Please use this identifier to cite or link to this item:
https://hdl.handle.net/2440/130272
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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 2162-2388 |
Statement of Responsibility: | 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 |
Published version: | http://dx.doi.org/10.1109/tnnls.2019.2952427 |
Appears in Collections: | Aurora harvest 8 Australian Institute for Machine Learning publications Computer Science publications |
Files in This Item:
File | Description | Size | Format | |
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hdl_130272.pdf | Accepted version | 7.75 MB | Adobe PDF | View/Open |
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