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Rank-Adaptive Tensor Completion Based on Tucker Decomposition

Tensor completion is a fundamental tool to estimate unknown information from observed data, which is widely used in many areas, including image and video recovery, traffic data completion and the multi-input multi-output problems in information theory. Based on Tucker decomposition, this paper propo...

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Detalles Bibliográficos
Autores principales: Liu, Siqi, Shi, Xiaoyu, Liao, Qifeng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955114/
https://www.ncbi.nlm.nih.gov/pubmed/36832592
http://dx.doi.org/10.3390/e25020225
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author Liu, Siqi
Shi, Xiaoyu
Liao, Qifeng
author_facet Liu, Siqi
Shi, Xiaoyu
Liao, Qifeng
author_sort Liu, Siqi
collection PubMed
description Tensor completion is a fundamental tool to estimate unknown information from observed data, which is widely used in many areas, including image and video recovery, traffic data completion and the multi-input multi-output problems in information theory. Based on Tucker decomposition, this paper proposes a new algorithm to complete tensors with missing data. In decomposition-based tensor completion methods, underestimation or overestimation of tensor ranks can lead to inaccurate results. To tackle this problem, we design an alternative iterating method that breaks the original problem into several matrix completion subproblems and adaptively adjusts the multilinear rank of the model during optimization procedures. Through numerical experiments on synthetic data and authentic images, we show that the proposed method can effectively estimate the tensor ranks and predict the missing entries.
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spelling pubmed-99551142023-02-25 Rank-Adaptive Tensor Completion Based on Tucker Decomposition Liu, Siqi Shi, Xiaoyu Liao, Qifeng Entropy (Basel) Article Tensor completion is a fundamental tool to estimate unknown information from observed data, which is widely used in many areas, including image and video recovery, traffic data completion and the multi-input multi-output problems in information theory. Based on Tucker decomposition, this paper proposes a new algorithm to complete tensors with missing data. In decomposition-based tensor completion methods, underestimation or overestimation of tensor ranks can lead to inaccurate results. To tackle this problem, we design an alternative iterating method that breaks the original problem into several matrix completion subproblems and adaptively adjusts the multilinear rank of the model during optimization procedures. Through numerical experiments on synthetic data and authentic images, we show that the proposed method can effectively estimate the tensor ranks and predict the missing entries. MDPI 2023-01-24 /pmc/articles/PMC9955114/ /pubmed/36832592 http://dx.doi.org/10.3390/e25020225 Text en © 2023 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Liu, Siqi
Shi, Xiaoyu
Liao, Qifeng
Rank-Adaptive Tensor Completion Based on Tucker Decomposition
title Rank-Adaptive Tensor Completion Based on Tucker Decomposition
title_full Rank-Adaptive Tensor Completion Based on Tucker Decomposition
title_fullStr Rank-Adaptive Tensor Completion Based on Tucker Decomposition
title_full_unstemmed Rank-Adaptive Tensor Completion Based on Tucker Decomposition
title_short Rank-Adaptive Tensor Completion Based on Tucker Decomposition
title_sort rank-adaptive tensor completion based on tucker decomposition
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9955114/
https://www.ncbi.nlm.nih.gov/pubmed/36832592
http://dx.doi.org/10.3390/e25020225
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AT shixiaoyu rankadaptivetensorcompletionbasedontuckerdecomposition
AT liaoqifeng rankadaptivetensorcompletionbasedontuckerdecomposition