Randomized Algorithms for Multilinear UTV Decomposition

doi:10.1002/nla.70000

	Randomized Algorithms for Multilinear UTV Decomposition
	Liu, Guimin 1; Zhao, Ruijuan2 ; Zheng, Bing 1; Yang, Fanyin 1
	2025-02
发表期刊	NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
卷号	32 期号:1
摘要	Truncated multilinear UTV decomposition (TMLUTVD) is an efficient method to extract the most dominant features of a given tensor in various practical applications, such as tensor tracking. However, the computation of TMLUTVD can be time-consuming, especially for large-scale data. Randomized methods are known for their ability to reduce computational costs, particularly when dealing with the low-rank approximation of large tensors. Therefore, in this paper, we develop randomized algorithms for computing the multilinear UTV decomposition. Specifically, we propose randomized versions of TMLUTVD using randomized sampling schemes and the power method technique, which is an extension of the existing randomized matrix method. They are more efficient when applied to very large datasets compared with deterministic methods, and a detailed probabilistic error analysis of these algorithms is provided. We further introduce two novel variants of these randomized algorithms, based on distinct computational challenges inherent in processing large-scale datasets. The first variant can adaptively find a low-rank representation that satisfies a given tolerance when the target rank is not known in advance. The second variant preserves the original tensor structure and is particularly effective for managing large-scale sparse tensors that are challenging to load into memory. Some numerical results are presented to illustrate the efficiency and effectiveness of the proposed methods.
关键词	low multilinear rank approximation multilinear UTV decomposition randomized algorithm tensors
DOI	10.1002/nla.70000
收录类别	SCIE
ISSN	1070-5325
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:001412776900001
出版者	WILEY
原始文献类型	Article
EISSN	1099-1506
引用统计	被引频次[WOS]：0 [WOS记录] [WOS相关记录]
文献类型	期刊论文
条目标识符	http://ir.lzufe.edu.cn/handle/39EH0E1M/38742
专题	信息工程与人工智能学院
通讯作者	Liu, Guimin
作者单位	1.Lanzhou Univ, Sch Math & Stat, Lanzhou, Peoples R China; 2.Lanzhou Univ Finance & Econ, Sch Informat Engn & Artificial Intelligence, Lanzhou, Peoples R China
推荐引用方式 GB/T 7714	Liu, Guimin,Zhao, Ruijuan,Zheng, Bing,et al. Randomized Algorithms for Multilinear UTV Decomposition[J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,2025,32(1).
APA	Liu, Guimin,Zhao, Ruijuan,Zheng, Bing,&Yang, Fanyin.(2025).Randomized Algorithms for Multilinear UTV Decomposition.NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS,32(1).
MLA	Liu, Guimin,et al."Randomized Algorithms for Multilinear UTV Decomposition".NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 32.1(2025).