-237X2162-2388http://hdl.handle.net/2440/130272Date of publication December 30, 2019; date of current version October 6, 2020Low-rank representation-based approaches that assume low-rank tensors and exploit their low-rank structure with appropriate prior models have underpinned much of the recent progress in tensor completion. However, real tensor data only approximately comply with the low-rank requirement in most cases, viz., the tensor consists of low-rank (e.g., principle part) as well as non-low-rank (e.g., details) structures, which limit the completion accuracy of these approaches. To address this problem, we propose an adaptive low-rank representation model for tensor completion that represents low-rank and non-low-rank structures of a latent tensor separately in a Bayesian framework. Specifically, we reformulate the CANDECOMP/PARAFAC (CP) tensor rank and develop a sparsity-induced prior for the low-rank structure that can be used to determine tensor rank automatically. Then, the non-low-rank structure is modeled using a mixture of Gaussians prior that is shown to be sufficiently flexible and powerful to inform the completion process for a variety of real tensor data. With these two priors, we develop a Bayesian minimum mean-squared error estimate framework for inference. The developed framework can capture the important distinctions between low-rank and non-low-rank structures, thereby enabling more accurate model, and ultimately, completion. For various applications, compared with the state-of-the-art methods, the proposed model yields more accurate completion results.en© 2019 IEEEAdaptive low-rank representation; automatic tensor rank determination; tensor completionJournal article100001228010.1109/tnnls.2019.29524270005764366000322-s2.0-85092680306515535Shi, Q. [0000-0002-9126-2107]van den Hengel, A. [0000-0003-3027-8364]