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Type: Journal article
Title: Accurate tensor completion via adaptive low-rank representation
Author: Zhang, L.
Wei, W.
Shi, Q.
Shen, C.
van den Hengel, A.
Zhang, Y.
Citation: IEEE Transactions on Neural Networks and Learning Systems, 2020; 31(1):4170-4184
Publisher: Institute of Electrical and Electronics Engineers
Issue Date: 2020
ISSN: 2162-237X
Statement of
Lei Zhang, Wei Wei, Qinfeng Shi, Chunhua Shen, Anton van den Hengel, and Yanning Zhang
Abstract: Low-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.
Keywords: Adaptive low-rank representation; automatic tensor rank determination; tensor completion
Description: Date of publication December 30, 2019; date of current version October 6, 2020
Rights: © 2019 IEEE
DOI: 10.1109/tnnls.2019.2952427
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