{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:23:28Z","timestamp":1776720208913,"version":"3.51.2"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T00:00:00Z","timestamp":1674518400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12071291"],"award-info":[{"award-number":["12071291"]}]},{"name":"National Natural Science Foundation of China","award":["20JC1414300"],"award-info":[{"award-number":["20JC1414300"]}]},{"name":"National Natural Science Foundation of China","award":["20ZR1436200"],"award-info":[{"award-number":["20ZR1436200"]}]},{"name":"Science and Technology Commission of Shanghai Municipality","award":["12071291"],"award-info":[{"award-number":["12071291"]}]},{"name":"Science and Technology Commission of Shanghai Municipality","award":["20JC1414300"],"award-info":[{"award-number":["20JC1414300"]}]},{"name":"Science and Technology Commission of Shanghai Municipality","award":["20ZR1436200"],"award-info":[{"award-number":["20ZR1436200"]}]},{"name":"Natural Science Foundation of Shanghai","award":["12071291"],"award-info":[{"award-number":["12071291"]}]},{"name":"Natural Science Foundation of Shanghai","award":["20JC1414300"],"award-info":[{"award-number":["20JC1414300"]}]},{"name":"Natural Science Foundation of Shanghai","award":["20ZR1436200"],"award-info":[{"award-number":["20ZR1436200"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/e25020225","type":"journal-article","created":{"date-parts":[[2023,1,25]],"date-time":"2023-01-25T03:53:18Z","timestamp":1674618798000},"page":"225","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Rank-Adaptive Tensor Completion Based on Tucker Decomposition"],"prefix":"10.3390","volume":"25","author":[{"given":"Siqi","family":"Liu","sequence":"first","affiliation":[{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]},{"given":"Xiaoyu","family":"Shi","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2033-6356","authenticated-orcid":false,"given":"Qifeng","family":"Liao","sequence":"additional","affiliation":[{"name":"School of Information Science and Technology, ShanghaiTech University, Shanghai 201210, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109326","DOI":"10.1016\/j.jcp.2020.109326","article-title":"Rank adaptive tensor recovery based model reduction for partial differential equations with high-dimensional random inputs","volume":"409","author":"Tang","year":"2020","journal-title":"J. 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