{"title":"An extrapolation trust-region alternating least-squares algorithm for triple decomposition of third-order tensors","authors":"Xuejuan Zhang, Jinling Zhao","doi":"10.1007/s10479-025-06614-8","DOIUrl":null,"url":null,"abstract":"<div><p>Triple decomposition, which is a novel decomposition for the third order tensors, decomposes a third order tensor into a product of three third order low rank tensors. Alternating least-squares (ALS) is one of the most commonly used algorithms for tensor decomposition. In this paper, we combined the trust region method with the ALS algorithm to establish an extrapolation trust-region alternating least-squares algorithm for triple decomposition (TD-ETRALS). Different from the fixed regularization parameters in the modified alternating least-squares method (EMALS), TD-ETRALS adjusts the trust-region parameters in each iteration to achieve the preset accuracy of triple decomposition faster and more accurately. Theoretically, we prove that the sequence generated by TD-ETRALS converges to a critical point. Numerical experiments show that TD-ETRALS preforms better than EMALS in triple decomposition for the tensors generated by a uniform distribution in the relatively narrow interval and the tensors with Gaussian noise. In the example of image processing, TD-ETRALS also shows some advantages in low rank decomposition.</p></div>","PeriodicalId":8215,"journal":{"name":"Annals of Operations Research","volume":"349 3","pages":"1933 - 1955"},"PeriodicalIF":4.5000,"publicationDate":"2025-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Operations Research","FirstCategoryId":"91","ListUrlMain":"https://link.springer.com/article/10.1007/s10479-025-06614-8","RegionNum":3,"RegionCategory":"管理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Triple decomposition, which is a novel decomposition for the third order tensors, decomposes a third order tensor into a product of three third order low rank tensors. Alternating least-squares (ALS) is one of the most commonly used algorithms for tensor decomposition. In this paper, we combined the trust region method with the ALS algorithm to establish an extrapolation trust-region alternating least-squares algorithm for triple decomposition (TD-ETRALS). Different from the fixed regularization parameters in the modified alternating least-squares method (EMALS), TD-ETRALS adjusts the trust-region parameters in each iteration to achieve the preset accuracy of triple decomposition faster and more accurately. Theoretically, we prove that the sequence generated by TD-ETRALS converges to a critical point. Numerical experiments show that TD-ETRALS preforms better than EMALS in triple decomposition for the tensors generated by a uniform distribution in the relatively narrow interval and the tensors with Gaussian noise. In the example of image processing, TD-ETRALS also shows some advantages in low rank decomposition.
期刊介绍:
The Annals of Operations Research publishes peer-reviewed original articles dealing with key aspects of operations research, including theory, practice, and computation. The journal publishes full-length research articles, short notes, expositions and surveys, reports on computational studies, and case studies that present new and innovative practical applications.
In addition to regular issues, the journal publishes periodic special volumes that focus on defined fields of operations research, ranging from the highly theoretical to the algorithmic and the applied. These volumes have one or more Guest Editors who are responsible for collecting the papers and overseeing the refereeing process.