Accurate tensor completion via adaptive low-rank representation

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dc.contributor.authorZhang, L.
dc.contributor.authorWei, W.
dc.contributor.authorShi, Q.
dc.contributor.authorShen, C.
dc.contributor.authorvan den Hengel, A.
dc.contributor.authorZhang, Y.
dc.date.issued2020
dc.descriptionDate of publication December 30, 2019; date of current version October 6, 2020
dc.description.abstractLow-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.
dc.description.statementofresponsibilityLei Zhang, Wei Wei, Qinfeng Shi, Chunhua Shen, Anton van den Hengel, and Yanning Zhang
dc.identifier.citationIEEE Transactions on Neural Networks and Learning Systems, 2020; 31(1):4170-4184
dc.identifier.doi10.1109/tnnls.2019.2952427
dc.identifier.issn2162-237X
dc.identifier.issn2162-2388
dc.identifier.orcidShi, Q. [0000-0002-9126-2107]
dc.identifier.orcidvan den Hengel, A. [0000-0003-3027-8364]
dc.identifier.urihttp://hdl.handle.net/2440/130272
dc.language.isoen
dc.publisherInstitute of Electrical and Electronics Engineers
dc.rights© 2019 IEEE
dc.source.urihttps://doi.org/10.1109/tnnls.2019.2952427
dc.subjectAdaptive low-rank representation; automatic tensor rank determination; tensor completion
dc.titleAccurate tensor completion via adaptive low-rank representation
dc.typeJournal article
pubs.publication-statusPublished

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