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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...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2023
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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. |
format | Online Article Text |
id | pubmed-9955114 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT liusiqi rankadaptivetensorcompletionbasedontuckerdecomposition AT shixiaoyu rankadaptivetensorcompletionbasedontuckerdecomposition AT liaoqifeng rankadaptivetensorcompletionbasedontuckerdecomposition |